Attempts to develop a quantum theory of gravity continue to falter and stagnate. Given this, it is worth considering approaches that start with what we know about gravity at the macroscale and investigate whether it provides any hints about some underlying more microscopic theory. One such approach was taken by Thanu Padmanabhan and is elegantly described and summarised in a book chapter.
Gravity and Spacetime: An Emergent Perspective
Insights about microphysics from macrophysics
Padmanabhan emphasises Boltzmann's insight: "matter can only store and transfer heat because of internal degrees of freedom". In other words, if something has a temperature and entropy then it must have a microstructure.
The approach of trying to surmise something about microphysics from macrophysics has a long and fruitful history, albeit probably with many false starts that we do not hear about. Kepler's snowflakes may have been the first example. Before people were completely convinced about the existence of atoms, the study of crystal facets and of Brownian motion provided hints of the atomic structure of matter. Planck deduced the existence of the quantum from the thermodynamics of black-body radiation.
Arguably, the first definitive determination of Avogadro's number was from Perrin's experiments on Brownian motion which involved macroscopic measurements.
Comparing classical statistical mechanics to bulk thermodynamic properties gave hints of an underlying quantum structure to reality. The Sackur-Tetrode equation for the entropy of an ideal gas hints at the quantisation of phase space. The Gibbs paradox hints that fundamental particles are indistinguishable. The third law of thermodynamics hints at the idea of quantum degeneracy.
Puzzles in classical General Relativity
Padmanabhan reviews aspects of the theory that he considers some consider to be "algebraic accidents" but he suggests that they may be hints to something deeper. These include the role of boundary terms in variational principles and he suggests hint at a classical holography (bulk behaviour is determined by the boundary). He also argues that the metric of space-time should not be viewed as a field, contrary to most attempts to develop a quantum field theory for gravity.
Thermodynamics of horizons
The key idea that is exploited to find the microstructure is that can define a temperature and an entropy for null surfaces (event horizons). These have been calculated for specific systems (metrics) including the following:
For accelerating frames of reference (Rindler) there is an event horizon which exhibits Unruh radiation with a temperature that was calculated by Fulling, Davies and Unruh.
The black hole horizon in the Schwarschild metric has the temperature of Hawking radiation.
The cosmological horizon in deSitter space is associated with a temperature proportional to the Hubble constant H. [This was discussed in detail by Gibbons and Hawking in 1977].
Estimating Avogadro's number for space-time
Consider the number of degrees of freedom on the boundary, N_s, and in the bulk, N_b.
On the boundary surface, there is one degree of freedom associated with every Planck area (L_p^2) where L_p is the Planck length, i.e, N_s = A/ L_p^2, where A is the surface area, which is related to the entropy of the horizon (cf. Bekenstein and Hawking).
In the bulk equipartition of energy is assumed so the bulk energy E = N_b k T/2 where
An alternative perspective on cosmology
He presents a novel derivation of the dynamic equations for the scale factor R(t) in the Friedmann-Robertson-Walker metric of the universe in General Relativity. His starting point is a simple argument leading to
The right-hand side is zero for the deSitter universe, which is predicted to be the asymptotic state of our current universe.
Possible insights about the cosmological constant
One of the biggest problems in theoretical physics is to explain why the cosmological constant has the value that it does.
There are two aspects to the problem.1. The measured value is so small, 120 orders of magnitude smaller than what one estimates based on the quantum vacuum energy!
Aside. In the same book, there is also a short and helpful chapter, Quantum Spacetime on loop quantum gravity by Carlo Rovelli. He explicitly identifies the "atoms" of space-time as the elements of "spin foam".
On page 224, "This equivalence is highly nontrivial (and not understood at a deeper level) and arises from the mathematical similarity of vacuum fluctuations and thermal fluctuations," the focus is on the equivalence of zero acceleration and minimal temperature.
ReplyDeleteA different focus, which I have not seen emphasized in the literature(?), is that vacuum fluctuations and thermal fluctuations are different for QFT in a flat space-time because they have different symmetry properties: vacuum fluctuations are Lorentz invariant, thermal fluctuations are not invariant under boosts. Entropy, however, is a thermodynamic dual of temperature, so it feels as if there should be a different concept of a thermodynamic dual of Planck's constant, that being what determines the amplitude of vacuum fluctuations for QFT in the absence of gravity. Something comparable to this, 'Quantropy', is suggested by Baez &Pollard in Entropy 2015, 17, 772-789; doi:10.3390/e17020772, however I must admit to not much liking the mathematics they use.
The introduction of 'quantropy' as well as entropy seems to me to introduce pertinent conceptual issues that Padmanabhan's chapter does not approach. The idea that there can be a thermodynamic dual of Planck's constant is part of my motivation for a different kind of approach to quantum gravity, which I can still discuss only all too briefly as part of a discussion of the relationship between classical random fields and quantum fields, as in the last but one slide of a talk I gave to the Oxford Philosophy of Physics Seminar on October 24th, https://youtu.be/61H0o8W9xg8 (there's a link to a PDF of the slides in that video's description).
Emergent gravity is really one of the most interesting ideas since the mid 90s for quantum gravity, although it did not really progress as we expected. One could hope that condensed matter has something to teach us here, so I will point two curious things involving Kerr black holes:
ReplyDeleteLow-temperature behavior: as in a solid state system, one could argue that as you get closer to zero temperature more of the quantum effects you can see. For Kerr BH zero-temperature is a critical black hole, which is well behaved. So much so that you can have zero-temperature BHs of arbitrary mass (and area), and if area is proprotional to entropy, then we can have an zero-temperature BH of arbitrary entropy. Maybe this says something about degenerate ground states?
Phase-transitions: the Kerr BH has a well-known phase transition from low angular momentum to high angular momentum, called a Davies transition in the literature. The high angular momentum phase has a positive heat capacity, while the low angular momentum phase has negative heat capacity. It's easy to see that the heat capacity diverges at the critical point, indicating a second order transition of some sort. I've never been able to find a reasonable order parameter to try to calculate the critical exponent, but I can tell you that the heat capacity diverges as a polynomial, not a logarithm, which at least suggests that we're not dealing with mean-field theory here.
Hope this is useful complement
Hello Cesar, Thanks so much for the helpful comment. I did not know anything about these phase transitions. It sounds fascinating. Is there a good introductory reference that you would recomnend to readers?
DeleteHi professor McKenzie, sorry for the delay, I'm 10 years removed from academia, so I needed to reread my masters' thesis, which was on this topic. Sadly the phase transition did not generate a lot of interest, so I must refer you to Paul Davies' "Thermodynamics of black holes" (Rep. Prog. Phys., Vol. 41, 1978). It's old, but the first 20-so pages reviews all aspects of black hole thermodynamics without delving too much in GR, and should be accessible to an average physicist. The parts on Hawking radiation are more technical, but can be ignored at first.
DeleteYou say that emergent gravity "did not really progress as we expected". What do you mean? Do you see problems with Padmanabhan's approach? Or is the field too dominated by AdS/CFT for alternatives to gain traction?
ReplyDeleteI think that a consensus emerged in the 80s that black hole thermodynamics offers the most concrete clues to quantum gravity, and so any QG theory should 1)reproduce BH thermodynamics and 2) explain the information loss paradox/resolve singularities. Padmanabhan's approach (as well as everybody inspired by Ted Jacobson's 1995 paper) is great because 1) becomes trivial, but since the argument is that thermodynamics is insensitive to microscopic details this approach didn't sprouted a good idea on how to deal with 2), since it did not informed people on what kind of dynamics there is in quantum gravity, in a sense Padmanabhan's approach is too strong. Or, if you are of a more cynic persuasion, you could say AdS/CFT is a tool, so people can generate lots of articles applying it to different hamiltonians/situations, while emergent gravity is a broad concept that does not translate into industrial-grade publishing, so university management likes one better than the other. I will note tough that in early 2010s a trend emerged in which people argued that AdS/CFT is an instance of the emergent gravity scheme and advocated dropping strings as a fundamental theory and using just AdS/CFT or similar things. Having attended conferences I'll say that the emergent gravity idea is one of the few things both string and anti-string people consider an important concept to some extent, I guess the attitude is that it just doesn't give a more detailed direction on where to go from there.
DeleteI have a naive question. How does this emergent spacetime approach avoid the problems of emergent gravity, i.e., gravity as entropic force (which seems to disagree with experiment)?
Delete