Spacetime Is Doomed: Time Is an Artifact

It is well known that spacetime has no operational meaning beyond the Planck scale. In consequence, many high-energy theoretical physicists are seeking, and finding, new structures entirely beyond spacetime. In light of these advances, we propose that time is not fundamental. The arrow of time is an artifact of projection of a stationary dynamics, entirely beyond spacetime and quantum theory, whose entropy does not increase


Introduction
What is time?Physics, neuroscience, and subjective experience offer answers that appear discrepant.The target articles for this issue admirably canvas the discrepancies and possible resolutions.Here I sketch a different resolution.
Physics tell us that spacetime is 'doomed' .Space and time fail to have operational meaning beyond the Planck scale -roughly 10 -33 cm and 10 -43 s (Gross, 2005;Arkani-Hamed et al., 2016).Spacetime therefore cannot be not fundamental reality: it is a limited data structure.It is frugal, sporting a mere handful of dimensions.It is shallow, failing at just 10 -33 cm rather than a more impressive, say, 10 −10 33 cm .Proper time, block universes, and Riemann curvature tensors describe a useful data structure, not objective reality.Evolution by natural selection agrees: perceived space and time are data structures that evolved to guide adaptive behavior, not to reveal objective reality (Hoffman, 2019;Prakash et al., 2020).If spacetime is not fundamental reality, then neither are its contents, such as particles, neurons, and brains.They are useful data structures, nothing more.
Many high-energy theoretical physicists have moved on (see, e.g., Bain, 2020).In the last decade they have found new structures deeper than spacetime and quantum theory.Amplituhedra, for instance, are geometric structures that are logically prior to spacetime and Hilbert spaces.Their volumes are scattering amplitudes.Their faces encode locality and unitarity, key properties of spacetime and quantum theory.Amplituhedra reveal a simplicity and symmetry in scattering amplitudes that cannot be seen within spacetime (Arkani-Hamed et al., 2021).In this new physics, spacetime and quantum theory emerge, together, as a projection of amplituhedra.
Physicists find, to their surprise, that much of the invariant physical information in amplituhedra is coded by permutations that are 'decorated' to distinguish moves left and right (Arkani-Hamed et al., 2016).But permutations of what, and why?What dynamics might hide behind amplituhedra?
It turns out that decorated permutations classify dynamical systems called Markov chains, by compactly describing their 'communicating classes' (Hoffman et al., 2023).In the Twitterverse, for instance, each user in a communicating class eventually sees every tweet of every user in that class.
It's easy to construct stationary Markov chains whose entropy does not increase.For these chains there is no entropic arrow of time.It's also easy to show that projecting such a chain, by conditional probability, yields a new chain that has an entropic arrow of time (Cover & Thomas, 2006).This arrow of time is not an insight about the original chain.It is merely an artifact of projection.
It should be noted that an entropy-nonincreasing Markovian dynamics can be one in which entropy (information) is conserved, i.e., one that satisfies the principle of unitary.Such processes are not beyond quantum theory but are rather its subject matter.However, the set of such unitary Markovian dynamics has measure zero in the set of all entropy-nonincreasing Markovian dynamics.That is, almost all Markovian dynamics that are entropy-nonincreasing are also not unitary, and thus are beyond the unitary formalism of quantum theory.
Spacetime is a projection of a deeper reality.In that projection, an arrow of time can arise as an artifact.Markov chains have a notion of sequence, but need neither relativistic time nor entropic time.
To specify a Markov chain, we must first write down a probability space describing all possibilities for its dynamics.This probability space is a timeless structure prior to any specific dynamics.It is a timeless framework of all possibilities, in which specific events appear and disappear.Perhaps this is the source of our feeling that it is always now.Beyond spacetime lurk amplituhedra and decorated permutations.Beyond decorated permutations may be a Markovian dynamic outside of time, on a probability space perhaps experienced as the now.
The question then arises: A Markovian dynamics of what?
D.D.Hoffman / Timing & Time Perception 12 (2024)  189-191 Downloaded from Brill.com 05/04/2024 12:51:04AM via Open Access.This is an open access article distributed under the terms of the CC BY 4.0 license.https://creativecommons.org/licenses/by/4.0/So proper time and entropic time are doomed because spacetime is doomed.
This is an open access article distributed under the terms of the cc by 4.0 license.