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Condensed Matter Lessons About the Origin of Time

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Abstract

It is widely hoped that quantum gravity will shed light on the question of the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have naturally evolved from general relativity, on the one hand, and from particle physics, on the other hand. A third important branch of twentieth century ‘fundamental’ physics, condensed-matter physics, also offers an interesting perspective on quantum gravity, and thereby on the problem of time. The bottomline might sound disappointing: to understand the origin of time, much more experimental input is needed than what is available today. Moreover it is far from obvious that we will ever find out the true origin of physical time, even if we become able to directly probe physics at the Planck scale. But we might learn some interesting lessons about time and the structure of our universe in the process. A first lesson is that there are probably several characteristic scales associated with “quantum gravity” effects, rather than the single Planck scale usually considered. These can differ by several orders of magnitude, and thereby conspire to hide certain effects expected from quantum gravity, rendering them undetectable even with Planck-scale experiments. A more tentative conclusion is that the hierarchy between general relativity, special relativity and Newtonian physics, usually taken for granted, might have to be interpreted with caution.

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Notes

  1. Weyl topologies include Fermi points in 3+1 dimensions, and Dirac points in 2+1 dimensions.

  2. Mathematically, one could still define Lorentz transformations for such a system. However, the relativistic “corrections” compared to the Newtonian physics obtained from Galilean transformations would be irrelevant in practice. One may think, e.g., of a phase transition in a background system where all the velocities involved are necessarily much smaller than the relativistic speed characteristic of the background spacetime. This in fact is what happens in most laboratory systems which display effective acoustic gravity, and where \(c_\mathrm{sound}\ll c_\mathrm{light}\). For all practical purposes, the background system may therefore be described as Newtonian, even though the “internal” physics in the effective gravity is naturally Lorentzian and governed by \(c_\mathrm{sound}\). Note that it is not required for the emergence of an effective acoustic gravity that the background system be Newtonian. Analogue gravity also emerges, e.g., in relativistic Bose–Einstein condensates [18].

  3. In fact, at this point, \(\tau _\mathrm{ch}\) can best be interpreted as a length scale, i.e. \(\tau _\mathrm{ch}=\xi _\mathrm{ch}/c\) with \(\xi _\mathrm{ch}\) some characteristic length scale of the system and \(c\) a dimensional conversion factor.

  4. The fourth-order derivatives of the first part of Eq. (8) imply that the global behaviour will in general be determined by it, and not by the second part. The conditions for the second part to become dominant in the limit when \(a\rightarrow 0\) are actually mathematically quite subtle, but this is just meant as a simple pedagogical example to illustrate the point of obtaining a hyperbolic structure from an underlying non-hyperbolic one. More involved examples, including a discussion of the mathematical conditions for the obtention of a low-energy hyperbolic structure, can be found in [19].

  5. General Relativity can be formulated as a gauge theory, and should therefore be invariant under the transformations of the relevant gauge group, namely the diffeomorphism group. For our discussion, the relevant issue is that physical states which differ only by a time reparametrization should be physically equivalent. One can take this as a fundamental point when attempting to quantize GR, which leads to the idea that time should be absent altogether in a fundamental (“quantum”) description of gravity. The problem then is how to recover time at the classical, “effective” level, and in particular how the evolution of the universe comes about. See e.g. [20, 21] for broad reviews on the problem of time in quantum gravity, including a dicussion of timeless models, and [22, 23] for introductions to two of the more popular approaches to timeless (quantum) gravity.

  6. The bosonisation scale for the standard model interactions considered in [26] need not coincide with the gravitational bosonisation scale. In fact, [26] finds \({\sim }10^{13}-10^{15}\,\hbox {GeV}\) for the former, i.e. \(10^{-6}-10^{-4} E_{Pl}\). Note that, in a laboratory condensed matter system such as \(^3\)He-A, different types of collective bosons also need not necessarily appear at the same temperature, external magnetic field etc.

  7. These analogue graviton masses are curiously related to the value of the analogue cosmological constant in \(^3\)He-A, see [14].

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Acknowledgments

I thank F. Barbero, C. Barceló and G.E. Volovik for useful comments. Financial support was provided by the Spanish MICINN through the project FIS2011-30145-C03-01.

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  1. Modelling & Numerical Simulation Group, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911, Leganés, Spain

    Gil Jannes

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Jannes, G. Condensed Matter Lessons About the Origin of Time. Found Phys 45, 279–294 (2015). https://doi.org/10.1007/s10701-014-9864-3

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