tag:blogger.com,1999:blog-64723337249584678962024-03-08T10:22:15.313-08:00PhysicsFMPhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.comBlogger47125tag:blogger.com,1999:blog-6472333724958467896.post-15881091891449025292022-06-17T09:41:00.039-07:002023-01-02T12:42:07.178-08:00YouTube Book ReveiwsRationale: I need to know what books I've reviewed on YouTube. <br>
<font color = blue>[Update 1/2/23: really, I was about to do a review for one of these.]</font><br><br>
Below is a catalog of those reviews and an Amazon link to the book. The text link <i>above</i> the Amazon link is a link to the review video flip through. I may try to integrate text book reiviews later.
<br><br>
I have categorized these into non-exculsive sets of either (1) Topics and (2) Book Series. All books in the second set appear in at least one topic, and some books appear in multiple topics. At some point I'll probably say why I included these particular series (that is, why I like them).
<hr>
<b>The Frontiers Collection</b><br><br>
<table><tr><td>
Schlosshauer, Maximillian, <br><br>
<a href = https://youtu.be/mtm_frbhVms>Dechoherence and<br>the Quantum to<br> Classical Transition</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3642071422&asins=3642071422&linkId=da6e8416505a9d42780fe51f6606c5ef&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Petkov, V <br><br>
<a href = https://youtu.be/_emTSq57zLE>Relativity and<br>The Nature of<br>Spacetime</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3642242359&asins=3642242359&linkId=cd1cacc33a0b2900fc19950460fd9c00&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Zeh, H.D. <br><br>
<a href = https://youtu.be/-SCeZn9oEF0>The Physical Basis<br>of the<br>Direction of Time</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3642087604&asins=3642087604&linkId=3f91c3e57279d230b06dca6af1404e77&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>General Physics/Physics Surveys</b><br><br>
<table><tr><td>
Leonhardt and Philbin<br><br>
<a href = https://youtu.be/RCIxqUWOFbA>Geometry and Light</a><br><br><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0486476936&asins=0486476936&linkId=07affa8df0f75b8aa3a5f5f6ab2fa0cb&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Moore, Thomas<br><br>
<a href = https://youtu.be/FpZ-6YIZkzM>Six Ideas That Shaped<br> Physics: Unit C:<br> Conservation Laws</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0073513946&asins=0073513946&linkId=08f9f5c952f228093b9b6597f0c78ad8&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Moore, Thomas<br><br>
<a href = https://youtu.be/FpZ-6YIZkzM>Six Ideas That Shaped<br> Physics: Unit N:<br> Lawas of Physics are Universal</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0077600932&asins=0077600932&linkId=e5474f7290eb73f3bbf2ca85a30fe18a&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Zeh, H.D. <br><br>
<a href = https://youtu.be/-SCeZn9oEF0>The Physical Basis<br>of the<br>Direction of Time</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3642087604&asins=3642087604&linkId=3f91c3e57279d230b06dca6af1404e77&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr><tr><td>
Padmanabhan<br><br>
<a href = https://youtu.be/5SfkRHn41_4>Sleeping Beauties<br>in<br>Theoretical Physics</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3319134426&asins=3319134426&linkId=26bcc7620599cf22b97166507cdd3a38&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Schwartz, M.<br><br>
<a href = https://youtu.be/leNOBDXyyDY>Principles of <br> Electrodynamics</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0486654931&asins=0486654931&linkId=9beeb32786df635a7594395732214880&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Lemons, Don<br><br>
<a href = https://youtu.be/2QkzbgdJr9k>Perfect Form</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=B087Z32M9K&asins=B087Z32M9K&linkId=a417361c52e0844a810c966768f5437a&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>Relativity</b><br><br>
<table><tr><td>
Lawden, D.F.<br><br> <a href = https://youtu.be/jIpsHiEbWyQ>Introduction to <br> Tensor Calculus,<br>Relativity and Cosmology</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0486425401&asins=0486425401&linkId=51258fb6b906fb1d75c6f4742e6d3ca0&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Petkov, V <br><br>
<a href = https://youtu.be/_emTSq57zLE>Relativity and<br>The Nature of<br>Spacetime</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3642242359&asins=3642242359&linkId=cd1cacc33a0b2900fc19950460fd9c00&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Will, Clifford<br><br>
<a href = https://youtu.be/MXHY38m1vEs>Theory and<br>Experiment in<br>Graviational Physics</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=1107117445&asins=1107117445&linkId=238a013270d9afbd13eaa1acffc9e0ea&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>Quantum Mechanics</b><br><br>
<table><tr><td>
Ahronov and Rohrlick, <br> <a href = https://youtu.be/A-zoCIdrmpU>Qunatum Paradoxes</a><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3527403914&asins=3527403914&linkId=d7878d39507b7aa8fcb34a031e60a3cb&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Basdevant and Dalibard,<br> <a href = https://youtu.be/Qps6C74ATZU>The Quantum Mechanics Solver</a><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3030137260&asins=3030137260&linkId=2beeb57ad8dd2a4ddfc533cd1c324ec9&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Schlosshauer, Maximillian, <br> <a href = https://youtu.be/mtm_frbhVms>Dechoherence and the<br> Quantum to Classical Transition</a><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3642071422&asins=3642071422&linkId=da6e8416505a9d42780fe51f6606c5ef&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Cohen, David W., <br> <a href = https://youtu.be/M8zcoMX0cwI>An Introduction to<br> Hilbert Space and Quantum Logic</a><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=1461388430&asins=1461388430&linkId=147238bf130dc7391f1a6f0a7d0bfa29&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr><tr><td>
<hr>Norsen, Travis<br><br>
<center><a href = https://youtu.be/M8zcoMX0cwI>Foundations of<br>Quantum Mechanics</a></center><br><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3319658662&asins=3319658662&linkId=a12ec0a4a2a274cbd4c8e8cc09e0bd47&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
<hr>Sakurai, J.J.<br><br>
<center><a href = https://youtu.be/COWUT4OMHsM>Modern<br>Quantum Mechanics<a></center><br><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=1108473229&asins=1108473229&linkId=a8a4fc6b7bd4b0a569eaa1882202a375&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
<hr>Sudbery, A.<br><br>
<center><a href = https://youtu.be/Dgwtag3XeCA>Quantum Mechnicas<br>and the Particles<br>of Nature</a></center><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0521277655&asins=0521277655&linkId=9a7ca149edff5e4b19e6090e0852a9a6&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
<hr>Tomonaga, S.-I.<br><br>
<center><a href =https://youtu.be/Phjh-gBP7o8>The Story of<br>Spin</a></center><br><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0226807940&asins=0226807940&linkId=4a37f4c09fe8fce3cb4a956a43bdcd7c&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>Statistical Physics</b><br><br>
<table><tr><td>
<hr>Ben-Naim, Arieh<br><br>
<a href = https://youtu.be/QEoz59t604g>Entropy and the Second Law</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=981437489X&asins=981437489X&linkId=3a2d79edf3851d8865fc9b23f2bdd31f&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
<hr>Ben Naim, Arieh<br><br>
<a href = https://youtu.be/QEoz59t604g>Entropy Demystified</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=B010WEL6TC&asins=B010WEL6TC&linkId=a7a26d71da3bc0662a96258bd8fb07ee&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
<hr>Krauth, W.<br><br>
<a href = https://youtu.be/FQWeo_TH8vE>Statistical Mechanics:<br>Algorithms and<br>Computation</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0198515367&asins=0198515367&linkId=6f06a8d33e75a4d04b3f3b4052b150e4&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>Applied Phyiscs and Engineering</b><br><br>
<table><tr><td>
Feynman, Richard <br> <a href = https://youtu.be/rDNzWBJMg-Q>The Feynman Lectures<br> on Compuation</a><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0738202967&asins=0738202967&linkId=9d34f9faf80e9959c30fbcba216ac11f&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Hubert and Schaefer, <br> <a href = https://youtu.be/WkM1GACRYTs > Magnetic Domains</a><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3540641084&asins=3540641084&linkId=8b619f59636792424fbba59e957a5a87&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Coleman, Charles<br><br>
<a href = https://youtu.be/Db52S0w2Ohs> Modern Physics for<br>Semiconductor Science</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3527407014&asins=3527407014&linkId=ad11e535194789ffefb3d0bcaf46ada0&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr><tr><td>
</td><td>
Szirtes, Thomas, <br> <a href = https://youtu.be/2s6rjHZo7mg>Applied Dimensional<br> Analysis and Modeling</a><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=B005H89K9C&asins=B005H89K9C&linkId=e6059de6b6663285053dc38bb0ed1d59&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>Mathematics</b><br><br>
<table><tr><td>
Farlow, Stanley<br><br>
<a href = https://youtu.be/3tYz6Owi1YU> Partial Differential <br>Equations for<br> Scientists and Engineers</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=048667620X&asins=048667620X&linkId=d7123ae9bd40ed219aa56af1f8780bca&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Gardiner, Anthony<br><br>
<a href = https://youtu.be/A3l3npZddk0>Understanding Infinity</a><br><br><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=048642538X&asins=048642538X&linkId=967be8af004389680345a024954d6a7a&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Cohen, David W. <br><br>
<a href = https://youtu.be/M8zcoMX0cwI>An Introduction to <br>Hilbert Space and <br>Quantum Logic</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=1461388430&asins=1461388430&linkId=147238bf130dc7391f1a6f0a7d0bfa29&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
Tapp, K<br><br>
<a href = https://youtu.be/eRsa1a8XTAU>Matrix Groups for<br>Undergraduates</a><br><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=1470427222&asins=1470427222&linkId=4ba5531a3f1364ec921cd67affddefa9&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>Mechanics</b><br><br>
<table><tr><td>
</td></tr></table>
<br><br>
<hr>
<b>Dover Books</b><br><br>
<table><tr><td>
<hr>Farlow, Stanley<br><br>
<a href = https://youtu.be/3tYz6Owi1YU> Partial Differential <br>Equations for<br> Scientists and Engineers</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=048667620X&asins=048667620X&linkId=d7123ae9bd40ed219aa56af1f8780bca&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
<hr>Gardiner, Anthony<br><br>
<a href = https://youtu.be/A3l3npZddk0>Understanding Infinity</a><br><br><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=048642538X&asins=048642538X&linkId=967be8af004389680345a024954d6a7a&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
<hr>Leonhardt and Philbin<br><br>
<a href = https://youtu.be/RCIxqUWOFbA>Geometry and Light</a><br><br><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0486476936&asins=0486476936&linkId=07affa8df0f75b8aa3a5f5f6ab2fa0cb&show_border=true&link_opens_in_new_window=true"></iframe>
</td><td>
<hr>Lawden, D.F.<br><br>
<a href = https://youtu.be/jIpsHiEbWyQ>Introduction to <br> Tensor Calculus,<br>Relativity and Cosmology</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0486425401&asins=0486425401&linkId=51258fb6b906fb1d75c6f4742e6d3ca0&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr><tr><td>
<hr>
Schwartz, M.<br><br>
<a href = https://youtu.be/leNOBDXyyDY>Principles of <br> Electrodynamics</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=0486654931&asins=0486654931&linkId=9beeb32786df635a7594395732214880&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>Lecture Notes in Physics </b><br><br>
<table><tr><td>
Padmanabhan<br><br>
<a href = https://youtu.be/5SfkRHn41_4>Sleeping Beauties<br>in<br>Theoretical Physics</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3319134426&asins=3319134426&linkId=26bcc7620599cf22b97166507cdd3a38&show_border=true&link_opens_in_new_window=true"></iframe>
<td><td>
Norsen, Travis<br><br>
<a href = https://youtu.be/M8zcoMX0cwI>Foundations of<br>Quantum Mechanics</a><br><br>
<iframe sandbox="allow-popups allow-scripts allow-modals allow-forms allow-same-origin" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3319658662&asins=3319658662&linkId=a12ec0a4a2a274cbd4c8e8cc09e0bd47&show_border=true&link_opens_in_new_window=true"></iframe>
</td></tr></table>
<br><br>
<hr>
<b>Multiversal Journeys </b><br><br>
<hr>
<b>Student Mathematical Library </b><br><br>
<hr>
<b>Oxford Master Series</b><br><br>
PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-70034598831328101802022-02-26T16:10:00.001-08:002022-02-26T19:03:44.944-08:00Answering Aristotle - IndexI am reading Aristotle's <a href = https://amzn.to/3Hvho8p>Physics</a>, and as I do with non-technical books, I try to write a topic sentence (here, "summary") for each section. The "chapters" in Aristotle are approximately the size of a good section. This is a list of those sentences. The chapter links, however, have me doing something different: when Aristotle makes assertions or predictions, and where I think that contemporary physics has something to say about them, I try to make some notes about that.<br><br>
Book I
<table>
<tr>
<td width = 75 align = "center"> Chapter </td> <td> Summary </td>
</tr><tr>
<td align = "center"> <a href = https://physicsfm-master.blogspot.com/2021/12/answering-aristotle-i1.html> I.1 </a> </td> <td> <hr align = center width = 25%> Although understanding something means we can reason from first principles, discovering these principles requires us to sort them out from the aggregate observations we are built to apprehend. </td>
</tr>
<tr>
<td align = "center"> <a href = https://physicsfm-master.blogspot.com/2021/12/answering-aristotle-i2-there-is-more.html> I.2 </a> </td> <td> <hr align = center width = 25%> There must be more than one thing because the ways in which all reality can be made of one thing each require there to be multiple things.</td>
</tr>
<tr>
<td align = "center"> <a href = https://physicsfm-master.blogspot.com/2022/01/answering-aristotle-i3-there-is-more.html> I.3 </a> </td> <td> <hr align = center width = 25%> The definition of a whole cannot be found in the definition of its parts, so that things exist does not mean that there is an existence that they are a part of.</td>
</tr>
<tr>
<td align = "center"> <a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-i4-there-cannot-be.html> I.4 </a> </td> <td> <hr align = center width = 25%> The number of kinds of things must be finite since the infinite is unknowable and a finite body cannot be composed of an infinite number of finite bodies.</td>
</tr>
<tr>
<td align = "center"> I.5 </td> <td> <hr align = center width = 25%> All principles must be opposites that admit admixtures of opposites, and the properties of an object may consist of combinations of these principles. </td>
</tr>
<tr>
<td align = "center"> I.6 </td> <td> <hr align = center width = 25%> </td>
</tr>
<tr>
<td align = "center"> I.7 </td> <td> <hr align = center width = 25%> </td>
</tr>
<tr>
<td align = "center"> I.8 </td> <td> <hr align = center width = 25%> </td>
</tr>
<tr>
<td align = "center"> I.9 </td> <td> <hr align = center width = 25%> </td>
</tr>
<tr>
<td align = "center"> I.10 </td> <td> <hr align = center width = 25%> </td>
</tr>
</table>
<br>
Book II
<br><br>
Book III
<br><br>
Book IV
<br><br>
Book V
<br><br>
Book VI
<br><br>
Book VII
<br><br>
Book VIIIPhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-18269498181977437302022-02-26T15:30:00.005-08:002022-02-26T19:03:21.388-08:00Answering Aristotle I.4 - There Cannot Be an Infinite Number of Things<table style="width: 100%;"><tbody><tr><td align="left" width = 33%><a href="https://physicsfm-master.blogspot.com/2022/01/answering-aristotle-i3-there-is-more.html"> ← Previous ( Physics I.3 ) </a></td><td align = "center" width =34%><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a></td><td align="right" width = 33%> <text align="right">( Physics I.5 ) Next → </text><br /></td></tr></tbody></table><br />
<hr width = 66%><br>
<blockquote><b>Physics I.4</b> The number of kinds of things must be finite since the infinite is unknowable and a finite body cannot be composed of an infinite number of finite bodies.</blockquote><br>
Again Aristotle is arguing against someone to prove his point. In this case, Anaxagoras. Aristotle presents this as since "it is impossible for something to come into being from non-being," so everything that exists is made up of smaller constituents. And if <i>everything</i> comes from smaller constituents, then there cannot be a smallest object -- it, itself, would need to be composed of even smaller things. Aristotle, disagrees. Although there must be more than one thing, or even one kind of thing, there cannot be an infinite number of things, let alone an infinite number of kinds of things that the finite things we see are composed of. <br><br>
It is a little difficult to keep track of things here, because sometimes Aristotle seems to be talking about the number of things that exist; at other times, he seems to being talking about the the number of kinds of things that exist; and at still other times, he seems to be arguing about the number of different properties that a thing can hold.<br><br>
Aristotle's argument that there cannot be an infinite number of things has five parts, of different quality:<br><br>
(1) <b>The infinite is unknowable.</b>
<dd> This is rather technical in the sense that it makes a strong point about the limitations of what we can perceive in thought. However, it is not really true that "if an object consists of an infinite number of things and forms, its nature is unknowable." This is a little strong, since something that consists of an infinite regularity could be understood in principle without apprehending its nature as a whole. That is in fact what we do in science. We don't perceive the entire array of atoms in a crystal lattice. For the most common measurements of the lattice, from X-ray diffraction, we don't even directly look at the regular array. Instead, we look at the regularities in the array of atoms making up a sample, and learn about its constituents that way.</dd><br>
(2) <b>If an object has a finite size, then its parts must also be finite.</b>
<dd>Zeno would be proud. This is a classic piece of the Dichotomy. However, Aristotle didn't buy Zeno's paradoxes any more than we do. In fact, many of his reasons are good enough to refute Zeno in any but a pedantic way (today, even the pedants should understand these paradoxes are refuted even at the more fundamental levels*). The parts of a homoeomerous substances <i>could</i> be made of ever smaller parts if you take a continuum model or even an infinitesimal model of matter. </dd><br>
(3) <b>That some of every constituent is present in every object is inconsistent.</b>
<dd>The best way I can present this argument is that if an object has a finite number of (kinds of) constituents, and if those constituents are differentiated and their relative preponderance determines the object's nature, then at some point when you reduce the size of a sample below a certain volume, you will have a sample of the object with an insufficient amount of one of its constituents to be the same kind of thing as it reduces in size. The divided objects cease to be of the kind of the original object. This would be equally true with random fluctuations in small samples.</dd><br>
(4) <b>Nothing material can be extracted from the smallest instance of a substance.</b>
<dd>Once you reach the limit above, you cannot make a smaller copy of the thing you're dividing. This is a direct response to Anaxagoras. </dd><br>
(5) <b>An infinite collection must be both divided and connected simultaneously.</b>
<dd>The infinite number of things that Aristotle is talking about are the constituents of other things.</dd><br>
Now that I try to explain them, I don't think any of them are very good. I think many of the reasons he discussed earlier are much better than his discussion here, but the conculsions he came to were wrong. And ironically, on this one Aristotle is right. <br><br>
Nothing is composed of an infinite number of things, to our knowledge.[2] It seems like there are a finite number of kinds of things that something can be composed of at the smallest level (standard model) and even a finite number of possible elements something can be made of (periodic table). So although a copper ball has an impossible number of atoms in it (maybe 10<sup>25</sup> or so), it is still a finite number, and although the atoms that make up the ball have constituents, they have a small number of constituents (say, around 250). <br><br>
____________________________<br>
[1] Although, as philosophers, they do continue to find value in them. See Salmon, <a href = https://amzn.to/3Ir5uOt>Zeno's Paradoxes</a> and Sainsbury, <a href = https://amzn.to/3phw051>Pardoxes</a>. [Amazon] <br><br>
[2] But there could be preons inside of quarks (but probably not). And if there are preons inside of quarks, then what's inside the preon?<br>
<hr width = 66%><br>
<table style="width: 100%;"><tbody><tr><td align="left" width = 33%><a href="https://physicsfm-master.blogspot.com/2022/01/answering-aristotle-i3-there-is-more.html"> ← Previous ( Physics I.3 ) </a></td><td align = "center" width =34%><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a></td><td align="right" width = 33%> <text align="right">( Physics I.5 ) Next → </text><br /></td></tr></tbody></table><br />PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-35285159666365259182022-02-22T19:05:00.000-08:002022-02-22T19:05:01.576-08:00The Two Ockham'sIn reading the first chapter of Bostrom's <I>Anthropic Bias: Observation Selection Effects in Science and Philosophy</I>,[1] his overview dealing with multiple worlds makes me feel as if there are two ways in which Ockham's Razor[2] are being used in science. That is, the general maxim of reducing the number of "entities" to a minimum is applied in two opposing ways, one of which is evident in anthropic reasoning. One of these ways is to reduce the number of actual things that you suppose to exist and the other is to reduce the number of postulates required to make predictions with a theory. <br><br>
How does that work? <br><br>
<b>Fine tuning</b> is a modern sin in theoretical physics. A theory that has a large number of free parameters, but only a few of which could lead to observed consequences, needs to have additional assumptions about those parameters. If these are unexplained, then the theory is fine tuned. This is generally felt to be a flaw because it is <i>surprising</i> that an otherwise successful theory should require a large number of ancillary assumptions -- 31 in the case of particle astrophysics[3] -- to predict the existence of the universe. Although not strictly a error, taking an elegant and insightful theory and clothing it in hand-me-down experimental parameters is a bit gauche.<br><br>
This is where the <b>anthropic principle</b> comes in. This principle, in this case, states that the universe has to be the kind of universe where you and me can exist. We're pretty sure that we do. This constrains overly loose theories, theories that require fine tuning, so that they can make predictions. This method was famously used by Steven Weinberg to predict the approximate magnitude of the cosmological constant. This has also recently been used to try to shore up string theory as it has become looser, parameter-wise, than once thought. Anthropic reasoning is an end around fine tuning.<br><br>
The expansion of possible string theories from five to an infinite number has made anthropic arguments possible in that each particular universe that would be associated with a string theory[4] (with different parameters) exists, and the reason why we are in <i>this</i> universe with <i>these</i> fundamental constants is not because of any finely tuned assumptions that we have to make, but rather it is because of the existing universes, we have to be in a universe that supports our existence. This can be true with parallel universes, sequential universes, and so on, just as long as there is an infinite reservoir and the proportion of those universes is a subset of the same transfinite cardinality of the reservoir.<br><br>
This is what brings me to Ockham's razor. This is usually stated as "entities must not be multiplied beyond necessity" or "plurality should not be posited without necessity." If there is no necessity to postulate a soul in order to understand consciousness, then don't postulate a soul. Normally, you would think that this would exclude a string theory landscape, that in order to explain the values of the universal constants that we measure, we need to postulate not just a soul, but an infinite number of souls.<br><br>
But that's just one way to think about it. Another one is Aquinas' maxim, "It is superfluous to suppose that which can be accounted for by a few principles has been produced by many." In this case, the anthropic principle is <i>supported</i> by Ockham's razor. We have literally reduced the number of assumptions we need to make from 31 <i>ad hoc</i> interpretations of experiments to a single proven principle. <br><br>
Both cases have a claim to be following the spirit of Ockham, and to me neither is obviously right. At least, neither seems to be the better argument in all cases. So, we have a situation where the same, admittedly somewhat subjective[5], principle would require us to take opposite approaches to the same problem. How do we decide which to follow? <br><br>
_____________________<br>
[1] <a href = https://amzn.to/3HOjgKw>Anthropic Bias: Observation Selection Effects in Science and Philosophy</a>, Nick Bostrom. [Amazon]<br><br>
[2] I prefer the ckh over the cc. How can Occam's Razor be named for Isaac of Ockham?<br><br>
[3] See for example Tegmark, Aguirre, Rees, and Wilczek's "Dimensionless Constants, Cosmology and Other Dark Matters." [<a href = https://arxiv.org/abs/astro-ph/0511774>arXiv</a>] See also Physics Frontiers 55: <a href = https://physicsfm-frontiers.blogspot.com/2020/12/multiversality.html>Multiversality</a>.<br><br>
[4] <a href = https://arxiv.org/abs/hep-th/0302219>Anthropic Landscape of String Theory</a>, Leonard Susskind. <a href = https://amzn.to/3HOjgKw> Extrad Dimensions in Space and Time</a> [Amazon], Bars and Terning, Multiversal Journeys Series. See also: Physics Frontiers 35: <a href = http://physicsfm-frontiers.blogspot.com/2018/09/the-string-theory-landscape.html>The String Theory Landscape</a>.<br><br>
[5] But Ockham's razor is no less subjective than the beauty of a physical theory, and a lot of people give that a lot of weight. PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-51215784118113136962022-01-03T09:42:00.008-08:002022-02-26T19:03:05.170-08:00Answering Aristotle I.3 - There Is More than One Thing II<table style="width: 100%;"><tbody><tr><td align="left" width = 33%><a href="https://physicsfm-master.blogspot.com/2021/12/answering-aristotle-i2-there-is-more.html"> ← Previous ( Physics I.2 ) </a></td><td align = "center" width =34%><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a></td><td align="right" width = 33%> <text align="right"><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-i4-there-cannot-be.html>( Physics I.4 ) Next → </a></text><br /></td></tr></tbody></table><br />
<hr width = 66%><br>
<blockquote> <b>Physics I.3</b> The definition of a whole cannot be found in the definition of its parts, so that things exist does not mean that there is an existence that they are a part of. </blockquote><br>
This reminds me of my first encounter with Aristotle, which happened to be when I was taking a graph theory course as an undergraduate. In the <i>Posterior Analytics</i>, Aristotle propounded that an argument that had to be made case by case wasn't a true derivation, or "...we often fall into error because our conclusion is not in fact...universal in the sense we thing we prove it so." When we prove a proposition case-by-case, instance-by-instance, "then the the demonstrations will be true of the individual instances...and will hold in every instance of it, yet the demonstration will not be true of this subject commensurately and universally." Aristotle's example, as so many it the text, is geometric: if the proof is shown for isosceles, scalene, and equilateral triangles, or if it is true of acute, right, and obtuse angles, then even though it is true for every triangle or for every angle, it is not true of triangles themselves because the proof does not follow from the nature of the triangle.<br><br>
Aristotle always seems to say that kind of thing.<br><br>
There is something reasonable about this. If there is a property of an object or a situation, then it should be derivable from the qualities of the object. If you need to bring in other conditions, then maybe it's the combination that has the property. Humans don't look like bushes, but humans wearing camouflage clothes and makeup can. The property of bush-likeness is a property of the clothing, not the man. Furthermore, I could create a situation where I found tofu dishes everyone likes: some people like tofu hot dogs, some people like tofutti, and even I like gelatinous tofu with beef in a szechwan sauce. However, people don't like the tofu, they like the flavorings around the tofu. Very few people eat plain dehydrated tofu bars.<br><br>
But remember, as I was reading this, I was taking a graph theory course. It was taught by the math department, but the course was a required course computer science majors, but it did use proofs.* Proof courses often had themes that were not explicit in the content, techniques for proofs that are useful in the field. For probability theory, it was condition and uncondition. For graph theory, proof by cases. For example, if you can prove that a process works for all even number cases, then you can do the same for all odd number cases, then you can say the process works for all cases. This was even true of the four color theorem, which I think we will all say is a property of maps -- it is not a different property for different kinds of maps. <br><br>
So I think that Aristotle has a point, but he's taken it a little too far: proof through cases, if you can demonstrate that you have exhausted all the cases, can still show that a derived property is a property of the system. <br><br>
Some of what Aristotle is saying in I.3 has a similar feel.**<br><br>
Unfortunately, that feel is very hard to follow. Aristotle talks about qualities like "paleness" as if paleness is to humans as quarks are to protons, and he does so with the object to show that there must be more than one thing. He does so mostly while arguing against positions that aren't clearly defined, so it feels like he's not arguing directly -- but since he doesn't restate the positions he is attacking. <br><br>
Here Aristotle feels he has successfully defended against two propositions:<br><br>
<dd>(1) Non-being has being.</dd>
<dd>(2) There exist indivisible magnitudes.</dd><br>
both of which have some merit, today.(*3) That non-being might have being means something like that the vacuum has some properties, but today we think that gravity is the theory of space-time, that mass can bend its fabric. Furthermore, quantum gravity is an attempt to find the quantum mechanical properties of this fabric. We think that this is true. The second is the atomic hypothesis, which wouldn't be accepted until the late 19th century, and today the standard model is full of indivisible, but not immutable, magnitudes.<br><br>
____________________________________<br>
* "Pure math" courses are proof-based somewhat like high school geometry, they aren't the endless calculations of algebra and calculus classes. You are expected to demonstrate that something works, or is a kind of mathematical tool, using logic. When the courses were required for other majors, computer science and math ed., they ended up being very, very simple.<br><br>
** I thought I would give an example here of Aristotle saying something similar in I.3 as I quoted in the <i>Posterior Analytics</i>, but the prose is quite convoluted, and the long, ellipsis-laden quotes I can find in the <i>Physics</i> say almost the same thing.<br><br>
(*3) Giving examples like this and those I did in I.2 are not what I wanted to be doing here.<br>
<hr width = 66%><br>
<table style="width: 100%;"><tbody><tr><td align="left" width = 33%><a href="https://physicsfm-master.blogspot.com/2021/12/answering-aristotle-i2-there-is-more.html"> ← Previous ( Physics I.2 ) </a></td><td align = "center" width =34%><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a></td><td align="right" width = 33%> <text align="right"><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-i4-there-cannot-be.html>( Physics I.4 ) Next → </a></text><br /></td></tr></tbody></table><br />PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-59195743305618087572021-12-20T19:05:00.005-08:002021-12-21T14:51:08.864-08:00Geometric IronyThis morning on my drive to work, I was listening to an old (May 2018) episode of Conversations with Tyler, the second half of which was a discussion between <a href = https://conversationswithtyler.com/episodes/nassim-nicholas-taleb-and-bryan-caplan/>Nassim Nicholas Taleb and Bryan Caplan</a> on the problems with education. The recurrent examples of these problems are poetry and geometry, at least one of which probably scares you. Their issue wasn't that there's anything inherently wrong with poetry and geometry, in fact they think that both are perfectly good hobbies that everyone should have (Taleb, I should say, was a little more tolerant of your poetry classes, but not that much). But they worry about the practical problem that very few students will pursue a career in them, and students graduate from school at eighteen or twenty-two having forgotten approximately 100% of the poetry and geometry that they "learned"<sup>1</sup> in class and having no idea what kind of career will suit them. There aren't many poets in the world, and there are even fewer that have learned to convert verse into cash with ab efficacy sufficient to fill a refrigerator. And what fifteen year olds need to do is to sample the <i>possibilities</i> of how they can fit into the world, like plumbing and customer service.<sup>2</sup><br><br>
The liberal arts are best left to Sunday afternoons on the porch and autumn walks in the park.<br><br>
I had finished the first half (where Tyler Cowen interviewed Taleb) and started on the part where Taleb talked with Caplan about his book <a href = https://conversationswithtyler.com/episodes/nassim-nicholas-taleb-and-bryan-caplan/ >The Case Against Education</a> (both segments included a lot of talk about Taleb's books, especially <a href = https://conversationswithtyler.com/episodes/nassim-nicholas-taleb-and-bryan-caplan/>Antifragile</a>),<sup>4</sup> when it was time to stop and get my cup of coffee.<sup>2</sup> I pulled out a paper on the history of the renormalization group and a pad of Bristol board, and started the day off by working on a cartoon for class and a bikini girl for Instagram while waiting for the caffine to get me attentive enough to read an academic paper. While I was drawing the cartoon, which is about integrating to find a volume, a local antique dealer, J., came by and we talked about finding volumes a little bit. <br><br>
<dd><img src = "http://www.physicsfm.com/images/Integration.png" width = 500></dd><br><br>
The cartoon, I hope you can see,<sup>5</sup> shows the Riemannian process behind the integral for finding the volume of the pyramid. J. saw the point right away ("what about the steps?"), and pulled out a problem for his store. The way he'd have to solve the problem was, he said, to weigh a stick of butter, then to carve a scale model out of it, weigh again, and then do some ratios. This is a very good method.<sup>6</sup> <br><br>
When he was in Versailles and saw a structure whose somewhat triangular shape he wanted to reproduce for his store, where he would put featured paintings at one point, antiquities on another, and books on the third. <img src = "http://www.physicsfm.com/images/Base.png" align = right width = 300> The shape was an equilateral triangle with the tips cut off (so, a hexagon), where the long edges had a slight inward curve. He'd add some walls and french doors as well, but what he wanted to know is that if the distance between next nearest points was 16' and the size of the cut was 4', what is the volume of concrete required to build the 1' thick base of the structure? I calculated it out with a little geometry, the quadratic formula, and a rather annoying bit of vector calculus (which was overkill).<sup>7</sup> Then C., the old Airforce master sergeant, came by and we talked about history books and historical novels until the larger group started coming in. J. took the sketch and calculation, I went back to drawing, and some girls sat behind me watching me draw the leopard print on the pinup's bikini.<br><br>
Then, when I got back into my car to get to work, I listened to the next fifteen minutes of the discussion, where Bryan Caplan and Nassim Nicholas Taleb continued their discussion on how unlikely it was that you'd end up using things like geometry or art in your day to day life, and thought about the wisdom of their words.<br><br>
______________________________<br>
<sup>1</sup> In fact, students lose the factoids they memorize for high school and undergraduate texts with a half life of about two weeks. So they'll always "remember" something from your class. <br><br>
However, it might be the wrong thing. I remember talking to a high school friend just a year or two after graduation who was sure that Lamrkian evolution was correct, because he'd read it in the HS biology textbook. He even remembered the specific example: proto-giraffe mommies stretched their necks to reach higher leaves, and so their babies had longer necks. And then this repeated over generations until giraffes were the long necked freaks of nature we see in zoos today. This was in fact in the book (I remembered it, although I never studied in high school, so I don't know why), but it was there as a historical contrast to Darwinian evolution.<br><br>
<sup>2</sup> And if you know me, especially if you knew me twenty years ago, you might remember my old rants against mindless education. And I still feel that way. I think, on the whole, Caplan and Taleb are correct. I'm not a fan of the pyramid schemes of psychology, but education kids love them, especially Maslow's heirarchy of needs. Poetry, art, and music are offerings to the sacraficial altar of self-actualization at the top of the pyramid. Caplan, and to a lesser extent Taleb, want the schools to focus more on the bottom steps of the pyramid, helping kids build the skills to keep themselves fed, housed, and safe. Those are the fertile soil for spiritual growth.<br><br>
On the other hand, whenever I hear someone say "it would be better to teach kids EXCEL instead of calculus," I think, "You have to do the calculus before you use EXCEL."<br><br>
<sup>2½</sup>If you're cool, then you know Iggy Pop's feelings are also in tune with Caplan and Taleb from reading his liner notes on the reissue of Raw Power (which I did, of course). <br><br>
...if you both like Iggy Pop and are literate (which I do and am, of course), which is not guaranteed (and that's the way he likes it; check out his liner notes).<br><br>
<sup>3</sup> I own a copy of Caplan's book and now I want a copy of Taleb's (I've read two others), but I'm about 40 books behind over the course of the pandemic. I usually read at least 50 books a year, but have gone down to a little over 30 each in 2020 and 2021. <br><br>
<sup>4</sup> I have a long commute which interacts with a complex morning routine, so this is a very simplified version. I've discussed the jalapeno boudin kolaches elsewhere. <br><br>
<sup>5</sup> Hopefully I'll get a way to put images up here.<br><br>
I did! Ha! Although the screw ups on the cartoon make me nervous. I've spared you the pinup, which is beautiful, but you're not authorized for that kind of titillation. Bring a note to me during office hours from your psychiatrist saying that it's mentally safe for you to view such things, and I'll give you a link.<br><br>
<sup>6</sup> Before there was a lot of computer time available, and even when computers were reasonably slow, this was how experimentalists would do numerical integrations on their data. They'd plot out the spectrum on their plotter, very carefully cut out the shape of the specturm, and then weigh it. That weight would be compared with the weight of the paper and the untis on the axes to find the integral.<br><br>
This is exactly J.'s butter technique.<br><br>
<sup>7</sup> If you are Nassim Nicholas Taleb and you really do enjoy doing geometry on your porch on Sunday afternoons, then this is a good little problem for you.PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-14115102387171166162021-12-13T08:14:00.006-08:002022-02-26T19:04:46.789-08:00Answering Aristotle I.2 - There Is More Than One Thing I <table style="width: 100%;"><tbody><tr><td align="left" width = 33%><a href="https://physicsfm-master.blogspot.com/2021/12/answering-aristotle-i1.html"> ← Previous ( Physics I.1 ) </a></td><td align = "center" width =34%><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a></td><td align="right" width = 33%> <text align="right"><a href = https://physicsfm-master.blogspot.com/2022/01/answering-aristotle-i3-there-is-more.html>( Physics I.3 ) Next → </a></text><br /></td></tr></tbody></table><br />
<hr width = 66%><br>
<blockquote> <b>Physics I.2</b> There must be more than one thing because the ways in which all reality can be made of one thing each require there to be multiple things.</blockquote> <br><br>
Aristotle is agnostic about the kind of thing that is the one thing. Is it a substance, a property, an element?* It doesn't matter. If there is only one of them, then he asserts there will be a contradiction. Although most of his arguments are directed against Parmenides and Melissus, they are of a kind: find what seems to be a logical contradiction, e.g. the skinny man is fat, that comes from some assumptions. One that he asserts are that something cannot be finite and infinite at the same time. <br><br>
These do not feel very compelling. For example,"...so there will be a substance as well as a quality, in which case it is twofold..." feels, at least in the translation, as if there is some confusion here. The two things are of such different kinds that I don't know how you can call them "two things," really. <br><br>
What this brings to mind, though, is string theory. In the standard model of particle physics, you have a number of fields corresponding to two kinds of particle: bosons and fermions. The fermions are leptons (electrons) and quarks, which constitute matter. The bosons, photons, gluons, and W & Z particles, constitute the fundamental forces of nature (sans gravity), the connections between matter particles, in a way. <br><br>
String theory makes all of these particles one kind of thing. <br><br>
And because we can envision these particles as excitations in their corresponding fields. That is, whenever the electron field gains energy, a new electron is born. This is a little bit weird to think about in fundamental physics, because we don't have an independent concept of an electron field. But in condensed matter physics, we do have strong classical ideas about the meaning of some of the fields that appear in matter. We know about sound waves, we know about spin waves (magnetization waves). These waves are continuous and extend through the body. They have standing states, just like the standing waves on a string or a membrane that you might be able to envision. <br><br>
And they're quantum mechanical. <br><br>
The physics of these waves are describes as excitations in their corresponding fields. A spin wave is an excitation in the local magnetic polarization (magnetization) of a ferromagnet, and these excitations can only happen for certain multiples of a fundamental oscillation mode, just like the vibrating string. However, unlike the vibrating string,** there is a minimum energy necessary to excite a single vibration, and increasing the amplitude of the vibration requires additional quanta of that vibration mode. The amplitude of the spin wave is an integer number of of these quanta. <br><br>
How much energy is this minimum energy? A ferromagnet (like your refrigerator magnets) is a material whose atoms' magnetic moments tend to align so that there is a net magnetic moment of the material. The minimum energy of a spin wave is exactly the amount of energy required to take one of these aligned moments and flip it 180 degrees. If you flip a spin like this, it can propagate through the material by successive mutual flips between neighbors. And we can examine the behavior of these spin flips, and their interactions with defects and oscillations <br><br>
The spin wave and spin flip are two aspects of the same thing: a magnon. <br><br>
This is the kind of quantum mechanical dualism you're used to, but it also shows the dualism between particle and field. The spin wave is an excitation over the entire field of atomic spins and the particle is an excitation at a single point, and depending on what we're investigating at the time. <br><br>
This is how I still envision fields. <br><br>
The difference between this and fundamental fields is that there's no substrate for the quantum field. There is no aether serving the role of the electromagnetic field that has some property that we excite electromagnetic waves in, and whose interactions with electrons are particulate photons. There is just the electromagnetic field. The same is true of the gluon field and weak fields. However just as water waves give you an analogy for water waves, the atoms in a material give you an idea about how a field works. <br><br>
And it's more than a simple analogy. Many of the big "verifications" of high energy theorists that we've seen in recent years, Dirac and Majorana fermions, for example, are coming out of materials and metamaterials research in condensed matter. Experimentalists can construct systems with the correct symmetries to realize the particles. It's like creating universes on demand, universes that contain the thins you want to find. <br><br>
In material, it's even easy to see something that becomes difficult to envision: how do these (at least) 25 fundamental fields of the standard model superpose over the entire universe? In our crystal lattice, quasiparticle fields correspond to different properties of the atomic and material structure. Lattice vibrations become phonons. Magnetic exicitations are magnons. And there are many others, but they all have this character of being related to properties of the collective properties of the material. <br><br>
You can view string theory in a similar way: there is this fundamental structure of the string, and the 25 fields are all different manifestations of the properties of the string. Is it open or closed? How does it vibrate? In string theory there is just one kind of thing, the string, and since the different manifestations of this kind of string are all conceptualized as excitations in universal fields. So, there may be only a single, universal field. <br><br>
Both of these interpretations, every particle is a string or every particle is an excitation in the stringy field, would count as Aristotle's "one principle."* String theory is a monist theory, the kind that Aristotle tries to disprove here. I don't think that the arguments he propounded in Physics I.2 really refute string theory, partly because many of them are arguments against specific philosophers and partly because many of them have mistaken logic of Greek mathematics. <br><br>
For example, if I change a line in Physics I.2 to read "if there is a continuous fundamental field, then immediately it must be many fields because anything continuous must be divisible," then we have string theory exactly as I described it. But, string theory is logically consistent. It is also logically coherent. There is no obvious logical problem with string theory as mathematics. It's only possible problem is correspondence: even though it's currently the best guess at a unified theory of the world, it may never be shown to actually predict anything. But although string theory might not be correct, and there may even be no theory of everything,(*3) the field theoretic structure has both the continuity (say, the electromagnetic field) and the divisibility (say, the photon) built in. In some way. And in some way, it is a counterexample to Aristotle's assertions against monism in Physics I.2.
<br><br>
So, it seems to me, string theory refutes these assertions by Aristotle. <br><br>
Monism is at least possible. <br><br>
_____________________________________ <br>
* In the translation the, Aristotle is arguing against the idea that there is only one "principle," whether that principle is "a substance, a quantity, or a quality." Democritus has an "infinite number of principles," because his atomic theory had atoms of "all shapes" -- and there are no limits on the number of shapes there could be (If I recall, Epicurus would have a limited number in the form of regular polygons, when he finally got around to being born, if I recall). Heraclitus, apparently, had zero principles. So the wording here made life difficult for me: I wanted a principle to be something like Newton's Law, rather than a substance like water or air. <br> <br>
** I think. There probably should be a quantum mechanical description of transverse mechanical waves on strings, although I don't know what its use would be, or how you'd do an experiment to detect it.<br> <br>
This would be like building up the vibration of a guitar string by adding transverse vibrations to individual atoms, one at a time. That would probably make them phonons.<br> <br>
(*3) Although I should go through these arguments on the <a href = https://en.wikipedia.org/wiki/Theory_of_everything>TOE page</a> for Wikipedia before I say that.<br>
<hr width = 66%><br>
<table style="width: 100%;"><tbody><tr><td align="left" width = 33%><a href="https://physicsfm-master.blogspot.com/2021/12/answering-aristotle-i1.html"> ← Previous ( Physics I.1 ) </a></td><td align = "center" width =34%><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a></td><td align="right" width = 33%> <text align="right"><a href = https://physicsfm-master.blogspot.com/2022/01/answering-aristotle-i3-there-is-more.html>( Physics I.3 ) Next → </a></text><br /></td></tr></tbody></table><br />
PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-30072799909697515372021-12-10T11:15:00.006-08:002022-02-26T19:11:00.408-08:00Answering Aristotle I.1 - The Basic Process<table style="width: 100%;"><tbody><tr><td align="left" width = 33%>.<td align = "center" width =34%><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a></td><td align="right" width = 33%> <text align="right"><a href = https://physicsfm-master.blogspot.com/2021/12/answering-aristotle-i2-there-is-more.html>( Physics I.2 ) Next → </a></text><br /></td></tr></tbody></table><br />
<hr width = 66%><br>
<blockquote> <b>Physics I.1</b> Although understanding something means we can reason from first principles, discovering these principles requires us to sort them out from the aggregate observations we are built to apprehend.</blockquote> <br><br>
And do that over and over a hundred times per book. I only rarely go back to them. I thought what I'd do here is to extend this a little by discussing how Aristotle's insights hold up, how they compare to what I've been told they are, and so on. <br><br>
There are two things that Physics I.1 brings to mind. The first is the actual evolution of physics, which in some places follow Aristotle's insight and in some placed doesn't. The other is that this discussion reflects the advice of Arnold Arons on the teaching of physics. <br><br>
<hr align = center width = 66%> <br>
When I wrote about operational definitions (or will write about in the past), I used an example from Arnold Arons, most likely, that describes how the concept of temperature arose in physics. This is a relatively new idea, and we know exactly how it developed. And it definitely follows Aristotle's process. "The natural way" to proceed is to "start with that which is intelligible <i>to us</i> and then to move toward what is intelligible to the thing <i>in itself</i>." That is, we start with what we perceive about the world, and then we try to use that to determine the way the world actually works. <br><br>
The first instance is temperature. This is a concept we all have a fairly intuitive understanding of, right? Well, not really. We have an understanding of "hot" and "cold," which was always a fairly ill-defined idea until Galileo. In order to construct a notion of temperature, we need to define a reliable way to compare "hot" and "cold," which is quite difficult. If you hold a book that has been sitting in a room for a long time, it feels neither hot nor cold, but if you touch marble, it feels cool. Finding a common understanding under such conditions is difficult. At the turn of the 17th century, Galileo invented his thermoscope, an instrument that held a glass bulb containing air and suspended in water that would rise and fall with changes in the state of the air (both the temperature and pressure state variables would cause these changes). It was only qualitative, but it was the first way in which our subjective idea of hot and cold could be related to the internal state of the things we called "hot" and "cold." <br><br>
It would be another hundred years before Fahrenheit constructed reliable thermometers based on the relative thermal expansion of air to that of mercury or alcohol. This allowed a science of thermodynamics and a theory of engines to rise, but it did not tell us what temperature is. What was needed for that was the kinetic theory of gases, a statistical examination of the motion of air molecules. This would wait for another 200 years, after the atomic theory of matter was accepted and probability theory was on a sound footing. The temperature of the air became the average kinetic energy in the translational motion of its molecules. Which is not what your feeling, your apprehension, of hot and cold is about. <br><br>
"Hot" and "cold" is about the rate of energy transfer from a material to you, which is why your book feels neutral and the marble feels hot. But, this too is explained by statistical mechanics. So, our basic ideas, the categories of our experience, led us to discover the idea of a measurable temperature, which in turn allowed us to discover what this meant to the air, and finally to even explain what our experience is really measuring. <br><br>
This mirrors the point of Aristotle's Physics I.1 exactly. <br><br>
I was going to offer a second example of the kind, the nineteenth's century's development of the idea of energy, which displaced the "imponderable fluids" of the 18th century (caloric, etc.). I think the story would further support Aristotle. <br><br>
A counterexample, however, might be the late 20th century's search for fundamental particles. Here, the big minds theorized the existence of fundamental particles, but rather vaguely based on precise theories, and provided the material experimentalists, who then searched for them with amazingly powerful and expensive machines. At meetings, you would see maps of the parameter space, regions blocked off from where different experiments could measure. Experiments verified, experiments falsified, but experiments didn't drive the science. And neither did our perceptions. I cannot see how this follows Aristotle's program, although perhaps a longer view could make a good story of it. <br><br>
It seems though, for most of its existence, physics followed something close enough to that program. <br><br>
<hr align = center width = 66%> <br>
The other comparison that this brought to mind was an educational one. Maybe two, in fact. The first from Arnold Arons and the other from Edward Redish, although many of these insights I've seen elsewhere. <br><br>
One of the more interesting admonishments of Arons' <i>Teaching Introductory Physics</i> is his insistence that concepts come before names [2]. This is part of his Socratic attempt to build students' physical intuition. The idea is to use identify the need for a concept, to start using the concept, before naming it. Even going to the point of admonishing students who use the term (e.g., "energy") before it is fully defined. Naming things gives people a feeling of understanding when they do not, and it relieves them enough that they ignore the rest of what's being said ("oh, that's energy -- let's get back to the important things, like "Hearthstone"). But you'll notice, this teaching style mirrors Aristotle's Physics I.1. <br><br>
<hr align = center width = 66%> <br>
So it looks like Aristotle's approach to physics looks like the same approach physicists usually use both to investigate phenomena and to teach physics. This, at least, is a good sign for the rest of the book, despite its reputation. <br><br>
___________________ <br>
[1] Most of this comes from Arnold Arons' <i><a href = https://amzn.to/3pJRdnF>Teaching Introductory Physics</a></i> Part III: Introduction to the Classical Conservation Laws. <br><br>
[2] This comes mostly from part I. I just skimmed Arons and couldn't find what I remembered. Is it Knight's <a href = https://amzn.to/3Gt3m7a>Five Easy Lessons</a>? Can't find it there, either. Probably Arons. <br><br>
[3] He may also have said many of the same things in his <a href = https://amzn.to/3pJRdnF>Teaching Physics with the Physics Suite</a>, which is also good (despite much very particular advice relating to the Physics Suite). The references for the articles are: <br><br>
<dd>0. Redish, E.F., "Using Math in Physics: Overview." [<a href = https://arxiv.org/abs/2009.14271>arXiv</a>] <br>
<dd>1. Redish, E.F., "Using Math in Physics: 1. Dimensional Analysis." [<a href = https://arxiv.org/abs/2011.12760>arXiv</a>]<br>
<dd>2. Redish, E.F., "Using Math in Physics: 2. Estimation." [<a href = https://arxiv.org/abs/2011.12699>arXiv</a>]<br>
<dd>3. Redish, E.F., "Using Math in Physics: 3. Anchor Equations." [<a href = https://arxiv.org/abs/2011.12761>arXiv</a>]<br>
<dd>4. Redish, E.F., "Using Math in Physics: 4. Toy Models." [<a href = https://arxiv.org/abs/2011.12700>arXiv</a>]<br>
<dd>5. Redish, E.F., "Using Math in Physics: 5. Functional Dependence." [<a href = https://arxiv.org/abs/2012.00794>arXiv</a>]<br>
<dd>6. Redish, E.F., "Using Math in Physics: 6. Reading the Physics in a Graph." [Not Yet Published]<br>
<dd>7. Redish, E.F., "Using Math in Physics: 7. Telling the Story." [Not Yet Published] <br><br>
<hr width = 66%><br>
<table style="width: 100%;"><tbody><tr><td align="left" width = 33%>.<td align = "center" width =34%><a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a></td><td align="right" width = 33%> <text align="right"><a href = https://physicsfm-master.blogspot.com/2021/12/answering-aristotle-i2-there-is-more.html>( Physics I.2 ) Next → </a></text><br /></td></tr></tbody></table><br />
PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-31117035072123214562021-11-28T11:20:00.003-08:002021-11-28T11:27:07.562-08:00Critical Thinking v Problem Solving II - Problem Solving from Start to FinishIn order to explore problem solving and critical thinking a little more, I would like to talk about problem solving. Mainly, I'll talk about a 1963 paper by Slagle, who programmed the first symbolic integrator using punch cards. And a very clever algorithm. It was able to solve 52 of 54 integrals on what sounds like a Calculus II final at MIT* using a ladder of proximate goals reaching up to an ultimate goal, the solution of the integral. It needed, to mimic some aspects of human problem solving by implementing two sets of rules: those that are always good and those that are heuristics and sometimes break down. But it does get to the answer. This isn't so surprising in itself, since commercial products, e.g., Mathematica, have been doing so for decades, but the fact that it could be done with a 1959 mainframe computer and with so few rules is an astounding fact. I will use this algorithm as the backbone for how to think about problem solving. <br><br>
The general way that people solve math problems is by a searching method.** You start with what you're given and then you search the space with known rules and inspiration and try to move forward, one step at a time. From time to time you get stuck, and then you take a few steps back and try another likely path. One of the differences between an expert and a novice is how they react to a setback: a novice usually chooses one way of doing a problem, then never steps back.*** An expert tries several tactics, until they complete the task. Matthew Shoenfeld's work quantified this behavior, and private discussions make it clear that many people consider this searching, <i>a la</i> Polya,(*4) almost a moral imperative of reasoning. <br><br>
Slagle's system worked on a method of proximate goals. That is, you start with a main goal, where you'd like to get to, and then as you work towards it, you sometimes identify a subgoal. When you do, you keep track of that subgoal. Sometimes as you work, you can reach a point where several directions are possible. In these cases you keep all of the goals, and place them in your tree. You don't try to work all of the goals together. Instead, you use various methods to assign the goals priority. Some goals can be reached through automatic processes, processes that are guaranteed to move you toward the main goal. You do these first. Others are heuristics, and you look to those only when there is no automatic option. Furthermore, for heuristics, you need to judge how costly each one is in the given situation: how hard it is compared to the goal. And you try the least costly first, as long as its line remains the least costly. When you find a way to reach the main goal, you have solved the problem. <br><br>
This should remind you of the method that people use to solve problems in the real world, as observed on Betamax by Shoenfeld: you search the space with known rules, trying to move forward, and when you get stuck, you take a few steps back and try a likelier path. <br><br>
There were three types of methods used by the program to solve the integrations problem. The first was a short integration table, a list of "Standard Forms." If you came to a standard form, then you had effectively solved the problem. In effect, the rest of the edifice is built to put a non-standard form in the image of a standard form. The second set of methods were those that always improved the situation. Whenever you came to one of these you tried it, and then checked it against the standard forms. These had no deviations and didn't really require any interesting tracking. You tried one after another until there were no obvious steps to try. Finally, there were the heuristics. These are rules that sometimes improve the situation, but sometimes do not (sometimes, trying them makes matters worse). When you came to this point, the program would try all of the applicable variants, and then assess the character of each try to judge which is the best way to proceed. And as I said, it worked in 52 of the 54 cases, and the other two could not be solved because the IBM 7090 didn't have enough memory for more entries in its integral table. <br><br>
This goal-directed reasoning is what I'll use as a paradigm for problem-solving. I often characterize it as a tangram in my classes: physics gives you a set of tiles with which to form the shape of the solution. The tiles are limited, but the forms are infinite.(*5) Arranging the tiles into the correct form is called thinking. <br><br>
_____________________________<br>
* At MIT, it's part of 18.01 Single Variable Calculus. 'most everywhere else, it's Calculus II - Methods of Integration -- with some idiosyncratic identifier cataloged by the inane, parochial system used by universities (a college catalog is a definitive, smack-down, irrefutable argument against expert judgement, although listening to the faculty senate is even better). I first learned of this algorithm from a very good lecture by Patrick Winston from 6.034, <a href="https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-034-artificial-intelligence-fall-2010/lecture-videos/lecture-2-reasoning-goal-trees-and-problem-solving/">Reasoning: Goal Trees and Problem Solving.</a> A short description of the algorithm can be found in Winston's <i><a href = https://amzn.to/3FVH7Xy>Artificial Intelligence</a></i> textbook. <br><br>
** See <i><a href = https://amzn.to/315m2dW>Mathematical Problem Solving</a></i>, Matthew Shoenfeld. I would like to show some diagrams from his work, but at this time I don't have a way to use images. <br><br>
*** A college freshman thinks that problems should take 2-3 minutes to solve, and literally thinks that a problem that takes more than 10 minutes is impossible. <br><br>
(*4) See, e.g., <i><a href = https://amzn.to/3I0K9LR>How to Solve It</a></i>, George Polya. <br><br>
(*5) Well, not really. Firstly, of course, there is room for disagreement about how many tiles there are, and what constitutes a different tile. I am sure there are many fewer than the 60-odd list of things the engineering college says it wants the students to learn (about one per 25 minutes of instruction), since "solve a quadratic equation," "Newton's Third Law," and "Kepler's Laws" are all very different types of things. Also, I think that there aren't technically an infinite number of solutions. I am 95% sure there are only seven one-dimensional kinematics problems for one process on one object (and 100% certain for uniformly accelerated motion). Well, I guess, then, if I allow an infinite number of processes and an infinite number of objects, I could end up with an infinite number of kinematics problems. Probably. And these can be sutured onto more complicated dynamics problems, which unlike kinematics, are really physics.PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-80409784030391782992021-11-17T19:51:00.006-08:002021-12-20T09:09:46.740-08:00How Long Does It Take to Do an Infinite Number of Things?Infinite processes shred our intuition to Hell like nothing other than probabilities and relativity. This was the infernal currency of Zeno of Elea, who proposed devilish paradoxes in order to prove the conjecture that movement is impossible. Zeno would construct a simple scenario that would show that everyday aspects of life, like chasing a tortoise or shooting an arrow. We really only have accounts from other authors, basically Aristotle, who disagree with him. Some of these arguments intertwine ideas about space and time, the arrow argues that an object is motionless at any instant, and both the dichotomy and Achilles and the Tortoise make arguments about the impossibility of doing an infinite number of things. I will eventually move on to an example to calculate the total time that it takes for a ball to bounce an infinite amount of time, but I will first describe the dichotomy using Philocetes' Arrow as a story (rather than Aristotle's bare-boned description from the Physics [1]).<br><br>
<blockquote>Philocetes looses an arrow from the Bow of Heracles at the Trojan prince, Paris. In order for the arrow to strike the Son of Priam, first, it must fly half the distance between the heroes. But, it is clear that in order for an arrow to travel half way to the midpoint before it can get to the midpoint. And it has to travel half way to the point before that, <i>ad infinitum</i>. Therefore, in order to move from one spot to another, no matter how close, you have to move an infinite number of times in a finite amount of time to get anywhere, so the arrow never flies and Trojan War never ends.</blockquote><br>
This is paradox because we do move, but at least the first time your hear the argument, you don't have a good reason why it is wrong. The arrow must move, but logically it cannot. And this is applicable to every kind of motion. Before you can eat your Wheaties in the morning, you have to get out of bed and get into the kitchen. But, you have to move through an infinite number of small separations to get there. <br><br>
And you can't do an infinite number of things before breakfast.<br><br>
Or can you?<br><br>
Most people think that the invention of Calculus resolved Zeno's paradoxes. This is certainly true in the case of the dichotomy: Leibniz used and even dirtier trick with infinity than Zeno did. Leibniz built calculus out of the idea of an infinitesimal to align with his cosmological ideas. An infinitesimal is a chunk of the universe that is smaller than the smallest division, basically the reciprocal of infinity. The integral calculus would define the distance that the arrow must travel as a sum of all of the infinitesimal chunks of space between Philocretes and Paris. The nature of infinitesimals is that they are smaller than the smallest fraction, there are an infinite number of them between each rational number. The infinity of the infinitesimals is that of the real numbers (the continuum) and the infinity of the dichotomy is that of the rational numbers (countable). So, if you can construct a theory of motion that adds up all the infinitesimal points, it will automatically encompass the infinity of halves used by Zeno.<br><br>
This solve the dichotomy, but it does so indirectly with an end around.<br><br>
By subsuming the motion of the dichotomy into a single, continuous process that can be analyzed separately, we show that motion can exist. We solve the riddle by changing the problem, though. However, this leaves Zeno's premise unchallenged: an infinite number of processes take an infinite amount of time. What I'd like to do here is take on the premise that an infinite number of discrete, sequential processes needs to take an infinite amount of time. You could do the same thing with the dichotomy, as well, but since that is an arbitrary partition of a single, continuous process, which I feel is a little different.<br><br>
The specific question I ask is: how long does it take a rubber ball to stop bouncing? The physics here is quite simple. It can be done with kinematics using the simplest of deflection theories: the coefficient of restitution. The model uses the simple rule that the velocity of the rebound of an object is proportional to its original speed, and that proportionality (the coefficient of restitution) remains the same after each bounce. The duration of the air time of the ball is given by uniformly accelerated motion. The sum of a sequence of such bounces will lead to an infinite series with a known sum (thanks again, calculus), and this sum will be finite.<br><br>
Where can this go wrong? Well, it's not in the assumption of uniform acceleration. Yes, it's not quite true, but it's pretty accurate at low velocities for short times, which a rubber ball acts in. If we complicate the problem by adding in air resistance, that will give us a slightly more accurate estimate at the cost of an annoying integral (no thanks, calculus). This accuracy will give us a time that is strictly smaller than the uniform acceleration version by giving us a factor similar to the coefficient of restitution itself. The significant assumption that would break this analysis, if it were relevant, would be that the time of the bounce itself will be the same each time the ball hits the ground if the bounce is modeled on an elastic restoring force, which is probably the best model available. Even though this will be small, at some point it will be larger than the air time per bounce, and since it remains the same, adding an infinite number of them would create an infinite time for the bounce.<br><br>
But, to answer the basic question, can an infinite number of processes be completed in a finite amount of time, eliminating the time of the bounce is justifiable.<br><br>
So what happens in this case? Well, from basic kinematics, we find that the time of an individual flight is proportional to the initial speed of that bounce.* Since the initial speed of each process is the coefficient of restitution is just the initial speed of the previous process, the duration of the subsequent process is scaled down by the sane proportionality,<br><br>
<dd>t<sub>n</sub> = r t<sub>n-1</sub> = r<sup>n</sup> t<sub>0</sub></dd><br>
which means that flight is scaled down by a power of the coefficient of restitution.<br>
When these are summed, we find an infinite series in powers of the coefficient of restitution that has a known sum: the inverse of one less the coefficient [ 1/(1-r) ]. So, the total time the ball bounces is finite if r < 1 (which is must be unless it is gaining energy from the environment somehow). <br><br>
So, an infinite number of bounces takes a finite amount of time<br><br>
<dd> t = 1/(1-r) t<sub>0</sub>.</dd><br>
This is a reasonable answer because if r = 1 the bouncing goes on forever and if r = 0 it stops after the first flight. This should be the same result you'd find if you were to sum the time to travel each segment of the arrow's path, but here we have distinctive processes represented by the flights between bounces. Our hero Leibniz has defeated Zeno of Elea's Satanic dichotomy.<br><br>
So the Trojan War terminates, and you can do an infinite number of things before breakfast. <br><br>
<br><br>
________________________________________________<br><br>
* The proportionality constant is 2/g.<br><br>
[1] All of my Aristotle is missing. Most of what I know about this comes from Sainsbury's Paradoxes, >although I was using the Stanford Encyclopedia of Philosophy.PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-4280274520925985172021-11-10T11:54:00.004-08:002021-11-10T12:37:17.465-08:00Critical Thinking vs. Problem Solving I - How Are They Different?I've spent a lot of time thinking about critical thinking and problem solving. Nominally, my course is required to include a critical thinking component by the university so that it order to satisfies a distribution requirement. Over the past five years, I have never really been able to discern the difference between critical thinking and problem solving, a more common term for what we "teach" in physics. Some papers explicitly say that problem solving is a kind of critical thinking, [1] others say that it's a separate skill. [2] I don't really know the proportion. I originally just went for a rather strict <a href = https://groups.spa.umn.edu/physed/Research/CGPS/GreenBook.html>problem solving format</a> from the University of Minnesota* that I feel shows me how a student is thinking about problems,and based on Force Concept Inventory scores, I implemented it well (gain around 35-45%).<br><Br>
The students hated it, but my job isn't to be adored. <br><br>
However, one spring day in 2020, I was informed that my course was to be reviewed for its critical thinking component.** When reviewing a course, all I have to do is to submit a product for each student that shows their critical thinking skills. This product can be a test question, a homework problem, a paper. I have a section on the tests where students individually provide an explanation of how to solve a problem, and I felt that this would do. It is a little stilted. What do you want to do? "Find the velocity." How are you going to do it? "Use conservation of energy." How do you represent that? "1/2 m v^2 = 1/2 m u^2 + mgh." It shows exactly what the student is thinking and how they utilize the data. I felt it would be a good way to show the development of the students' problem solving capabilities over the semester. <br><br>
But I was given a rubric, and the rubric told me that I was wrong. <br><br>
These are some highlights from the rubric: <br><br>
<dd><b>Explanation of Issues</b>. Problem is stated clearly and described comprehensively, including all relevant information.</dd>
<dd><b>Evidence</b>. Viewpoints of experts are questioned thoroughly.<dd>
<dd><b>Context</b>. Thoroughly analyzes assumptions and carefully evaluates the relevance of contexts when presenting a position.</dd>
<dd><b>Student's Position</b>. Position is imaginative and other's views are synthesized within it.</dd>
<dd><b>Conclusions</b>. Conclusions are logical and reflect the evidence and perspectives in priority order.</dd><br>
Try that with conservation of energy. <br><br>
For some of this, expanding the selection from just he planning phase of the problem solving process would probably do. For others, it seems irrelevant. In fact, some of the categories seem to be completely irrelevant to the course ("Influence of Context and Assumptions" is the full title). But, looking at the rubric for the curriculum component, I feel at minimum it requires a term paper, and probably a thesis. The school implicitly takes the side that problem solving is not a part of critical thinking. <br><br>
Critical thinking, as described by the rubric, is really separate from problem solving. <br><br>
However, I still think that there should be some overlap. I think in come coming posts, I'll talk about what I think problem solving and critical thinking are, possibly in several posts each, and then I'll talk about some specific problem-solving tools for first year physics students. <br><br>
___________________________________________________ <br><br>
* That, I think, they don't use it any more. <br><br>
** And just after I wrote this, they told me that this was the evaluation of the engineering students' "written communication." <br><br>
___________________________________________________ <br><br>
[1] Willingham, D., "Critical Thinking: Why Is It So Hard to Teach?" American Educator (2007). <br><br>
[2] Pasquinelli, E., M. Farina, A. bedel, and R. Casati, "Naturalizing Critical THinking: Consequences for Education, Blueprint for Future Research in Cognitive Science." Mind, brain, and Education 15, 168 (2021).PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-72014197321880205202020-05-02T17:39:00.001-07:002020-05-02T17:39:57.888-07:00Alain Aspect's Quantum Optics on Coursera<a href="https://www.amazon.com/Introduction-Quantum-Optics-Semi-classical-Quantized/dp/0521551129/ref=as_li_ss_il?dchild=1&keywords=alain+aspect&qid=1588454912&sr=8-1&linkCode=li1&tag=physicsfm00-20&linkId=91a2711ddfb11e2c37806e093e801a5a&language=en_US" target="_blank"><img border="0" align="right" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=0521551129&Format=_SL110_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=physicsfm00-20&language=en_US" ></a><img src="https://ir-na.amazon-adsystem.com/e/ir?t=physicsfm00-20&language=en_US&l=li1&o=1&a=0521551129" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />I finally got done with finals, and as a reward, I decided to see if I could find a <a href = http://www.coursera.org>Coursera</a> course to play with. I had been looking to see if there was a quantum computing MOOC available (and there are many), but among the search results was <a href = https://www.coursera.org/learn/quantum-optics-single-photon#syllabus>
Alain Aspect's Quantum Optics</a> course on Coursera. This is, he says, the first of two MOOCs based on his textbook (at right*). It's a short course (4 weeks, basically four lectures), and so, just right for me.<br><br>
The subject is interesting (and very similar to a special topics course I took as an undergraduate called "The Quantum Mechanics of the Laser" -- I wish I'd kept those notes when I moved), but the lectures are dense. They do go over a lot of the material in <a href = https://amzn.to/2z3NMBP>Sakurai's Modern Quantum Mechanics</a>*, which I worked through two summers ago, but of course with a focus on the meaning in terms of quantum optics. Already, some things I haven't heard of before, some that relate to experimental design (quantization volume), some straightforward interpretations of mathematical expressions (the energy of a single photon). The understand in terms of experimental parameters is particularly helpful to me (since I understand things in terms of experiments, due to my training).<br><br>
The course, however, is not for those who are afraid of mathematics. Aspect's discussion in mathematically dense. Really dense. My students think I use too much mathematics in university physics classes, but this is all math. And Aspect expects you to have seen it all before: many times he references your prior knowledge. He doesn't quite say that you're an uneducated ignoramus if you can't recall trivialities like the photon energy or the uncertainty relations (he calls them dispersion relations, an aspect of his philosophy -- it's nice to hear an expert talk explain the mechanics of physics in a way that makes it clear he has opinions). And the homework is tough. Not as tough as it sounds when you read it, but pretty tough.[1] Even on the internet, you're expected to know your stuff.<br><br>
<a href="https://www.amazon.com/Statistical-Mechanics-Algorithms-Computations-Physics/dp/0198515367/ref=as_li_ss_il?dchild=1&keywords=krauth&qid=1588465407&sr=8-2&linkCode=li1&tag=physicsfm00-20&linkId=da106d4d632051e389d1688c8ddb1843&language=en_US" target="_blank"><img border="0" align = right src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=0198515367&Format=_SL110_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=physicsfm00-20&language=en_US" ></a><img src="https://ir-na.amazon-adsystem.com/e/ir?t=physicsfm00-20&language=en_US&l=li1&o=1&a=0198515367" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />I have found that I had to speed his lectures up. I don't know if it's him, if it's because he's European, or because Coursera makes everyone speak like someone shilling their latest book in a bad TED talk, but he talks slowly. Last summer, I took <a href = https://www.coursera.org/learn/statistical-mechanics>Werner Krauth's MOOC</a>,[2] from the same school but a different country, and he spoke with the same cadence. I found I had to speed up the lecture to 1.5x so that they spoke at a normal speed.<br><br>
This minor technical problem aside, I certainly am enjoying the break this provides before I start preparing for my summer courses (How did I let myself get roped into summer courses? At least they're on-line so I can get a lot of the work out early).<br><br>
[1] I didn't pay the $49.99, or whatever, it costs in order to get it graded, but I did work it. And it reinforced the advice I give to my students: try the homework before class, then the class will be more useful to you.
[2] Which was serendipitous, since I'd begun setting up to work through the book it was based on, <a href = https://amzn.to/3dg79Xb>Statistical Mechanics: Algorithms and Computation</a>,* when Coursera sent me an e-mail about it. I get the feeling there's as much shilling on Coursera as there is at TED talks. But it couldn't be more: a TED talk is just an advertisement for a book. If you're lucky, there's more to the book than just the TED talk. Obviously, though, there's more to a physics textbook than eight hours of lecture. Hell, there's more to a physics textbook than the forty hours of lecture in a semester.<br><br>
* Note: These links are to Amazon pages. Purchases on those pages from the links will give me a commission (at least for now -- every time I've tried to use the Amazon Associates program they've kicked me off for not selling anything, but I do like having the links in the show notes so that you can pick up the books we might reference in a discussion).PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-56133510172422078922020-04-22T08:28:00.029-07:002024-01-28T19:22:23.853-08:00Most Recent Podcasts<table><tbody><tr><td valign = top>
<strong><a href="http://physicsfm-frontiers.blogspot.com/">Physics Frontiers</a></strong><br /><br />
Episode 76: <a href="http://frontiers.physicsfm.com/76">Undecidability and Theories of Everything with Claus Kiefer</a><br /><br />
<a href="http://physicsfm-master.blogspot.com/2017/09/physics-frontiers-index.html">All Physics Frontiers Episodes</a><br /><br />
<a href="https://physicsfm-master.blogspot.com/2018/08/physics-frontiers-most-popular-episodes.html">Most Popular Physics Frontiers Episodes</a>
</td><td width="100"><br />
</td><td valign = top>
<strong><a href="https://weeklyelectronicpaper.blogspot.com/">The Weakly Electronic Paper</a></strong><br /><br />
Episode 5: <a href="http://papers.physicsfm.com/5">Counting Universes</a><br /><br />
<a href="https://physicsfm-master.blogspot.com/2020/04/weekly-electronic-paper-index.html">More Episodes</a></td></tr>
</tbody></table>
<br /><br />
<a href="http://physicsfm-master.blogspot.com/">Blog</a><br />
Latest Blog Entry: <a href="https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-i4-there-cannot-be.html">Answering Aristole I.4 - There Cannot Be an Infinite Number of Things</a><br>
Series: <a href = https://physicsfm-master.blogspot.com/2022/02/answering-aristotle-index.html>Answering Aristotle</a>
<font color = White>Series:</a> <a href = https://physicsfm-master.blogspot.com/2022/06/youtube-book-reveiws.html> YouTube Book Reviews</a>
<br /><br />
Retired Podcasts:<br /><br />
<a href = http://paradoxes.physicsfm.com>Quantum Paradoxes</a><br><br>
<p align = right><font color = blue>Update: 2023/01/02</font></p>PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-68194152738075028942020-04-22T08:21:00.002-07:002020-06-18T20:28:04.912-07:00Weekly Electronic Paper Index<a href="https://weeklyelectronicpaper.blogspot.com/">Podcast Home</a><br /><br />
Posted Shows:<br /><br />
4. <a href = https://weeklyelectronicpaper.blogspot.com/2020/06/entropy-v-entropy.html>Entropy v. Entropy</a> (2020/06/18)<br><br>
3. <a href="https://weeklyelectronicpaper.blogspot.com/2020/04/uploaded-20200419-i-discuss-qbism-or.html">The Machine in the Ghost</a> (2020/05/13)<br /><br />
2. <a href="https://weeklyelectronicpaper.blogspot.com/2020/04/itty-bitty-physics.html">Itty Bitty Physics</a> (2020/04/28)<br /><br />
1. <a href="https://weeklyelectronicpaper.blogspot.com/2020/04/uploaded-20200419-i-discuss-qbism-or.html">The Quantum Bookie</a> (2020/04/19)<br /><br />
PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-12764610231763152962018-09-01T10:07:00.002-07:002019-07-15T18:30:52.954-07:00Quantum Sense and Nonsense by Jean Bricmont<a href="https://www.amazon.com/Quantum-Sense-Nonsense-Jean-Bricmont/dp/3319652702/ref=as_li_ss_il?keywords=sense+and+nonsense+about+quantum&qid=1563240345&s=books&sr=1-1&linkCode=li2&tag=physicsfm0e-20&linkId=33ef12c646c13513f3211f5a1436b093&language=en_US" target="_blank"><img border="0" align = right src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=3319652702&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=physicsfm0e-20&language=en_US" ></a><img src="https://ir-na.amazon-adsystem.com/e/ir?t=physicsfm0e-20&language=en_US&l=li2&o=1&a=3319652702" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />I don't really know why I picked up <a href = https://amzn.to/2lCbyOx>Quantum Sense and Nonsense</a> or when. I'm pretty sure it was in the last year when I was looking for some popular books to read after I finished <a href = http://physicsfm-master.blogspot.com/2018/05/the-wave-function-essays-on-metaphysics.html>The Wave Function</a>, and this one, written by Jean Bricmont and published by Springer, stood out. The cover, and likely the description, seems a little misleading since it seems to say that the book will focus on crazy and unfounded assertions of psychic and mystical properties attributed to quantum mechanics (and as Bricmont has published with Sokal, that's exactly what you'd think), but instead the book focuses on two experiments (double slit experiments and EPR-type experiments, both of which seem to be recurring themes on <a href = http://physicsfm-frontiers.blogspot.com/>Physics Frontiers</a>) and the interpretation of each. Bricmont follows Bell in asserting that EPR-experiments like the Aspect experiment show that there is some kind of non-locality at play in quantum mechanics and that the best way to interpret the meaning of the wave function (that is, what the wave function, itself, is) is to look toward an interpretation like the de Broglie-Bohm vision of the wave function (see Bell's, <a href = http://physicsfm-master.blogspot.com/2017/09/speakable-and-unspeakable-in-quantum.html>Speakable and Unspeakable in Quantum Mechanics</a>).<br><br>
Despite being much different than what I thought the book would be, this made the Quantum Sense and Nonsense an excellent read.<br><br>
The double slit experiment as performed by Thomas Young in the first decade of the 19th century showed that coherent light from the sun interfered with itself, showing that light is, in fact, a wave -- and brought about the belief in a mysterious Ether in which the light waves propagated. When Einstein showed the photoelectric effect requires quantization of light,* this made the interpretation more difficult. And de Broglie's prediction that electrons, really all material objects, have a wavelength and the subsequent discovery of electron diffraction,
brought the same problem to all matter. And the interference is so strong that when a single photon or a single electron is sent through the slits, and the results of the experiments accumulated, the interference fringes are still seen. Material objects interfere with themselves. <br><br>
A very strange property, and one that leads to many strange interpretations of quantum mechanics, is that if you set up a detector at one of the slits in the double slit experiment to see which slit the particle passes through, then the interference fringes will disappear. This leads to the idea that <I>observation</I> causes a change in the wave function, what is termed the wave function collapse. Many strange ideas come out of this, even from physicists (Bricmont's target). People use this idea to give consciousness a role in the measurement of quantum systems, Bricmont uses quotes from the following physicists to show the sloppy thinking on these points: d'Espagnat, Wheeler, and Mermin (to name only those I've heard of): they all give some role to the human mind in the collapse of the wave function. To be fair, understanding the collapse is impossible in the standard "Copenhagen" interpretation of quantum mechanics, which is what Schroedinger's cat was intended to show.<br><br>
The EPR experiments, violations of Bell's theorem, are the second cause of sloppy thinking because they show one of two things: either (1) quantum mechanics is non-local or (2) quantum mechanics is non-causal. Those are the two assumptions that Bell uses to derive his inequalities beyond ordinary statistics and quantum theory. If you have to choose one of the two assumptions to invalidate, (1) is the more likely (although we recently published a podcast on <a href = http://physicsfm-frontiers.blogspot.com/2018/07/retrocausality.html>retrocausality</a> and Yakir Aharonov has a different version of a locality-preserving assumption, presented in his <A href = http://physicsfm-master.blogspot.com/2018/07/quantum-paradoxes-by-aharonov-and.html>Quantum Paradoxes</a> book as well as old papers). But once you remove locality from your assumptions about the world, people start babbling about telepathy and similar nonsense. <br><br>
As befits someone of Bricmont's station, the descriptions of these experiments are exemplary, and Quantum Sense and Nonsense would be worth a read if only they were presented here. However, he does us another service by giving us a rich, logical and convincing description and defense of the de Broglie-Bohm pilot wave theory of quantum mechanics. In this theory, the wave and particle are broken up into two objects, an oscillation in space time that drives the motion of an otherwise deterministic particle. The randomness of quantum mechanics then ceases to be the mystical randomness associated with Bohr and Heisenberg and Copenhagen in general and becomes the deterministic randomness of statistical mechanics.** Bricmont goes so far to say that because of this and the fact that it can be mathematicised, de Broglie-Bohm is the only interpretation of quantum mechanics;*** the others (including statistical, Copenhagen, and many-worlds) don't meet that bar. Obviously, it doesn't mean that Bricmont is right, since he's delved into philosophy or worse in the comparison of interpretations by their linguistic characterizations, but it is a good way of thinking about the interpretations.<br><br>
So I would recommend this book. I do think that it is a little too popular for most people that would read this, and he often refers to his own, more technical <a href = https://amzn.to/2k5gDOU>Making Sense of Quantum Mechanics</a> quite a bit for more quantitative details. He also says that this is only "slightly" more rigorous and would probably point you to P. Holland's <a href = https://amzn.to/2k4jTKn>The Quantum Theory of Motion</a> for a really rigorous treatment. I haven't read either of those two books, however, so I can't recommend them to you.<br><br>
-------------------------------------------------------------<br><br>
I wrote this review a little faster than I'd like because I'd just finished the book yesterday and Google sent me a "<a href = https://motls.blogspot.com/>news story</a>" on my phone today, which I read over my morning coffee. It was a rather infantile post by Luboš Motl, someone I've never heard of, who calls himself a "freelance string theorist" (but who has a reasonably impressive pedigree) reviewing books by science journalists. It makes me sad when a physicist does as bad a job of presenting science as a science journalist does.<br><br>
The blog does a good job of showing two very bad ways to think about the interpretations of quantum mechanics. The first is from the book he reviews (or really, the blog post that he reviews of the book that it reviews). In that case, the science journalist author, whose name is of no importance, suggests that all interpretations are valid. This seems quite odd to me, especially when most of them are logically contradictory: if you believe in a wave function collapse, then you can't coherently believe in the universal wave function of Everett. You can make up a pretty complex and silly rationale if you want to, but it will always end up being incoherent somewhere (and I'm not going to read it to find out where). The reason you would want to hold multiple conceptions in your head is to find out places where they disagree -- and then to find an experiment that distinguishes them.<br><br>
Motl himself presents to us the second version, which is to deny all interpretations. But that is clearly unsatisfactory. Although it is called the Copenhagen interpretation (by some, what is meant by that changes from philosopher to philosopher, physicist to physicist), you still have to have some interpretation. You have to have some ontological vision of the wave function to assert that information cannot travel faster than light during its collapse, for example, or to state that it would be impossible to ever use it for long distance communication. That you refuse to examine your beliefs doesn't mean that they're not there.<br><br>
Bricmont does a good job of showing how to deal with interpretations without getting so dogmatic that his assertions become meaningless, just the opposite of Motl<br><br>
------------------------------------------------------------
<br><Br>
* Planck's experiments don't show this. Since the quantized electromagnetic waves are coming out of an enclosed chamber, black body radiation could be interpreted as having something to do with standing waves in the oven. <br><br>
** Interestingly, though, the roles of randomness are reversed. In statistical mechanics we measure macroscopic parameters associated with microstates. In quantum mechanics, and especially in the de Broglie-Bohm interpretation, the wave function is the microstate and the measurement is of the particle, or the microstate.<br><br>
*** I should mention that de Broglie-Bohm is not excessively popular among physicists. Reading The Wave Function, however, I came out of it thinking it was extremely popular among professional philosophers of science.PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-27491114097370305842018-08-02T19:54:00.009-07:002023-04-23T18:38:27.634-07:00Physics Frontiers: Most Popular Episodes<b>All Time</b><br>
1. Physics Frontiers 45: <a href = http://frontiers.physicsfm.com/45>Loop Quantum Gravity</a><br>
2. Physics Frontiers 60: <a href = http://frontiers.physicsfm.com/46>Warp Bubbles</a><br>
3. Physics Frontiers 55: <a href = http://frontiers.physicsfm.com/55> Multiversality</a><br>
4. Physics Frontiers 53: <a href = http://frontiers.physicsfm.com/53>Electromagntic-Gravitational Repulsion</a><br>
5. Physics Frontiers 44: <a href = http://frontiers.physicsfm.com/44>Spooky Action at a Distance></a><br>
<br><br>
<b>2022</b><br>
1. Physics Frontiers 69: <a href = http://frontiers.physicsfm.com/69>The Flavor Puzzle</a><br>
2. Physics Frontiers 68: <a href = http://frontiers.physicsfm.com/68>Qunatum Resource Theories</a><br>
3. Physics Frontiers 65: <a href = http://frontiers.physicsfm.com/65>Time and Causality</a><br>
<br>
<b>2021</b><br>
1. Physics Frontiers 60: <a href = http://frontiers.physicsfm.com/60>Warp Bubbles</a><br>
2. Physics Frontiers 59: <a href = http://frontiers.physicsfm.com/59>The Hubble Crisis</a><br>
3. Physics Frontiers 57: <a href = http://frontiers.physicsfm.com/57>Quantum Effects in Gravity Waves</a><br>
<br>
<b>2020</b><br>
1. Physics Frontiers 55: <a href = http://frontiers.physicsfm.com/55>Multiversality</a><br>
2. Physics Frontiers 53: <a href = http://frontiers.physicsfm.com/53>Electromagnetic-Gravitational Repulsion</a><br>
3. Physics Frontiers 54: <a href = http://frontiers.physicsfm.com/54>The ANITA Experiment</a><br>
<br><br>
<b>2019</b><br>
1. Physics Frontiers 45: <a href = http://frontiers.physicsfm.com/45>Loop Quantum Gravity</a><br>
2. Physics Frontiers 44: <a href = http://frontiers.physicsfm.com/44>Spooky Action at a Distance</a><br>
3. Physics Frontiers 46: <a href = http://frontiers.physicsfm.com/46>Wigner's Friend</a><br>
<br><br>
<b>2018</b><br>
1. Physics Frontiers 38: <a href = http://frontiers.physcisfm.com/38>The Dimensionality of Space-Time</a><br>
2. Physics Frontiers 33: <a href = http://frontiers.physicsfm.com/33>The String Theory Landscape</a>
3. Physics Frontiers 40: <a href = http://frontiers.physicsfm.com/40>The Octonions</a><br><br>
<br><br>
<b>2017</b><br>
1. Physics Frontiers 17: <a href = http://frontiers.physicsfm.com/17>The Physics of Time Travel</a><br />
2. Physics Frontiers 9: <a href = http://frontiers.physicsfm.com/9>f(R) Theories of Gravity</a><br />
3. Phyiscs Fronteirs 6: <a href = http://frontiers.physicsfm.com/6>Genreal Relativity for the Experimentalist</a><br />
<br><br>
<a href = https://physicsfm-master.blogspot.com/2017/09/physics-frontiers-index.html>Physics Frontiers Index</a><br><br>
[Edited 1/1/2023]PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-64480260962021720502018-07-25T20:10:00.004-07:002021-05-02T15:43:54.122-07:00Quantum Paradoxes by Aharonov and RohrlichYou might think I like <i>Quantum Paradoxes</i> [<a href="https://amzn.to/3beCIlF">Amazon</a>] by Yakir Aharonov and Daniel Rohrlich. I mean, I started a <a href="http://paradoxes.physicsfm.com/">podcast</a> about it. I might even finish it someday.*<br /><br />
This book explores the meaning of quantum mechanics through paradoxical thought experiments. It uses a few standard ones, like Schrodinger's cat, and a lot of interesting variations of the double slit experiment and electron diffraction. The first eight chapters motivate mainly how quantum mechanics works using paradoxes. The last ten chapters motivate Aharonov and Rohrlich's interpretations.<br /><br />
<iframe align = "right" style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm02-20&language=en_US&marketplace=amazon®ion=US&placement=3527403914&asins=3527403914&linkId=7a0013284d9090faf76103ec5e68b3b3&show_border=true&link_opens_in_new_window=true"></iframe>
I am very enamored of the format.<br /><br />
Each chapter follows a formula. After a short preamble, a paradox is presented in detail. The paradoxes are presented as thought experiments, first. This means that a detailed, if not physically possible, experiment is described, and then its physics discussed. The physics leads to two possible interpretations, such as: there is no physical difference in the dynamics of an electron on either side of a charged capacitor, but quantum mechanics predicts a phase shift in the wave function of the electron. How can that be?<br /><br />
Next, aspects of the physics are discussed in mathematical detail. In this case, what is the relationship between the gauge and the phase of the wave function. This leads to a choice, clarification, or reconciliation. The most interesting part of this for me has been the use of modular variables to clear up some points that have to do with the use of gauges, although the general set-up of the interference experiments Aharonov and Rohrlich are discussing requires a bit of careful reading. Sometimes, a section or two follows with implications and real, physical experiments.<br /><br />
The second half of the book deals with the interpretation of quantum mechanics in the context of weak measurements. I really don't have a great idea about how to explain a weak measurement, but the two important facets are: (1) they allow you to measure the wave function without (completely) destroying it and (2) they are only approximations to the wave function. Aharonov and Rohrlich mainly deal with their own interpretation, and (a) the Copenhagen interpretation (a favorite among users of quantum mechanics) and (b) the many-worlds hypothesis (a favorite among string theorists). Mainly, I think, because these are their main competitors. <br /><br />
Their own interpretation has to do with temporal boundary conditions, which is very appealing to me because it's compatible with the block universe idea of relativity, at least conceptually. It's very important to remember that every fundamental physical theory must be compatible with every other fundamental physical theory -- if two theories that should apply to a situation don't, you have a paradox. So, any interpretation of quantum mechanics must be compatible with relativity. This hasn't been a problem with the theory -- quantum electrodynamics is exactly the integration of quantum mechanics and special relativity. It has been a major problem with interpretations, and the authors detail some of those problems in the book.<br /><br />
I don't want to go into more detail, but if you want to get more detail, then over the next thirty-four-odd weeks, I discuss each chapter with a friend of mine in a podcast. Contact me for the address if you're not already subscribed.<br /><br />
So, I just love this book. It's a great way to not only explore quantum mechanics, but to explore what it means to be an interpretation of quantum mechanics in a rigorous and technical, but not exceedingly technical (to a physicist). If you have the mathematical background to play with differential equations, or even the intellectual fortitude to not be scared of them, I highly recommend this book. If you don't have that knowledge, then check out the podcast. It'll probably be more than enough for you.<br><br>
* Update (5/24/2020): To be clear here: I've read through the book three times, once to get ideas for teaching well before I'd started any podcast, once when Randy agreed to do the Quantum Paradoxes podcast, and finally, once when we started the podcst over. I think we've given up hope on finishing the <a href="http://paradoxes.physicsfm.com">Quantum Paradoxes</a> podcast.
PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-65522901107015082452018-05-22T20:26:00.002-07:002020-05-13T19:53:00.719-07:00The Wave Function: Essays on the Metaphysics of Quantum Mechanics<br /><iframe style="width:120px;height:240px;" marginwidth="0" marginheight="0" align = "right" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ss&ref=as_ss_li_til&ad_type=product_link&tracking_id=physicsfm00-20&language=en_US&marketplace=amazon®ion=US&placement=019979054X&asins=019979054X&linkId=4de8e22e64cd79d67a336ac2f37462a2&show_border=true&link_opens_in_new_window=true"></iframe><br /><div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";"><a href = https://amzn.to/3cwHwkO> The Wave Function</a> is a philosophy anthology about the wave function of
quantum mechanics.<span style="margin: 0px;"> </span>The wave function
specifies the state of the quantum mechanical system in a way similar to how
the ideal gas law specifies the state of a dilute gas.<span style="margin: 0px;"> </span>You can make more or less of that, if you
wish.<span style="margin: 0px;"> </span>But if you’re a philosopher, you’ll
make more.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">This book is not really about the wave function, what it
does, and how to care for it, it is a discussion of David Albert’s thesis
exposited in the 1996 paper, “Elementary Quantum Mechanics.”<span style="margin: 0px;"> </span>In this paper he looked the wave function as
a real thing, and said that if it is real, then the universe must exist in
3N-dimensions, where N is the number of particles in the universe.<span style="margin: 0px;"> </span>This is because the wave function a system of
particles is a collection of positions for those particles.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">I’ll discuss each chapter in turn.<span style="margin: 0px;"> </span>You might think the description is a little short
for some of them, but the review has gotten pretty long.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">1. David Albert, “Wave Function Realism”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">In this essay, David Albert of the philosophy department of
Columbia University discusses his idea on how to view the wave function
realistically.<span style="margin: 0px;"> </span>Realist, in the
philosophical sense, of the wave function is a real thing, and so its nature
can be used to tell us something about the nature of the rest of the world.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Since this is the view that most of the remainder of the
essays discuss, and all address, it’s a good thing to go into detail about this
here.<span style="margin: 0px;"> </span>If the wave function is a real,
physical object, it is a kind of field.<span style="margin: 0px;">
</span>In physics, the word field refers to an object that can be represented
as a function, which can be scalar, vector, or tensor-valued, that has
different values at different points in space.<span style="margin: 0px;">
</span>The velocity field of a stream, for example, is a vector field that
tells you how fast and in what direction the water in that stream is moving at
that point.<span style="margin: 0px;"> </span>In a steady state, even
though the water is different at every instant, the current is the same at every
point.<span style="margin: 0px;"> </span>Its domain is the physical, three
dimensional space that composes the stream (technically, it could be all
space), and its range is the three dimensional velocity vectors that the water
can travel at (magnitudes and directions.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">What Albert noticed is that the domain of the field is, in
all of physics, the 3D space that we live in or a subset of it.<span style="margin: 0px;"> </span>All of physics, that is, except in quantum
mechanics, where the domain of the wave function is the possible positions of
each of the particles that the wave function describes (is that true?*), and so
instead of being a 3-dimensional space, it is a 3N-dimensional space with N
being the number of particles.<span style="margin: 0px;"> </span>Albert’s
leap was to say that since quantum mechanics is the foundational theory of the
world, this 3N-dimensional space is the REAL world whereas our usual
3-dimensional space is an apparition based on the relationships between large
number of particles.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">The reason why we don’t see the 3N world is basically a
brain-in-a-vat type of problem.<span style="margin: 0px;"> </span></span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">2. Valia Allori, “Primitive Ontology and the Structure of
Physical Theories”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Valia Allori, a philosopher at Northern Illinois University,
tries to understand all this in a very philosophical way.<span style="margin: 0px;"> </span>She invents sub-categories within categories
that you’d never heard of.<span style="margin: 0px;"> </span>In this case,
she starts talking about the “primitive ontology” of a theory.<span style="margin: 0px;"> </span>This is all, if I recall, along the same
program as Albert.<span style="margin: 0px;"> </span></span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">An ontology in the philosophy of science is the collection
of thing in the world on which the theory can function, whether they be atoms
or charges or point particles.<span style="margin: 0px;"> </span>A
primitive ontology is the minimum ontology for the theory to function.<span style="margin: 0px;"> </span>This varies from theory to theory, and it has
a set of “primitive variables” which create the minimum parameterization that
allows you to translate the objects of the primitive ontology into mathematics.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Allori analyzes three and a half theories with this system:
Bohmian mechanics, the Ghirardi-Rimini-Weber (2x versions), and the many-worlds
interpretation.<span style="margin: 0px;"> </span>These three
interpretations keeps coming up, and not very many more, so I wonder if most of
the philosophy of quantum mechanics is a detailed response to John Bell,
especially the collection The Speakable and Unspeakable in Quantum Mechanics –
since those were, really the three that he detailed in that book.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">3. Steven French , “Whither Wave Function Realism”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Steven French, a philosopher at the University of Leeds,
wonders whether the wave function is the right thing for the realist
philosopher of science to consider as part of the ontology of the theory.<span style="margin: 0px;"> </span>He feels that overestimating the importance
of the wave function in using quantum mechanics to tell us about the world
underdetermines the theory and leaves us with a rather vague idea about what
really exists.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">4. Sheldon Goldstein and Nino Zanghi, “Reality and the Role
of the Wave Function in Quantum Theory”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Sheldon Goldstein, a mathematician at Rutgers, and Nino
Zanghi, a physicist at the University of Genoa,<span style="margin: 0px;">
</span>wonder just what it is that a wave function can be, and there are
several things that look at.<span style="margin: 0px;"> </span>First of
all, there can be no such thing as the wave function in the world.<span style="margin: 0px;"> </span>It is just a computational tool.<span style="margin: 0px;"> </span>Next, it could be an epistemic representation
of our subjective knowledge of the system.<span style="margin: 0px;">
</span>That is, it isn’t physical but it has something to do with the state of
something physical – basically, the state of our brains.<span style="margin: 0px;"> </span>Or it can be some fact or object in the world
– a thing in the world.<span style="margin: 0px;"> </span>That it, the
wave function could be nothing, it could be epistemic, or it could be real.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">The main point of most of these papers is to analyze and
criticize Albert’s wave function realism, so it is the last that is
interesting.<span style="margin: 0px;"> </span>If the wave function is
real, there are two possibilities: it could be nomological or material, or at
least partially one or the other will a little subjectiveness or nothingness
thrown in.<span style="margin: 0px;"> </span>If it is nomological, it is
a fact about the world, like Gauss’ Law.<span style="margin: 0px;">
</span>If it is material, it is a real thing, like a changed pith ball.<span style="margin: 0px;"> </span>But again, they give themselves a little
wiggle room by allowing the wave function to be either quasi-nomological or
quasi-material.<span style="margin: 0px;"> </span>It might be factish or
thinglike.<span style="margin: 0px;"> </span></span>
</div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Just like the Allori paper, Goldstein and Zanghi analyze a
group of different interpretations of quantum mechanics to determine what role
the wave function plays in each according to this categorization.<span style="margin: 0px;"> </span>If you’re interested enough in which is what
and what is which, you’re probably interested enough to read the book, so I’ll
save myself some time and not make out a table.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">5. Peter Lewis, “Dimension and Illusion”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Peter Lewis, a Dartmouth philosopher that was at the
University of Miami when The Wave Function was published, gives a pragmatic
analysis of Albert’s thesis.<span style="margin: 0px;"> </span>And it’s no
surprise what a pragmatist will think about a 3N-dimensional world.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">6. Tim Maudlin, “The Nature of the Quantum State”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Time Maudlin, New York University Philosopher, provides the
most direct assault on Albert in this book.<span style="margin: 0px;">
</span>That is, he goes after the main method of analysis – producing an
ontology from the mathematics – in order to show that 3N-dimensional space isn’t
necessary.<span style="margin: 0px;"> </span>He does this both by careful
analysis of Alberts 1996 paper and with an analogy to Fourier’s Analytical
Theory of Heat, which provided a metaphysical cover for the caloric fluid model
of heat.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">That particular induction was natural.<span style="margin: 0px;"> </span>The equations in the theory of heat flow are
the same as those as for current flow in liquids.<span style="margin: 0px;"> </span>So, if you don’t have any idea about
statistical mechanics, it’s the most natural thing in the world to see heat as a
current of some sort of fluid instead of just energy transfer.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">And of course, that didn’t work.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Maudlin’s conclusion is justified: looking at the
mathematical form that a theory has to take does not require you to take
implications of the mathematics to be real – to be in the ontology of the
theory, as the philosophers put it. <span style="margin: 0px;"> </span>Not
only is not necessary, it’s not even a good reason.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">7. Bradley Monton, “Against 3N-Dimensional Space”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Bradley Monton, who worked at the University of Colorado at
Boulder at the time but now philosophizes at Wuhan University, sets the tone
for this one with his first section “Quantum Mechanics is False.”<span style="margin: 0px;"> </span>Why does he say that? Because he feels that General
Relativity is the more fundamental theory of the two, mostly because quantum
mechanics synchronize their watches.<span style="margin: 0px;"> </span>This
may seem trivial, but it’s a major problem in using string theory to construct
a theory of gravity.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">His main argument against the 3N-dimensional space and in
favor of 3-dimensional space as being the fundamental dimensionality of the
world is that 3-dimensional space more accurately reflects what physicists think
about the world and how they carry out experiments.<span style="margin: 0px;"> </span>And, Monton argues, unless 3N-dimensional
space can make itself useful, then there’s no good reason to take it as
fundamental.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">8. Alyssa Ney, “Ontological Reduction and the Wave Function
Ontology”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Alyssa Ney, a philosopher at the University of California at
Davis, gives an account of “ontological reduction,” how one set of things can
be reduced to another set of things.<span style="margin: 0px;"> </span>In
this case, she gives an account of how our 3-dimensional experience can reduce
to the 3N-dimensional space of the wave function.<span style="margin: 0px;"> </span>You can think of this in analogy to
scientific reductionism where biology can be reduced to chemistry, for example,
for a certain idea about what biology is.<span style="margin: 0px;">
</span>Chemistry never gives you the full picture of biology, but we have faith
that between chemistry and physics, everything about living things can be
explained in some reasonable way – although not predicted.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">9. Jill North, “Structure of the Quantum World”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">Jill North, now of Rutgers, once of Cornell, discusses how
Albert’s program is supported by the dynamics of the world.<span style="margin: 0px;"> </span>If the wave function changes in
3N-dimensions, then a 3N-universe is the best explanation of it.<span style="margin: 0px;"> </span>I didn’t see it before, but I see it now:
North’s view of the wave function is of the universal variety, and the
universal wave function is the most physical assumption of the many-world’s
hypothesis.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">10. David Wallace, “A Prolegomenon to the Ontology of the
Everett Interpretation”</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";">David Wallace moved from Oxford to the University of
Southern California to do his philosophizing.<span style="margin: 0px;">
</span>Here, he talks a lot about the many-worlds interpretation.</span></div>
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: "calibri";"><span style="margin: 0px;"> </span>* In the case of
identical particles, the wave function gives the probability amplitude of
finding *a* particle there.<span style="margin: 0px;"> </span>It doesn’t
tell you which one.</span></div>
PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-18031846620083602982018-04-25T19:34:00.000-07:002018-09-01T13:07:30.047-07:00Book Review Index<ol>
<li><a href = http://physicsfm-master.blogspot.com/2018/09/quantum-sense-and-nonsense-by-jean.html>Qunatum Sense and Nonsense</a> by Bricmont</la>
<li><a href = http://physicsfm-master.blogspot.com/2018/07/quantum-paradoxes-by-aharonov-and.html>Quantum Paradoxes</a> by Aharonov and Rohrlich</li>
<li><a href = http://physicsfm-master.blogspot.com/2018/05/the-wave-function-essays-on-metaphysics.html>The Wave Function: Essays on the Metaphysics of Quantum Mechanics</a>, Ney and Albert, Eds.</li>
<li><a href= http://physicsfm-master.blogspot.com/2018/04/cosmic-update-by-adams-buchert-and.html>Cosmic Update</a> by Adams, Buchert, and Mersini-Houghton </li>
<li><a href = http://physicsfm-master.blogspot.com/2018/03/the-nature-of-space-and-time.html>The Nature of Space and Time</a> by Hawking and Penrose</li>
<li><a href =http://physicsfm-master.blogspot.com/2017/10/extra-dimensions-in-space-and-time-by.html>Extra Dimensions in Space and Time</a> by Bars and Terning</lI>
<li><a href = http://physicsfm-master.blogspot.com/2017/09/theory-and-experiment-in-gravitational.html>Theory and Experiment in Gravitational Physics</a> by Will </li>
<li><a href = http://physicsfm-master.blogspot.com/2017/09/speakable-and-unspeakable-in-quantum.html>Speakable and Unspeakable in Quantum Mechanics</a> by J.S. Bell</li>
</ol>
PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-67402007897480838072018-04-24T11:22:00.001-07:002018-07-28T19:46:40.602-07:00Cosmic Update by Adams, Buchert, and Mersini-Houghton<a href="https://amzn.to/2Aj2G7v">Cosmic Update: Dark Puzzles, Arrow of Time, Future History</a> is the second book in the <a href="http://www.mvjs.org/">Multiversal Journeys</a> series run by <a href="https://fqxi.org/grants/large/awardees/view/__details/2006/nekoogar">Farzad Nekoogar</a> and published through Springer. Like its predecessor in the series, <a href="http://physicsfm-master.blogspot.com/2017/10/extra-dimensions-in-space-and-time-by.html">Extra Dimensions in Space and Time</a>, this is an accessible, semi-technical discussion about different matters in theoretical physics by experts. In this case, the three main essays are about cosmology, especially: if the universe is expanding due to an unidentifiable force, what does that mean about our physics. All of these topics are perfect topics for Physics Frontiers, and some probably have been and will be.<br />
<br />
<a href="https://www.amazon.com/Cosmic-Update-Puzzles-Multiversal-Journeys/dp/1489994130/ref=as_li_ss_il?_encoding=UTF8&me=&qid=1532832262&linkCode=li2&tag=physicsfm0a-20&linkId=750c6b9da193785137b811cd5ecd66f8&language=en_US" target="_blank"><img border="0" align = right src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=1489994130&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=physicsfm0a-20&language=en_US" ></a><img src="https://ir-na.amazon-adsystem.com/e/ir?t=physicsfm0a-20&language=en_US&l=li2&o=1&a=1489994130" width="1" height="1" border="0" align = right alt="" style="border:none !important; margin:0px !important;" />The first essay, "Dark Energy and Dark Matter Hidden in the Geometry of Space?" by Thomas Buchert describes how gravitational theory is being modified to accommodate the expansion of the universe. In particular, it describes the attempt to look at how the structure we see in the universe aids in creating an apparent cosmological constant. Standard cosmology usually assumes uniform values for the energy density and pressure of the universe, although we know that to be untrue. It's "true enough," they say, "on average." Buchert and coworkers have been looking at how that average model breaks down in the presence of known structure, and what the implications of that structure are, and apparently those nonuniformities might account for the dark energy field and dark matter halos observed by astronomers. The process that does this is the gravitational backreaction against cosmic evolution. Exactly how this works, I'd need to delve into, but it's an interesting way to model what's happening to the cosmos that gives a physical explanation to some ghostly phenomena.<br />
<br />
The second essay, "The Arrow of Time in a Universe with a Positive Cosmological Constant Λ" by Laura Mersini-Houghton identifies the direction of thermodynamic processes based on the expansion on the universe. And what apparently happens is that in a de Sitter universe, the gravitational entropy eventually exceeds the matter entropy, and time reverses. Worse, when it happens, there is a "tachyonic instability" from (or by?) "super-Hubble" modes, which results in a violent transition at the boundary. At the conclusion of the chapter Mersini-Houghton says that the result of her theoretical inquiry into the direction of time is that we cannot have a "pure" Λ for dark energy, the cosmological constant has to vary in space and time, in order to avoid a breakdown of general relativity in the infrared regime.<br />
<br />
The last of the original essays, "The Future History of the Universe" by Fred Adams is an updated physical eschatology accounting for the presence of dark energy. He discusses the fate of stars of different sizes, black holes, and so on. It's entropically depressing, of course. The universe is young now, in its "stellariferous" era with its fancy stars and pretentious galactic clusters, but in the long run, it's going to be a bleak, black place. In just another 10<sup>33</sup> years, though, the universe will be quite unfashionable and enter into the degenerate era, full of brown dwarfs, white dwarfs, blue dwarfs, and any other dwarf that found a way to get out. The scary, lonely thing is that some of these blue dwarfs will have habitable worlds. But there won't be anything out there in the sky for them to see. Going over my notes, I didn't really get where the changes were, except that there were supposed to be difference from what you'd have read in 1995, but it is an interesting discussion.<br />
<br />
An added bonus is a reprint of a paper by Lawrence Krauss and Robert Scherrer, "The Return of the Static Universe and the End of Cosmology" that supplements the last essay by saying that there will be a point in future where an observer will not be able to tell that the universe is expanding.<br />
<br />
All in all very interesting. It's a little expensive, unlike the next book in the series, <a href="https://amzn.to/2K9osLA">Quantum Physics, Mini Black Holes, and the Multiverse: Debunking Common Misconceptions in Theoretical Physics</a> (just out) but if you can get a copy, it's worth a read.PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-67413490980404286802018-03-16T20:31:00.000-07:002020-05-14T06:08:35.408-07:00The Nature of Space and Time by Hawking and PenroseStephen Hawking died two days ago, and I have a copy of <I><a href = https://amzn.to/2Lv463Z>The Nature of Space and Time</a></I> sitting in my review pile waiting its turn. It doesn't have to wait its turn, though, because (1) Stephen Hawking recently died, and so it would be nice to review something of his as a homage, and (2) It's short and so easy to review.<br><br><a href="https://www.amazon.com/Nature-Space-Newton-Institute-Lectures/dp/069116844X/ref=as_li_ss_il?s=books&ie=UTF8&qid=1532832415&sr=1-1&keywords=the+nature+of+space+and+time&linkCode=li2&tag=physicsfm0a-20&linkId=de85e6f204c50db639cd498881b06141&language=en_US" target="_blank"><img border="0" align = right src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=069116844X&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=physicsfm0a-20&language=en_US" ></a><img src="https://ir-na.amazon-adsystem.com/e/ir?t=physicsfm0a-20&language=en_US&l=li2&o=1&a=069116844X" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
The premise of the book is that it is a series of lectures by Hawking and his mentor Roger Penrose. This was "the high point of a six month program held in 1994 at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge." I'm not sure where Cambridge is or what it's famous for, but I'm sure this was the hottest thing going in that half-year. The book itself is not a debate, only the last of the seven chapters. The first six are lectures alternately by Hawking and Penrose building up to the debate. If the seventh lecture was the high point of the program, the lectures certainly built up the dramatic tension in exactly the way universities don't build up dramatic tension.<br><Br>
The lectures are semi-non-technical. By that I mean that Hawking and Penrose can't help themselves and they put the pretty equations in the text for you to admire, but they aren't used for anything. So, really, they're nothing more than window dressing for the topic at hand. The topics are the classical theory of space and time (what is the future, what is the past, do they always exist?), singularities in space time (and some ideas about them), many varieties of quantum mechanical stuff (quantum black holes, quantum cosmology, quantum gravity), and twistor theory. Not necessarily light subjects, but presented in a way that most anyone should be able to understand.<br><br>
And here both Hawking and Penrose get a chance to discuss some of their theories, like: why, exactly, would nature abhor a singularity? How exactly does it go about hiding them?<br></br>
To be honest, the debate doesn't seem to be very heated when you get to it. It's just a restatement of the positions outlined beforehand, mostly. Not much "here's why I'm right and you're wrong." So, if you were waiting to find out who won the debate, I'm sorry: it wasn't that kind of debate.<br><Br>
-----------------------------------------------------
I just noticed that Princeton is now putting this is a series call "The Isaac Newton Institute Series of Lectures," which is awesome. I want to read all of the books in that series. It's just that I have: there's only one in it so far, and that's this one -- which I read in its old Princeton Science Library format (a series that I love)<br><br> I'm sure the Isaac Newton Institute has brought some very engaging speakers in, and I was wondering if you'd help me bother them for more.<br><br>
Mostly for myself, what I'm thinking about reading:<br>
<ul>
<li><a href = http://amzn.to/2G3rKkn>Quantum Physics, Mini Black Holes, and the Multiverse: Debunking Common Misconceptions in Theoretical Physics (Multiversal Journeys) by Yasunori Nomura (Author), Bill Poirier (Author), John Terning (Author), Farzad Nekoogar (Editor) </a></li>
<li><a href = http://amzn.to/2HGTIQe>Quantum Sense and Nonsense</a> by Jean Bricmont</li>
<li><A href = http://amzn.to/2FG175y> Quantum-Classical Analogies (The Frontiers Collection) by Dragoman and Dragoman</a>
<a href = https://amzn.to/2GxjlXn>A</a> [started, actually, 7/28/2018]
</ul>PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-88366696135300405822018-01-22T09:56:00.001-08:002018-02-15T07:41:38.005-08:00StubThis is a stub for show notes.<br />
<br />
The link you're looking for will be redirected to the show notes for the episode you're interested in as soon as it is about 50% ready.<br><br>
Until then, go <a href =http://physicsfm-master.blogspot.com/2017/09/physics-frontiers-index.html>HERE</a> for an index of all Physics Frontiers shows.PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-50469557889003746362017-11-12T17:45:00.001-08:002017-11-12T17:45:17.452-08:00Video: Physics Frontiers Episode 2Finally got a video together for Physics Frontiers 2 - The de Broglie - Bohm Interpretation of Quantum Mechanics.
It's available on YouTube: <a href = https://youtu.be/Y0PBlvfrVbE>PhysicFrontiers0002.mp4</a>
Tell me what you think. I'm trying to add some illustrations that I think might be helpful.
PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-41064185527885717982017-10-31T19:53:00.000-07:002017-10-31T19:53:11.449-07:00Happy Birthday, Physics FrontiersPhysicsFM was 3 years old October 20th, and the first Physics Frontiers episode came out one year ago today!<br />
<br />
We've had over 20,000 downloads in our first year, plus almost 3,000 embedded plays through Podomatic.<br />
<br />
Thank you for listening to our podcast. Randy and I are just a little bit happier every time you play one of our podcasts, and twice as happy every time you share it with a friend!<br />
<br />
Thanks again!<br />
<br />
JimPhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0tag:blogger.com,1999:blog-6472333724958467896.post-85404807727193470872017-10-17T12:00:00.000-07:002018-07-29T08:26:24.090-07:00Extra Dimensions in Space and Time by Itzhak Bars and John Terning<a href="https://amzn.to/2K4GopB"><i>Extra Dimensions in Space and Time</i></a> is a wonderful find. A few months ago, Randy and I talked about Itzhak Bars' 2T theory of space and time for a <a href="https://physicsfm-frontiers.blogspot.com/">Physics Frontiers</a> podcast (it's two podcasts up in the editing queue and will come out about a month from when I publish this), and it was one of the hardest this for us to get a handle on. Randy is really excited about Bars' theory (and not just because he went to USC), but reading the papers he selected left us a little confused about how it worked. When I saw that Springer had a book by Bars on the subject, I decided to take the $125.00 hit. Maybe a longer form text would help me figure out what was going on, and maybe choose a couple of different papers for another podcast that were a little more understandable.<br />
<a href="https://www.amazon.com/Extra-Dimensions-Space-Multiversal-Journeys/dp/0387776370/ref=as_li_ss_il?s=books&ie=UTF8&qid=1532877907&sr=1-1&keywords=extra+dimensions+in+space+and+time&linkCode=li2&tag=physicsfm0a-20&linkId=174f2d332da4314a52e757e9301fca06&language=en_US" target="_blank"><img border="0" align = right src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=0387776370&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=physicsfm0a-20&language=en_US" ></a><img src="https://ir-na.amazon-adsystem.com/e/ir?t=physicsfm0a-20&language=en_US&l=li2&o=1&a=0387776370" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
<br />
And I was pleasantly surprised by this book.<br />
<br />
<i>Extra Dimensions in Space and Time</i> is the first in the <i>Multiversal Journeys</i> series, edited by Farzad Nekoogar. This series of books is fulfilling the purpose of the <a href="http://www.mvjs.org/">Multiversal Journeys</a> organization:<br />
making theoretical physics easy for the public. In that, the two halves of this book are non-technical introductions to their topics. The first hundred pages, by Itzhak Bars, talks about a theory of particles and interactions that uses two different time-like dimensions. The next sixty pages, by John Terning, discusses what the proliferation of spatial dimensions in string theory means. And they don't hurt your brain.<br />
<br />
In Itzhak Bars' "Two-Time Physics: The Unified View from Higher Dimensional Space and Time," Bars discusses the reasons for his 2T physics. This includes an insightful development of physics, including string theory itself, building up to the rationale for the second time dimension. And then he discusses the implications of the theory.<br />
<br />
Interestingly, two-time physics was the result of Bars' postulation of a symmetry. His postulate is this: there is a phase-space symmetry between different space-time dimensions without affecting the physics. Any particular direction at any particular event can be swapped with any other. Furthermore, this works with the energy-momentum tensor. On top of that, an energy can be swapped with a time and a spatial dimension can be swapped with a momentum component. Although his figure does not include cross arrows, I'd expect this to be true with the other possible reconfigurations. He calls this the Sp(2,R) symmetry.<br />
<br />
Again, physics does not change when you regard a spatial dimension as being time-like, as long as you switch a time dimension to be space-like.<br />
<br />
If this symmetry is indeed a law of nature, like translational or rotational symmetries, then there must be two time dimensions (no more and no less) and four space dimensions (at least, maybe you can have more, I don't remember, but you can't have less) to prevent anomalies like ghost particles -- the real universe is the 4+2 universe. These two extra dimensions are macroscopic, not the microscopic curled-in dimensions of string theory. And this leads to all of the interesting physics. The big, interesting analogy is that the universe you and I reside in, the 3+1 universe, is a holographic shadow of the 4+2 universe. And it is the way in which 4+2 objects project into 3+1 space-time that determines how we view them. <br />
<br />
The eight ways in which Bars had shown these objects to project into our space are as:<br />
<ol>
<li>Dirac Particles </li>
<li>Particles in a Robertson-Walker Universe</li>
<li>Massive Particles</li>
<li>Particles in Maximally Symmetric Spaces</li>
<li>The Hydrogen Atom</li>
<li>Particles in a Conformally Flat Space</li>
<li>The Harmonic Osciallator</li>
<li>Twistors</li>
</ol>
<div>
which isn't everything, but its a lot.</div>
<div>
<br /></div>
<div>
Bars claims for 2T-Physics are the following:</div>
<ol>
<li>Sp(2,R) gauge symmetry of phase space is a fundamental property of nature.</li>
<li>2T-field theory, free of ghosts, has be successfully constructed and applied.</li>
<li>Grand unified theories and supersymmetric 2T-field theory have been constructed as 2T-field theories.</li>
<li>2T-physics provides new technical computation tools for 1T-physics.</li>
<li>2T supergravity, 2T strings, 2T branes, 2T M-Theory are only partially constructed in 2T-physics at this time.</li>
<li>A deeper phase space formulation of field theory is likely to exist.</li>
<li>The extra space and time dimensions in 2T-physics are neither small nor hidden.</li>
</ol>
<div>
John Terning's "Extra Dimensions of Space" is of a similar level, if not anywhere near as weird. This is because Terning focusses on the strings and branes in M-Thoery, and stays just as far away from the scary math, ending, more-or-less, at the Higgs. When the book was written, in 2009, the Higgs particle hadn't been discovered at the LHC, but it was expected. Although nowhere near as detailed and nowhere near as out there as Bars' discussion, Terning does a good job of explaining why you need something like a string theory, and why the string theories that are limits of M-Theory satisfy those issues. </div>
<div>
<br /></div>
<div>
He builds up from the standard modern physics story, through symmetry and gravity, and then discusses string theory. How do strings manifest as particles? How do they interact with each other and with branes? How do branes deform, and what are the implications of such a deformation? Those are the questions Terning answers, just a little bit more exactly than you're used to in an equation-free account.</div>
<div>
<br /></div>
<div>
There is also a final chapter for those of you who feel like equation-free is to physics as Diet Pepsi is a Coca-Cola, "The Equations behind the Words." The thing is, I expect that for most of you that are interested in the exactness that mathematics provides a concept, the equations provided are things you're already familiar with.</div>
<br />
But since that's the 13th chapter, you're going to skip it anyway.<br />
<br />
So, this is a great book, especially given my expectations from Bars' papers, and I recommend it to people who want a deeper understanding about the theories that require additional dimensionality for the world. It's a step up from a popular book, and I think it's exactly the sort of thing that someone who listens to our podcast to enjoy.PhysicsFMhttp://www.blogger.com/profile/13134018651176248475noreply@blogger.com0