APS April Meeting 2020
Volume 65, Number 2
Saturday–Tuesday, April 18–21, 2020;
Washington D.C.
Session C15: Quantum Theory of Gravity
1:30 PM–3:18 PM,
Saturday, April 18, 2020
Room: Virginia B
Sponsoring
Unit:
DGRAV
Chair: David Craig, Oregon State University
Abstract: C15.00004 : Some Implications of Invariant Boltzmann Statistical Mechanics to Quantum Gravity and Noncommutative Geometry of Physical Space and its Fractal Spectral Dimension.
2:06 PM–2:18 PM
On Demand
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Abstract
Author:
Siavash Sohrab
(Northwestern University)
According to invariant Boltzmann statistical mechanics [1], Kelvin absolute
temperature T [K] is identified as Wien wavelength $\lambda
_{\mathrm{w\beta -1}}$ [m] of thermal oscillations leading to \textit{internal} \textit{measures} of
spacetime $(\lambda_{w\beta -1} ,\tau_{w\beta -1} )$ and \textit{external} \textit{measures} of space and
time $(x_{\beta } =N_{x} \lambda_{w\beta -1} ,t_{\beta } =N_{t} \tau
_{w\beta -1} )$. Therefore, temperature of space or Casimir vacuum fixes
local measures of \textit{spacetime} $(\lambda_{w\beta -1} ,\tau_{w\beta -1} )$that are not
\textit{independent} because $v_{ws} =\lambda_{ws} /\tau_{ws} $ must satisfy the vacuum
temperature. Since Wien displacement law $\lambda_{w}
T=0.29\mbox{\thinspace \thinspace cm-K\thinspace =\thinspace
0.0029\thinspace [m}^{2}]$ requires the change of units [m/cm] $=$ 100, the
classical temperature conversion formula becomes
$T[m]=^{o}\mbox{C[m]}\mbox{\thinspace +\thinspace 2.731}$ with 2.731 close
to Penzias-Wilson [1965] cosmic microwave background radiation temperature
$T_{CMB} \simeq 2.73\mbox{\thinspace [m}]$. The role of analytic functions,
Cauchy-Riemann conditions, and possible imaginary nature of internal
spacetime coordinates, due to connections to Riemann surfaces at lower scale
$\beta \quad -$1, on path-independence of trajectories of quantum transitions
and Heisenberg equation of motion are discussed. Finally, some implications
of the hydrodynamic model to quantum gravity as a dissipative deterministic
system [2] and fractal spectral dimension of noncommutative geometry of
space [3] are examined.
$^{\mathrm{1}}$ Sohrab, S. H.,\textit{ ASME J. Energy Resoures Technology} \textbf{138}, 1-12 (2016).
$^{\mathrm{2}}$ `t Hooft, G., \textit{Quantum Grav}. \textbf{16}, 3263 (1999).
$^{\mathrm{3\thinspace }}$Connes, A., \textit{Lett. Math. Phys}. \textbf{34}, 238 (1995).