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The Thermal Substructure of General Relativity | | Manfred Requardt
; | | Date: |
3 Jan 2023 | | Abstract: | In a first step we will provide arguments for the understanding of quantum
space-time (QST), that means, the microscopic substructure which is assumed to
underly ordinary smooth classical space-time, as a thermal system at each
(macroscopic) point $x$ of the classical space-time manifold (ST). In this
context we exploit among other things some recent findings in the foundations
of quantum statistical mechanics.
We argue that the classical metric tensor field $g_{ij}(x)$ plays the role of
an order parameter field, signalling the existence of a primordial phase
transition in which both space-time and (quantum) matter emerged, accompanied
by the spontaneous symmetry breaking (SSB) of diffeomorphism invariance which
is induced by the existence of quantum excitations in QST.
We then analyze the role the Einstein equations (EEQ) are playing in this
context and relate them to the local thermodynamical heat influx into QST at
point $x$, thus defining the Einstein tensor or Ricci tensor as local heat
tensor. We also define local gravitational temperature, entropy and internal
energy.
Finally, we give a thermodynamic interpretation of the conserved Noether
current which derives from diffeomorphism invariance, separating it into heat
contributions and work terms. In this connection we discuss the role and nature
of tensor and non-tensor quantities and relate our investigation to the
socalled energy vector of Hilbert’s classical analysis. | | Source: | arXiv, 2301.00980 | | Services: | Forum | Review | PDF | Favorites | |
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