[FOM] Infinitely divisible spacetime?

[Stephen Paul King]

Hi,

   On Sat, 27 Aug 2016 10:35:54 -0400 , Harvey Friedman
​ posting ​
To: Foundations of Mathematics
​on the
Subject: [FOM] Remarks on Church's Thesis
​
wrote:​


" I doubt if any substantial number of physicists today believe in any kind
of
infinitely divisible space or time or spacetime."

   I should point out the following. Spacetime is necessarily smooth
otherwise there will be an energy dependence for the speed of a photon.
Gerard ’t Hooft has a very nice paper cover most of the other issues and
some neat ideas.

  Observations seem to have ruled out any such energy dependence to very
high energies. See:
arxiv 1109.5191

​
Bounds on Spectral Dispersion from Fermi-detected Gamma Ray BurstsRobert J.
Nemiroff, Ryan Connolly, Justin Holmes, Alexander B. Kostinski
*(Submitted on 23 Sep 2011 *(v1)*, last revised 18 Apr 2012 (this version,
v2))*

Data from four Fermi-detected gamma-ray bursts (GRBs) is used to set limits
on spectral dispersion of electromagnetic radiation across the universe.
The analysis focuses on photons recorded above 1 GeV for Fermi detected GRB
080916C, GRB 090510A, GRB 090902B, and GRB 090926A because these
high-energy photons yield the tightest bounds on light dispersion. It is
shown that significant photon bunches in GRB 090510A, possibly classic GRB
pulses, are remarkably brief, an order of magnitude shorter in
​ ​
duration than any previously claimed temporal feature in this energy range.
Although conceivably a >3σ fluctuation, when taken at face value, these
pulses lead to an order of magnitude tightening of prior limits on photon
dispersion. Bound of Δc/c<6.94 x 10−21 is thus obtained. Given generic
dispersion relations where the time delay is proportional to the photon
energy to the first or second power, the most stringent limits on the
dispersion strengths were k1< 1.61 x10−5 sec Gpc−1 GeV−1 and k2< 3.57
x 10−7 sec
Gpc−1 GeV−2 respectively. Such limits constrain dispersive effects created,
for example, by the spacetime foam of quantum gravity. In the context of
quantum gravity, our bounds set M1c2 greater than 525 times the Planck
mass, suggesting that spacetime is smooth at energies near and slightly
above the Planck mass.

​I would like to see more observations of such photons, to be sure, but
this finding hints that spacetime just might be nice and continuous after
all... I am very much learning a lot from the conversations about the
Church-Turing thesis!


-- 

Kindest Regards,

Stephen Paul King

Senior Researcher

​ProvenSecure Solutions, inc
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