Friday, June 15, 2018

Post-Newtonian Gravitation

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Recorded: 11/12/2017 Released: 6/8/2018

Randy and Jim discuss the Parameterized Post-Newtonian Framework, a generalized way to compare metric theories of gravity to experiment in a standardized way. In this episode we discuss several theories of gravity and how they hold up under the light of experimental data.

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A Guide to the Parameters


  • γ (gamma) - Coupling of matter to curvature, GR = 1 , Newton = 0
  • β (beta) - Linearity of superposition, GR = 1 - Superposition linear
  • ξ (xi) - Preferred location effects, GR = 0 - Spatially homogeneous
  • α1 (alpha) - Preferred frame effects, GR = 0 - Lorentz invariant
  • α2 (alpha) - Preferred frame effects, GR = 0 - Lorentz invariant
  • α3 (alpha) - Preferred frame effects, GR = 0 - Lorentz invariant
  • ζ1 (zeta) - Momentum changes, GR = 0 - Momentum conserved
  • ζ2 (zeta) - Momentum changes, GR = 0 - Momentum conserved
  • ζ3 (zeta) - Momentum changes, GR = 0 - Momentum conserved
  • ζ4 (zeta) - Momentum changes, GR = 0 - Momentum conserved


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Notes:

1. The paper we read for this program (only sections 3 and 4):
2. My review of Will's book. This paper serves as something of an update of it. A true update is scheduled to come in December 2018.

3. Related Episodes of Physics Frontiers:

4. If you have any information about good packages for numerical relativity for Randy, please leave them in the comments.

5. Our subreddit.

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Thursday, May 24, 2018

The Consistent Histories Interpretation of Quantum Mechanics


Recorded: 10/29/2017 Released: 5/24/2018

Jim and Randy investigate the Consistent Histories interpretation of quantum mechanics. This highly logical interpretation was conceived of by Robert Griffiths and is based on bundling possible histories for a particle together and only using those histories that are consistent with the measurements we perform to winnow out the possible states of the particle. Although Griffiths calls this "Copenhagen done right," the interpretation is based on the idea the quantum particles have definite values for observables in the intervening space.

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Notes:

1. The papers we read for this program:

2. Griffith's book Consistent Quantum Theory, which we mention in the podcast because he continually refers to it in the podcast.

3. My review of Speakable and Unspeakable in Quantum Mechanics by John Bell, which includes the paper in which he formulates Bell's Theorem -- the testable version of the EPR Paradox, which is based on the first tractable formulation of the paradox by David Bohm. I also recently reviewed a book on wave function realism, which seems to be a response to a response to Bell.

4. I haven't quite got the Patreon I promised Randy in this episode up and running, but it is at least limping.

5. Our subreddit.

Tuesday, May 22, 2018

The Wave Function: Essays on the Metaphysics of Quantum Mechanics



This is a philosophy anthology about the wave function of quantum mechanics.  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.  You can make more or less of that, if you wish.  But if you’re a philosopher, you’ll make more.
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.”  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.  This is because the wave function a system of particles is a collection of positions for those particles.
I’ll discuss each chapter in turn.  You might think the description is a little short for some of them, but the review has gotten pretty long.
1. David Albert, “Wave Function Realism”
In this essay, David Albert of the philosophy department of Columbia University discusses his idea on how to view the wave function realistically.  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.
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.  If the wave function is a real, physical object, it is a kind of field.  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.  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.  In a steady state, even though the water is different at every instant, the current is the same at every point.  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.
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.  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.  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.
The reason why we don’t see the 3N world is basically a brain-in-a-vat type of problem. 
2. Valia Allori, “Primitive Ontology and the Structure of Physical Theories”
Valia Allori, a philosopher at Northern Illinois University, tries to understand all this in a very philosophical way.  She invents sub-categories within categories that you’d never heard of.  In this case, she starts talking about the “primitive ontology” of a theory.  This is all, if I recall, along the same program as Albert. 
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.  A primitive ontology is the minimum ontology for the theory to function.  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.
Allori analyzes three and a half theories with this system: Bohmian mechanics, the Ghirardi-Rimini-Weber (2x versions), and the many-worlds interpretation.  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.
3. Steven French , “Whither Wave Function Realism”
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.  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.
4. Sheldon Goldstein and Nino Zanghi, “Reality and the Role of the Wave Function in Quantum Theory”
Sheldon Goldstein, a mathematician at Rutgers, and Nino Zanghi, a physicist at the University of Genoa,  wonder just what it is that a wave function can be, and there are several things that look at.  First of all, there can be no such thing as the wave function in the world.  It is just a computational tool.  Next, it could be an epistemic representation of our subjective knowledge of the system.  That is, it isn’t physical but it has something to do with the state of something physical – basically, the state of our brains.  Or it can be some fact or object in the world – a thing in the world.  That it, the wave function could be nothing, it could be epistemic, or it could be real.
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.  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.   If it is nomological, it is a fact about the world, like Gauss’ Law.  If it is material, it is a real thing, like a changed pith ball.  But again, they give themselves a little wiggle room by allowing the wave function to be either quasi-nomological or quasi-material.  It might be factish or thinglike. 
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.  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.
5. Peter Lewis, “Dimension and Illusion”
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.  And it’s no surprise what a pragmatist will think about a 3N-dimensional world.
6. Tim Maudlin, “The Nature of the Quantum State”
Time Maudlin, New York University Philosopher, provides the most direct assault on Albert in this book.  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.  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.
That particular induction was natural.  The equations in the theory of heat flow are the same as those as for current flow in liquids.  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.
And of course, that didn’t work.
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.  Not only is not necessary, it’s not even a good reason.
7. Bradley Monton, “Against 3N-Dimensional Space”
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.”  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.  This may seem trivial, but it’s a major problem in using string theory to construct a theory of gravity.
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.  And, Monton argues, unless 3N-dimensional space can make itself useful, then there’s no good reason to take it as fundamental.
8. Alyssa Ney, “Ontological Reduction and the Wave Function Ontology”
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.  In this case, she gives an account of how our 3-dimensional experience can reduce to the 3N-dimensional space of the wave function.  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.  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.
9. Jill North, “Structure of the Quantum World”
Jill North, now of Rutgers, once of Cornell, discusses how Albert’s program is supported by the dynamics of the world.  If the wave function changes in 3N-dimensions, then a 3N-universe is the best explanation of it.  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.
10. David Wallace, “A Prolegomenon to the Ontology of the Everett Interpretation”
David Wallace moved from Oxford to the University of Southern California to do his philosophizing.  Here, he talks a lot about the many-worlds interpretation.
 * In the case of identical particles, the wave function gives the probability amplitude of finding *a* particle there.  It doesn’t tell you which one.

Tuesday, May 15, 2018

Gravitational Alternatives to Dark Energy


Recorded: 10/15/2017 Released: 5/15/2018

Jim and Randy discuss the ways in which different modified gravities mimic the observed dark energy in the universe, contra a cosmological constant hypothesis. They talk about various forms of modified gravity theories and the particles associated with their "fifth fields."

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Notes:

1. The papers we read for this program:

2. My review of Will's book, which I talk about a little too much in this podcast.

3. Related Episodes of Physics Frontiers:

4. Our subreddit.

Wednesday, April 25, 2018

The Quantum Vacuum and the Casimir Effect


Recorded: 9/16/2017 Released: 4/24/2018

Jim and Randy review two very convincing papers that make the claim that the Casimir effect is due to materials fluctuations and not the zero point energy

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Notes:

1. The papers we read for this program:

2. We discuss an earlier episode on the Casimir Effect and van der Waals forces repeatedly in this episode.

3. Our subreddit.

Book Review Index

  1. The Wave Function: Essays on the Metaphysics of Quantum Mechanics, Ney and Albert, Eds.
  2. Cosmic Update by Adams, Buchert, and Mersini-Houghton
  3. THe Nature of Space and Time by Hawking and Penrose
  4. Extra Dimensions in Space and Time by Bars and Terning
  5. Theory and Experiment in Gravitational Physics by Will
  6. Speakable and Unspeakable in Quantum Mechanics by J.S. Bell

Tuesday, April 24, 2018

Cosmic Update by Adams, Buchert, and Mersini-Houghton

Cosmic Update: Dark Puzzles, Arrow of Time, Future History is the second book in the Multiversal Journeys series run by Farzad Nekoogar and published through Springer. Like its predecessor in the series, Extra Dimensions in Space and Time, 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.

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.

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.

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 1033 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.

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.

All in all very interesting. It's a little expensive, unlike the next book in the series, Quantum Physics, Mini Black Holes, and the Multiverse: Debunking Common Misconceptions in Theoretical Physics (just out) but if you can get a copy, it's worth a read.