[FOM] Infinitely divisible spacetime?

[katzmik at macs.biu.ac.il]

The idea that spacetime really is continuous is very interesting but how does
this square with the common perception that infinite divisibility breaks down
at the Planck scale?  Do we have to attribute this to the fact that
gravitation and quantum theory have not been reconciled yet?  I am writing as
a complete commoner as far as physics goes so if the above comments reveal
fundamental misconceptions I would like to hear about it.   MK

On Wed, August 31, 2016 03:50, Stephen Paul King wrote:
> 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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