On Thu, Sep 15, 2011 at 11:28 PM, Stephen P. King <stephe...@charter.net>wrote:

>
>     Hi Jesse,
>
>     Any physically significant boost would act to alter the scale of
> "Plankian effects", that is what general covariance basically tosses out any
> physically real notion of space-time points what ever their size might be.
>


Naively this might seem to be true, but this would mean that all the
physicists who think string theory and loop quantum gravity can be
Lorentz-invariant despite having a minimum length scale are just complete
idiots who have collectively failed to notice a very simple argument that
blows apart their theories. I think this is rather unlikely to be the case;
can you point to any mainstream physicists who argue that a minimum length
scale is fundamentally incompatible with all Lorentz-invariant theories, or
is this your own original argument?

Additionally, string and brane theories *require* a fixed and flat
> space-time to act as a base space for the fibration of compatified torii,
> orbifolds or what have you. The same is true for all quantum field theories
> that depend of the fiber bundle formulation.
>

Due to various string dualities (see
http://en.wikipedia.org/wiki/String_duality ), as well as the holographic
principle, there is the widespread idea that precisely the same physical
theory can be stated in very different background spacetimes (sometimes
involving different numbers of spatial dimensions), which is thought to
indicate that the background geometry is not really fundamental (see the
first paragraph after the heading "Black holes and branes in string theory"
at http://superstringtheory.com/blackh/blackh5.html for example). There is
therefore some hope that a future version of "M theory" will be formulated
in a "pregeometrical" form--see (i) on p.1 of
http://www.ias.ac.in/jarch/jaa/20/149-164.pdf for instance. And despite the
use of continuous background spacetime, apparently it is not really
physically meaningful to talk about phenomena smaller than the planck length
in string theory, for reasons discussed on p. 249-255 of "The Elegant
Universe" by Brian Greene (all but 252 and 254 can be read on google books
starting at
http://books.google.com/books?id=jYHtp6kx8qgC&lpg=PP1&pg=PA249#v=onepage&q&f=false).
As explained there, there are two different approaches to measuring
"distance" depending whether we use strings that are wound or unwound in the
compact dimension, and on pp. 253-254 Greene writes:

'And in this case, when R shrinks to sub-Planck length but we continue to
use the unwound strings (even though they have now become heavier than the
wound strings), we are employing the "hard" approach to measuring distance,
and hence the meaning of "distance" does not conform to our standard usage.
However, the discussion is far more than one of semantics or even of
convenience or practicality of measurement. Even if we choose to use the
nonstandard notion of distance and thereby describe the radius as being
shorter than the Planck length, the physics we encounter—as discussed in
previous sections—will be identical to that of a universe in which the
radius, in the conventional sense of distance, is larger than the Planck
length'

So it sounds like Greene is describing another sort of "duality" here, which
makes it so any physical description of phenomena below the Planck length is
physically identical to a different description of phenomena above the
Planck length, and thus there is no new physics to be found at these scales.

 A 'money quote' from page 8 of that paper:
>
> "The observation of the highest energy gamma rays up to 31 GeV from
> a distant gamma ray burst GRB 090510 also shows that there are no ob-
> servable quantum effects of spacetime down to the Planck scale [15]. The
> result therefore rules out those quantum gravity theories in which the
> speed
> of light varies linearly with photon energy. There is no evidence of
> violation
> of Lorentz invariance down to the Planck length. Spacetime is continuous
> and special relativity is right. The greatest mystery is why spacetime is
> man-
> ifestly so smooth and classical all the way to the smallest conceivable
> level."
>
>
>


That quote specifically says "no evidence of violation of Lorentz
invariance", so again there's no reason to think it's ruling out
Lorentz-invariant theories which do have the Planck length as the minimum
length scale.

Jesse

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