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
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).