REVIEW
Non-existence of Irreversible Processes in Compact Space Time
High Energy Physics - Theory · Submitted 19 Feb 2006 · 16 references
Pith's reading: Compact spacetime would make irreversible processes extremely unlikely because the classical field equations would permit only one solution, eliminating the freedom to choose the special initial conditions the second law requires.
The paper
The paper claims
Compact spacetime would make irreversible processes extremely unlikely because the classical field equations would permit only one solution, eliminating the freedom to choose the special initial conditions the second law requires.
The reading
This paper asks what would happen if spacetime were compact, meaning it loops back on itself like the surface of a ball, including the time direction. The authors argue that in a compact spacetime, a discretized version of the classical field equations would have exactly as many equations as unknown field values. Each equation then cuts down the number of possible field configurations by the same factor, leaving roughly one solution that satisfies all equations. There is no room to choose initial conditions, because the equations alone determine the entire history.
If only one history exists, the authors say, it is overwhelmingly unlikely that this single history would be the extremely special one needed to show entropy increase over time. That is because the special histories are a tiny fraction of all possible histories. So irreversible processes would be essentially absent in a compact spacetime. Since we do observe entropy increase, the paper concludes that spacetime cannot be compact in the way proposed by some cosmological models, such as the no-boundary idea extended to the future.
Extended reading notes
Core claim
The paper's central claim is that 'if the space time is compact there cannot be irreversible processes, in the classical approximation' (Section I). More explicitly, compact spacetime leads to essentially one solution to the classical field equations, and such a unique solution is overwhelmingly unlikely to be one of the special histories that exhibit entropy increase. If true, compact spacetime is not phenomenologically viable.
Load-bearing premise
The argument treats the discretized field equations as effectively random relations, so that each equation cuts the number of possible field configurations by an independent factor and the resulting solution is 'typical' (Section II). It then adds that the random part of the Hamiltonian shuffles micro states inside a macro state without changing macro-state transitions (Section V.A). If the real equations are not random in this sense, or if the random part can move the history into the special subset required for irreversible processes, the unique-solution counting does not imply the absence of entropy increase.
Original abstract
It is shown that if physical space time were truly compact there would only be of the order of one solutions to the classical field equations with a weighting to be explained. But that would not allow any peculiar choice of initial conditions that could support a non-trivial second law of thermodynamics. We present a no-go theorem: Irreversible processes would be extremely unlikely to occur, for the almost unique solution for the intrinsically compact space time world, although irreversible processes are well known to occur in general.What we here assume -- compact space time -- excludes that universe could exist eternally.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
It is shown that if physical space time were truly compact there would only be of the order of one solutions to the classical field equations with a weighting to be explained. But that would not allow any peculiar choice of initial conditions that could support a non-trivial second law of thermodynamics. We present a no-go theorem: Irreversible processes would be extremely unlikely to occur, for the almost unique solution for the intrinsically compact space time world, although irreversible processes are well known to occur in general.What we here assume -- compact space time -- excludes that universe could exist eternally.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is shown that if physical space time were truly compact there would only be of the order of one solutions to the classical field equations with a weighting to be explained. | result 0.98 | 0.81 | 0.16 | asserted 0.97 |
| s1 | But that would not allow any peculiar choice of initial conditions that could support a non-trivial second law of thermodynamics. | interpretation 0.79 | 0.42 | 0.13 | asserted 0.61 |
| s2 | We present a no-go theorem: Irreversible processes would be extremely unlikely to occur, for the almost unique solution for the intrinsically compact space time world, although irreversible processes are well known to occur in general.What we here assume -- compact space time -- excludes that universe could exist eternally. | result 0.58 | 0.85 | 0.89 | asserted 0.85 |
What was examined, and what was not
- arXiv listing abstract v4
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Figures
Figures reproduced from arXiv:hep-th/0602186 by the authors.
Human review
References
How the literature uses it
1 arXiv paper cite this in 1 sentence
Discussion
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