http://www.pbase.com/scalarp6/image/45314188/original

To Bjoern in particular and other Bjoern level veterans in
in general. Early this year I mentioned Brian Greene talking
about how spaces are turbulent in the microscopic plank realms
and why it is not compatible with General Relativity which
has smooth spaces and the core reasons for the interest in
M-theory. Bjoern wrote the following (dated Jan 20, you could
use search to get the thread if needed):

"I mean that what scientists mean when they say that
General Relativity is not compatible with Quantum Theory,
they do not mean that "spaces are in turbulence in the
microscopic Plank realms".

The problems are totally different. They are mainly
mathematical, not conceptual."

---------

I was supposed to discuss it last time but because we had so
many topics, I didn't pursue. Now let me do it as I re-read Brian
Greene book "The Elegant Universe" yesterday and I find it
puzzling how Bjoern or others can't agree with Greene
on the core of it.

Refer to this illustration:

http://www.pbase.com/scalarp6/image/45314188/original

And the following text (note how it is contrary to Bjoern comment
above since Greene is saying it is literal and not just
mathematical)

Brian Greene argued:

"The Need for a New Theory

General Relativity vs. Quantum Mechanics

The usual realm of applicability of general relativity is that of
large, astronomical distance scales. On such distances Einstein's
theory implies that the absence of mass means that space is flat,
as illustrated in Figure 3.3. In seeking to merge general
relativity with quantum mechanics we must now change our focus
sharply and examine the microscopic properties of space. We
illustrate this in Figure 5.1 by zooming in and sequentially
magnifying ever smaller regions of the spatial fabric. At first,
as we zoom in, not much happens; as we see in the first three
levels of magnification in Figure 5. 1, the structure of space
retains the same basic form. Reasoning from a purely classical
standpoint, we would expect this placid and flat image of space
to persist all the way to arbitrarily small length scales. But
quantum mechanics changes this conclusion radically. Everything
is subj ect to the quantum fluctuations inherent in the
uncertainty p rinciple-even the gravitational field. Although
classical reasoning im plies that empty space has zero
gravitational field, quantum mechanics shows that on average it
is zero, but that its actual value undulates up and down due to
quantum fluctuations. Moreover, the uncertainty principle tells
us that the size of the undulations of the gravitational field
gets larger as we focus our attention on smaller regions of
space. Quantum mechanics shows that nothing likes to be cornered;
narrowing the spatial focus leads to ever larger undulations.

As gravitational fields are reflected by curvature, these quantum
fluctuations manifest themselves as increasingly violent
distortions of the surrounding space. We see the glimmers of such
distortions emerging in the fourth level of magnification in
Figure 5. 1. By probing to even smaller distance scales, as we do
in the fifth level of Figure 5. 1, we see that the random quantum
mechanical undulations in the gravitational field correspond to
such severe warpings of space that it no longer resembles a
gently curving geometrical object such as the rubber-membrane
analogy used in our discussion in Chapter 3. Rather, it takes on
the frothing, turbulent, twisted form illustrated in the
uppermost part of the figure. John Wheeler coined the term
quantum foam to describe the frenzy revealed by such an
ultramicroscopic examination of space (and time) - it describes
an unfamiliar arena of the universe in which the conventional
notions of left and right, back and forth, up and down (and even
of before and after) l ose the ir meaning. It is on such short
distance scales that we encounter the fundamental incompatibility
between general relativity and quantum mechanics. The notion of a
smooth spatial geometry, the central principle of general
relativity, is destroyed by the violent fluctuations of the
quantum World on short distance scales. On ultramicroscopic
scales, the central feature of quantum mechanics-the uncertainty
principle-is in direct conflict with the central feature of
general relati vity-the smooth geometrical mo del of space (and
of spacetime).

In practice, this conflict rears its head in a very concrete
manner. Calculations that merge the equations of general
relativity and those of quantum mechanics typically yield one and
the same ridiculous answer: infinity. Like a sharp rap on the
wrist from an old-time schoolteacher, an infinite answer is
nature's way of telling us that we are doing something that is
quite wrong. The equations of general relativity cannot handle
the roiling frenzy of quantum foam. Notice, however, that as we
recede to more ordinary distances, (following the sequence of
drawings in Figure 5. 1 in reverse), the random, violent
small-scale undulations cancel each other out-in much the same
that, on average, our compulsive borrower's bank account shows no
evidence of his compulsion-and the concept of a smooth geometry
for the fabric of the universe once again becomes accurate. It's
like what you experience when you look at a dot-matrix pictu
From fa r away the dots that compose the pic ture blend together
and create the impression of a smooth image whose variations in
lightness seamlessly and gently change from one area to another.
When you inspect the picture on finer distance scales you
realize, however, that it markedly differs from its smooth,
longdistance appearance. It is nothing but a collection of
discrete dots, each quite separate from the others. But note that
you become aware of the discrete nature of the picture only when
you examin e it on the smallest of scales., from far awa y it
looks smooth. Similarly, the fabric of spacetime appears to be
smooth except when examined with ultramicroscopic precision. This
is why general relativity works on large enough distance (and
time) scales-the scales relevant for many typical astronomical
applications - but is rendered inconsistent on short distance
(and time) scales. The central tenet of a smooth and gently
curving geometry is justified in the large but breaks down due to
quantum fluctuations when pushed to the small.

The basic principles of general relativity and quantum mechanics
allow us to calculate the approximate distance scales below which
one would have to shrink in order for the pernicious phenomenon
of Figure 5. 1 to become apparent. The smallness of Plancks
constant-which governs the strength of quantum effects-and the
intrinsic weakness of the gravitational force team up to yield a
result called the Planck length, which is small almost beyond
imagination: a millionth of a billionth of a billionth of a
billion th of a centimeter (10^-33 centimeter). The fifth level
in Figure 5.1 thus schematically depicts the ultramicroscopic,
sub-Planck length landscape of the universe. To get a sense of
scale, if we were to magnify an atom to the size of the known
universe, the Planck length would barely expand to the height of
an average tree.

And so we see that the incompatibility between general relativity
and quantum mechanics becomes apparent only in a rather esoteric
realm of the universe. For this reason you might well ask whether
it's worth worrying about. In fact, the physics community does
not speak with a unified voice when addressing this issue. There
are those physicists who are willing to note the problem, but
happily go about using quantum mechanics and general relativity
for problems whose typical lengths far exceed the Planck leng th,
as their research requires. There are other physicists, however,
who are deeply unsettled by the fact that the two foundational
pillars of physics as we know it are at their core fundamentally
incompatible, regardless of the ultramicroscopic distances that
must be probed to expose the problem. The incompatibility, they
argue, points to an essential flaw in our understanding of the
physical universe. This opinion rests on an improvable but pro
foundly felt view that the universe, if understood at its deep
est and most elementary level, can be described by a logically
sound theory whose parts are harmoniously united. And surely,
regard, less of how central this incompatibility is to their own
research, lost physicists find it hard to believe that, at rock
bottom, our deepest theoretical understanding of the universe
will be composed of a mathematically inconsistent patchwork of
two powerful yet conflicting explanatory frameworks.

Physicists have made numerous attempts at modifying either
general relativity or quantum mechanics in some manner so as to
avoid the conflict, but the attempts, although often bold and
ingenious, have met with failure after failure.

That is, until the discovery of superstring theory."

p6:

And the following text (note how it is contrary to Bjoern comment
above since Greene is saying it is literal and not just
mathematical)

Then, let me restate it in a more obvious way. The (apparent)
incompatibility between general relativity and quantum mechanics
refers to the attempts to develop a quantum theory of gravity
that reduces to general relativity in the classical limit. It
has little to do with the question of doing quantum theory in
curved spacetime. Hawking radiation, for example, is predicted
from doing quantum field theory in curved spacetime.

Brian Greene argued:

"The Need for a New Theory

General Relativity vs. Quantum Mechanics
[...]
as illustrated in Figure 3.3. In seeking to merge general
relativity with quantum mechanics we must now change our focus
sharply and examine the microscopic properties of space.

Precisely. General relativity is generally considered to be the
classical limit of some quantum theory of gravity. One would expect
a something analogous to ehrenfest's theorem, which essentially
says that you recover the classical variables in the limit that
the operators can be replaced by their expectation values. Hence
one might expect the existence of the spacetime we observe to be
only a limiting case of theory in which space and time lose their
classical meaning.

[...]
quantum fluctuations. Moreover, the uncertainty principle tells
us that the size of the undulations of the gravitational field
gets larger as we focus our attention on smaller regions of
space. Quantum mechanics shows that nothing likes to be cornered;
narrowing the spatial focus leads to ever larger undulations.

Which begs the question of whether it's meaningful to talk about
anything in the limit that those regions become arbitrarily small.
Bekenstein has shown that he uncertainty principle places a limit on such
regions due to considerations of entropy. Coincidentally, the quantum
limit coincides with the entropy of a black hole derived from general
relativity, thus providing a connection in terms of quantizing the
entropy.

[...]
uppermost part of the figure. John Wheeler coined the term
quantum foam to describe the frenzy revealed by such an
ultramicroscopic examination of space (and time) - it describes
an unfamiliar arena of the universe in which the conventional
notions of left and right, back and forth, up and down (and even
of before and after) l ose the ir meaning.

You can find some non-technical commentary from wheeler himself on
this idea in terms of bekenstein's results in the introduction to
``Entropy and the Physics of Information,'' ed. Zurek, W. (1989).

[...]
And so we see that the incompatibility between general relativity
and quantum mechanics becomes apparent only in a rather esoteric
realm of the universe. For this reason you might well ask whether
it's worth worrying about. In fact, the physics community does
not speak with a unified voice when addressing this issue.

Naturally. No one has come up with a theory of quantum gravity that can
be tested (or is even complete), so there wil obviously be a great deal of
disagreement on how to do it. So much for the assertion that physicists
represent some sort of establishment which conspires to maintain the
status quo. It's very easy to find physics about which considerable
disagreement exists. All you have to do is pick a topic and address it at
the level where there is no experimental data that can choose between
competing theories which haven't been rendered untenable by the data that
does exist.


There
are those physicists who are willing to note the problem, but
happily go about using quantum mechanics and general relativity
for problems whose typical lengths far exceed the Planck leng th,
as their research requires.

Physics is just like other professions. Not all physicists are
theorists studying quantum gravity, just as all physicians aren't
orthopaedic surgeons. Nuclear physicists, for example, don't have
a professional interest in planck length physics, because it's
irrelevant to nuclear structure, although some nuclear physics
experiments might place constraints on physics developed later.

There are other physicists, however,
who are deeply unsettled by the fact that the two foundational
pillars of physics as we know it are at their core fundamentally
incompatible, regardless of the ultramicroscopic distances that
must be probed to expose the problem.

So far, your article has not made a case for incompatibilty. It's made
the well known observation that we have no quantum theory of gravity due
to our lack of understanding physics at the planck length. That is hardley
a crisis that should raise a great deal of concern. Prior to quantum
theory and general relativity, there was a great deal more physics that to
be appeared incompatible. Physics has never progressed by the proposal of
a theory which required a radical ``paridigm shift'' except in the minds
of crackpots. Quantum theory, for example, is not the radical departure
from classical theory it is often depicted to be in popular magazines.
Quantum theory made extremely rapid progress because the physicists who
invented it understood classical mechanics extremely well. Apart from the
factor of i\hbar that appears when replacing classical variables with
hermitian operators in a classical poisson bracket, much of classical
physics carried over directly.

[...]
Physicists have made numerous attempts at modifying either
general relativity or quantum mechanics in some manner so as to
avoid the conflict, but the attempts, although often bold and
ingenious, have met with failure after failure.

Considering the sheer amount of physics that has been explained this
century, I think lenting over the failure to find a ``theory of
everything,'' is a bit over the top. At the beginning of the twentieth
century, the sum total of what we knew about nature was essetially
contained in two theories. We had a theory of electromagnetism which
wasn't well understood and was incapable of describing all electromagnetic
effects. We had a theory of gravity which contained the concept of of mass
that layed the groundwork for general relativity, but was otherwise only
empirical. In only 75 years, we discovered two new forces that no one
prior to the twentieth century even knew existed and we have combined
those forces with a more complete theory of E&M into one theory. We also
have a more comprehensive theory of gravity. By comparison, coulomb
postulated the inverse square law in 1785. It took another 80 years before
a satisfactory (but incomplete) theory of E&M existed. It took another 10
years before anyone (maxwell) actually states that light is an
electromagnetic phenomenon. It took another 15 years before hertz was able
to demonstrate the prediction of electromagnetic radiation experimentally.
The last 30 years might be somewhat disappointing in comparison to the
first 75 years of the twentieth century, but that's only because you've
become conditioned to a pace of development that is rather anomalous
compared with history of physics up until the twentieth century.

That is, until the discovery of superstring theory."

While string theory is a potential candidate for some future
quantum theory of gravity, there exists no experimental evidence
for physics beyond the standard model and general relativity at
the moment. While it's extremely unlikely that general relativity
and the standard model are the last word, what is needed are
predictions which are experimentaly accessible. Since the obvious
predictions require energies far beyond what will be realizable
in the near future, if ever, in a laboratory, string theory will
need to be understood much better than it is now to gain wide
spread acceptance as more than a candidate.

Bjoern Feuerbacher wrote:
p6 wrote:

Bjoern Feuerbacher wrote:


Physicists have made numerous attempts at modifying either
general relativity or quantum mechanics in some manner so as to
avoid the conflict, but the attempts, although often bold and
ingenious, have met with failure after failure.

That is, until the discovery of superstring theory."

Stop confusing explanations of physics on a popular science level
with what the theories actually say.


Bye,
Bjoern


Pop-sci said that everything is subject to the quantum
fluctuations inherent in the uncertainty principle.
This means that in microscopic space. There is quantum
fluctuations opposing the smooth or uniform space properties
of GR. What is wrong with this description?? Does actual
theories say otherwise??

No. You are right that QT and GR are inconsistent on this point.

There is NO experimental proof of any inconsistentcy,
none is apparent I know of.

But *this is not the problem* in reconciling them, from a mathematical
point of view.

Not really, the quantum of charge "q" is
expressed in GR by,

2q = F_uv a^u b^v

in accord with q=E*r^2, where
"a" and "b" define r and E=F_10.

From "q" one gets action like h=q^2 both of
which underwrite QT.
Ken

"p6" wrote in message
ups.com...


Bjoern Feuerbacher wrote:

Physicists have made numerous attempts at modifying either
general relativity or quantum mechanics in some manner so as to
avoid the conflict, but the attempts, although often bold and
ingenious, have met with failure after failure.

That is, until the discovery of superstring theory."

Stop confusing explanations of physics on a popular science level
with what the theories actually say.


Bye,
Bjoern

Pop-sci said that everything is subject to the quantum
fluctuations inherent in the uncertainty principle.
This means that in microscopic space. There is quantum
fluctuations opposing the smooth or uniform space properties
of GR. What is wrong with this description?? Does actual
theories say otherwise??

The actual theories say that QM and GR are reconcilable up to a certain
cutoff at about the plank scale - http://arxiv.org/abs/gr-qc/9512024.
Even QED has the same problem i.e. it is only true up to a certain cutoff
when another theory takes over (the electroweak theory). The only
difference is that QED is what is called renormaliseable - which means the
cutoff can be eliminated from the equations and instead expressed in terms
of physically measurable quantities (such as the renormalized charge and
mass that in fact turn out to depend on the cutoff). The problem is finding
a theory that peeks behind the cutoff at the plank scale - not that GR and
QM are inherently incompatible.

Thanks
Bill



p6

Bill Hobba wrote:
"p6" wrote in message
ups.com...


Bjoern Feuerbacher wrote:

Physicists have made numerous attempts at modifying either
general relativity or quantum mechanics in some manner so as to
avoid the conflict, but the attempts, although often bold and
ingenious, have met with failure after failure.

That is, until the discovery of superstring theory."

Stop confusing explanations of physics on a popular science level
with what the theories actually say.


Bye,
Bjoern

Pop-sci said that everything is subject to the quantum
fluctuations inherent in the uncertainty principle.
This means that in microscopic space. There is quantum
fluctuations opposing the smooth or uniform space properties
of GR. What is wrong with this description?? Does actual
theories say otherwise??

The actual theories say that QM and GR are reconcilable up to a certain
cutoff at about the plank scale - http://arxiv.org/abs/gr-qc/9512024.
Even QED has the same problem i.e. it is only true up to a certain cutoff
when another theory takes over (the electroweak theory). The only
difference is that QED is what is called renormaliseable - which means the
cutoff can be eliminated from the equations and instead expressed in terms
of physically measurable quantities (such as the renormalized charge and
mass that in fact turn out to depend on the cutoff). The problem is finding
a theory that peeks behind the cutoff at the plank scale - not that GR and
QM are inherently incompatible.

Thanks
Bill


Do you agree with the assumptions of M-theory that the strings can
increase the cutoff by smearing it out so that it's resolution is
less than point particles making the chaotic quantum fluctuations
at sub-planck size a non-issue.

What is your personal thought about strings. You think they exist?

p6

"p6" wrote in message
oups.com...


Bill Hobba wrote:
"p6" wrote in message
ups.com...


Bjoern Feuerbacher wrote:

Physicists have made numerous attempts at modifying either
general relativity or quantum mechanics in some manner so as to
avoid the conflict, but the attempts, although often bold and
ingenious, have met with failure after failure.

That is, until the discovery of superstring theory."

Stop confusing explanations of physics on a popular science level
with what the theories actually say.


Bye,
Bjoern

Pop-sci said that everything is subject to the quantum
fluctuations inherent in the uncertainty principle.
This means that in microscopic space. There is quantum
fluctuations opposing the smooth or uniform space properties
of GR. What is wrong with this description?? Does actual
theories say otherwise??

The actual theories say that QM and GR are reconcilable up to a certain
cutoff at about the plank scale - http://arxiv.org/abs/gr-qc/9512024.
Even QED has the same problem i.e. it is only true up to a certain
cutoff
when another theory takes over (the electroweak theory). The only
difference is that QED is what is called renormaliseable - which means
the
cutoff can be eliminated from the equations and instead expressed in
terms
of physically measurable quantities (such as the renormalized charge and
mass that in fact turn out to depend on the cutoff). The problem is
finding
a theory that peeks behind the cutoff at the plank scale - not that GR
and
QM are inherently incompatible.

Thanks
Bill


Do you agree with the assumptions of M-theory that the strings can
increase the cutoff by smearing it out so that it's resolution is
less than point particles making the chaotic quantum fluctuations
at sub-planck size a non-issue.

Reference please


What is your personal thought about strings. You think they exist?


I do not take theories that have yet to have any experimental confirmation
too seriously. It however has increased our knowledge of a theory I do take
seriously - QFT.

Bill


p6

p6:
Bill Hobba wrote:

The actual theories say that QM and GR are reconcilable up to a certain
cutoff at about the plank scale - http://arxiv.org/abs/gr-qc/9512024. Even
QED has the same problem i.e. it is only true up to a certain cutoff when
another theory takes over (the electroweak theory). The only difference
is that QED is what is called renormaliseable - which means the cutoff can
be eliminated from the equations and instead expressed in terms of
physically measurable quantities (such as the renormalized charge and mass
that in fact turn out to depend on the cutoff). The problem is finding a
theory that peeks behind the cutoff at the plank scale - not that GR and
QM are inherently incompatible.


Thanks
Bill


Do you agree with the assumptions of M-theory that the strings can
increase the cutoff by smearing it out so that it's resolution is
less than point particles making the chaotic quantum fluctuations
at sub-planck size a non-issue.


That isn't quite what string theory does. String theory eliminates
the point interaction that corresponds to the vertex of a feynman
diagram by treating point particles as strings which trace out a
world sheet that looks like a tube. Draw a feynman diagram with
tubes, rather than lines. You'll see that there is no single point
that corresponds to the vertex of the feynman diagram. The interaction
takes place of a world sheet. The point interaction is not merely
``smeared out.'' The point interaction at the vertex is completely
eliminated.

Bilge wrote:
Then, let me restate it in a more obvious way. The (apparent)
incompatibility between general relativity and quantum mechanics
refers to the attempts to develop a quantum theory of gravity
that reduces to general relativity in the classical limit.

That's not a problem at all, and (in fact) doesn't even require quantum
gravity. As Jacobson showed in 1995, the mere imposition of the
Bekenstein bound in conjunction with the laws of thermodynamics,
implies general relativity. To quote his conclusion: gravity need not
be quantized as a fundamental field any more than phonons do.

The way he showed this is to employ the Raychaudhuri equation for
volume contraction at a local "Rindler horizon". This gives you an
equation expressing the horizon area in terms of the energy
influx/outflux.

The imposition of the Bekenstein bound equates the horizon area, up to
proportion, to the entropy associated with the phase averaging over the
horizon. Using this expression, a formulation of the 2nd law: d(heat)
= (Temperature) d(Entropy) is formed, the temperature being that
associated with the thermal state arising from the relative state phase
averaging over the horizon -- thus being expressible in terms of the
Ricci tensor.

This gives you the right hand side of the Einstein equation. The left
hand side (d(Heat)), is equated to the flux of matter/energy. This
gives you the left hand side of the Einstein equation -- up to a term
proportional to the metric. The extra term is fixed (up to a
cosmological constant) by invoking the conservation of energy -- as is
usually done in the derivation of the field equations.

Any quantum theory which admits a formulation of thermodynamics + a
Bekenstein bound -- regardless of whether it explicitly includes a
theory of gravity or not -- will therefore yield Einstein's equations
of gravity as a consequence of the compatibility requirements for local
Rindler horizons.

It has little to do with the question of doing quantum theory in
curved spacetime. Hawking radiation, for example, is predicted
from doing quantum field theory in curved spacetime.

In a way, Jacobson's result is a major generalization of the earlier
Hawking result, going the extra step further to FULLY bring the field
equations under the scope of thermodynamics.

Precisely. General relativity is generally considered to be the
classical limit of some quantum theory of gravity.

The end result is that GR is shown to be the classical limit of
*GENERIC* quantum theory, with no special need for any quantum theory
of gravity.

The two missing elements from Jacobson are
(1) extension of the foregoing to globally non hyperbolic spacetimes
(2) an implementation of the Bekenstein bound.

Item (2) is where string theory may come into play, for instance. As
for item (1), in fact, is something Jacobson is ideally suited for!
Since you generally don't have a global "t" parameter in the absence of
global hyperbolicity (nor a universal state space), you're forced to
treat everything locally.

You can still, then, talk about locally hyperbolic regions. Such a
region R is characterized as follows. It has associated with it a
time-like vector field X of compact support. The region is bounded by
2 spacelike hypersurfaces: Boundary(R) = R(1) - R(0). Associated with
this is a flow exp(tX), which maps the initial hypersurface R(0) -
R(t) for t between 0 and 1. On each hypersurface is a (n-1) form,
n(t), such that n(t) ^ X gives you a volume form.

This is, in fact, the standard prescription (e.g. Lecture Notes in
Physics, 107) for setting up a symplectic structure.

The Hamiltonian is given by an expression of the form
H = Lie_X(phi) dL/d(phi) - X L
where Lie_X is the Lie derivative associated with X. On each
hypersurface R(t) this gives you an integral (integrated using n(t)),
H(t). The commutator [F, H(t)] = i h-bar F'(t) gives you the
Heisenberg equations.

Since the boundary of the region is R(1) - R(0), then all the layers
R(t) share a common frontier, Boundary(R(t)) = H, for all t. This "H"
plays the role of Jacobson's local Rindler Horizon.

Considering all the possible ways of setting up regions, you get a
requirement for compatibility from imposing the Bekenstein bound on
each such H. This translates into Jacobson's arguments.

The novel element not in Jacobson is how compatibility is enforced
between the overlapping parts of two locally hyperbolic regions. Since
the spacetime in general need not be globally hyperbolic, then what
passes for timelike within one region may be spacelike or even timelike
with the opposite orientation, seen from the perspective of another
region.

This is, in fact, a form of the "time-traveller paradox".

Taking two points x, y; which are timelike in region R1, and spacelike
in region R2; the commutators [A(x),A(y)]_{R1} != 0, while
[A(x),A(y)]_{R2} = 0!

Invariably, this means that the state space must be thermal! What
passes for quantum noise from the perspective of region R1 in virtue of
the non-commutatitivy of the operators, will be seen as thermal noise
form the perspective of R2.

The best way to see how this works is as follows.

If you think of a time-like path traversing from x to y wholly
contained in R1, at some point it has to exit R2 and reenter it. Those
two points cross one or both of the boundary hypersurfaces, R2(1) or
R2(0). The quantum noise seen from the perspective of R1, shows up as
thermal noise associated with the cut-off that took place on the
boundary, and shows up as a boundary fluctuation. In other words, the
extra information corresponding to the correlation between A(x), A(y)
is encoded into the boundary R2(1), R2(0).

The usual, Wightmann, formalism of QFT is the first casualty. In place
of the axiom that the vacuum be a pure state that is Poincare'
invariant, you have the axiom that it is a thermal state. If you also
impose the condition that it be a thermal state at positive
temperature, then this may be enough to also subsum the Wightmann
"spectral axiom", thereby rendering its ad hoc formulation unnecessary.

The first two laws of thermodynamics, applied locally to the region,
give you the Einstein equations.

The third law may (via a general argument posted in s.p.r. not too long
ago, concerning the nature of negative temperature and negative energy)
give you a spectral gap away from 0 energy -- a prerequisite to
establishing a particle interpretation and a scattering theory
formalism. In Wightmann this needs to be separately postulated. Here,
it may arise as a consequence.

So, with the extension and with a way of implementing the Bekenstein
bound, you have a general approach to quantum theory that automatically
subsumes general relativity, thereby achieving the desired goal through
the back door without the need to "quantize gravity" -- exactly as
Jacobson foretold.

Bilge wrote:
p6:
Bill Hobba wrote:

The actual theories say that QM and GR are reconcilable up to a certain
cutoff at about the plank scale - http://arxiv.org/abs/gr-qc/9512024. Even
QED has the same problem i.e. it is only true up to a certain cutoff when
another theory takes over (the electroweak theory). The only difference
is that QED is what is called renormaliseable - which means the cutoff can
be eliminated from the equations and instead expressed in terms of
physically measurable quantities (such as the renormalized charge and mass
that in fact turn out to depend on the cutoff). The problem is finding a
theory that peeks behind the cutoff at the plank scale - not that GR and
QM are inherently incompatible.


Thanks
Bill


Do you agree with the assumptions of M-theory that the strings can
increase the cutoff by smearing it out so that it's resolution is
less than point particles making the chaotic quantum fluctuations
at sub-planck size a non-issue.


That isn't quite what string theory does. String theory eliminates
the point interaction that corresponds to the vertex of a feynman
diagram by treating point particles as strings which trace out a
world sheet that looks like a tube. Draw a feynman diagram with
tubes, rather than lines. You'll see that there is no single point
that corresponds to the vertex of the feynman diagram. The interaction
takes place of a world sheet. The point interaction is not merely
``smeared out.'' The point interaction at the vertex is completely
eliminated.

Yes. Brian Greene used the same description as you do. I'm just
using his description "smearing" as when Brian stated: (page 152)

"String theory softens the violent quantum undulations by "smearing"
out the short-distance properties of space. There is rough and a
more precise answer to the question of what this really means and
how it resolves the conflict. We discuss each in turn"

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Interesting book. I forgot if he described this in graphical sense
in his Nova 3 part DVD. I only saw it once. Maybe got to watch it
again this weekend.

p6