VSL (Variable Speed of Light) Relativity
Perfectly Innocent
I've looked at many papers on VSL (Variable Speed of Light) Relativity
on the Internet and they are all beyond me. I've asked about VSL at
the newsgroup sci.physics.relativity and have never received a
specific answer.
Surely you know the answer.
What are the transformation equations between "inertial" frames of
reference that modify SR and preserve a variable speed of light? What
are the physical interpretations and implications of these equations
that make sense to students of physics and math at the undergraduate
level? Do these equations imply that the relative velocities between
different "inertial" frames of reference are speeding up or slowing
down? And finally, is there any possibility that VSL justifies the
unorthodox "tired light" hypothesis?
Thanks.
Eugene Shubert
http://www.everythingimportant.org/relativity/
John Devers
> I've looked at many papers on VSL (Variable Speed of Light)
Hi there, you might like my little file/tutorial I've put together on
current measurments of light.
Lab tests tenets' limits
http://www.nature.com/nsu/030428/030428-20.html
Seven years ago, the US physicist Freeman Dyson looked at the
radioactive decay products of a spontaneous nuclear chain reaction
about two billion years ago in natural uranium deposits in Gabon. He
used the results to estimate the value of alpha at that time. He
concluded that it could not have differed from the present-day value
by a factor of more than one ten-billionth - a rate of change of
around 0.5x10-16 per year.
Harold Marion and colleagues at the Observatoire de Paris in France,
and James Bergquist and co-workers at the National Institute of
Standards and Technology in Boulder, Colorado, have ruled out any
change greater than between 7x10-15 and 7x10-16 per year.
New Experimental Limit on the Photon Rest Mass with a Rotating Torsion
Balance
http://link.aps.org/abstract/PRL/v90/e081801
New upper limit on photon mass of 1.2×10-51g
A New Limit on Photon Mass
http://www.aip.org/enews/physnews/2003/split/625-2.html
A new limit on photon mass, less than 10-51 grams or 7 x 10-19
electron volts, has been established by an experiment in which light
is aimed at a sensitive torsion balance
The speed of light is constant in all directions
Lorentz Violations? Not Yet
http://www.aip.org/enews/physnews/2003/split/623-2.html
The Stanford group sees no such anisotropy at the level of 10-13 for
velocity-independent terms, and at the 10-9 level for
velocity-dependent terms.
Finding the Speed of Light with Marshmallows
Marc Millis
Perfectly Innocent Eugene Shubert wrote:
-snip-
> What are the transformation equations between "inertial" frames of
> reference that modify SR and preserve a variable speed of light?
An indirectly related theme to the idea of VSL is something that is
sometimes called the "Optical-Analogy." Within GR, there exists some
"Euclidean" interpretations, one of which is the "optical analogy." In
this interpretation, the gravitational field is represented as an
optical medium with an effective index of refraction [7-9]. Although
different from the more common Geometric interpretation, this
interpretation has been shown to be consistent with physical observables,
and transformation rules between these two perspectives have also been
published [8]. Little attention is typically focused on this
perspective because it does not predict any new effects that aren't
already covered by the more common Geometric perspective of GR, and
because it raises unanswered issues with coordinate systems choices.
I hope that this adds to your repertoire of knowledge rather than to
your confusion. This particular approach is easier to visualize.
7. de Felice, ?On the Gravitational Field Acting as an Optical Medium?,
in Gen. Rel. and Gravitation, 2, 347-357, (1971). 8. Evans, J., Nandi,
and Islam, ?The Optical-Mechanical Analogy in General Relativity: Exact
Newtonian Forms for the Equations of Motion of Particles and Photons?,
In General Relativity and Gravitation, 28, 413-439, (1995). 9. Nandi,
Kamal and Islam, ?On the optical-mechanical analogy in general
relativity?, In Am. J. Phys. 36 (3) (March 1995)
Also, I welcome comments from the other readers to highlight the
strengths and weaknesses of this perspective. In particular, does
anyone know a reference that critiques these from the point of view of
issues with coordinate systems choices?
Marc
Bill Hobba
Inertial reference frames are homogeneous and isotropic in space and
homogeneous in time. Homogeneous means exactly the same experiment yields
exactly the same results. This means if I shine a torch at time t and
measure the speed of light I will measure exactly the same speed as if I
shine it at another time. The way the speed of light can vary under normal
SR is it having a very small mass which means its speed is not the same as
the speed in the Lorentz transformation. That speed must, by its
definition, remain unchanged.
Although I have not gone into the details of the papers Bilge and others
have referred you to as far as I can make out they 'modify' the property's
of inertial reference frames. Just why do you want a variable light speed
when it is at such odds with the homogeneity property? The papers you were
referred to cited applications to cosmological models. Is that your reason?
If so why?
Thanks
Bill
Uncle Al
Let's ask some questions outside the box to challenge the ansatz where
it lacks a Chobham armor glacis plate.
1) Does the optical model include birefringence? If one can erect
one refractive index in a medium, one can erect multiple refractive
indices (anisotropic in space) by the same mechanism. Gravitation
suddenly has new testable predictions. Spatial anistropy
symmetry-breaks conservation of angular momentum.
2) If you can have birefringence then you can have circular
birefringence (optical chirality, gyrotropy) by at least three
internal physical mechanisms fundamental to a lattice (J. Chem. Phys.
65(4) 1522 (1976)):
1. Pseudoscalar, from local chirality that persists in
disordered distribution (e.g., solution).
2. Vector. A property of pyroelectric lattices.
3. Pseudodeviator, from lattice symmetry - requires absence of
a point of symmetry but tolerates mirror planes of symmetry (optical
chirality without physical chirality). Silver thiogallate (J. Appl.
Cryst. 33 126 (2000)), AgGaS2 with non-polar achiral tetragonal space
group I-42d (#122), has immense optical rotatory power: 522
degrees/millimeter along [100] at 497.4 nm, reversed along [010].
plus external field-imposed asymmetries - Faraday effect,
electrogyration, piezogyration, electro-Faraday effect,
magneto-activity, and magneto-electrogyration.
Mica crystal (muscovite, phlogopite) is birefringent and it easily
splits into supremely thin atomically-smooth layers (isinglass). Make
a compressed stack of mica films each plane being slightly rotated
about the same axis vs. the previous one, all in the same helical
sense. You now have a powerful optical rotator crafted of a sheaf of
*achiral* components.
If we erect an optical model then all the attendant optical baggage
tags along as potential observables. If we erect an optical model,
then we have a potent handle into quantitatively modeling optical
properties of a lattice-based medium (J. Appl. Cryst. 19 108 (1986)).
If we erect an optical model, then we can geometrically assault its
geometric basis and look for unavoidable outputs,
http://www.mazepath.com/uncleal/eotvos.htm
It uses the same apparatus and the same experimental protocol. The
novel test masses cost about the same as those in a classical
experiment. Somebody should look.
--
Uncle Al
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)
Tom Roberts
> An indirectly related theme to the idea of VSL is something that is
> sometimes called the "Optical-Analogy." Within GR, there exists some
> "Euclidean" interpretations, one of which is the "optical analogy." In
> this interpretation, the gravitational field is represented as an
> optical medium with an effective index of refraction [7-9]. Although
> different from the more common Geometric interpretation, this
> interpretation has been shown to be consistent with physical observables,
> and transformation rules between these two perspectives have also been
> published [8]. Little attention is typically focused on this
> perspective because it does not predict any new effects that aren't
> already covered by the more common Geometric perspective of GR, and
> because it raises unanswered issues with coordinate systems choices.
And also, I suspect, because such an Euclidean interpretation cannot
possibly hold in a region with strong gravitation....
[I have not looked at your references.]
Tom Roberts tjro...@lucent.com
Perfectly Innocent
I deeply appreciate your contribution. I believe that interpretations
like the "optical analogy" and the "Fermat metric" are directly
related to VSL. Up until now I was only familiar with my own
mathematical wonderment and some interesting but unprofessional
speculations that I've read on the Internet. I agree that the "optical
analogy" is easier to visualize. Isn't "an effective index of
refraction" just another way to say "gravitational potential as a VSL
theory?"
If the interpretation you mentioned is, in a large degree, "consistent
with physical observables" then I think it should be carefully studied
by everyone. We should have as many competing theories as possible if
for no reason than to gauge the better ones. Didn't Einstein say
"Physical theories should be made as simple as possible--but no
simpler." I know that a healthy diet requires variety.
I can understand the offense of abandoning curvature for "Euclidean"
interpretations but don't recent cosmological observations suggest
that that is a reasonable direction? I look forward to reading the
literature you cited and the expert responses to the points you have
made.
Eugene Shubert
http://www.everythingimportant.org
> 7. de Felice, "On the Gravitational Field Acting as an Optical Medium",
> in Gen. Rel. and Gravitation, 2, 347-357, (1971). 8. Evans, J., Nandi,
> and Islam, "The Optical-Mechanical Analogy in General Relativity: Exact
> Newtonian Forms for the Equations of Motion of Particles and Photons",
> In General Relativity and Gravitation, 28, 413-439, (1995). 9. Nandi,
> Kamal and Islam, "On the optical-mechanical analogy in general
> relativity", In Am. J. Phys. 36 (3) (March 1995)
Perfectly Innocent
> Just why do you want a variable light speed when it is at such odds
> with the homogeneity property?
> The papers you were referred to
> the papers Bilge and others have referred you to
Joao Magueijo asserts in his book, "Faster Than the Speed of Light:
The Story of a Scientific Speculation", Perseus Publishing, 2003, that
revisions to special relativity that do not contradict the relativity
of motion are possible.
I quote:
"IT'S DIFFICULT to sum up where VSL stands, as I finish this book,
because it is still well within the maelstrom of scientific inquiry.
VSL is now an umbrella for many different theories, all predicting, in
one way or another, that the speed of light is not constant, and that
revisions to special relativity are required. Some of these theories
contradict the relativity of motion--for example, the model Andy and I
first proposed--but others don't. Some predict that the speed of light
varies in space-time, such as my Lorentz-invariant VSL theory and
Moffat's theory." (p. 256).
I can easily imagine all "inertial" frames of reference being
equivalent in a space that is homogeneous and isotropic, abandoning
the homogeneity of time requirement and allowing a variable speed of
light.
If that's the claim being made then I want to see a concrete
example--an explicit transformation equation--expressing how
space-time events transform in different "inertial" frames of
reference, preserving the principle of relativity. I didn't ask for
links citing a vast collection of VSL papers; I asked for someone to
write down even one of these alleged transforms explicitly for the
easy case of one spatial dimension. I explicitly asked for a
coordinate transformation of the form: x'=f(x,t), t'=g(x,t) with all
the required properties on the level of Rindler's relativity books.
I can't imagine there being so much published about VSL and the
subject not being translatable into an undergraduate-level
presentation of the physics, with clocks and rulers.
I have an interest in simple generalizations of SR. I also have a
curiosity about all viable, logically consistent, alternative SR type
theories.
http://www.everythingimportant.org/viewtopic.php?t=605
Eugene Shubert
Marc Millis
-snip-
> Let's ask some questions outside the box to challenge the ansatz where
> it lacks a Chobham armor glacis plate.
>
> 1) Does the optical model include birefringence? If one can erect
> one refractive index in a medium, one can erect multiple refractive
> indices (anisotropic in space) by the same mechanism. Gravitation
> suddenly has new testable predictions. Spatial anistropy
> symmetry-breaks conservation of angular momentum.
-snip-
Uncle Al,
I am not proficient in all the optical analysis tools you suggest.
Would you care to distill this down into something akin to a thought
experiment that we could apply to the "optical analogies"?
Thanks.
Marc Millis
In <bibsgg$p...@netnews.proxy.lucent.com> Tom Roberts wrote:
-snip-
> And also, I suspect, because such an Euclidean interpretation cannot
> possibly hold in a region with strong gravitation....
This would be an interesting analysis, but I suspect one would have to
be careful with starting assumptions in trying to figure out how to
appropriately apply this optical model in cases such as black holes.
That, by itself, would be a challenging task.
I am definitely under the impression that wormholes or warp drives are
not describable from this perspective, but this is just an impression,
not a reliable conclusion on my part.
For example, to consider the back hole case, here is just one detail
that muddies up the works: Time. One would have to be careful on how
one defines the propagation of time. For clocks that are based on an EM
phenomena (remember that c varies with respect to the gravitational
potential in the optical model), one has to be careful on which clocks
to use as a reference. So long as it is all applied consistently, any
selection should suffice (uh, maybe). Perhaps a master clock at
infinity (far from sources of gravitational potential), but there are
multiple ways to treat this too.
BTW, one of the optical analogy papers I cited earlier describes the
phenomenon of gravitational red-shift using the optical analogy.
I have not seen a reference that attempts this or that uses such an
attempt to refute such optical perspectives. If anyone knows of such a
reference, I would greatly appreciate having it pointed out to me.
Thanks,
Marc
Uncle Al
> In <bidvqi$rhk$1...@lfa222122.richmond.edu> Uncle Al wrote:
> > 1) Does the optical model include birefringence? If one can erect
> > one refractive index in a medium, one can erect multiple refractive
> > indices (anisotropic in space) by the same mechanism. Gravitation
> > suddenly has new testable predictions. Spatial anistropy
> > symmetry-breaks conservation of angular momentum.
> I am not proficient in all the optical analysis tools you suggest.
> Would you care to distill this down into something akin to a thought
> experiment that we could apply to the "optical analogies"?
Stipulated that one creates an empty spacetime as an optical
analogue. It can be very symmetric and simple in structure, giving
straighforward answers. Analogous to ray tracing, it can still be
rich with content. If you want to do anything interesting in physics
you have to add stuff to the spacetime. Adding stuff breaks
symmetries, certainly locally. When you lower the symmetry of the
medium by adding stress, what are the implications? If it is an
optical medium the implications are profound. If you create one
"refractive index," then that identical mechanism is applied again by
the adopted rules. The properties of an optical medium are
exquisitely sensitive to symmetry.
The symmetry of a crystal lattice determines its refractive behavior.
Said symmetry can be intrinsic (space group) or imposed (symmetry
lowering by applied stress; or magnetic or electric fields). Table
salt and diamond are highly symmetric, homogeneous, isotropic solids.
If you take a crystal and rotate it between crossed linear polarizers,
the field stays dark. (If you stress the crystal, or a glass, the
symmetry lowering makes the medium active toward polarized light).
Hydrated magnesium sulfate, Epsom salt, has three optical axes and
three refractive indices (1.433, 1.455, 1.461). If you rotate a
crystal of Epsom salts between crossed polarizers you get alternate
brightening and darkening from the birefringence. Certain crystal
directions will split an image into an ordinary and an extraordinary
ray with different polarization directions. Engineers who use a
single crystal alumina (white sapphire) window for its great strength
and hardness get a doubled image unless they look along the
crystallographic c-axis.
If the lattice lacks an inversion point of symmetry it can be
birefringent (two or more refractive indices) and it can be
gyrotropic, too - rotating the plane of polarized light propagating
through it. The symmetry lowering creates additional phenomena like
piezoelectric (charge separation with stress), pyroelectric (charge
separation with temperature) and ferroelectric (latching of
polarization states) responses.
An optical model of spacetime contains awesome potential complexities
as soon as asymmetry (gravitation of a body) is intoduced, and
therefore empirically testable consequences. General Relativity (GR)
was built to be as simple and "flat" as possible, assuming the
Equivalence Principle (EP) and spacetime curvature therefrom,
possessing parity-symmetric rank-2 tensors. Metric spacetime begins
isotropic and homogeneous, going beyond conformal symmetry (scale
independence) to symmetry under all smooth coordinate transformations
- general covariance. Affine/teleparallel models are rigorously
identical to almost all GR predictions, not assuming the EP,
substituting spacetime torsion for curvature. The slim non-overlap
can include parity-antisymmetry. A parity EP test could therefore
falsify metric theories. Somebody should look.
Optical models of spacetime cannot be that simple. They must
implicity include a wealth of phenomena wildly in excess of metric or
affine theories' contents. Polarized light propagating through free
space empirically ignores hundreds of megagauss magnetic fields or
millions of lightyears of more modest fields (Carrolls' work).
Polarized light propagating through a refractive medium plus even a
fractional gauss magnetic field detectably Faraday rotates.
My opinion is that any treatment of spacetime as an optical analogue
that does not address the inescapable baggage of optical media is
selling false goods. Creating a hugely publishable model of
gravitation is no big deal - loop quantum theory,
brane/string/M-theory, Lorentzian lattice quantum gravity, a whole
pile of stuff
http://www.mazepath.com/uncleal/eotvos.htm#b25
Creating a empirically testable/credible model of gravitation is a big
deal. If you can create a bulk transparent strong ferromagnet, a
whole lot of folks want to talk with you.
Perfectly Innocent
Just for the record, what follows below is a corrected version of your
footnotes. In your second reference the year is 1996, not 1995 and in
the third, it's Vol. 63, not 36.
Thanks for bringing this to my attention:
7. de Felice, "On the Gravitational Field Acting as an Optical
Medium", in General Relativity and Gravitation, 2, 347-357, (1971).
8. Evans, J., Nandi, and Islam, "The Optical-Mechanical Analogy in
General Relativity: Exact Newtonian Forms for the Equations of Motion
of Particles and Photons", In General Relativity and Gravitation, 28,
413-439, (1996).
9. Nandi, Kamal and Islam, "On the optical-mechanical analogy in
general relativity", In American Journal of Physics, Volume 63, No. 3
(March 1995)
Eugene Shubert
http://www.everythingimportant.org/viewtopic.php?t=533
Eric Baird
<marc.g...@nasa.gov> wrote:
>
>Perfectly Innocent Eugene Shubert wrote:
>-snip-
>> What are the transformation equations between "inertial" frames of
>> reference that modify SR and preserve a variable speed of light?
>-snip-
>
>An indirectly related theme to the idea of VSL is something that is
>sometimes called the "Optical-Analogy." Within GR, there exists some
>"Euclidean" interpretations, one of which is the "optical analogy." In
>this interpretation, the gravitational field is represented as an
>optical medium with an effective index of refraction [7-9].
Hi Marc!
Yep, this approach goes back at least as far as Isaac Newton, but
IN inverted some key relationships and after his version was
disproved, the idea was discredited for a long time. Newton wanted to
be able to say that both particles and waves fall at the same rate in
a gravitational field and both get "diffracted" by a lightspeed
gradient by the same amount, so he was going for a sort of double
duality.
Since his trajectories were the same for particles and waves, I guess
we might even think of him as a pioneer of the geometrical approach.
Kip Thorne's "popular" black holes book refers to the "gravity-as-
curvature" and "gravity-as-lightspeed-variation" ideas as totally
interchangeable, but I don't know how far KT considered that
equivalence to go. Obviously if you have a geometry in which a surface
ends up curving through 90 degrees or more, or is multiply-connected,
projecting that onto a flat surface is going to be problematic unless
you start tiling or using overlays or something.
>Although
>different from the more common Geometric interpretation, this
>interpretation has been shown to be consistent with physical observables,
>and transformation rules between these two perspectives have also been
>published [8]. Little attention is typically focused on this
>perspective because it does not predict any new effects that aren't
>already covered by the more common Geometric perspective of GR, and
>because it raises unanswered issues with coordinate systems choices.
It raises a lot of questions, but part of that is due to the way that
existing physics already breaks down. I think those breakdowns are
sometimes more obvious and more difficult to hide in the "optical"
descriptions.
One point about the optical approach is that it doesn't work properly
for moving-body situations if you just assign simple "refractive
index" values to points in spacetime. That might give you a
description of the behaviour of stationary bodies, but once you have
relative motion, you need to include some sort of additional direction
and magnitude properties to deal with lightspeed anisotropies due to
nearby moving particles.
GR includes Machian effects like frame-dragging around rotating and
accelerating masses, and so a compatible optical description needs to
include lightspeed-dragging effects to replicate those effects. And to
include the Fizeau effect, you seem to have to include similar
dragging effects for particles that have simple constant-velocity
relative motion (and perhaps to include "rotational direction"
information in rotating-body problems?).
Trouble is, SR doesn't include velocity-based dragging effects, and I
don't think you can retrofit them cleanly without breaking the theory,
so it seems that for this sort of description to be consistent, it
needs to have a degree of incompatability with SR. Velocity-dragging
can be the basis of a relativistic model where velocity-shifts and
gravity-shifts are fully interchangeable, but SRseems to be too
strongly founded on flat spacetime to work in that sort of context.
Re: black hole problems involving QM, there are a number of papers
that describe the QM phenomenology outside the horizon by saying that
we can treat the horizon as a conventional radiating surface
supporting a conventional (very rarefied) atmosphere, so you can use
conventional classical "pre-SR" methods and get good "post-GR"
predictions ["Black holes: The Membrane Paradigm", eds Thorne, Price,
Macdonald]. But the equivalence of these descriptions breaks down at
the horizon. Again, the culprit seems to be special relativity,
because to be able to have a classical radiation model that _spans_
the horizon, velocity shifts seem to need to be able to follow a
different set of shift laws to the ones that are included with SR.
Unruh produced a few papers on indirect radiation through a sonic
horizon, but to turn the sonic model into an optical one, we need our
choice of optical rules to include the ability of particles to drag
lightspeed locally in their vicinity. Again, we are back to the
velocity-dependent dragging, the Fizeau effect, propagation
nonlinearities and some derivational and numerical incompatabilities
with special relativity.
Matt Visser has produced an interesting paper on Hawking radiation in
non-SR physics [ gr-qc/9712010 ], and the sorts of "modern" Lorentz
group relationships that can crop up in an archaic dark-star-type
model.
Re: warp drives (which you mention in a later post) ... again,
optical-type descriptions do seem to be workable for warp drive
problems, but only if we drop the condition that the physics has to
reduce to special relativity.
Impose SR-compliance, and you get horizon problems and issues about
how fast a warpdrive wavefront (which is supposed to represent an
increase in the speed of light in the direction of ship travel) is
supposed to propagate. If the wavefront propagates at cBACKGROUND, you
have problems, if it propagates at cWARP you have problems, and if
different parts of the wavefront propagate at their own local nominal
lightspeeds, you have problems with the "fast-c" rear of the wavefront
trying to overtake the "slow-c" front edge. These problems aren't down
to the optical description, they are there as part of the cost of
including SR in our model. We can try to reintroduce nonlinearity
non-classically by saying that perhaps gravitational information
tunnels forwards across the wavefront in a manner analogous to black
hole radiation, but then we are inventing a new "warpdrive version" of
the existing Black Hole Information Paradox, for which there's
currently no SR-compatable solution AFAIK.
To get around the "coordinate system choices" issue, you need some way
if imposing local lightspeed constancy, and once again the answer
seems to be to incorporate velocity-dragging. Unfortunately there's
more overhead this way in that you can't then abstract away the
particulate matter that represents your emitter and observer and just
talk about idealised empty frames as you can in SR ... in this sort of
model, lightspeed constancy depends on there actually being a mass at
a specified location with a specified velocity in order for you to be
able to take the measurement. Any attempt to extract new information
from a region results in a change of the region's geometry.
Re: Cosmological issues (which again you mention in a later post) ...
I did make some progress with an approach that seemed to allow Hubble
shifts to also be totally interchangeable with velocity-shift and
gravity-shift descriptions (so that a cosmological horizon ended up
being treatable as a conventional radiating black hole horizon
shielding us from a supposed initial singularity), but once again, for
all the descriptions to be interchangeable, and the indirect radiation
mechanisms to be the same, you had to lose the SR shift equations.
Indirect radiation through a cosmological horizon looks just like
conventional Hawking radiation, but when you think about it,
cosmological indirect radiation has to also be describable using
mundane non-QM methods, so it seems to correspond to the "primitive"
dark-star version of the effect.
It's easier to imagine than the QM pair-production description, but
it's not SR-compatable (I think the conventional view is that Hubble
shifts fall into a separate category and don't have to follow the SR
rules).
So I think there are two possible approaches with the "optical" method
of attack: make it compatable with the largest number of basic
principles and descriptions (but lose special relativity), or force it
to be compatable with SR, but lose all the cool new stuff and end up
with a description that tells you only what you already know, but
makes the inconsistencies more glaring.
Given that most relativists are brought up on SR, I think the most
likely attitude they'd take would be the second one, concluding that
the optical approach is interesting but problematic and doesn't tell
us anything new.
Personally, I think the supposed problems (and the apparent pattern
behind them) suggest a hell of a lot, but that's just me.
>I hope that this adds to your repertoire of knowledge rather than to
>your confusion. This particular approach is easier to visualize.
>
>
>7. de Felice, ?On the Gravitational Field Acting as an Optical Medium?,
>in Gen. Rel. and Gravitation, 2, 347-357, (1971). 8. Evans, J., Nandi,
>and Islam, ?The Optical-Mechanical Analogy in General Relativity: Exact
>Newtonian Forms for the Equations of Motion of Particles and Photons?,
>In General Relativity and Gravitation, 28, 413-439, (1995). 9. Nandi,
>Kamal and Islam, ?On the optical-mechanical analogy in general
>relativity?, In Am. J. Phys. 36 (3) (March 1995)
>
>
>Also, I welcome comments from the other readers to highlight the
>strengths and weaknesses of this perspective. In particular, does
>anyone know a reference that critiques these from the point of view of
>issues with coordinate systems choices?
>
>Marc
I think Visser's paper on non-SR relativistic models and Hawking
radiation is interesting [ http://arxiv.org/abs/gr-qc/9712010 ], but I
don't know of any other similar work from mainstream folks.
I think that if you want one of these descriptions to work
consistently with black hole and warpdrive problems, you seem to
almost inevitably end up doing something that conflicts with SR, and I
think that is likely to have stumped a lot of the people who might
have tried writing something on the subject.
But I haven't been following things for the last year or so (I'm
trying to go physics "cold turkey" in order to get myself a life), so
perhaps I've missed some new developments, dunno.
=Erk= (Eric Baird)
: "We seek to [do these] things, not because they are easy, but
: because they are hard ..."
: -- JFK
Eric Baird
>Newton wanted to
>be able to say that both particles and waves fall at the same rate in
>a gravitational field and both get
[????] "diffracted" [????]
>by a lightspeed
>gradient by the same amount,
Sorry ... I meant to type
... "refracted" ...
Newton's refactive index arguments are discussed in
http://xxx.lanl.gov/abs/physics/0011003
( or, you can have fun by putting a copy of "Opticks" side by side
with a copy of "Principia" and piecing together his masterplan
yourself <grin> )
=Erk= (Eric Baird)
Robert Clark
program. Nice to see you as a contributor to this group, though I
might suggest putting some type of spam blocker to your address if
this is a usable email address for you.
I remember reading that Kip Thorne first worked out the mathematics
of wormholes at the request of Carl Sagan as background for Sagan's
book "Contact". Since Thorne also suggested that the material medium
description is equivalent to the warped space-time description of GR
in his book "Black Holes and Time Warps: Einstein's Outrageous
Legacy", he would probably be a good source to find out if black holes
can be described this way.
However, since the book was about black holes I can't imagine he would
say the two descriptions were equivalent if he was not also including
the possibility of black holes.
Also I recall seeing recently there is some work on creating "lab
versions" of black holes. I think it was by using the material medium
analogy to GR.
If the material medium description is equivalent to the space-time
description of GR then we should also expect phenomena that occur in
fluid dynamics to occur in GR.
One that I'm interested in is the Magnus effect:
The Magnus Effect.
http://www.geocities.com/k_achutarao/MAGNUS/magnus.html
This is an effect that produces a transverse force on a rotating body
in a fluid.
There is an effect in GR known as "frame dragging". But in the
descriptions I've seen, only the precession of the orbit of a
satellite is described. However, from the mathematical similarity of
the equations of general relativity to those of motion through a
material medium we might also expect there to be a force produced that
drags the satellite in toward the parent body.
Detecting this inward force in addition to the normal GR
gravitational effect (without rotation) would be one test of this
effect. Another possible test would come from the origins of the
Magnus effect: it's due to the fluid being dragged along with the
rotating body. This results in the speed of propagation of a wave in
that fluid being increased or decreased, depending on direction. Then
light speed should be increased or decreased near a massive rotating
body depending on direction in GR as well.
I found another interesting comparison to the Magnus effect after a
Google search:
===========================================================================
From: paul vose (para...@bluesky.net.au)
Subject: Lorentz Force and Magnus Effect compared (and a gif) -
the_same.gif (0/1)
Newsgroups: sci.physics
Date: 1996/12/29
Has anyone ever noticed the similarities between the Lorentz Force and
the Magnus Effect ?
For those who have never heard of either term, a simple definition of
each follows.
---> The Lorentz Force is the centripetal force experienced by a
MOVING CHARGED particle as it travels through a magnetic field. Only
that component of the particle velocity at right angles to the field
is involved. The field does not add any energy to the particle
velocity. The field, the velocity, and the force are always at right
angles to each other, so as the direction of travel of the particle
changes the force also rotates accordingly. The particle ends up
travelling in a circle or a spiral path, depending on the angle at
which it enters the magnetic field. Loss of kinetic energy should also
be taken into consideration. For those who prefer an equation, here it
is..
F = Bq (V sinq), where B is the field strength, q is charge, V is
velocity, and q is the angle between the (total) velocity and the
field. If all of the particle velocity is at right angles to the
field, then sin90 = 1, means maximum force experienced by the
particle.
---> The Magnus Effect is the centripetal force experienced by a
MOVING SPINNING object as it travels through a fluid medium. (The
proviso is that the object be capable of dragging some of the
surrounding fluid around it's 'equator' as it spins - i.e. it needs to
have a rough surface...like a golf ball or a tennis ball). Only that
component of the object velocity at right angles to the spin axis is
involved. The rate of spin does not add any energy to the object
velocity. The spin axis, the velocity, and the force are always at
right angles to each other, so as the direction of travel of the
object changes the force also rotates accordingly. The object would
end up travelling a full circle if gravity and fluid fluctuations did
not act upon it. Golfers and tennis players use the Magnus Effect all
the time, when they use backspin or sidespin to good effect for their
game. Assuming a spinning golf ball travels through the air and drags
some of that air around its equator, it creates a slight vacuum on one
side (at the surface of the ball) where the air is hauled away from
the oncoming wind. On the opposite side, the fluid is thrown into the
oncoming wind and the pressure is increased. The net force on the ball
causes it to change direction continuously. The equation describing
the Magnus Effect is a little complicated for me to describe here.
These two phenomena are extraordinarily similar I think, and it aint
just a coincidence !
=====================================================================
Then perhaps there is an actual physical interpretation of the
electrons spin as a rotation. There were some attempts to do this
mathematically early on but it was found to require rotation speeds
greater than the speed of light. However, if light speed is no longer
an absolute maximum or if it is allowed to vary this is no longer an
legitimate objection.
Bob Clark
Marc Millis <marc.g...@nasa.gov> wrote in message
news:<20030828160...@newsread.grc.nasa.gov>...
Big Bird
> I can easily imagine all "inertial" frames of reference being
> equivalent in a space that is homogeneous and isotropic, abandoning
> the homogeneity of time requirement and allowing a variable speed of
> light.
You can imagine that? I can't.
First off, it seems you'd be abandoning the concept of spacetime
itself if you demand that space but not time be homogenous. Surely
this seems to say that the two are independent concepts -- and how,
then, could there be Lorentz-like transforms that link the two?
Then, of course, abandoning homogeneity of time means abandoning
conservation of energy via Noether's theorem. Certainly conservation
of energy has all the experimetal backup I could imagine any physical
principle to have.
Thirdly I'd be curious to hear just what it would mean to write
something as fundamental as "F = dp/dt" for an inhomogenous "t".
Derivative with respect to what? Or how would the Hamiltonian of a
free particle look like?
This is approximately where my teeth start hurting just thinking about
this and hence the question how you manage to imagine these things...
Igor
My somewhat educated guess would be that the Lorentz transformation as
a coordinate transformation would not change form. However, the
corresponding linear transformation has no choice but to change its
form, since one of the elements in the transformation, namely c,
varies possibly as a function c ( x, y, z, t ). This possibly could
lead to some rather interesting consequences for GR based cosmology,
perhaps even explaining why the distant reaches of the universe are
not slowing down relative to us but speeding up instead.
Just a guess...
John Devers
rgrego...@yahoo.com (Robert Clark) wrote in message news:<832ea96d.03090...@posting.google.com>...
> Also I recall seeing recently there is some work on creating "lab
> versions" of black holes. I think it was by using the material medium
> analogy to GR.
Event horizon dawns on desktop
http://www.nature.com/nsu/020121/020121-7.html
A laboratory analogue of the event horizon using slow light in an
atomic medium
ULF LEONHARDT
School of Physics and Astronomy, University of St Andrews, North
Haugh, St Andrews, Fife KY16 9SS, UK
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Refraction in Media with a Negative Refractive Index
Bilge
Perfectly Innocent:
>news:<3f3c9...@news.iprimus.com.au>...
>
>> Just why do you want a variable light speed when it is at such odds
>> with the homogeneity property?
>
>> The papers you were referred to
>
>> the papers Bilge and others have referred you to
[...]
>I can easily imagine all "inertial" frames of reference being
>equivalent in a space that is homogeneous and isotropic, abandoning
>the homogeneity of time requirement
How so? Inertial frames have to be equivalent under time translations
to be inertial. If time translation symmetry is not valid, then energy
is not conserved. Furthermore, time translation invariance is what
implies that experiments are repeatable.
> and allowing a variable speed of light.
You seem to be hung up on the idea that the speed of light somehow
essential for relativity. The speed of light is rather peripheral.
What matters is the equivalence of inertial frames. The speed of light
is only relevant if it coincides with that definition when taken to
be constant. There are reasons for believing it's true, but you seem
to be uninterested (or unaware) as to how the speed of light fits
intp special relativity physically. This is the reason you have no idea
why a number line differs from a ruler and you "invented" your "schubertian
clock" without regard to the physics implied by rulers and clocks.
Rulers and clocks are physical markers for distance and time, not
mathematical abstractions without physical consequences.
>If that's the claim being made then I want to see a concrete
>example--an explicit transformation equation--expressing how
>space-time events transform in different "inertial" frames of
>reference, preserving the principle of relativity. I didn't ask for
>links citing a vast collection of VSL papers; I asked for someone to
>write down even one of these alleged transforms explicitly for the
>easy case of one spatial dimension. I explicitly asked for a
>coordinate transformation of the form: x'=f(x,t), t'=g(x,t) with all
>the required properties on the level of Rindler's relativity books.
(1) I referred you to the exact page in magueijo's paper where you
will find an example,
(2) I wrote down the transformation after you kept whining about
wanting to see one (as you are still doing).
Since you seem to perceive yourself as having superior knowledge in
this area (except when you post the same question to sci.physics.research),
why don't you just do what us idiots did and read the papers for yourself?
>I can't imagine there being so much published about VSL and the
>subject not being translatable into an undergraduate-level
>presentation of the physics, with clocks and rulers.
Since you seem to think that the lorentz transforms violate the principle
of relativity[1], I would say that variable speed of light theories are
best left until non-variable speed of light theories have sunk in.
[1] From your website:
...
x' = x cosh(\theta) - t sinh(\theta)
t' = -x sinh(\theta) + t cosh(\theta)
"The problem with the given, very general solution is that it violates
the principle of relativity, i.e., the equivalence of all inertial
frames of reference."
Well, no, it doesn't. Those equations are derived from the principle
of relativity and the derivation which makes it most obvious gives
the form above, most naturally.
Perfectly Innocent
sci.physics.research, then so is my rebuttal.
dub...@radioactivex.lebesque-al.net (Bilge) wrote in message news:<slrnbku1ci....@radioactivex.lebesque-al.net>...
> Perfectly Innocent:
>
> You seem to be hung up on the idea that the speed of light somehow
> essential for relativity. The speed of light is rather peripheral.
> What matters is the equivalence of inertial frames. The speed of light
> is only relevant if it coincides with that definition when taken to
> be constant. There are reasons for believing it's true, but you seem
> to be uninterested (or unaware) as to how the speed of light fits
> intp special relativity physically. This is the reason you have no idea
> why a number line differs from a ruler and you "invented" your "schubertian
> clock" without regard to the physics implied by rulers and clocks.
> Rulers and clocks are physical markers for distance and time, not
> mathematical abstractions without physical consequences.
The degree of your misrepresentation is staggering. If you want to
criticize me in a respectable way, please start with the untangled
version of what I say, http://www.everythingimportant.org/relativity ,
paragraph by paragraph. Then let me answer the criticisms of actual
quotes in a logical order, by paragraph, sentence, fragment, equation
or whatever. That way, everyone will easily see just how meaningful
(or confused and meaningless) your many accusations are.
Thank you.
> >If that's the claim being made then I want to see a concrete
> >example--an explicit transformation equation--expressing how
> >space-time events transform in different "inertial" frames of
> >reference, preserving the principle of relativity. I didn't ask for
> >links citing a vast collection of VSL papers; I asked for someone to
> >write down even one of these alleged transforms explicitly for the
> >easy case of one spatial dimension. I explicitly asked for a
> >coordinate transformation of the form: x'=f(x,t), t'=g(x,t) with all
> >the required properties on the level of Rindler's relativity books.
>
> (1) I referred you to the exact page in magueijo's paper where you
> will find an example,
>
> (2) I wrote down the transformation after you kept whining about
> wanting to see one (as you are still doing).
If you wrote down transformation equations of the form x'=f(x,t),
t'=g(x,t), allegedly containing the required properties of a VSL
relativity theory, then please write them down again. I missed it.
And the readers of sci.physics.research didn't see it.
> Since you seem to perceive yourself as having superior knowledge in
> this area (except when you post the same question to sci.physics.research),
> why don't you just do what us idiots did and read the papers for yourself?
http://www.everythingimportant.org/viewtopic.php?t=580
> >I can't imagine there being so much published about VSL and the
> >subject not being translatable into an undergraduate-level
> >presentation of the physics, with clocks and rulers.
>
> Since you seem to think that the lorentz transforms violate the principle
> of relativity[1], I would say that variable speed of light theories are
> best left until non-variable speed of light theories have sunk in.
>
> [1] From your website:
>
> ...
>
> x' = x cosh(\theta) - t sinh(\theta)
>
> t' = -x sinh(\theta) + t cosh(\theta)
>
> "The problem with the given, very general solution is that it violates
> the principle of relativity, i.e., the equivalence of all inertial
> frames of reference."
>
> Well, no, it doesn't. Those equations are derived from the principle
> of relativity and the derivation which makes it most obvious gives
> the form above, most naturally.
Nowhere do I say that the Lorentz transforms violate the principle of
relativity. You have taken what I've said out of context.
http://www.everythingimportant.org/relativity/generalized.htm
Eugene Shubert