On Thu, 15 May 2008 22:12:09 -0700, "N:dlzc D:aol T:com \(dlzc\)"
wrote:

Dear Eric Baird:

Eric Baird wrote in message
.. .
...
Perhaps Hawking radiation might be expected under
//someone else's// general theory, but I don't see
how the effect can appear classically in a model
that's supposed to reduce to the SR equations of
motion, as Einstein's was.

How fortuitous...
http://groups.google.com/group/sci.a...c52e34b1d93586
... just posted on sci.astro.

Oh, that's really cool!

I shall bookmark it and examine it at leisure!



See the approximations that reduce GR to SR involve the patching
technique to connect little bits of spacetime for forming a
"solution space". GR allows curvature (the patches can be
slightly skew), and SR does not.

Yeah, I understand the idea that a curved model has to reduce to
effectively-flat regions if you zoom in on it far enough ... what I'd
take issue with is whether that geometrical reduction has to
correspond to a reduction to the //physics// of special relativity.


One could make the case that if all energy is associated with
curvature, and if lightspeed is regulated between particles by
gravitomagnetic effects, then all physics would be curvature-based,
and there wouldn't be any such thing as "the physics of flat
spacetime" left for SR to describe.

SR might still be a decent first approximation in some ways, but if
you zoomed in far enough to get flatness, you'd then have zoomed in so
far that your region wouldn't contain any particles moving with
significant relative velocities (or any particles at all!).

In that scenario, you could certainly zoom in and get your little flat
"facets" or "patches", but the physics of moving bodies wouldn't then
be described by the internal geometry of any of those facets, it'd be
described by the cumulative mismatches between facets that'd produce
the curvature effects associated with the particles and the distortion
fields between them.

In that hypothetical situation, we'd still be able to have a general
theory of relativity based on the idea of spacetime curvature, but it
wouldn't seem to reduce to the flat-spacetime-generated relationships
of special relativity.



The connection to Hawking radiation is that whle acoustic metrics seem
to be happy to generate indirect radiation through a horizon,
Einstein's implementation of a general theory doesn't seem to want to
cooperate.
Hence the black hole information paradox, and the last few decades
that Thorne, Hawking, Wheeler and the others have spent trying and
failing to find some way to reconcile QM with GR1915.


We'd seem to be able to resolve the black hole information paradox,
and allow GR to tackle classical indirect radiation by allowing it to
reduce to an acoustic metric rather than to a Minkowski metric, but if
we swap out the Minkowski metric, we lose our original justification
for believing that some of the relationships of special relativity are
correct.

If we then wanted to continue using SR as foundation theory, we'd have
to find a new way to derive it without falling back on the idea of a
reduction to flat spacetime, and that seems to be rather difficult.

I don't personally think that a proper solution to the information
paradox is likely to be achievable without deleting special relativity
out from under GR, and I think that it's physicists' reluctance to
contenance that final option that has been holding them back for the
last thirty years and preventing them from solving this thing.

I think that it's great that the "quantum gravity" guys are now
steaming ahead at such a rate, with their work on acoustic metrics ...
they can get away with this because everyone knows that the rules for
quantum gravity aren't quite settled yet, so if the QG guys are
exploring ideas that don't seem to be SR-compatible //yet//, the SR
community don't cry foul ... they expect that, at the last moment, the
final implementation of QG will pull some masterstroke and magically
become compatible with both SR/GR1915 and QM.

I think that when the QG guys get to the logical conclusion of their
current work, the SR guys (and some of the GR guys) are liable to get
a horrible shock.


Not entirely as mysterious as
you imagine...

Oh, I don't regard the situation as mysterious at all!



=Erk= (Eric Baird) www.relativitybook.com
: " Why should I care about Posterity? What's Posterity
: ever done for me? "
: -- Groucho Marx

Dear Eric Baird:

On May 19, 6:31*am, Eric Baird wrote:
On Thu, 15 May 2008 22:12:09 -0700, "N:dlzcD:aol T:com \(dlzc\)"

wrote:
Dear Eric Baird:

Eric Baird wrote in message
.. .
...
Perhaps Hawking radiation might be expected under
//someone else's// general theory, but I don't see
how the effect can appear classically in a model
that's supposed to reduce to the SR equations of
motion, as Einstein's was.

How fortuitous...
http://groups.google.com/group/sci.a...c52e34b1d93586
... just posted on sci.astro.

Oh, that's really cool!

I shall bookmark it and examine it at leisure!


See the approximations that reduce GR to SR
involve the patching technique to connect little
bits of spacetime for forming a "solution space".
GR allows curvature (the patches can be
slightly skew), and SR does not. *

Yeah, I understand the idea that a curved model
has to reduce to effectively-flat regions if you
zoom in on it far enough ... what I'd take issue
with is whether that geometrical reduction has to
correspond to a reduction to the //physics// of
special relativity.

No. All it does is limit the "extent" of "frame". "Local" suddenly
becomes important.

One could make the case that if all energy is
associated with curvature, and if lightspeed is
regulated between particles by gravitomagnetic
effects, then all physics would be curvature-based,
and there wouldn't be any such thing as "the
physics of flat spacetime" left for SR to describe.

Such a model is incapable of describing a flat spacetime. Which the
Universe is "in the large".

SR might still be a decent first approximation
in some ways, but if you zoomed in far enough
to get flatness, you'd then have zoomed in so
far that your region wouldn't contain any particles
moving with significant relative velocities (or any
particles at all!).

GR fails at this scale. In fact, gravitation drops off such that SR
is the classical tool of choice at that scale.

In that scenario, you could certainly zoom in
and get your little flat "facets" or "patches", but
the physics of moving bodies wouldn't then be
described by the internal geometry of any of
those facets, it'd be described by the cumulative
mismatches between facets that'd produce the
curvature effects associated with the particles
and the distortion fields between them.

Which entirely fails in flat space.

snip a bunch

GR does not give up the first postulate of SR, namely that the laws of
physics are the same for all observers. It only adds the word "local"
when evaluating the laws of physics.

...
I think that when the QG guys get to the logical
conclusion of their current work, the SR guys
(and some of the GR guys) are liable to get a
horrible shock.

I doubt that it will be a horrible shock, since it must make
predictions that describe what we already see. What it should do is
extend the domain of applicability, and predict some things that we
assumed were random noise, or anomalous. Frankly, I think anyone that
really knows relativity, is ready for something different that works.

Not entirely as mysterious as
you imagine...

Oh, I don't regard the situation as mysterious
at all!



OK.

David A. Smith

Eric Baird wrote:
On Thu, 15 May 2008 22:12:09 -0700, "N:dlzc D:aol T:com \(dlzc\)"
wrote:
See the approximations that reduce GR to SR involve the patching
technique to connect little bits of spacetime for forming a
"solution space". GR allows curvature (the patches can be
slightly skew), and SR does not.

Yeah, I understand the idea that a curved model has to reduce to
effectively-flat regions if you zoom in on it far enough ... what I'd
take issue with is whether that geometrical reduction has to
correspond to a reduction to the //physics// of special relativity.

Some presentations (e.g. MTW, IIRC) take the attitude that ALL of SR is
taken as a postulate for local physics. This is, in essence, where the
constant "c" comes from in GR :-).


One could make the case that if all energy is associated with
curvature,

No, one cannot -- one must use GR when one is examining GR. In GR this
simply is not true. Not even close, as gravitation involves no energy or
force at all.


SR might still be a decent first approximation in some ways,

SR _IS_ a "decent" first approximation to GR, in a suitable limit.


In that hypothetical situation, we'd still be able to have a general
theory of relativity based on the idea of spacetime curvature, but it
wouldn't seem to reduce to the flat-spacetime-generated relationships
of special relativity.

You sure use words funny. This would not be GR, so you have no business
calling it "a general theory of relativity" -- we ALREADY have that, and
it is not at all what you describe. A "generalized" GR is not GR.


Tom Roberts

On Mon, 19 May 2008 07:08:53 -0700 (PDT), dlzc wrote:

Dear Eric Baird:

On May 19, 6:31*am, Eric Baird wrote:
On Thu, 15 May 2008 22:12:09 -0700, "N:dlzcD:aol T:com \(dlzc\)"

wrote:
Dear Eric Baird:

Eric Baird wrote in message
.. .
...
Perhaps Hawking radiation might be expected under
//someone else's// general theory, but I don't see
how the effect can appear classically in a model
that's supposed to reduce to the SR equations of
motion, as Einstein's was.

How fortuitous...
http://groups.google.com/group/sci.a...c52e34b1d93586
... just posted on sci.astro.

Oh, that's really cool!

I shall bookmark it and examine it at leisure!


See the approximations that reduce GR to SR
involve the patching technique to connect little
bits of spacetime for forming a "solution space".
GR allows curvature (the patches can be
slightly skew), and SR does not. *

Yeah, I understand the idea that a curved model
has to reduce to effectively-flat regions if you
zoom in on it far enough ... what I'd take issue
with is whether that geometrical reduction has to
correspond to a reduction to the //physics// of
special relativity.

No. All it does is limit the "extent" of "frame". "Local" suddenly
becomes important.

Agreed.
But there's a potential loophole in the usual argument that a general
theory must reduce to the physics of SR over small regions, in that we
still have to consider whether or not a situation involving particles
whizzing past each other at significant relativistic velocities
//should// count as a flat-spacetime problem.

If we think that it should, then we get special relativity.
If we think that it shouldn't, we seem to be on a path leading to
Something Else (apparently to a model in which gravitomagnetic
regulation of lightspeeds is important).

In the second case, the extent of the "flat frame" regions that SR
would be mathematically valid for would have to be reduced so far that
none of those interesting particle interactions would be happening in
any individual local frame. It'd be like zooming in so far on a
computer image that you see the pixels. The pixels are //there// in
our description, but they represent an idealisation that doesn't
appear in the object being photographed, and the interior region of a
pixel isn't interesting. A pixel only has a few basic properties,
crudely corresponding to the alignment and scale of an SR "facet" in a
gravitomagnetic model. But it has no interior detail.
If we were to go down the gravitomagnetic route, and then break a
"g-m" curved description into an equivalent collection of flat facets,
the facets would be interesting only because of their boundary
properties. There wouldn't be any interior physics of a facet, just as
there's no image contained inside a pixel.

So although such a model could still be said to reduce mathematically
and geometrically to flat-spacetime geoemtry, it couldn't be said to
reduce to the //physics// of special relativity, because in this case,
"the physics of flat spacetime" would be a null concept.
Any "significant" physics (in that sort of model) would be represented
as a significant //departure// from flat spacetime.



I'm not saying that stepping away from special relativity would be
easy, or that we wouldn't need to develop a raft of new theoretical
infrastucture to do it, and I'm not expecting people who like SR to
welcome the idea with open arms ... but when when people say that we
know that any curved-spacetime model //has// to reduce to the physics
of SR, as a geometrical certainty, I have to respond, no, I donl
tthink that we know that. Not yet.

Before we could be in a position to say //that//, we'd probably need
to find some way to prove that a gravitomagnetically-based alternative
can't work, and so far there doesn't seem to be any mainstream
research on that subject. At least, not that I've seen.



One could make the case that if all energy is
associated with curvature, and if lightspeed is
regulated between particles by gravitomagnetic
effects, then all physics would be curvature-based,
and there wouldn't be any such thing as "the
physics of flat spacetime" left for SR to describe.

Such a model is incapable of describing a flat spacetime. Which the
Universe is "in the large".

If you mean, the way that there doesn't seem to be a preferred frame
for the propagation of light at solar-system scales, then that's a
good argument.

There does seem to be a counter-argument, though:
When I was originally looking into this, there seemed to be two
catastrophic problems associated with a gravitomagnetically-based
description, neither of which seemed to be avoidable.

:: Problem One ...
.... was those medium-and large-scale bulk dragging effects.

If the motion of any matter was associated with a lgiht-dragging
effect, then although we'd get the right sort of behaviour for things
like the Fizeau experiment, over much larger scales we'd expect the
cumulative effect of moving background matter to be significant.
If we flew a spaceship though the background universe at high speed,
and if every "moving" star and galaxy showed a dragging effect, we'd
expect these effects, all acting in the same direction, to create a
field that would cause the ship to decelerate.
We'd then have an absolute preferred frame for the propagation of
light at any location at medium scales, and even standard Newtonian
mechanics would fail, because there wouldn't be equivalence between
physics carried out in different inertial frames. We'd even seem to
lose Newtonian/Galilean relativity!

That would be pretty appalling

:: Problem Two ...
.... was gravitational aberration.
If we go back to our spaceship example, the faster the ship moves wrt
the background starfield, the more that relativistic aberration
effects would make that starfield appear to distort. The viewed
positions of the stars, as seen from the ship, would appear to be
deviated so that they appeared increasingly to be congregating ahead
of the ship. The faster the ship went, the more the background stars
would appear to be concentrated ahead of the ship, and the visible
universe would appear to have an increased mass-concentration ahead of
the ship and a decreased one behind it.

If the ship's occupants felt the gravitational effect due to each
star to be coming from the same direction that the star was //seen//
to have ... if each star had a single observed position that didn't
depend on whether we used optical or gravitaitonal equipment to view
it ... then they'd probably expect the ship to undergo a natural
freefall acceleration towards the region of highest apparent density,
which would be forwards.

So the passengers would tend (by default) to expect the ship to
accelerate in the same direction that it was already moving in, which
would make the apparent distortion of the starfield even worse, and
we'd end up with a horribly unstable effect where any object with any
motion at all wrt the background stars would end up with an
uncontrollable positive-feedback forward acceleration.

This would be catastrophic for any attempt at sensible physics, and it
obviously can't be right.


:: Current Theory

The current approach seems to be to tackle both problems sequentially,
and to say that since //each// of these arguments produces stupid
results that don't correspond to the universe that we see around us,
that both of them must obviously be wrong.

::: problem one ...
We say that velocity-dependent dragging effects can't possibly be
significant, even though they appear to exist at small scales, because
at larger scales their cumulative effects would make any moving object
appear to experience a //decelerational// gravitational field. We'd
lose the background flat-spacetime "arena" that conventional inertial
phsyics is played out in.

If dragging effects are then reckoned //not// to be significant, our
attempt to apply the principle of relativity to simple mechanics then
tends to assume totally flat spacetime, and that gives us Einstein's
special theory.

::: problem two ...
We then say that the "gravitational aberration" idea is even worse,
and also deserved to be rejected.
It makes any moving object appear to experience an //accelerational//
gravitational field, and since we obviously don't see anything of that
sort happening, we say that the gravitational effect of a moving body
is therefore is known (somewhat counter-intuitively) //not// to be
affected by aberration.


:: A Gravitomagnetic Approach
::: cancellation

If we're trying a non-SR approach and trying to make gravitomagnetic
effects fundamental, then we don't have the luxury of deleting
cumulative large-scale dragging effects. They have to be there. It's
also more difficult to justify saying that gravitational aberration
effects don't happen.
However, when we look at both problems, together, they seem to cancel
each other out. One predicts a forward acceleration for any moving
object, the other predicts a deceleration for any moving object, and
the magnitudes of the two opposing "problem" effects //seem// to be
about the same. They might actually be identical.

In which case, neither of these "problems" would actually actually be
a problem, both effects would be required, together, to make the
system work.
We'd then say that for the spaceship's occupants, they'd see the
region ahead of them to be populated by a greater number of
blueshifted stars, each pulling more weakly, and the region behind
them to contain a smaller number of redshifted stars, each pulling
more strongly.
Provided that the initial distribution of distant mass in the universe
was reasonably uniform, the two things would then cancel out.

So instead of saying
"Dragging is forbidden, gravitational aberration is forbidden, and
spacetime must be flat at larger scales, because that's what we see",
we allow both effects to do their thing, and to hopefully cancel out,
and that cancellation would then become the reason why spacetime
appears flat at medium scales.

Instead of flatness being an arbitrary condition that we have to
impose, with distortion effects being set "by hand" to zero,
distortion effects would become the underlying reason why that
flatness appears, as an emergent effect, within 3+1 dimensions. It's
perhaps a more complicated description, but less arbitrary.

::: electromagentic analogue

There seems to be a precedent for this sort of cancellation in
electromagnetic theory (although I've lost the textbook reference that
I used to have for it).
If you have a charged test-particle inside a hollow charged sphere,
the sphere's charge is supposed to cancel at every point inside the
cavity. The field obviously cancels when the test particle is centred,
but as we offset it towards one side of the sphere, two opposing
factors play off against each other so that the cancellation is
preserved.
If we offset the test particle along the x-axis, and cut the sphere
into two parts perpendicular to the x-axis, through the particle's
position, then we can try to calculate the summed effects of the
fields due to each of the two pieces, and take these as representing
the opposing forces applied by the shell along the x-axis.

We have a smaller piece of shell wall that is on average closer to the
particle's position, and which therefore exerts a stronger force per
shell-atom, and we have a larger piece of shell that has a larger
average distance from the particle, and therefore a weaker affect per
atom.
The positional offset causes the atoms in the shell to have a
different angular distribution around the test change, that could be
used to argue an acceleration in one direction, while the altered
distances let us argue for a net acceleration fo the test change in
the opposite direction. Both things cancel out.

(I think there's also reckoned to be electromagnetic counterparts of
Coriolis and centrifugal fields within the sphere when it's spun
around the centre that the test particle is offset from, or when the
test particle circles within the sphere, but as I said, I've lost the
reference, and now I can't remember what the effect's supposed to be
called).



SR might still be a decent first approximation
in some ways, but if you zoomed in far enough
to get flatness, you'd then have zoomed in so
far that your region wouldn't contain any particles
moving with significant relative velocities (or any
particles at all!).

GR fails at this scale. In fact, gravitation drops off such that SR
is the classical tool of choice at that scale.

Currently, yes. But a gravitomagnetic version of GR might have a
fighting chance of also working at these smaller scales. It'd need to
apply curved-spacetime principles right down to the particle scale.

Of course, things'd get more complicated with additional fields being
involved, but that's probably not avoidable.


In that scenario, you could certainly zoom in
and get your little flat "facets" or "patches", but
the physics of moving bodies wouldn't then be
described by the internal geometry of any of
those facets, it'd be described by the cumulative
mismatches between facets that'd produce the
curvature effects associated with the particles
and the distortion fields between them.

Which entirely fails in flat space.


Yep!
At small scales, a "g-m" model would have to describe interactions
between particles in terms of curvature effects.

At larger scales we'd seem to get cancellation of background effects,
to produce a flat "stage" in which physics could then be played out,
but when we put particles into that region and bounced them off each
other, their interactions would again have to be describable as
small-scale distortions set against that larger-scale flat background.
It'd be a little like a theatre stage, with a flat floor, and flat
stage scenery, but three-(four-?)dimensional actors playing out the
scene within those surroundings.

As far as an outsider was concerned, the distortions caused by those
particles would be miniscule, and the region would still be
effectively flat.
But as far as the particles themselves were concerned, the signals
that they excahanged would be passing through the regions of maximum
distortion, and the resulting physics might not then be flat-spacetime
physics.


GR does not give up the first postulate of SR, namely that the laws of
physics are the same for all observers. It only adds the word "local"
when evaluating the laws of physics.

Yep. But textbook GR also tends to add the condition that that local
physics has to operate according to the laws of special relativity.

The assumption that everything has to reduce to the physics of SR is
pretty pervasive, it's even started appearing in textbook definitions
of the equivalence principle ("over small regions of spacetime, the
laws of physics must reduce to the their nongravitational special
relativistic form")

I'm querying whether the GR guys have actually done enough background
work to justify that assumption that a reduction to SR physics is
compulsory.
I understand the argument that a curved surface neccessarily has to
reduce to a flat one over sufficiently small regions, but from the
earlier argument, it doesn't //automatically// follow from this that a
relativistic curved-spacetime theory of physics has to reduce to the
physics of special relativity over small regions.
It might instead be that in order to zoom in sufficiently far to
achieve "effective flatness", we have to focus on such a small region
that no meaningful physics is taking place inside it.

The idea that we "know" that physics has to be flat over small regions
seems to me to be based on tradition and convention, and on the fact
that that's how current theory requires things to be. But if we were
building a curved-spacetime model right now, from scratch and with the
benefit of hindsight, I don't see how we could justify the idea that
reduction to SR is compulsory, based on what we currently know.

It seems to me that once we step away from SR's idea of global
lightspeed constancy, and allow lightbeams to deflect and change
velocity (provided that a particulate observer can still measure the
same value for the local round-trip speed of light), then all bets are
off -- it opens up the possibility of curvature-regulated local
c-constancy between bodies as an alternative to special relativity's
description.


Once we have the possibility of //two// different types of model that
would seem to be able to explain local c-constancy within conventional
mechanics, the decision to only consider solutions that reduce to SR
needs further justification.
If we're only looking at inertial mechanics, Occam's Razor would seem
to favour SR, and would seem to suggest that the idea of spacetime
curvature is an unneccessary complication and probably shouldn't be
used unless there's some compelling reason to do so. But if we're
looking at a full gravitational model that already uses spacetime
curvature, then Occam's Razor might apply differently, and say that
since we're having to tackle curvature effects anyway, why not make
them general? Why have a two-stage theory with a GR layer that allows
curvature built built on top of an SR layer that doesn't, if we could
have a theory that applied GR-style principles all the way down, and
didn't make this distinction?

The apparent logical possibility of an overlooked relativistic
alternative to SR-GR1915 doesn't mean that the current system is
necessarily wrong, but it does suggest that we might have a lot more
work to do before we could say that the current system was
neccessarily right.

...
I think that when the QG guys get to the logical
conclusion of their current work, the SR guys
(and some of the GR guys) are liable to get a
horrible shock.

I doubt that it will be a horrible shock, since it must make
predictions that describe what we already see. What it should do is
extend the domain of applicability, and predict some things that we
assumed were random noise, or anomalous. Frankly, I think anyone that
really knows relativity, is ready for something different that works.


Reading that last sentence made me happy!
Thank you!


=Erk= (Eric Baird) www.relativitybook.com
: " ... all attempts to obtain a deeper knowledge of the
: foundations of physics seem doomed to me unless the basic
: concepts are in accordance with general relativity from
: the beginning. This situation makes it difficult to use
: our empirical knowledge, however comprehensive, in
: looking for the fundamental concepts and relations of
: physics, and it forces us to apply free speculation to a
: much greater extent than is presently assumed by most
: physicists. I do not see any reason to assume that the
: heuristic significance of the principle of general
: relativity is restricted to gravitation and that the rest
: of physics can be dealt with separately on the basis of
: special relativity, with the hope that later on the whole
: may be fitted consistently into a general relativistic
: scheme. I do not think that such an attitude, although
: historically understandable, can be objectively justified.
: The comparative smallness of what we know today as
: gravitational effects is not a conclusive reason for
: ignoring the principle of general relativity in theoretical
: investigations of a fundamental character. In other words,
: I do not believe that it is justifiable to ask: What would
: physics look like without gravitation? "
: -- Albert Einstein, Scientific American, April 1950

Eric Baird wrote:
But there's a potential loophole in the usual argument that a general
theory must reduce to the physics of SR over small regions, in that we
still have to consider whether or not a situation involving particles
whizzing past each other at significant relativistic velocities
//should// count as a flat-spacetime problem.

The issue does not directly involve the speed of the particles, merely
the size of the region of spacetime involved and the strength of gravity
there. For instance, at the CDF detector at Fermilab, protons and
antiprotons moving at 0.999999 c collide head on, and their interactions
produce many secondary and tertiary particles moving at speeds 0.9 c.
The detector fits inside a sphere that is 20 meters in radius, so the
maximum duration of an event in the detector is about 100 ns (not
counting electronic delays, which are not subject to gravity). In order
to analyze an event in a locally inertial frame, that frame must be in
freefall; the simplest one to use is at rest relative to the detector at
the start of the event.

Exercise: compute how far that frame will fall during 100 ns,
and compare to the resolution of the detectors (take this as
~1 micron, which is smaller than their actual resolution but
will do).

Exercise: do the same for the rotation of the earth during
the event.

These experimenters are fully justified in neglecting gravity and
rotation, and using SR to analyze their events.


If we think that it should, then we get special relativity.
If we think that it shouldn't, [...]

There's no sensible way to "think that it shouldn't".


BTW in attempting to distinguish between "GR1915" and "GR", you attempt
to make a distinction without a difference. We have learned A LOT since
1915, but the theory is still that of Einstein in 1915.


Tom Roberts

On Sun, 25 May 2008 07:59:20 -0500, Tom Roberts
wrote:

Eric Baird wrote:
But there's a potential loophole in the usual argument that a general
theory must reduce to the physics of SR over small regions, in that we
still have to consider whether or not a situation involving particles
whizzing past each other at significant relativistic velocities
//should// count as a flat-spacetime problem.

The issue does not directly involve the speed of the particles, merely
the size of the region of spacetime involved and the strength of gravity
there. For instance, at the CDF detector at Fermilab, protons and
antiprotons moving at 0.999999 c collide head on, and their interactions
produce many secondary and tertiary particles moving at speeds 0.9 c.
The detector fits inside a sphere that is 20 meters in radius, so the
maximum duration of an event in the detector is about 100 ns (not
counting electronic delays, which are not subject to gravity). In order
to analyze an event in a locally inertial frame, that frame must be in
freefall; the simplest one to use is at rest relative to the detector at
the start of the event.

Exercise: compute how far that frame will fall during 100 ns,
and compare to the resolution of the detectors (take this as
~1 micron, which is smaller than their actual resolution but
will do).

Exercise: do the same for the rotation of the earth during
the event.

These experimenters are fully justified in neglecting gravity and
rotation, and using SR to analyze their events.


Yeah, I think its fully justified to ignore the effects of
//background// curvature when we're dealing with such small regions
that that background curvature fades away to almost nothing.


What I'm more concerned about is that we've neglected the idea of
curvature caused by the relative motion of the particles themselves.
If you fly two particles past each other at 0.999c, it's not
unreasonable to expect that the lightbeam geometry of the region may
distort as they skim past each other, and its possible to conceive of
a model in which these sorts of distortions are responsible for
regulating local lightpseed constancy.

If we were to try to test for the existence of velocity-dependent
light-dragging effects, one way would be to pack a large number of
particles together into a region, and move them all together in a
given direction, and then look for a corresponding offset in the speed
of any light passed through that region.
That's what Fizeau did in the 1850's to test Fresnel's theory that
light was dragged by moving particles, and he came up with a positive
result. The result has been replicated since, and nobody seems to be
disputing it.

While some SR enthusiasts are adamant that we know that the speed of
light isn't affected by the motion of particles, the physical evidence
seems to say the opposite.



Was it legitimate to try ignoring these complicating effects, and try
to construct an idealised, flat-spacetime theory (SR) in the hope that
it'd get things mostly right, and that any problems due ot
over-edealisation might be fixable later? Yes. Was it legitimate to
try to take that special theory as far as it could possibly go? Yes.

Is it then legitimate for us to to say that since this idealised
theory seems to work pretty well in a lot of situations, we therefore
know that the SR idealisations are 100% correct, and that moving
particles have zero effect on the propagation of light, despite any
apparent physical evidence to the contrary? No.


With a theory that depends on idealised assumptions, we're supposed to
eventually go back and test which parts of the theory are sensitive to
small deviations from those idealised assumptions, and which aren't.
Special relativity has now been around for over a century ... if the
SR community were as thorough as some other scientific research
communities, by now I //should// be able to go to a library and look
up a study that'll tell me how the relaxation of SR's condition of
perfectly flat spacetime affects the resulting mathematical and
geometrical structure. I should be able to find a research paper that
asks, "If the principle of relativity is correct, but moving bodies
drag light, then does the theory remain unchanged, and if not, which
parts of it change, and by how much?"


That study doesn't seem to exist in the mainstream literature.



If we think that it should, then we get special relativity.
If we think that it shouldn't, [...]

There's no sensible way to "think that it shouldn't".



Sure there is: Spacetime curvature as a function of relative velocity
between moving bodies.

Under general relativity, we have three major classes of
gravitomagnetic effect for objects with significant gravitation:
we have
[1] light-dragging between relatively-rotating bodies,
[2] light-dragging between relatively-accelerating bodies, and
[3] light-dragging between bodies with relative velocity.

The first effect's well-known (rotational frame-dragging), the second
is slightly more obscure because its more difficult to test, but
nobody really seems to dispute it. The third is more controversial ...
I've come across GR people who insist that no such effect exists, but
all the phenomenology //associated// with that effect seems to exist
in general relativity when bodies have "significant" gravitation.
Bodies moving past each other can exchange momentum, they're supposed
to be able to donate momentum to nearby test-bodies, and from that we
should expect them also to be able to supply momentum to passing
light, which translates into the existence of light-dragging effects.
If a mini black hole shoots past you, you should feel it, and feel a
tug yanking you in the direction that the hole is moving.

When we then move on to consider objects whose conventional
gravitational effects aren't supposed to be significant, we still find
effects [1] and [2], and we can say that this is okay, because it's
okay for forcibly-accelerated bodies to warp spacetime. According to
the GPoR, the "physical" rotation or acceleration of masses //has// to
mangle flat lightbeam geometry, because those masses experience
geeforces that seem to them to be evidence of an associated
gravitational field, and this effect has to be mutual. If rotating the
background starfield relative to a body causes gravitomagentic effects
on that body, then rotating the body relative to the starfield must
cause the body to exert similar (smaller!) gravitomagnetic effects on
the starfield, and on the rest of the region around it.

Acceleration and rotation of //any// masses should distort spacetime.
The SR guys don't get too upset about this suggestion, because we know
that special relativity didn't attempt to "relativise" acceleration or
rotation, so when these things break SR's geoemtry, we shrug and say
that SR itself hasn't broken, we're simply looking at effects that are
outside SR's strict remit. We can use SR as a first approximation, or
switch to GR is we want a more logically-consistent explanation.
Fair enough.

But the final thing that we have to deal with is the possibility of
effect #3 for the case of "gravitationally insignificant" bodies.

This is where things get more difficult.


There seem to be two ways of attacking this problem:

APPROACH #1
We can say that the success of Newtonian/Galiean relativity means that
we know that an isolated body moving through a "flat" background
should coast indefinitely, which means that there are no obvious net
forces on the body due to its motion for us to analyse, which in turn
means that we're justified in saying that the most efficient
explanation is that there //are no// gravitomagnetic effects
associated with relative velocity.
If we assume that bodies passing each other with significant relative
velocities don't distort spacetime, then we end up with a perfectly
"flat" model of inertial physics, which gives us global c-constancy,
Minkowski spacetime and special relativity.

APPROACH #2
The second route is to work forwards from the other evidence and
backwards from the GPoR, and to see where the two things meet in the
middle. Real moving particulate matter seems to drag light along with
it (Fizeau), and the GPoR describes the receding side of a rotating
body as pulling more strongly than the approaching side, so a
generalisation of these effects and principles seems to lead to the
idea that effect #3 is general. Gravitational physics seems to include
the analogue of velocity-dependent dragging, and "mutuality" seems to
require that when we allow a mix of bodies with and without obvious
significant gravitation, that these effects should apply for all of
them, and that any modification of the equations of motion due to
gravitomagnetism that applies to "gravitational" bodies should then
apply to all bodies.
So the GPoR, by default, tends to suggest velocity-dependent
gravitomagentic effects as something fundamental, and our physical
evidence doesn't seem to be in conflict with that idea.

The one restriction that we have to take seriously with the second
approach is that we need to to make sure that any velocity-dragging
effects due to background material have to cancel perfectly in 3+1
dimensions when that background material is evenly distributed ... and
that does seem to be the default result when we set environmental
dragging effects against the effects of gravitational aberration.


So (, to me), we seem to have two distinct routes to a general theory
of relativity: We can either embrace the idea of spacetime curvature
wholeheartedly and try to build a single-stage general theory that's
designed around the idea that spacetime curvature is a fundamental
part of physics, or we can break the problem into two sections, attack
the "inertial physics" part by assuming flat spacetime (giving us SR),
and then construct GR1915 to handle the non-SR effects, but design it
to reduce to SR as a limiting case.



Historically, we took the second path. Mathematicians had certainly
been trying to come up with curved-space models back in the C19th, but
they failed, apparently because they didn't realise that time
coordinates had to be warped by gravitation as well as spatial
coordinates. A credible geometrically-based general theory doesn't
seem to have been achievable until after Einstein had pointed out that
gravitational shifts seemed to lead, trivially, to the idea of
gravitational time dilation.
Once we knew that gravity also warped //time//, we could go back and
dig up the old C19th curvature arguments and try to make them work.
But by this time Enstein had already developed special relativity, and
had decided to try to embed special relativity in his general theory
as a limiting case, so that he wouldn't have to design his GTR
completely from scratch. From that point onwards we seemed to be
locked into the idea that gravitational theory //had// to reduce to
special relativity, even though nobody seemed to stop to analyse
whether this was actually true or not.




If history had played out slightly differently ... if some bright
spark had pointed out the argument for the gravitational time dilation
effect back in 1820 or 1850 or 1880, then the smart math guys should
have been able to come up with some sort of general theory in the
//Nineteenth// Century, before Einstein came along. There wouldn't
have been an obvious reason why that theory would have been expected
to reduce to what we now understand as special relativity, because SR
wouldn't yet have appeared on the scene.
We might instead have ended up with a gravitomagnetically based theory
that made curvature the basis of all physics ... that certainly seemed
to be an idea that Clifford was campaigning for, and the idea of
dragging effects would have been something that physicists were
already familiar with from all those C19th aether-dragging models.
It'd have been a logical extension of the concepts and expertise of
the time.

So not only do we appear to have two separate potential routes to a
general theory of relativity ("flat plus curved" or "curved-only"), in
some ways, the path that we actually took seems the more improbable
one, and looks (IMO) as if it might be down to a freak accident of
history.




BTW in attempting to distinguish between "GR1915" and "GR", you attempt
to make a distinction without a difference.

I'm making a distinction between what a general theory of relativity
//can// predict, and the particular predictions that Einstein's
specific implementation forces upon us.

* A general theory based on an acoustic metric (rather than SR) will
predict indirect radiation from horizon-bounded objects.

* A general theory based on special relativity will argue that
radiation through gravitational horizons is geometrically impossible.

That's a significant difference.


Since QM agrees that information needs to be somehow leaking outwards
through a gravitational horizon, this puts Einstein's attempted
implementation of a general theory at odds with quantum theory. After
thirty years of our smartest guys trying to find a way to allow GR1915
to allow this sort of radiation, they've failed. I'd suggest that the
reason they can't persuade GR1915 to behave in this way, is that the
non-radiative nature of GR1915's gravitaitonal horizons is built
directly into the structure of the theory, thanks to its incorporation
of special relativity.

Can we apply general principles to argue that Hawking radiation ought
to be expected from a horizon? Yes.

Does GR1915 fully implement those principles? Since it can't make that
prediction, no.


We can try overlaying QM's Hawking radiation predictions onto a GR
background and say that the HR is due to separate QM effects, but the
result is rather artificial:
In an acoustic metric, QM's description of indirect radiation from a
horizon is a statistical description of effects that are already there
in the classical model. We can present the effect as something that
should be expected from acoustic horizons (which fluctuate and radiate
naturally of their own accord), and if we should decide that we'd
instead prefer to describe the effect statistically using QM, we have
that option. The "QM" and "classical" descriptions are dual.

But if we try to retrofit Hawking radiation to GR1915 as a separate QM
effect, there's nothing in the GR1915 model for those QM statistics to
relate to. The effect isn't predicted by GR1915. We can use QM's more
abstract principles to argue that a horizon //should// fluctuate, and
//should// radiate, and we can calculate the properties that we expect
the "missing" effects to have, using QM, and describe them in terms of
QM-style particle-pair production effects ... but if we then take
these QM predictions for how far GR1915 misses the correct answer, and
overlay them onto a GR1915 background asa correction, to bring the
GR1915 predictions back into line with what we've found out by other
means should be the right answers, we haven't really solved anything.



We have learned A LOT since
1915, but the theory is still that of Einstein in 1915.

Yes, I tend to agree ... because we're still using a version of
general relativity that's assumed to reduce to the physics of SR.


That's where I think the problem is.


=Erk= (Eric Baird)
www.relativitybook.com
: " Things ... fall ... apart.
: And it might not be down to you,
: It's just a thing that happens,
: Something they do. "
: -- "X-Directory"

Eric Baird wrote:
What I'm more concerned about is that we've neglected the idea of
curvature caused by the relative motion of the particles themselves.
If you fly two particles past each other at 0.999c, it's not
unreasonable to expect that the lightbeam geometry of the region may
distort as they skim past each other, and its possible to conceive of
a model in which these sorts of distortions are responsible for
regulating local lightpseed constancy.

The fact that the standard model reproduces essentially all particle
experiments indicates that neglecting such "distortions" down to 10^-18
meter or so is fully justified. At present, nobody knows what to do on
smaller scales, but expectations are that QFTs kinda-sorta ought to hold
down to near the Planck scale. But there are indications that the
specific QFT we call the standard model will need to be modified when we
achieve energies on the scale of a few TeV (i.e. in the next few years
as the LHC comes on line). It is of course possible that new information
will revise upward the length scale at which QFT is expected to fail
(smaller length scale corresponds to larger energy scale).


If we were to try to test for the existence of velocity-dependent
light-dragging effects, one way would be to pack a large number of
particles together into a region, and move them all together in a
given direction, and then look for a corresponding offset in the speed
of any light passed through that region.

Or alternately, put a similarly large number of particles into a similar
bunch and make the two bunches collide. I just described what we
actually do at several machines, including the Tevatron here at Fermilab
and the LHC at CERN.


That's what Fizeau did in the 1850's to test Fresnel's theory that
light was dragged by moving particles, and he came up with a positive
result. The result has been replicated since, and nobody seems to be
disputing it.

Physics is a QUANTITATIVE science. The densities achievable in water and
glass are ENORMOUSLY larger than those achievable in particle beams
(factors on the order of 10^10 or more). Work out Fresnel's formula for
an index of refraction that differs from 1 by one part in 10^10.


While some SR enthusiasts are adamant that we know that the speed of
light isn't affected by the motion of particles, the physical evidence
seems to say the opposite.

What "physical evidence"???? -- your non-quantitative guesses are not
"evidence" of anything.


Was it legitimate to try ignoring these complicating effects, and try
to construct an idealised, flat-spacetime theory (SR) in the hope that
it'd get things mostly right, and that any problems due ot
over-edealisation might be fixable later? Yes. Was it legitimate to
try to take that special theory as far as it could possibly go? Yes.

Is it then legitimate for us to to say that since this idealised
theory seems to work pretty well in a lot of situations, we therefore
know that the SR idealisations are 100% correct, and that moving
particles have zero effect on the propagation of light, despite any
apparent physical evidence to the contrary? No.

Nobody does that, except you in your straw-man arguments.


With a theory that depends on idealised assumptions, we're supposed to
eventually go back and test which parts of the theory are sensitive to
small deviations from those idealised assumptions, and which aren't.
Special relativity has now been around for over a century ... if the
SR community were as thorough as some other scientific research
communities, by now I //should// be able to go to a library and look
up a study that'll tell me how the relaxation of SR's condition of
perfectly flat spacetime affects the resulting mathematical and
geometrical structure. I should be able to find a research paper that
asks, "If the principle of relativity is correct, but moving bodies
drag light, then does the theory remain unchanged, and if not, which
parts of it change, and by how much?"

If the moving earth does not drag light, and it demonstrably does not do
so to very high accuracy, how can you expect a single proton to drag
light significantly?


That study doesn't seem to exist in the mainstream literature.

Nonsense. It's known as General Relativity.


If we think that it should, then we get special relativity.
If we think that it shouldn't, [...]
There's no sensible way to "think that it shouldn't".

Sure there is: Spacetime curvature as a function of relative velocity
between moving bodies.

Nope. Curvature is a tensor field on the manifold, and cannot depend on
such things.

One could imagine a completely different model, in which such relative
velocities are important and can "drag light" and such. But that is
utterly unrelated to the basis of SR and GR. You're on your own to try
to formulate such a theory. Good luck.


BTW in attempting to distinguish between "GR1915" and "GR", you attempt
to make a distinction without a difference.

I'm making a distinction between what a general theory of relativity
//can// predict, and the particular predictions that Einstein's
specific implementation forces upon us.

You MUST pick a different name. Attempting to use the same name only
confuses everybody. The name "general relativity" is already taken, and
is specifically Einstein's theory (as expanded and amplified through the
years).


Tom Roberts