Hi Jesse,

On 9/16/2011 1:58 AM, Jesse Mazer wrote:

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

I cannot point at the moment to any specific case of a published paper that makes that argument except for some comments by Penrose and other skeptics of Kaluza-Klein type theories but the argument that I am making is, AFAIK, not original with me. As it is the fact that Kaluza-Klein type theories are in fashion and recieve the lion's share of public funding for research and the kinds of mathematics that physicists have learned to use, there is a natural bias against alternatives. My personal view is motivated by my own need for a consistent total 'picture' and so far the current fashionable theories seem to be flailing attempts. It could be that my argument is flowing from an incomplete understanding but given alternatives, such as the work of Chris Isham et al on topos based theories, I think that we need to be a bit more open minded and remember always that explanatory models must never be confused with facts.

    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.

Sure but contrast that argument with the following. From http://arxiv.org/abs/1101.3910v3 "Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models" by Maxim Eingorn <http://arxiv.org/find/gr-qc/1/au:+Eingorn_M/0/1/0/all/0/1>, Orival R. de Medeiros <http://arxiv.org/find/gr-qc/1/au:+Medeiros_O/0/1/0/all/0/1>, Luís C. B. Crispino <http://arxiv.org/find/gr-qc/1/au:+Crispino_L/0/1/0/all/0/1>, Alexander Zhuk <http://arxiv.org/find/gr-qc/1/au:+Zhuk_A/0/1/0/all/0/1>

"We can summarize the main conclusion of our paper
as follows. For compact astrophysical objects with dust-
like equation of state in the external space (p0 = 0),
the demand of the agreement with the gravitational ex-
periments requires the condition (30), namely: τ =
−(2.1 ± 2.3) × 10−5. However, to be at the same level
of accuracy as general relativity, we must have τ = 0.
In other words, we should consider the latent solitons
with equations of state (32) in the internal spaces (in
the case d0 = 3). Moreover, the condition of stability of
the internal spaces singles out black strings/branes from
the latent solitons and leads uniquely to pi = −ε/2 as
the black string/brane equations of state in the internal
spaces, and to the number of the external dimensions
d0 = 3. The main problem with the black strings/branes
is to find a physically reasonable mechanism which can
explain how the ordinary particles forming the astrophys-
ical objects can acquire rather specific equations of state
(pi = −ε/2) in the internal spaces."

Basically, this paper argues that there seems to be a mismatch between the theoretical models based on KK constructions and observations of actual physical systems. See, for example, http://arxiv.org/abs/1010.5740v2 for more details. I have and continue to read the papers and books, such as B. Greene's, on the KK based theories, but I am becoming more and more convinced that there is a fundamental error in the ontological assumptions that these theories are built upon. I have identified this flaw as the 'assumption of substance' but that is my own argument based on philosophical considerations (informed by many other writers on the topic) and tempered by my understanding of experimental evidence that I can access. I am a complete amateur in the field of philosophy of science and can claim no professional accreditation so you are free to take or leave my considerations.

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 <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.

Does this not seem suspicious on its face? Claims that Nature is conspiring to hide phenomena that would contradict theory...hummmm.... That smacks of attempts to rescue the theory that might be, to quote Pauli via Peter Woit, 'not even wrong'; but this critisism can be hand wavved away due to the lack of a compelling alternative theory... If I can help contribute toward a viable alternative I would be a happy man. ;-)

     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
    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.

I just cannot reconcile in my thinking these two things. Why is it necessarily the case that the Plank scale is a fundamental lenght scalse of physical reality and not just some derivative on a minimum ability by observers and measurements, in other words we should be sure that the finiteness is in our ability to resolve information or in the world. We would hardly claim that the pixel resolution limit of a digital camera is caused by a granularity in the world that the camera can take pictures of!



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