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
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
--
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!
Onward!
Stephen
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