Sunday, September 24, 2017

Theory and Experiment in Gravitational Physics by Clifford M. Will

Theory and Experiment in Gravitational Physics is an excellent, if old, tract on the confrontation of general relativity and experiment (I read the revised edition of 1993).  The author, C. M. Will, however, gives regular updates in the literature (the last time was 2014, to my knowledge).  The theme of the book, really, is that General Relativity works and that, for the most part, its alternatives don't.  At least not very well.

This isn't to say that Will shortchanges alternative theories.  In fact, I'd say the opposite.  Will depicts a wide array of theories of gravity, mainly of the "metric theory" variety because only metric theories of gravity seems to be consistent with experiment -- and the Einstein Equivalence Principle (he hints that the earlier edition included more, and in a few places he includes more).  A metric theory satisfies three postulates:
  1. The underlying space-time structure is defined by a metric tensor field.
  2. The world lines of small objects are geodesics in space.
  3. The local space-time geometry approximates a Minkowski space.
If you've worked with general relativity in the past, you were working with a metric theory of gravity.  It sounds like this would be an extremely restrictive culling of theories, but it turns out that there were already a large number of such theories of gravity being explored in the 1980's.  And if you read the update, you'll find more (including the f(R) theories).  Every one of these theories needs to have a tensor metric like general relativity, but they differ in having secondary gravitational fields, sometimes of quite different character (scalar, vector, or tensor), which changes the way in which matter couples to the metric...and therefore produce measurable differences in how space-time responds to the presence of physical objects.

The tests are presented in various ways. 

There is an early description of tests of the Einstein equivalence principle (which states that a small object will follow a geodesic trajectory), since that eliminates all non-metric theories.  The most important such test is the Eoetvoes experiment, which is a Cavendish-like experiment with bodies of different compositions; if this acts just like the Cavendish experiment, then the weak equivalence principle is sound.  And that is about a third of what you need to show that the Einstein equivalence principle is sound.  The other two points are local Lorentz invariance, which is tested by the Hughes-Drever NMR experiment, and local position invariance, which is tested by gravitational red shift experiments.  These tests restrict gravity to be a metric theory.

Since only metric theories are valid, Will then discusses a parameterized post-Newtonian framework for stellar system tests of gravitational theories.  By performing perturbative expansions of the dynamical quantities in the various gravities, he creates a suite of parameters that describe how gravity changes near bodies that are just a little more massive than can be described by classical physics.  Each metric theory has a range for each of these parameters in which it is viable.  So when measurements are taken, these parameters can be calculated by the data and then used to put limits on, and in some cases disqualify, theories of gravity.  Furthermore, many of these parameters indicate symmetry and conservation laws that are valid or invalid in the theory.  So even if a theory is not ruled out by experiment, this formulation tells you if, say, the law of conservation of angular momentum holds in it.

Getting to this point is essentially the first half of the book, and the second half mainly describes how different theories fare when confronted with the physical world.

His first foray is into what he calls the classical tests of general relativity, which he modifies because the gravitational red shift experiment is really a test of the weak equivalence principle.  So he swaps that out, and uses the deflection of light, the time-delay of light, and the perihelion shift of Mercury as his tests.  He then worries about tests of the strong equivalence principle -- which is very like the Einstein equivalence principle, but self-gravitating bodies cannot react to their own effects on space.  He finishes up with tests of gravity waves (which oscillate differently in different theories of gravity), binary pulsars (whose neutron stars should be dense enough to affect their own trajectories, if such a things is possible), and a variety of cosmological tests (this was before the anisotropy of the cosmic microwave background was discovered).

And after all this, general relativity survives and most of the other theories really don't.  Theories with additional vector and tensor couplings are right out, and scalar-tensor theories looked very doubtful. This is astounding because general relativity, with no free parameters, is the most restrictive theory of the bunch, the one with the least wiggle room to respond to those occasional experiments that are likely to tell the poor theoretician that his baby isn't as beautiful as he thought. In a Popperian world, this makes Einstein's theory the strongest or the survivors, and makes the scalar-tensor theories look bad -- especially when some theorist says that it's all this doom and gloom experiment stuff is okay, because you can always play with the parameters of his theory so that it will work (as one did in one of the papers Randy and I are reading for next week's recording -- it will probably be out around March).  These experiments are very effective to be able to eliminate so many different kinds of theories, and with the exception of general relativity, those that survive only survive by being slippery.

And that was what everything looked like in 1993.  If you look at Will's 2014 update, general relativity looks even better. [edit - I just noticed a new edition is coming out at the end of 2018; if it's 2019 or later and you read this, could you e-mail me so I can update the links?]

Again, this is a wonderful book. We were going to use this, after Quantum Paradoxes, for the second book on PhysicsFM when we were doing that, and for good reason. It is little on the technical side, but if you've gotten through an undergraduate course in gravitation you should be okay (although there are a few chapters in the middle you might feel a little bit over your head in), and I recommend it heartily.

I need to find a better way to sign off.   I still sound like a recommendation letter.

I really hope this book gets into grad school.

Sunday, September 17, 2017

Physics Frontiers Index

Posted Shows:

1. G4V: The Gravitational 4-Vector Formulation of Gravity
(Recorded: 10/8/2016) (Published: 10/31/2017)  [video]
2. The de Broglie-Bohm Interpretation of Quantum Mechanics
(Recorded: 10/15/2016) (Published: 11/15/2017)  [video]
3. Graviteoelectromagnetism
(Recorded: 10/22/2016) (Published: 12/6/2017)  [video]
4. Phononics
(Recorded: 11/5/2016) (Published: 1/4/2017)
5. Pilot Wave Hydrodynamics
(Recorded: 11/20/2016) (Published: 1/20/2017)
6. General Relativity for the Experimentalist
(Recorded: 11/26/2016) (Published: 2/14/2017)
7. Virtual Gravitational Dipoles
(Recorded: 12/3/2016) (Published: 3/14/2017)
8. Vacuum Fluctuations and the Casimir Effect
(Recorded: 12/10/2016) (Published: 4/27/2017)
9. f(R) Theories of Gravity
(Recorded: 12/17/2016) (Published: 6/2/2017)
10. Requirements for Gravitational Theories
(Recorded: 1/15/2017) (Published: 6/30/2017)
11. Photonic Molecules and Optical Circuits
(Recorded: 1/21/2017) (Published: 7/16/2017)
12. A Gravitational Arrow of Time
(Recorded: 1/28/2017) (Published: 8/20/2017)
13. Exotic Photon Trajectories in Quantum Mechanics
(Recorded: 2/4/2017) (Published: 9/14/2017)
14. Stochastic Electrodynamics
(Recorded: 2/11/2017) (Published: 10/4/2017)
15. Five Proven Methods of Levitation
(Recorded: 3/5/2017) (Published: 10/21/2017)
16. Stochastic Resonance Energy Harvesting
(Recorded: 3/11/2017) (Published: 11/6/2017)
17. The Physics of Time Travel
(Recorded: 4/2/2017) (Published: 11/23/2017)
18. The 2T Physics of Itzhak Bars
(Recorded: 4/8/2017) (Published: 12/6/2017)
19. Exoplanets. [Lost track]
(Recorded: 4/15/2017)
20. Time Crystals
(Recorded: 4/22/2017) (Published: 12/21/2017)
21. The Origin of Inertia
(Recorded: 4/29/2017) (Published: 1/10/2018)
22. Weyl Quasiparticles
(Recorded: 5/7/2017) (Published: 1/18/2018)
23. Dark Energy
(Recorded: 5/20/2017) (Published: 2/8/2018)
24. The Island of Stability
(Recorded: 5/27/2017) (Published: 2/23/2018)
25. Gravitational Field Propulsion
(Recorded: 6/11/2017) (Published: 3/15/2018)
26. Antimatter Production at a Potential Boundary
(Recorded: 6/17/2017) (Published: 3/25/2018)
27. The Gravitational Equivalence Principles
(Recorded: 9/10/2017) (Published: 4/14/2018)
28. The Quantum Vacuum and the Casimir Effect
(Recorded: 9/16/2017) (Published: 4/24/2018)
29. Gravitational Alternatives to Dark Energy
(Recorded: 10/15/2017) (Published: 5/14/2018)
30. Consistent Histories Interpretation of Quantum Mechanics
(Recorded: 10/29/2017) (Pubished: 5/24/2018)
31. The Parameterized Post-Newtonian Framework
(Recorded: 11/12/2017) (Published: 6/8/2018)
32. Tunneling Time
(Recorded: 11/25/2017) (Published: 7/6/2018)
33. Retrocausality
(Recorded: 3/3/2018) (Published: 7/25/2018)
34. CPT Symmetry and Gravitation
(Recorded: 3/28/2018) (Published: 8/10/2018)

Coming Soon (in editing):

35. The Positive Energy Theorem (Recorded: 12/9/2017)

Upcoming Shows (recorded and unedited):

36. The String Theory Landscape (Recorded: 5/12/2018)
37. The Electromagnetic Stress Tensor in Metamaterials (Recorded: 5/26/2018)


Next Recording:

38. The Einstein-Cartan Theory

Thursday, September 14, 2017

Exotic Photon Trajectories in Quantum Mechanics.



Jim and Randy discuss strange trajectories observed in triple slit experiments with metallic plates. Photons seem to pass through one slit, come back through the middle slit, and out the third due to their interactions with surface plasmons. There are implications in this experiment about the way in which wavefunctions need to be interpreted in non-relativistic quantum mechanics.

-------------------------------------------

Notes:

1. The paper we read for this program: tbd.

2. Our subreddit.

Wednesday, September 6, 2017

Suggested Shows for Physics Frontiers

This post is a list of topics Randy and I have discussed, and is intended to be kept up to date in what should be an easily found spot so that I don't lose any more lists of possible show topics.

Please feel free to comment about topics you'd like to see discussed, especially if you have a reference for them.  Priority goes to references in refereed publications.

Also please feel free to suggest ways to narrow down or split the topics; many of these are too broad, especially when following a show format focuses on discussing one or two scientific papers.

Before suggesting a topic, make sure that we haven't already discussed it in the index. But, if there's something from the show that you'd like to hear more about, we're also willing to revisit topics, similar topics, and aspects of topics.

Possible topics:

Gravitation

Ghosts 1
Galileon 1
de Sitter Unvierse
Chameleon Fields 1 2
Bimetric Theories of Gravity
The Parameterized Post-Newtonian Framework
Post-Post-Newtonian Physics
Black Holes and Hawking Radiation
Mass, Gravitational Binding Energy, and Nuclear Mass Defect
massive gravity 1
Cosmological Constant 1
Gravitational Waves
More Experimental Evidence in Gravitation – Hafele Keating Exp., Precession of Perihelion of Mercury, Deflection of Starlight, time dilation, gravitational waves, frame dragging, etc (don't think we did enough on this one; some topics need more elaboration) Tests of Lorentz Invariance 1 2
Gravity Probe B and Gravitomagnetism 1 
Dark Energy Survey results 1
Unruh's Law
Bekenstein's Law
Bekenstein's Bound
Dark Matter 1
Inhomogeneous Cosmology 1
k-moufage 1 2
Unruh Effect


Quantum Mechanics

Consistent Histories Interpretation  (Griffiths, Omnes)
Multiple Worlds 1
Process Quantum Theory (David Finkelstein)
Nonlinear Schrodinger Equations and Wavefunction Collapse (still a thing?)
Rosenfeld Universe
Wheeler-Feynman Absorber Theory
Higgs Stuff
Wigner function and Weyl transforms –  transition from QM to classical
Double slit experiments with superconductors
Standard Model: What's Next? 1  (The squarkless gluiNO)
Stochastic Electrodynamics (time and quanta and GR) 1 2 3
Asymptotic Freedom
Quantum Gravity Oscillations


Vacuum

Mass for the Graviton 1
Space-Time Vacuum (specific theories?  which?)
Twistors ala Penrose 1 2
Superstring/Brane stuff (More specific?)
Non-commutative Geometry [Alain Connes] 1 2
Loop Quantum Gravity 1 2
Links between Loop Quantum Gravity and String Theory 1
Spin Networks 1
Holographic Principle  1 2 
Emergent Gravity (verlinde) 1
Qubits in Space 1
Consistent Histories and Relativity (Topos) (Christopher Isham) 1 2 3 4



Materials Physics

Bose-Einstein Condensation of Quasi-Particles
Massless Dirac Fermions (on the verge of exciton condensation)
Excitons in general.
Metamaterials (too broad)
Spin States in Quantum Fluid Analogy (analogy to what?)
Sonoluminescence and Sonofusion
Fusion Power
Superparamagentism
Thermionic Energy Harvesting


Uncategorized

Buesard-Poliwell Reactor (wuzzis?)

From Podomatic Comment:  Paul Corkum did a lecture entitled " a molecule takes a selfie". This was a lecture discussing his work with attosecond lasers. I'm not sure if you're familiar with this topic. It was fascinating in many respects. One being a new way of creating quantum computers. He only touched on that possibility during the lecture. 



People to Investigate:
Raphael Sorkin

[Last Updated 9/28/2017]



Posted Shows

Monday, September 4, 2017

Speakable and Unspeakable in Quantum Mechanics by J.S. Bell

John S Bell is well known because of his development of what is known as Bell’s theorem – a proof showing that quantum entanglement means that local causality does not exist. This book, Speakable and Unspeakable in Quantum Mechanics, is a collection of 24 technical and semi-technical papers written by Bell on that topic. Bell’s outlook is partially physical and partially philosophical, making these papers quite interesting reading. At this point I would say it’s incredibly well-written and accessible, but I remember trying to read this as an undergraduate in the 90’s (when there were only 22 papers; I picked this one up because I lost the old one in a postdoc-postdoc transition) and having quite a lot of trouble with it.   Many of the papers seem to be addressed to philosophers, whereas others are standard physics papers. But most of them lay in the no man’s land between theoretical physics and the philosophy of science.

Many of Bell’s concerns run throughout the book, with slight variations from paper to paper. One of them is the incoherence of quantum mechanics:

So long as wave packet reduction is an essential component [of quantum mechanics], so long as we don’t know exactly how and when it takes over for the Schrödinger equation, we do not have an exact and unambiguous formulation of our most fundamental theory.
And that cannot stand. In order to have a reasonably scientific quantum theory, you should be able to express exactly when the wavefunction collapses. This is for several reasons, but what Bell really wants to know is this: if I measure the magnetic moment of an electron in a magnetic field, when does the electron decide which Sz state it is in (up or down)? Here are some options, which aren’t all of them:

  • Does it do so when I turn on the static magnetic field?
  • Does it do so when the microwave detection field reaches it?
  • Does it do so when the response is felt by the field?
  • Does it do so when the inductive current is generated in the pick-up coil?
  • Does it do so when the microwave current passes through the diode detector?
  • Does it do so when the detector is read by the multimeter?
  • Does it do so after the multimeter output is analyzed by the computer?
  • Does it do so when the analysis is displayed on the screen?
  • Does it do so when the graduate student save the data?
  • Does it do so when the Ph.D. looks at the charts?
  • Does it do so when the paper is submitted or accepted?
  • Does it do so when the paper is printed or earns an award? 
The Ph.D. gag was Bell’s favorite sarcastic line in these papers (judging by the number of re-uses), which were drawn from publications like Reviews of Modern Physics, Foundations of Physics, and so on, as well as invited lectures and symposia and book chapters. The important thing is that “measurement,” resulting in the collapse of the wavefunction, is an essential part of quantum theory, but it is not well defined theoretically. In Bell’s words:
The Landau-Lifshitz formulation…when applied with good taste and discretion is adequate for all practical purposes,” but it is “still ambiguous in principle about exactly when and exactly how the collapse occurs…”
 This is the same problem that led Schrödinger to torture analogical cats late at night in obscure journals.* Furthermore, Bell feels that “highly idealized ‘measurements’ should be replaced by an interaction of continuous, if variable, character.” This is essentially the thing that Aharonov explores in the book that started PhysicsFM off, Quantum Paradoxes.

Bell returns again and again to the Einstein-Poldosky-Rosen paradox (EPR, in case I use it again), its reformulation by Bohm into a more physical experiment, and finally, the Aspect Experiment which was the first practical test of the EPR paradox (the introduction to the new edition was written by Alain Aspect himself). The Aspect Experiment really turned Bell’s Theorem into an experiment, but Bell’s theorem was one that elucidated the true importance of what had been an almost forgotten result by Bohm – for the practical reason that no one could figure out how to do the experiment with 1950’s technology. The experiment took entangled photons (rather than electrons in Bohm’s experiment) and looked at their correlations. If you are looking at just up vs. down, clockwise vs. counterclockwise, and so on, then the correlations are fairly simple and come directly from conservation laws. However, when you tilt the detectors with respect to each other, the classical and quantum predictions diverge in such a way that an inspired and talented experimental physicist can tickle out the subtle differences. And when he did that experiment, Alain Aspect fount that quantum mechanics won and Bell’s theorem implied that local causality** was lost.

And at that point, “the concept of ‘reality’ [became] an embarrassing one for many physicists,” according to Bell.

Much of the book also discusses the interpretation of quantum mechanics. Bell looks at interpretations differently than most. In “Six Possible Worlds of Quantum Mechanics,” Bell categorizes theories into a 3 x 2 matrix. Bell’s three main categories are a no-nonsense measurement-based approach that doesn’t attempt to understand what is happening between measurements, that the wavefunction collapse is a real thing that happens to the quantum system and changes it, and that there are two or more subsystems in any quantum system that account for wave-particle duality (hidden variables). The “x2” breaks three interpretation into unromantic and romantic pairs. The romantic dual makes the interpretation interesting without adding any true meaning.

Thus, you have this practical approach being paired with the Bohrian Copenhagen interpretation where the universe holds complimentary views, macroscopic and microscopic, simultaneously. The collapse interpretation is paired with a Wignerian dualistic interpretation where it is the act of intelligent observation that collapses the wave function. The de Broglie-Bohm hidden variable interpretation is paired with Everett’s multiversal interpretation where each possible way in which something can happen does happen – just in another universe.

This is a very different view of Everett. Specifically, Bell’s interpretation of the many-worlds interpretation is to say that the many-worlds part is inessential. It is comforting, he says, to cosmologists (because it allows them to ignore the collapse of the universal wavefunction), but the additional “worlds” don’t add any new physics or understanding of what is happening. So, he says, if you strip the romantic multiverse from Everett, you have a (possibly different) nonlinear hidden variable theory than conjured by Bohm. I’ve never seen anyone else say that. To everyone else the many-worlds of the many-worlds interpretation are the point.

The most annoying gripe Bell makes is to continually harp on his theory of “Be-ables,” which would be a subset of quantum mechanical observables with certain properties that make things less weird. I don’t think it helps so much as he thinks, and it certainly wasn’t clear what the different was, other than terminology, the in the first half-dozen papers he mentioned them in.

In sum, I very much like this book. It is wonderfully written, physically insightful, and historically important. Many of the points, especially those from lectures, are very much Bell’s own thoughts and just his own thoughts that no one else thinks (beables), but even there he is trying to make points about the unsuitability of quantum theory without refinements that tell us what several of these mathematical objects that we use refer to in the physical world.

* Well, not really obscure. But still.
** “Local causality” might seem to be a strange combination of words, but it is what we normally think of as causality. First, if P causes Q, then P occurs before Q. Second, if P causes Q, it should be close enough to affect Q by special relativity. That is P is close enough to Q that light can travel from P to Q. It really is what you’d think about as causality in relativity theory.