Are gravity and space-time emergent?

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 

V is the Hubble volume, 4pi/3H^3, where H is the Hubble constant, and L_P is the Planck length.

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!

2. The measured value seems to be finely tuned (to 120 significant figures!) to the value of the mass energy.

He presents an argument that the cosmological constant is related to the Planck length 

where mu is of order unity.

Details of his proposed solution are also discussed here.

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".