PDA

View Full Version : Gravitational effect on speed of light Q



DyerWolf
2007-Mar-05, 06:46 PM
If gravity warps spacetime, is it possible that light travels faster in low gravity areas, such as between the stars or between galaxies, than we measure it here in the well of a star?


May sound a little out there, but while reading this article, the question popped into my head. 13 Things That Don't Make Sense (http://space.newscientist.com/article/mg18524911.600-13-things-that-do-not-make-sense.html)

We already know that light travels slower through water than it does through air or a vacuum. If 3d gravity, instead of looking like the 2d "well" often seen on the cover of science magazines actually looked more like a "thickening" of space and time, is it possible that while light passes through the thicker soup it 'slows' to the speed we measure it at present, but speeds up while traversing a thinner gravitational soup?

Gsquare
2007-Mar-06, 02:53 PM
If gravity warps spacetime, is it possible that light travels faster in low gravity areas, such as between the stars or between galaxies, than we measure it here in the well of a star?




Of course, light does pass slower... through the gravitational field of a star for example. It is known as the Shapiro time delay after its discoverer, (it is actually predicted by Gen Relativity).

The test is done by bouncing radar beams off the surface of Venus or Mars as it passes behind the sun, and has even been done by radar reflections off the Viking spacecraft.
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1977JGR....82.4329S

The reduction of light speed is small, a few hundred microseconds, as measured from earth, (it is assumed that it's value is still c as measured from the local frame through which it passes).

BTW, the results can be calculated equivalently using time dilation effects without resorting to space-time curvature of GR.

Thanks for the post ; I always like a good scientific enigma....your link gave 13 ! ;)

Gsquare

publius
2007-Mar-07, 12:46 AM
I almost missed this question somehow.

Yes, one way to view things is the speed of light varies in a gravitational field. This is called the "coordinate speed of light", as it is the speed of a null vector at some point in a particular coordinate system. You can think in terms of a "density" that acts just like a change in the index of refraction.

However, the density also determines your own local ruler and clock, and any observer always sees the local speed of light, the speed he would measure a light pulse travelling by him as 'c'. So, locally, the density is always normalized to 1, and everybody else's rulers and clocks are different.

In Schwarzschild, the space-time of a spherically symmetric mass distribution, the coordinate speed of light is this:

c_r = c*(1 - R/r) in the radial direction; and
c_tan = c*sqrt(1 - R/r) in the tangential direction

where R is the Schwarzschild radius, and r is the coordinate radius. Light travelling at some angle in between will be a combination of these in between.

And as Gsquare mentioned, understand this is just one way to coordinatize the situation. There are others that sort of path together the local rulers and clocks all the way where the speed remains c the whole time. But they all agree on the final result of what some observer *would measure*.

-Richard

blueshift
2007-Mar-10, 01:58 AM
A very distant observer will measure the speed of light on earth as being slower than in a vacuum but the observer on the ground will not because his time is moving slower by just the right amount called for in stronger curvature and, hence, measures light traveling at c.

swansont
2007-Mar-11, 03:02 PM
Is it correct to say that the observed slowing, by a distant observer (with smaller gravity potential, e.g. in "flat" space), of the speed of light in a (larger) gravity potential, can be explained solely by the different geometries? I was under the impression that the Shapiro delay was just that; the path increase because some part of the path is not "flat" and so if the observer does not account for this, the speed of light appears to be smaller.

blueshift
2007-Mar-12, 11:03 PM
Is it correct to say that the observed slowing, by a distant observer (with smaller gravity potential, e.g. in "flat" space), of the speed of light in a (larger) gravity potential, can be explained solely by the different geometries? I was under the impression that the Shapiro delay was just that; the path increase because some part of the path is not "flat" and so if the observer does not account for this, the speed of light appears to be smaller.You most certainly can explain this as a consequence of the Shapiro delay. Kip Thorne used to use differing methods of approach as a mathematical tool to check his math. You can also perceive the universe to have no spacetime curvature at all but measure matter to rubbery and not rigid, becoming more rubbery in the vicinity of other matter. The math comes out the same.

There are two authors, Clifford Will and Lewis Carroll Epstein, who show how refraction can be considered to cause the bending of light and be even the cause of gravity. But one has to assume different speeds for light in different reference frames.

In fact, when general relativity was under attack by Dicke and Brans it was Irwin Shapiro who was involved with the critical experiments that proved GR would win out.

The trouble with those approaches is that there is no explanation for how light "accelerates back up" to c after it leaves the medium and returns to space. Quantum annihllations explain that.

publius
2007-Mar-13, 12:25 AM
Is it correct to say that the observed slowing, by a distant observer (with smaller gravity potential, e.g. in "flat" space), of the speed of light in a (larger) gravity potential, can be explained solely by the different geometries? I was under the impression that the Shapiro delay was just that; the path increase because some part of the path is not "flat" and so if the observer does not account for this, the speed of light appears to be smaller.
Swansont,

There is no correct answer to that. :) The vexing thing about General Relativity is all of this stuff is coordinate dependent, and what you say depends on what coordinates you are using to describe it.

Using Schwarzschild coordinates, firing a beam of light radially down in a (spherical) gravity well, I can say the light slows down as it "falls". If I give a non radial path, it will curve as well as slowing down (another complication is the coordinate speed of light depends on the direction -- it is slower in the radial direction than the tangential, which is a consequence of how the metric behaves).

So, using those coordinates, light follows a curved path with the speed varying along the way.

Now, that's just using one set of coordinates. One can adopt another set of coordinates (sort of patching together what stationary observers would say all the way), and have the speed being c the whole way. Here, the concept of the distance the light travelled will be something totally different.

And there are yet other ways to do it. But all will agree on what any observers will measure and observe.

That is not very comforting, but that's the way space-time works.

-Richard

Sam5
2007-Mar-13, 01:53 AM
Of course, light does pass slower... through the gravitational field of a star for example. It is known as the Shapiro time delay after its discoverer, (it is actually predicted by Gen Relativity).

This prediction was made in Einstein's 1911 Gravitational Redshift theory. I pointed this out on this board about 6 years ago.

Gsquare
2007-Mar-13, 03:30 AM
This prediction was made in Einstein's 1911 Gravitational Redshift theory. I pointed this out on this board about 6 years ago.

I think you misunderstood, Sam.

My parenthetical comment was merely to show that the effect is compatable with the predictions of Gen. Relativity, not to explain whose theory predicted it first.

If your are interested in the origin of the concept you will need to go back much farther than 1911 however.....

John Michell is generally credited with being the first to 'predict' the effect of gravity on light (in the 1780's) ....He predicted the "weakening of light" by gravity, and even predicted the inability of light to attain escape velocity from extremely high gravitational fields; IOW, black holes.

If that is your interest, you may be want to explore these references:

Clyde R Hardin "The scientific work of the Reverend John Michell"
Annals of Science, 22 27-47 (1966)

Gary Gibbons "The man who invented black holes -his work emerges out of the dark after two centuries."
New Scientist, 28 June pp.1101 (1979)

Gsquare

Sam5
2007-Mar-13, 03:53 AM
I think you misunderstood, Sam.

My parenthetical comment was merely to show that the effect is compatable with the predictions of Gen. Relativity, not to explain whose theory predicted it first.

If your are interested in the origin of the concept you will need to go back much farther than 1911 however.....

John Michell is generally credited with being the first to 'predict' the effect of gravity on light (in the 1780's) ....He predicted the "weakening of light" by gravity, and even predicted the inability of light to attain escape velocity from extremely high gravitational fields; IOW, black holes.

If that is your interest, you may be want to explore these references:

Clyde R Hardin "The scientific work of the Reverend John Michell"
Annals of Science, 22 27-47 (1966)

Gary Gibbons "The man who invented black holes -his work emerges out of the dark after two centuries."
New Scientist, 28 June pp.1101 (1979)

Gsquare

Thanks for the information. Perhaps I should have said the "Einstein approved" speed of light changes go back to his 1911 paper. Actually, I think he might have first mentioned it in a 1907 paper.

I have some early 19th Century references to John Mitchell's prediction. I have a set of Humboldt's "Cosmos" from the early 19th Century and that mentions it.

But so many people have latched on to the "constancy postulate" of SR theory, and variations of it, that has become quite a myth. Just a few years ago I was threatened with being banned for saying that the speed of light is not always constant and that the speed varies in areas of different gravitational potential, and I was criticized heavily for promoting the study of the history of physics. I've managed to hang on long enough to see the idea finally accepted here.

Gsquare
2007-Mar-13, 05:21 AM
"But so many people have latched on to the "constancy postulate" of SR theory, and variations of it, that has become quite a myth.
.

True; but we've still got a few good 'Myth Busters' here on BA. :D he, he.

swansont
2007-Mar-13, 11:25 PM
So it seems to me that if you measure the speed of light and don't get the expected answer, that's an indication that you are not in flat spacetime (over the region of the measurement)

Which is analagous to getting c+v and c-v answers in a rotating frame of reference it tells you you are not in an inertial frame.

publius
2007-Mar-13, 11:52 PM
So it seems to me that if you measure the speed of light and don't get the expected answer, that's an indication that you are not in flat spacetime (over the region of the measurement)

Which is analagous to getting c+v and c-v answers in a rotating frame of reference it tells you you are not in an inertial frame.

Swansont,

Well, you always get 'c' locally, save for some details about the Sagnac effect, which I'll get into in a bit. Every observer, locally (ie as the light is going past him where he is at) will measure every null geodesic to be 'c'.

The Sagnac Effect, as seen in the non-inertial Coriolis frame of reference (the metric for this is called the Born metric, after Max Born) is an effect of frame dragging (well, what looks like frame dragging -- it's really just a coordinate effect, which looks like frame dragging via Equivalence Principle logic).

And it also an effect of making light follow a non-geodesic path, as near as I can figure. The world line is still null, but it is a non-geodesic path.

Suppose we're on a centrifuge (and the rotating earth will suffice for this for long wavelengths, and one can observe the Sagnac effect by sending a radio signal from LA to NY for instance), and we have a little fiber optic cable strung along the circumference. Out there, we will measure the speed of light in that cable (assuming its index of refraction is unity) to be c +/- v in each direction.

That tells us we are rotating. Now, what I think will happen, but am not completely sure is if we let light go as it will, follow its geodesics, we will always measure 'c' locally. However, with frame dragging, you have "non time orthogonality", which means one of your spatial vectors isn't "perpendicular" to time. :lol: That is where the crazy non-c for a local null world line comes from, and it may not work out for all null geodesics, either, I'm not sure.

Frame dragging, non time-orthogonal coordinates get very weird and a lot of stuff you think holds good actually gets thrown out the window.

-Richard

publius
2007-Mar-14, 12:16 AM
Let me add this. Every *Lorentz observer* in any space-time measures the speed of light to be 'c' locally. A Lorentz observer is one who is following is geodesic, going completely with the flow of space-time so to speak.

Now, *accelerated observers*, do not see the coordinate speed of light as being a constant, but a function of position. As long as those observers have a time orthogonal coordinate system, they will measure the speed of light to be c locally, however, geodesic or not.

An observer who is rotating (or doing some other crazy thing where his clock his not perpendicular to all his rulers) may not always do that. I say may not.

-Richard

publius
2007-Mar-14, 12:29 AM
If there are any bright-eyed and bushy-tailed budding young relativists out here, and you want to do ol' Publius a big favor, hee-hee, do the following trivial little calculation for him.

From an inertial frame, we have relativistically rotating disc/centrifuge of radius r, speed 'w', and make rw get high. Now, shoot a beam of light so it just passes the edge of that disc. Problem, what speed will an observer on the edge measure the speed to be as it shoots past him.

To answer that we need to transform that r = ct straight line into Born coordinates and then see what it looks like. That will give us a null geodesic that, to us in the inertial frame, looks like it goes tangentially by the rotating observer. I want to see just what that looks like in the Born frame.

-Richard

blueshift
2007-Mar-16, 11:30 PM
From an inertial frame, we have relativistically rotating disc/centrifuge of radius r, speed 'w', and make rw get high. Now, shoot a beam of light so it just passes the edge of that disc. Problem, what speed will an observer on the edge measure the speed to be as it shoots past him.

To answer that we need to transform that r = ct straight line into Born coordinates and then see what it looks like. That will give us a null geodesic that, to us in the inertial frame, looks like it goes tangentially by the rotating observer. I want to see just what that looks like in the Born frame.

-RichardI am really not sure that I am prepared to answer your question at all. So one thing at a time...I am trying to make sure what you are saying first and then I will dive into Born frames if I can...

It is your first statement that has me puzzled...How can we have a relativistically rotating disc when a neutron star cannot even reach relativistic speed despite its high spin rate? I don't think that a disc of any sort can possibly hold together with such a great spin. Or do you know something that I do not know where I must plead ignorance?

publius
2007-Mar-17, 01:12 AM
Blueshift,

This is just a thought experiment, heck just about reference frames, really. We have a purely mathematical reference frame riding on the edge of a purely mathematical disc spinning at such high speed (and it is itself is rotating, keeping it's axis stationary relative to the disc). What is the coordinate speed of the light geodesic locally in that frame.

That speed is always 'c' for time-orthogonal frames, but I'm not sure for non time-orthogonal frames. In Born, time is orthogonal at the origin (Born is the coordinate of a rotating point, basically), because various factors go to zero. The guy at the origin measures it to be 'c' locally in all cases. However, frames riding out from the origin, and keeping their axes stationary with respect to Born are not time orthogonal locally.

-Richard

publius
2007-Mar-17, 01:29 AM
Let me add something about this. Rotation is just weird. It's "unnatural". :lol: As near as can figure with my still elementary school boy level in General Relativity, no "natural" coordinates of any observer, going along any possible world line will ever be non time orthogonal. The procedure for finding the local rulers and clocks along any path is called the "frame field" vectors. Frame fields, will they certainly may have a translational proper acceleration, they will never have a proper rotation.

The subtle thing here is there can be relative (coordinate) rotation between frame field systems (ie geodetic precession), but there will never be *proper* rotation, unless you require it.

IOW, if we specify a point on edge of a rotating disc and crank out the frame field for an obsever at that point, the natural axes will not be rotating. That is, they will just be going around in a circle, but pointing in the same inertial direction.

Local null geodesics are always 'c' there. However, if we make it rotate, we are doing something "unnatural".

-Richard

publius
2007-Mar-17, 04:36 AM
There is something here about "unnatural rotation" that is deep. If you recall some previous rambling, General Relativity does not handle intrinsic angular momentum, ie "spin" of quantum particles (for any lurkers not familiar with this, this does not mean GR can't handle rotation of mass systems which it does just fine. This has to do with "point angular momentum"). I think this is related to frame fields never having any proper rotation.

The version of GR that does include point angular momentum (or attempts to -- no one has yet figured out a way to test it as the effects are so small) is called Einstein-Cartan. I'll be E-C may indeed have more to say about rotation than regular GR.

For example, a really open question is what the gyro-gravitomagnetic ratio of a given particle with spin.

-Richard

blueshift
2007-Mar-18, 05:12 PM
publius,

I am presently combing over a group of pdf files so that I can respond with a little better understanding..


http://www.citebase.org/abstract?identifier=oai:arXiv.org:gr-qc/0103076&action=cite****s&cite****s=cocitedby

I am not sure if any of those answered the questions you raised but I think they might help me out.

I was under the impression in the past that Finkelstein coordinates did take into account the issue of rotating discs. Several gears then could be conceived all in the same reference frame if their axes did not change in distance and the rotation speeds were the same. In the case of two meshing gears I perceived there would be several frames where the meshed gears would be in one reference frame temporarily in both gears while gears 180* away from the meshed gears would share another reference frame temporarily during rotation. I only picked up a little of Finkelstein's view from reading Kip Thorne's "Black Holes and Time Warps".

publius
2007-Mar-18, 05:32 PM
Blueshift,

That link is interesting:



The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light, are not applicable to rotating frames. Different postulates based on the Sagnac experiment are proposed, and from these postulates a new relativistic theory of rotating frames is developed following steps similar to those initially followed by Einstein for rectilinear motion. The resulting theory agrees with all experiments, resolves problems with the traditional approach to the rotating disk, and exhibits both traditionally relativistic and non-relativistic characteristics. Of particular note, no Lorentz contraction exists on the rotating disk circumference, and the disk surface, contrary to the assertions of Einstein and others, is found to be Riemann flat. The variable speed of light found in the Sagnac experiment is then shown to be characteristic of non-time-orthogonal reference frames, of which the rotating frame is one. In addition, the widely accepted postulate for the equivalence of inertial and non-inertial standard rods with zero relative velocity, used liberally in prior rotating disk analyses, is shown to be invalid for such frames. Further, the new theory stands alone in correctly predicting what was heretofore considered a "spurious" non-null effect on the order of 10-13 found by Brillet and Hall in the most accurate Michelson-Morley type test to date. The presentation is simple and pedagogic in order to make it accessible to the non-specialist.

I don't know about that "no Lorentz contraction" part, though. But, that confirms that nagging thing that non-time orthogonal frames do not have to see the speed of light as 'c' locally.

-Richard

publius
2007-Mar-18, 06:08 PM
I read over that whole paper (and saved it of course, but will I remember where I put it?). Damn, I'm not as good as I used to be, and I wished I were so I could absorb stuff like that faster. I've got a chemical imbalance in the brain -- excess mollases or something. :lol:

Anyway, he comes up with the exact "peculiar result" for the *local* tangential speed of light that I pulled out playing with Born:

c_tan = (c +/- rw)/sqrt[1 - (rw/c)^2], the denominator being seen as "gamma" as viewed from an inertial frame.

The author also goes on to say something else extrordinary about "standard rods". That is, a ruler on the edge of the rotating disc is *NOT EQUAL* to the ruler of an instantaneous Lorentz observer tangent to the world line at that point. This is also a consequence of the non-time orhthogonality.

There's something subtle here to appreciate. This is an effect for an observer on the edge who himself is rotating. That is, he is keeping is own axies stationary with respect to the rotating coordinate system of the origin. An observer who is "stellar inertial" (NASA lingo for the axes of a spacecraft in orbit that is not properly rotating) would NOT see these effects. Those are the "natural coordinates", the ones you get from the "frame field vector" machinery. Again, rotation just isn't "natural". :)

The instantaneous Lorentz observer's ruler would agree with the "stellar inertial" ruler. Of course, "inertial" here is bad -- non-properly rotating, but still accelerating. The author's point is that previous analyses of the rotating disc problem (always been extremely vexing) get these mixed up.

-Richard

publius
2007-Mar-18, 07:57 PM
I encourage anyone with interest in this stuff to read over this paper:

http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Agr-qc%2F0103076


Keep in mind the difference I was rambling about above between the "stellar inertial" observer riding the edge of the disc who keeps his spatial axes pointed in the same (inertial) direction, and the "corotating" observer riding the edge who keeps his axes stationary with respect to the rotation.

Now, consider the typical Minkowsky diagram of the temporal and spatial axes of a moving observer. Minkowski, due to that minus sign makes "orthogonal" very non-Euclidean looking. The moving observer's T and X axes are very much "angled" according to the "stationary" frame and don't look perpendicular, with less than a 90 degree angle between them. As the observer's speed approaches c, those two axes just angle collapse onto each other at a 45 degree angle line.

Now, here is the funny business which is the author's point. In the corotating edge-riding frame, the local clock is equal to the instantaneous Lorentz observer clocks, ie on the T' axis angled to the inertial T. However, the *ruler* is aligned with that of an inertial observer who is not moving. That is the time non-orthogonality.

I'm struggling to find the words to make this as clear as possible. We, observer 'A' are watching observer 'B' on the edge of rotating disc. 'B' is corotating, not "stellar inertial". Now, B's *clock* is that of instantaneous Lorentz observer moving along his instantaneous velocity vector. But B's ruler is *our ruler*. This is way to see a "pedagogical reason" the local light speed is aniostropic. You're using rulers and clocks from two different "tangent frames" at the same time.

This is what the author means by "no length contraction". His point that there has been much confusion over this business.

Ken G, if you're reading this, I remember you remarked once how difficult rotating frames are in relativity. :) This is an example of that.

Something else that bugs me is the question of what a local Cavendish experiment on the corotating edge frame would do. This is "Strong Equivalence Principle" considerations. I have not found any authoritative commentary on that question.

-Richard

RussT
2007-Mar-19, 10:48 AM
None of the links above worked for me, so here is the PDF.

http://arxiv.org/abs/gr-qc/0103076

Richard, these are the very things I have tried to verbalize in several different threads and ways.

The discontinuity of time, the rotating earth for slower clocks at altitude, and the Schwarzschild problem I went into some length about. He is just doing what I suggested needed to be done (Of course there is no way I could formalize it like this).

However, when it gets to the theory and any cosmological implications/applications, there are deeper and more intimate considerations that need to be addressed.

publius
2007-Mar-19, 08:19 PM
Well, I still haven't found any authoritative commentary on my little "local Cavendish in the edge rotating frame" yet, so I just said what the heck, and sent some private queries to some of the authorities. :lol:. It will be interesting if any respond.

Thanks for posting this blueshift -- it really got me to thinking about "non time orthogonality" again. When your ruler ain't perpendicular to your clock, crap happens.

-Richard

publius
2007-Mar-19, 11:12 PM
If no one is interested in this, you can stop me from rambling, but this stuff just fascinates me to no end. Klauber above has quite a few papers on relativistic rotation and I've been smoking them over.

In one, he shows how a "stellar inertial" observer moving around in a circle will indeed see the local speed of light as 'c' always, yet the Sagnac effect is readily seen and agrees with the inertial frame result.

If you can imagine a guy with a "rotating Rindler" thing going on, the stellar inertial rotating observer will see the difference in light travel time as entirely an effect of *global* variation in light speed, in accord with his metric. But his local light speed is c, and his ruler and clock agree with that of the instantaneous co-moving Lorentz observer.

However, the rotating observer (not stellar inertial but facing the center of rotation) is very different. This point is what Klauber is fascinated with, and what has fascinated me.............

And BTW, DavidW was entirely correct and I was wrong there: the stellar inertial rotating observer sees absolutely no frame-dragging, no 'B_g' effects at all. His metric is globally time orthogonal.

-Richard

-Richard

JohnD
2007-Mar-19, 11:38 PM
Publius,
This question is closely allied to another thread: http://www.bautforum.com/showthread.php?t=55821

I tried to explain the way I think about BHs, but you have a much tighter handle on these things. Can you offer Niin any insight?

John

publius
2007-Mar-20, 12:29 AM
John,

I saw that, and I will look over it and see if I think I can add anything halfway helpful. Your reply that space is so curved it just turns back on itself is a spot on way to put it, really. I could try to explain things in several ways, but it would probably shed more confusion that light, really.

Inside the horizon, time and space are very different, indeed, for an observer inside where we think the horizon is, his clock "points in the direction of our radius", and his third spatial dimension "points in the direction of our clock". :lol: Inside, the singularity is in *time*. Outside, we say the singularity is in space, some distance to it. But inside, it's in time. You can no more accelerate to escape than you can accelerate and avoid next Wednesday coming. :) Any light shot by any observer in there follows some path according to whatever local coordinate you might be using and hits the "wall in time". It's radius never gets outside, no more than something can go bacwards in proper time.

According to our external notions (our coordinate time is invalid, all we can speak of is distance), everything just moves radially to oblivion. One can coordinatize by external radius vs proper time of a free-faller, and get radius vs proper free-fall time. Amazingly, that velocity value, dr/dtau is exactly equal to Newton as a function of 'r', sqrt(2GM/r), and that is valid all the way to r = 0. But that "speed" is really meaningless, because no observer could measure it. It's just a pure coordinate thing.

And that's (one of the) reason(s) the pure Newtonian calculation of escape velocity = c gives the correct value for the horizon. Externally, r(t), where t is the coordinate time is something very different.

Now, see what I mean about confusing "newbies" when I get to rambling. :)

-Richard

Sam5
2007-Mar-20, 12:39 AM
Of course, light does pass slower... through the gravitational field of a star for example. It is known as the Shapiro time delay after its discoverer, (it is actually predicted by Gen Relativity).

The test is done by bouncing radar beams off the surface of Venus or Mars as it passes behind the sun, and has even been done by radar reflections off the Viking spacecraft.
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1977JGR....82.4329S

Did you read that Kaptain K? Diamond?

publius
2007-Mar-20, 03:22 AM
Again, you all stop me if no one is interested, but here is Klauber's most recent paper:

http://arxiv.org/PS_cache/gr-qc/pdf/0604/0604118.pdf

Here is the first paragraph from the abstract:


Alternative theories of relativistic rotation considered viable as of 2004 are compared in the light of experiments reported in 2005. En route, the contentious issue of simultaneity choice in rotation is resolved by showing that only one simultaneity choice, the one possessing continuous
time, gives rise, via the general relativistic equation of motion, to the correct Newtonian limit Coriolis acceleration. In addition, the widely dispersed argument purporting Lorentz contraction in rotation and the concomitant curved surface of a rotating disk is analyzed and argued to be
lacking for more than one reason. It is posited that not by theoretical arguments, but only via experiment can we know whether such effect exists in rotation or not.


This is damnably subtle and interesting. Let me attempt to put what the above is saying (in a broader context) in my own little Romper Room level words:

Go into a Coriolis frame and consider an edge-riding observer, who is keeping his own little axes stationary. "Simultaneity choice" determines the rulers and clock of that observer. The only choice that will reduce to the Newtonian coriolis force in the newtonian limit is the Born type time non-orthogonal one.

The ruler cannot be orthogonal to the clock with this choice, and thus that observer does not agree with the instantaneous co-moving Lorentz observer. He is actually using the ruler of the inertial frame stationary with the origin of the rotating system, and thus sees no difference in circumference from the inertial observer.

This is fascinating stuff. Any other choice of coordinates will be "a different frame" and not what the corotating, edge riding observer naturally sees. If you are riding the edge of the disk and are "stellar inertial" with your axes, you do not see the disk as stationary, but moving around you. The only truly stationary frame is the time nonorthogonal one.

{ETA: Well beyond anything I remotely know about, but this Klauber guy also has a paper on dark energy and the cosmological constant, purporting to offer a way to make the "zero point energy" actually come out to reasonable value, and not way too large. Again, I don't know enough about that to make heads or tails out of it}

-Richard

RussT
2007-Mar-20, 09:47 AM
Please Publius, keep going.
Eventually all the scientists are going to have to work together to figure out exactly how what he is showing is 'really working'!

It appears that he is right in his analysis in the first part of his paper, and 'his
theory' does seem to be getting good answers to some of the things he is showing, BUT just like Cahill, he is getting some things wrong when he tries to apply this to the universe as a whole, because he is making incorrect assumptions about certain things.

Kaptain K
2007-Mar-20, 02:03 PM
Did you read that Kaptain K? Diamond?
Huh????? I haven't even posted to this thread. What the [heck] are you talking about?

Hornblower
2007-Mar-20, 04:07 PM
This discussion illustrates the perceived paradoxes that result from thinking in terms of classical mechanics while trying to visualize what happens under the extreme conditions near the event horizon of a black hole. In modern physics we need to forget some of these visualizations and trust the mathematical results of Einstein's general theory of relativity (GR), which have withstood exhaustive theoretical and experimental testing for most of a century to date.

If I had stayed in physics professionally for the past 40 years instead of switching to music, I could proceed lucidly at great length. Please bear with me as I do the best I can with what little I can remember, along with what I can find by browsing various online sources.

First, some fundamentals: Photons do not move in the same manner as projectiles in response to gravity. According to GR a photon in a vacuum always moves at the speed of light (c) as measured by an instrument at the location in question. We cannot observe from afar what the photon is doing while it is in an extremely deep gravitational well. We can only infer what it did if and when it escapes and eventually reaches us, by studying its arrival time and energy level.

It is well known that radio signals from interplanetary spacecraft are delayed when they pass very close to the Sun. See the following abstract concerning the Viking landers on Mars.

http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1977JGR....82.4329S

Gsquare summed this up very nicely in this thread a couple of weeks ago.

We normally visualize it as if the photon is moving slower while near the sun and returning to its normal speed upon getting out of the intense gravity. The actual circumstances have been described as space/time warp, time dilation, etc. Once again this is GR, not classical mechanics.

In our visualization we have an apparent paradox in which the photon seems to be speeding up as it escapes from the deep gravitational well, even though it is losing energy in the process. That energy loss is fundamentally different from the slowdown of a bullet on the same initial path, and we see it as dimming and redshifting of the light that reaches us.

I remember seeing an article in Sky and Telescope a few years ago, which described what we should see as a brilliant luminous object fell into a black hole. As the object approached the event horizon, the light would be dimmed and redshifted and its propagation would be delayed for the same reasons as the delay of the Viking telemetry. As the separation from the event horizon approached zero, the light's energy as seen by us would approach zero and the delay would increase without limit. Thus we would see the object approach the horizon asymptotically, fading rapidly as it proceeds. We would see it fade to invisibility but we would in principle never see it cross the event horizon, no matter how sensitive our light detectors might be.

I hope my memory of this article is reasonably accurate. If I am wrong on any of this, please link me to a reliable rebuttal.

For any further treatment of light sources at or below the event horizon I am lost. I must leave it to those who are up to date on the necessary math. Some of you in this thread have done it very nicely. I would attempt an analogy by describing the light as running in place but making no forward progress in our visualization from afar.

Sam5
2007-Mar-20, 04:56 PM
Huh????? I haven't even posted to this thread. What the [heck] are you talking about?

On another thread on this board in 2004 you told me I was wrong when I said that light speed is not always constant because it is slowed down by strong gravitational fields and when I said that the Shapiro effect proved that light speed slows down in the strong gravitational field of the sun and when I said that this is supported by GR theory.

publius
2007-Mar-20, 05:34 PM
Well, I got a response back from someone about the Cavendish in NTO frame thing. It was basically that it is an intriguing question that would require a lengthy research project from someone bright-eyed and bushy-tailed and rarin' to go. :lol:

I can't mention any more because he just wasn't sure and asked me not to quote him.

ETA: Well, I'll be dog-gone. I just got not one, bu *two* followup e-mails from this particular good doctor again. He said the "perspicaciousness" of this question hadn't really sunk in when he first responded, and now he can't get it out of his head. :lol:

-Richard

blueshift
2007-Mar-20, 11:30 PM
Well, I still haven't found any authoritative commentary on my little "local Cavendish in the edge rotating frame" yet, so I just said what the heck, and sent some private queries to some of the authorities. :lol:. It will be interesting if any respond.

Thanks for posting this blueshift -- it really got me to thinking about "non time orthogonality" again. When your ruler ain't perpendicular to your clock, crap happens.

-RichardDon't worry, I will be following this up and digging in over the next few weeks. I just want to go over it slowly and review a number of concepts from many other sources I have including a friend of mine in my astronomy club.

http://www.bio.aps.anl.gov/~dgore/

He likes hearing things like this.

Kaptain K
2007-Mar-21, 07:48 AM
On another thread on this board in 2004 you told me I was wrong when I said that light speed is not always constant because it is slowed down by strong gravitational fields and when I said that the Shapiro effect proved that light speed slows down in the strong gravitational field of the sun and when I said that this is supported by GR theory.
my emphasis

Hey! That was over two years ago! I was wrong then. Like most people here I'm here to learn! Believe me, I've learned a lot in the time I've been here!

Hornblower
2007-Mar-21, 12:56 PM
I just realized that I posted in this thread yesterday by mistake when that post was intended for the Why can't light escape a black hole thread. I am going to copy it over there now.

swansont
2007-Mar-21, 11:31 PM
On another thread on this board in 2004 you told me I was wrong when I said that light speed is not always constant because it is slowed down by strong gravitational fields and when I said that the Shapiro effect proved that light speed slows down in the strong gravitational field of the sun and when I said that this is supported by GR theory.

Interesting, because that's not what I took away from this discussion. It's not an absolutely true statement; it depends on how you've decided to look at things.


There is no correct answer to that. The vexing thing about General Relativity is all of this stuff is coordinate dependent, and what you say depends on what coordinates you are using to describe it.

and

Let me add this. Every *Lorentz observer* in any space-time measures the speed of light to be 'c' locally. A Lorentz observer is one who is following is geodesic, going completely with the flow of space-time so to speak.

Now, *accelerated observers*, do not see the coordinate speed of light as being a constant, but a function of position. As long as those observers have a time orthogonal coordinate system, they will measure the speed of light to be c locally, however, geodesic or not.

IOW, you'll measure c to be different if you choose some coordinate systems, but if you measure locally, you'll get c.

So when you say that the Shapiro effect shows that the speed of light has decreased, I say that's not an absolutely true statement. As I'm understanding it, you can explain the delay by c decreasing, in your coordinate system, but that coordinate system doesn't hold true over that whole path. A series of local observers would all measure c to be the expected value, but would measure a longer path length, which accounts for the delay.

Let me ask this: at the center of the gravity well, where you'd expect c to be smallest, there are a bunch of nuclear reactions going on. The energy they give off depends on c^2. What value of c^2 do you use?

Sam5
2007-Mar-22, 01:48 AM
So when you say that the Shapiro effect shows that the speed of light has decreased, I say that's not an absolutely true statement. As I'm understanding it, you can explain the delay by c decreasing, in your coordinate system, but that coordinate system doesn't hold true over that whole path. A series of local observers would all measure c to be the expected value, but would measure a longer path length, which accounts for the delay.



I explained this in 2004. Einstein explained it in 1911.

Atomic clocks slow down in the same gravitational potentials where light speed slows down. So an atomic clock runs slightly slow at the surface of the sun and light speed is slightly slower at the surface of the sun, but a clock at the sun would measure the speed at the sun to be c. Consequently, atomic clocks run slightly faster at the surface of the earth (than at the sun) and light speed is slightly faster at the surface of the earth (than at the sun).

Shapiro used an earth based clock to measure the travel time of his EM waves, and with that earth based clock the EM waves were measured to slow down as they passed near the sun, then they speeded back up again as they returned to earth.

publius
2007-Mar-22, 01:59 AM
Interesting, because that's not what I took away from this discussion. It's not an absolutely true statement; it depends on how you've decided to look at things.



Swansont,


It may be counterproductive to quote anything I've said to our good friend Sam5. He indicated in this post here,

http://www.bautforum.com/showpost.php?p=933550&postcount=172

that he doesn't read much of anything I say he doesn't like. Sam has strong misconceptions about relativity, both special and general, and no amount of explanation is going to change his mind. You'll note he says "atomic clocks" slow down. He doesn't believe "time itself", what we mean by proper time slows down at all, I don't think.

-Richard

swansont
2007-Mar-22, 01:45 PM
Swansont,


It may be counterproductive to quote anything I've said to our good friend Sam5. He indicated in this post here,

http://www.bautforum.com/showpost.php?p=933550&postcount=172

that he doesn't read much of anything I say he doesn't like. Sam has strong misconceptions about relativity, both special and general, and no amount of explanation is going to change his mind. You'll note he says "atomic clocks" slow down. He doesn't believe "time itself", what we mean by proper time slows down at all, I don't think.

-Richard


Sam5 and I are acquainted. :) I just wanted to note that what he said was not going to go unchallenged and somehow acquire "the quiet authority of the written word" (to quote from "North by Northwest")