# Does Gravity Slow Light Moving Vertically?

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I should also mention -- I appreciate your persistence and dedication in neg-reppring all of my posts. Occasionally, I think you might forget one, but you are very meticulous and I can appreciate that quality.

Any case... the length of the green line?

I asked you some questions, so please answer them. , I pointed out quite a few errors in your posts, may I suggest that you answer the points and stop trying to talk down to me?

Edited by xyzt

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I asked you some questions, so please answer them. , I pointed out quite a few errors in your posts, may I suggest that you answer the points and stop trying to talk down to me?

I'm not trying to talk down. I gave my reasoning and cited three sources to answer your Shapiro delay question in post 73.

Before before you "pointed out quite a few errors" in that post I asked a very straightforward question.

Given that the blue line is 0.5...

What is the distance of the green line in a v=0.6c frame?

You have told me repeatedly that my use of the length contraction formula won't work, so I'm very curious what solution you find. Can you give me a number. This is literally the simplest question you could get in special relativity, and I'm just looking for a number.

Could you please give me a number so we can be on the same page?

Edited by Iggy
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I'm not trying to talk down. I gave my reasoning and cited three sources to answer your Shapiro delay question in post 73.

That is false, you are trying to act as a "teacher" but you keep piling up mistakes. For example, the most serious link you cite , the C.M.Will one, you took the citation not out of the Shapiro delay explanation paragraph but out of the following paragraph, his refutation of the Kopeikin paper (the one that claims to be measuring the speed of gravity). This nullifies your appeal to authority and invalidates your explanation. On the other hand, I provided the mathematical derivation of the Shapiro effect, there is nothing in it about the speed of light "slowing down". I also pointed out that the rays of light do not come anywhere close to the event horizon, contrary to your claim, you chose to sweep this error under the rug. The rays of light in discussion pass by at distances that are many orders of magnitude larger than the EH.

Could you please give me a number so we can be on the same page?

I explained this as well to you several times, last time in this post, that there is no number since the proper distance between ships is a function of the proper time $\tau$. As such, it obviously varies with $\tau$. What you are calculating is not the proper distance between the ships. You are calculating something else, I'll let you think about it.

Edited by xyzt
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Here is a good presentation showing how the proper distance stays constant using the inversely proportional acceleration relationship that Iggy refers to. When you Lorentz transform to the ships' frame, they stay 0.25 apart (for the three ships in the second scenario) or 0.5 apart (for the two ships in the first scenario). http://www.csupomona.edu/~ajm/professional/talks/relacc.ppt

The whole presentation is useful, but slides 12-15 are the core for our discussion.

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Just chiming in to, hopefully, get this discussion back on topic. I've read some of the thread and only skimmed others. I am also probably not as knowledgeable about GR as xyzt is.

First note, primarily to Iggy:

Aside from any reasoning mistakes you may or may not have made, you appear to be using fairly specific (but not widely used) definitions of a number of terms that become somewhat ambiguous in general relativity. If these terms are used at all, they will often be context dependent and should be defined for the purposes of a discussion if they are to be used at all. Velocity (outside of local velocity) is one such.

You are also using terms like simultaneous and proper distance to refer to events relating to events that do not share an obvious inertial reference frame as if we are all on the same page (doing so is going to require further qualification).

Thirdly, you appear to be privileging results derived from a specific coordinate system. The words/definitions/results derived are frequently only going to be useful within said coordinate system.

These are all things that aren't really appropriate in a response to someone asking a question when they are learning SR/GR. Also presenting natural language interpretations/explanations of mathematical results that differs from the mainstream one is not really appropriate in a thread like this; regardless of whether or not the result is internally consistent with the definitions you've chosen.

xyzt:

If you encounter someone saying something that is likely to cause confusion or derail the thread, it can be better to suggest they take it up in private messages or another thread with you until you figure out your disagreement, or inform the mods early if this fails. The main thing I can see about Iggy's posts which is disruptive is his unstated assumptions and definitions which are a good reason to ask him to take his discussion elsewhere independently of whether his reasoning is internally consistent.

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Here is a good presentation showing how the proper distance stays constant using the inversely proportional acceleration relationship that Iggy refers to. When you Lorentz transform to the ships' frame, they stay 0.25 apart (for the three ships in the second scenario) or 0.5 apart (for the two ships in the first scenario). http://www.csupomona.edu/~ajm/professional/talks/relacc.ppt

The whole presentation is useful, but slides 12-15 are the core for our discussion.

Thank you, this is an interesting presentation, in the past I have argued with Mallinckrodt that his presentation was both misleading and incorrect. I can see he hasn't corrected it. As a senior editor of American Journal of Physics he was a disaster (though not as bad as the former editor in chief, Jan Tobochnik a hardened closet anti-releativist), I am glad to see him demoted to the status of consulting editor , where he can do less damage.

Anyway, here are the issues with his presentation (we are talking page 12):

-Mallinckrodt states, with no mathematical proof , that the points agree on simultaneity

-I pointed out to him that he produced no proof of his claim, he declared it by fiat

-Mallinckrodt states (correctly) on page 9 that the line of "instantaneous simultaneity" passes through the origin, this means that the two particles moving at different accelerations cannot share the same line of instantaneous simultaneity at all times as he incorrectly claims on page 12

-Mallinckrodt claims further down the page that "A and B agree that their proper separation is constant". Of course, he produces no proof of his claim.

-the only correct claim he makes is a trivial one "A and B agree at all times on their common velocity". Yes, this is obvious, so what?

-I tend to take exception to "proofs" based on drawings, the only "proof" he presents on page 12 is a .....drawing.

The takeaway from this is that you cannot believe presentations off the web (especially when they come from someone who's been teaching at CalPoly Pomona), you need to try to do the calculations yourself.

Anyway, we have taken a long detour through your scenario, you would have been much better off sticking with your first scenario, one single rocket shining rays of light towards mirrors at the aft and fore.

Finally, are you in clear with the fact that proper light speed is an invariant, it does NOT vary with the gravitational field?

It is the coordinate-dependent light that varies (as I explained in detail in my very first post in this thread). GR is a theory that was written from the ground up to be coordinate-INDEPENDENT, it deals with invariants only, so any coordinate-DEPENDENT , coordinate - VARIANT entities (like the coordinate-dependent light speed) are irrelevant (and, in stronger words, unphysical).

Just chiming in to, hopefully, get this discussion back on topic. I've read some of the thread and only skimmed others. I am also probably not as knowledgeable about GR as xyzt is.

First note, primarily to Iggy:

Aside from any reasoning mistakes you may or may not have made, you appear to be using fairly specific (but not widely used) definitions of a number of terms that become somewhat ambiguous in general relativity. If these terms are used at all, they will often be context dependent and should be defined for the purposes of a discussion if they are to be used at all. Velocity (outside of local velocity) is one such.

You are also using terms like simultaneous and proper distance to refer to events relating to events that do not share an obvious inertial reference frame as if we are all on the same page (doing so is going to require further qualification).

Thirdly, you appear to be privileging results derived from a specific coordinate system. The words/definitions/results derived are frequently only going to be useful within said coordinate system.

These are all things that aren't really appropriate in a response to someone asking a question when they are learning SR/GR. Also presenting natural language interpretations/explanations of mathematical results that differs from the mainstream one is not really appropriate in a thread like this; regardless of whether or not the result is internally consistent with the definitions you've chosen.

xyzt:

If you encounter someone saying something that is likely to cause confusion or derail the thread, it can be better to suggest they take it up in private messages or another thread with you until you figure out your disagreement, or inform the mods early if this fails. The main thing I can see about Iggy's posts which is disruptive is his unstated assumptions and definitions which are a good reason to ask him to take his discussion elsewhere independently of whether his reasoning is internally consistent.

Thank you, I will try to do that.

It was difficult for me to deal with the barging in claiming that

Exactly. Shapiro delay confirms it. Light passing a mass is slowed on approach and slowed likewise on departure. yep yep

I'll take Iggy aside next time he does that.

Edited by xyzt
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Aside from any reasoning mistakes you may or may not have made, you appear to be using fairly specific (but not widely used) definitions of a number of terms that become somewhat ambiguous in general relativity. If these terms are used at all, they will often be context dependent and should be defined for the purposes of a discussion if they are to be used at all. Velocity (outside of local velocity) is one such.

In post #3 xyzt identifies that post #1 is speaking of coordinate speeds. It seems like it's defined and understood early on in the thread, and only later (post #25?) is there issue taken with it, and since then stifled, even though it's used meaningfully throughout the thread.

Edit: It would have been clearer to call it "coordinate speed" throughout the thread.

If you encounter someone saying something that is likely to cause confusion or derail the thread,

Aren't Iggy and JVNY still discussing the core of the topic that was brought up in post #1, that of differently accelerating rockets that maintain a proper distance, while xyzt is complaining that it is too complicated and pushing for a discussion of a physically unrealistic uniformly accelerated rocket or nothing at all? All of xyzt's objections seem to only be directed against discussing the topic as it was introduced. Are you sure that others are derailing the thread, or is it possible that xyzt changed the subject but appears on topic due to insistence?

Edited by md65536
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In post #3 xyzt identifies that post #1 is speaking of coordinate speeds. It seems like it's defined and understood early on in the thread, and only later (post #25?) is there issue taken with it, and since then stifled, even though it's used meaningfully throughout the thread.

That's not true, I made it quite clear that coordinate speed is meaningless (unphysical). Besides, this is a well known FACT , present in textbooks. Read again, in case you missed it:

1. Vesselin Petkov is a crank, this is known in the physics community.

2.1 LOCALLY, the speed of light in a gravitational field is CONSTANT, if it weren't the whole GR theory would fall apart.

2.2. Nevertheless, the COORDINATE speed of light is variable. Indeed, start with the reduced Schwarzschild metric:

Edit: It would have been clearer to call it "coordinate speed" throughout the thread.

Didn't I make it clear enough from my first post, i.e. post 3 in this thread?

Aren't Iggy and JVNY still discussing the core of the topic that was brought up in post #1, that of differently accelerating rockets that maintain a proper distance, while xyzt is complaining that it is too complicated and pushing for a discussion of a physically unrealistic uniformly accelerated rocket or nothing at all? All of xyzt's objections seem to only be directed against discussing the topic as it was introduced.

That is false as well, my complaints have been two fold:

One, and most important, the falsity promoted by Iggy, that the speed of light slowdown explains the Shapiro delay. This is the crux of the disagreement.

Two, and less important, that the scenario presented by JVNY is not described correctly in the mathematical formalism.

Are you sure that others are derailing the thread, or is it possible that xyzt changed the subject but appears on topic due to insistence?

I think that the person who is attempting to derail the thread is you. I redlined some of your distortions of reality. Schrodinger's Cat has put this debate to bed, why are you attempting to re-ignite it , especially in the context of making false statements?

Edited by xyzt
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Xyzzy, on your question I do not know what you mean by coordinate speed. If you mean the time that it takes for light to travel a straight radial path toward a mass, reflect, then travel a straight radial path back to the source, as measured by an observer at the source, then I agree. That two leg path is slower as measured by an observer at the light source than the same flash takes for the same two legs absent the mass. But then I do not know what you mean by it being unphysical.

There is a very important disagreement here: how to transform the events from the illustrated inertial frame to the ships' frame (or each ship's frame, for those who conclude that the accelerating ships do not share a single reference frame). Iggy is not giving preference to a particular frame. The inertial frame is clear (it is illustrated), so all Iggy is doing is the transform to the ships' frame. Iggy and I draw three conclusions. First, that by accelerating each ship inversely to its distance from the front ship one keeps the ships at the same proper distance, that is the same distance in their accelerating reference frame. Each will have a vertical worldline in that frame, always the same distance apart (just as they would if they were in inertial motion with respect to the inertial frame). Second, that all ships agree at all times on their common velocity (just as they would if they were in inertial motion with respect to the inertial frame). Third, that the ships agree on the simultaneity of events in their frame (just as they would if they were in inertial motion with respect to the inertial frame).

Xyzt, am I correct in concluding that you agree with the second conclusion (but consider it unimportant), and that you disagree with the first and third?

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That is false, you are trying to act as a "teacher" but you keep piling up mistakes. For example, the most serious link you cite , the C.M.Will one, you took the citation not out of the Shapiro delay explanation paragraph but out of the following paragraph, his refutation of the Kopeikin paper (the one that claims to be measuring the speed of gravity). This nullifies your appeal to authority and invalidates your explanation. On the other hand, I provided the mathematical derivation of the Shapiro effect, there is nothing in it about the speed of light "slowing down". I also pointed out that the rays of light do not come anywhere close to the event horizon, contrary to your claim, you chose to sweep this error under the rug. The rays of light in discussion pass by at distances that are many orders of magnitude larger than the EH.

I will consider carefully what you say.

I explained this as well to you several times, last time in this post, that there is no number since the proper distance between ships is a function of the proper time $\tau$. As such, it obviously varies with $\tau$. What you are calculating is not the proper distance between the ships. You are calculating something else, I'll let you think about it.

The ships constitute a Born-rigid system, so the proper distance between them is not a function of $\tau$. But, that isn't what I'm asking.

I'm saying that the following is an inertial frame:

in which the spatial distance of the blue line is 0.5, and the spatial distance of the green line is 0.625. What is the distance of the green line in a v=0.6 inertial frame?

You say there is no number, but I assure you the question I just asked has a numerical answer.

First note, primarily to Iggy:

Aside from any reasoning mistakes you may or may not have made, you appear to be using fairly specific (but not widely used) definitions of a number of terms that become somewhat ambiguous in general relativity. If these terms are used at all, they will often be context dependent and should be defined for the purposes of a discussion if they are to be used at all. Velocity (outside of local velocity) is one such.

I've spoken of speeds in particular coordinate systems. For example, the first thing I said about the speed of light, and the first thing that found objection, and the thing that has been frequently quoted, is the following:

your diagrams in your pdf are Rindler coordinates. The speed of light in that case is $xg$ (where x is the x position and g is acceleration). As c and x are proportional in c = xg, the greater the x (i.e. the greater the distance from the mass) the greater the speed of light.

Is the speed in Rindler coordinates a coordinate speed? I dare say it is. But, I have not been ambiguous about what I was talking. From the start -- I didn't just say that it was a coordinate speed, I gave the specific coordinates to which I was referring, so I don't know why you are directing that comment at me.

You are also using terms like simultaneous and proper distance to refer to events relating to events that do not share an obvious inertial reference frame as if we are all on the same page (doing so is going to require further qualification).

If it isn't clear then I expect the following site would make it clear:

In other words, the accelerated clock's rate is identical to the clock rate in a "momentarily comoving inertial frame" (MCIF), which we can imagine is holding an inertial clock that for a brief moment slows to a stop alongside the accelerated clock, so that their relative velocity is momentarily zero.

Clock acceleration and timing

Any time I have spoken of simultaneity of an accelerating clock I have done so in the context of a 'momentarily comoving inertial frame'. I didn't think this was a problem because every participant in this thread spoke of light rays hitting distant accelerated objects simultaneously relative to accelerated observers before I joined the thread. I agreed with that conclusion, and spoke in the same terms.

Not to mention, you might note I wrote the following yesterday:

No doubt, any non-local speed in GR is ambiguous, but an ambiguous thing does not a constant and invariant thing make.

Thirdly, you appear to be privileging results derived from a specific coordinate system. The words/definitions/results derived are frequently only going to be useful within said coordinate system.

Indeed. If you open the PDF in the OP then you will see it is a diagram of a specific coordinate system. Subsequent questions asked by the OP dealt with that same coordinate system. It shouldn't be a surprise that I've been talking about that exactly.

These are all things that aren't really appropriate in a response to someone asking a question when they are learning SR/GR.

Let me ask you if post #3 is appropriate. It answers the OP entirely in terms of Schwarzschild coordinates which are irrelevant to the OP and the language of the OP -- like something copied out of the wrong book.

I'm glad you're here, and I welcome your participation in this thread immensely, but I think you've misjudged the previous discussion.

Edited by Iggy
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Let me ask you if post #3 is appropriate. It answers the OP entirely in terms of Schwarzschild coordinates which are irrelevant to the OP and the language of the OP -- like something copied out of the wrong book.

I can see that you continue with your personal attacks. The answer in terms of Schwarzschild coordinates is the standard, mainstream answer. Your insinuation that I copied it out (from the wrong book) it totally unacceptable. This is the second time you've done this in this thread, please cease and desist.

Xyzzy, on your question I do not know what you mean by coordinate speed. If you mean the time that it takes for light to travel a straight radial path toward a mass, reflect, then travel a straight radial path back to the source, as measured by an observer at the source, then I agree. That two leg path is slower as measured by an observer at the light source than the same flash takes for the same two legs absent the mass. But then I do not know what you mean by it being unphysical.

It is all explained in post #3.

In the Schwarzschild coordinate system, the expression $\frac{dr}{dt}$ represents coordinate speed. It is unphysical because it is not measurable, it represents what a distant observer "would" measure but measurements can only be made locally.

The particular $\frac{dr}{dt}$ obtained through the cancellation of the LHS of the metric, $ds=0$ represents the coordinate-dependent speed of light (because light follows null geodesics). It is not measurable because.....you can fill in the blanks now.

Edited by xyzt
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The answer in terms of Schwarzschild coordinates is the standard, mainstream answer.

Fair enough. Let's answer your Shapiro delay question in terms of Schwarzschild coordinates:

Q & A: How does Shapiro delay work

The rule about the speed of light being constant only applies locally to patches of spacetime small enough to be effectively flat, i.e. ones which can be described by special relativity. On a bigger scale, with gravity involved, phrases like "the same distance" become ambiguous.

Let's think of light from some distant star. There's an extra delay in how long it takes to reach us when the light happens to pass near the sun on its way. How come? We can describe it in a particular choice of coordinates, the Schwarzschild coordinates. Two things happen to the light as it goes near the sun:

1) Close to the sun, the effective rate at which time passes is slowed. According to local clocks there, the light is traveling at the usual speed, c, but we think those clocks are slow so from our point of view the light is going slower.

2. As it approaches and departs from the vicinity of the sun, the light travels extra distance, more than what you would calculate if you drew a big circle around the sun and took the diameter to be its circumference over 2pi. Space isn't Euclidean- the diameter of that circle is bigger than it should be based on the circumference. So the light has farther to go (as measured by local rulers) than it would if it weren't going near the sun.

These effects add up to give the Shapiro delay.

Should you say that under these circumstances the light travels farther? In our coordinate choice, that does account for half the effect.

Q & A: How does Shapiro delay work

You insisted earlier that Shapiro delay is due to light traveling farther than it would otherwise have to. In Schwarzschild coordinates that does account for half the effect. The other half is because "from our point of view the light is going slower".

Shapiro delay is an effect measured by our clocks here on earth, and it does indeed verify that light is slowed relative to our clocks here, and I am indeed happy that you accept Schwarzschild coordinates for proving this.

I ask the following question because you rejected my answer very aggressively: If a spatial distance is 0.625 in our frame, then what is the distance is a frame with a relative velocity of v=0.6c?

Edited by Iggy
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Fair enough. Let's answer your Shapiro delay question in terms of Schwarzschild coordinates:

Q & A: How does Shapiro delay work

The rule about the speed of light being constant only applies locally to patches of spacetime small enough to be effectively flat, i.e. ones which can be described by special relativity. On a bigger scale, with gravity involved, phrases like "the same distance" become ambiguous.

Let's think of light from some distant star. There's an extra delay in how long it takes to reach us when the light happens to pass near the sun on its way. How come? We can describe it in a particular choice of coordinates, the Schwarzschild coordinates. Two things happen to the light as it goes near the sun:

1) Close to the sun, the effective rate at which time passes is slowed. According to local clocks there, the light is traveling at the usual speed, c, but we think those clocks are slow so from our point of view the light is going slower.

2. As it approaches and departs from the vicinity of the sun, the light travels extra distance, more than what you would calculate if you drew a big circle around the sun and took the diameter to be its circumference over 2pi. Space isn't Euclidean- the diameter of that circle is bigger than it should be based on the circumference. So the light has farther to go (as measured by local rulers) than it would if it weren't going near the sun.

These effects add up to give the Shapiro delay.

Should you say that under these circumstances the light travels farther? In our coordinate choice, that does account for half the effect.

Q & A: How does Shapiro delay work

You insisted earlier that Shapiro delay is due to light traveling farther than it would otherwise have to. In Schwarzschild coordinates that does account for half the effect. The other half is because "from our point of view the light is going slower".

Shapiro delay is an effect measured by our clocks here on earth, and it does indeed verify that light is slowed relative to our clocks here, and I am indeed happy that you accept Schwarzschild coordinates for proving this.

I redlined all your non-mainstream, anti scientific repetitions of the "light is going slower". References to the pop-sci website hosted by U of Illinois are not valid references, why are you using it, are you going to school there? You copied word for word a totally fringe description. For a correct description (no fringe references to "light slowing down") see , for example , Rindler page 237. I would have written down the derivation but I am tired of you accusing me that I "copy from material I don't understand").

1) Close to the sun, the effective rate at which time passes is slowed. According to local clocks there, the light is traveling at the usual speed, c, but we think those clocks are slow so from our point of view the light is going slower.

Notwithstanding that the above claim cannot be found in any mainstream text or textbook, your error is obvious, the (correct) statement that time is running slower would imply that , contrary to your claim, "light speed should be running faster", "not slower", so , the effect that you are claiming does not exist. The Shapiro delay is not "made up of two effects", there is only one, the length of the geodesic arc described by the photon orbit grazing a large gravitating body is larger than the length of a straight line segment in the Euclidian sense.. This takes care of another one of your incorrect claims, the grazing happens at distance that is many orders of magnitude larger than the event horizon. I could recommend a few mainstream places for a solid derivation of the Shapiro delay, would you be interested in learning?

Edited by xyzt
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Md65536, do you wanna help us out?

A spatial distance of 0.625 in our frame is what in a frame of relative velocity v=.6c?

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Md65536, do you wanna help us out?

A spatial distance of 0.625 in our frame is what in a frame of relative velocity v=.6c?

0.625/gamma

gamma = 1.25

I don't want to be drawn into any hostile arguments, but I'll go along with it if it helps me figure stuff out.

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0.625/gamma

gamma = 1.25

You may not realize that what you tried to prove is that $x_2(t)-x_1(t) = x_3(t)-x_2(t)$, i.e. the distance between the rockets stays constant in the frame of the launch pad.

No, it apparently stayed constant in the v=.6c frame, not the frame of the launch pad. JVNY calculated it earlier, and Md verifies the math. Also, Born rigidity has been around for about 100 years, I don't think you're about to disprove it. So...

there is no number since the proper distance between ships is a function of the proper time $\tau$.

No, not a function of tau. It is well-established science that the proper distance between accelerating observers stays constant if their acceleration is inversely proportional to their distance.

I, nevertheless, appreciate your insistence otherwise. It's like Christopher Hitchens said in Canada I think... He said "it might, in any case, give people to think about why do they know what they already think they know. How do I know that I know this, except that I've always been taught this and never heard anything else. It's always worth establishing first principles"

You've certainly challenged us to establish first principles, and I welcome the challenge and hope I haven't disappointed in the result.

Thank you, Md.

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Light travels at the speed its allowed to travel , as to where and when it comes near to different objects ie : Planets , Stars . Gravity becomes stronger the closer o the planet or star clusters it gets so there-fore will slow down accordingly . In short light will go in any direction necessary for it to continual its endless journey forward. As in space the question becomes in what direction is the light going , as is there a vertical or a horizontal within space and the universe as when in space we are all in the middle of the solar system at one point no matter where we are , such as with space always rotating so the centre of space rotates . This is another subject

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Here is a recap and a reopening of the question of the coordinate speed of light in the accelerating frame as a function of the distance from the rear (which should be like the distance from a gravitational mass). I think that the result utilizes parts of the posts from each of md65536, Iggy and xyzt.

As md65536 suggests, consider a row of separate ships at rest in an inertial frame that are then simultaneously accelerated (rather than trying to accelerate a single object that has the same length as the row). Each ship accelerates at a proper rate inversely proportional to its distance from the origin. For example, the ship that starts at x=0.5 accelerates at a=1/0.5, or a=2. The ship that starts at a=1 accelerates at a=1/1, or a=1. As Iggy states, under these conditions the ships undergo "Born rigid" motion: they remain together in a shared accelerating reference frame; they keep their same proper distance in that accelerating frame; they agree on simultaneity; they always have the same velocity relative to the inertial frame; and their worldlines in the inertial frame are hyperbolas. Their clocks do not run at the same rate in their frame. The farther forward a ship is, the faster its clock runs. However, the rate is proportional to distance, so each ship behind the front can program its clock to automatically scale up its elapsed time proportionately and thus keep its clock synchronized with the front clock. Iggy advises that the front clock's time is the conventional measure of time in the accelerating frame; it is called the coordinate time of the frame. The time that we measure in that frame when we determine the speed of light in the frame is coordinate time, and so I think that the speed of light in that frame is its coordinate speed.

As the ships start to accelerate, the front ship flashes a light toward the rear. The Minkowski diagram for the inertial frame is as follows (ships' worldlines are hyperbolas; light flash's worldline is the arrow):

Because the ships are all in the same (accelerating) reference frame, we can Lorentz transform the light's path into the ships' frame. The light's worldline is no longer a straight 45 degree line. Rather, it is curved:

To make the effect clearer, we can diagram the marginal amount of coordinate time that it takes for the light to travel successive equal segments in the ships' frame (here done using distance increments of 0.02). It takes successively greater coordinate time to travel equal segments the farther toward the rear of the row (left in the diagram) that the light is traveling. In coordinate time, light is always traveling less than c, and increasingly less as it moves rearward:

Notice that the curve flattens out toward the front of the row (toward the right). This suggests that the coordinate speed of light over successive equal increments is higher toward the front (the right), but at a decreasing rate. It suggests that the coordinate speed will not exceed c. This agrees with xyzt, who states that the speed of light is not proportional to the distance from the origin, and more specifically that the speed of light will not exceed c at distances farther away from the rear. Xyzt prefers not to use calculations, but Iggy you can confirm that the coordinate speed of light does not exceed c as follows.

Start with two ships, one at x=99.98 and the other at x=100. They accelerate simultaneously and flash a light at each other. Their acceleration rates are 1/99.98 and 1/100, respectively. Next, as you did before use the relativistic rocket formulas to determine the coordinate time that each light flash takes to cross the 0.02 proper distance and strike the other ship. You should find it to be 0.020002 (same in both directions). The coordinate speed of light is still less than c (0.02/0.020002), but it is getting very close to c. This is just an example, but I expect that those of you with better math skills than I have can prove that at any distance away from the origin the coordinate speed will remain below c (I think that it will asymptotically approach c, but I cannot be sure).

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No, it apparently stayed constant in the v=.6c frame, not the frame of the launch pad. JVNY calculated it earlier, and Md verifies the math. Also, Born rigidity has been around for about 100 years, I don't think you're about to disprove it.

There is nothing special about "the v=0.6c frame". The motion , if Born rigid, is Born rigid in all frames.

Also what I said, is that you tried to demonstrate that the distance stayed constant in the launcher frame (and you failed).

The motion is not Born rigid and this problem has nothing to do with Born rigidity, you are dealing with three particles that all have different speeds in any frame you consider, so, there is relative motion between them. As such, their relative distances, contrary to your claims, cannot be constant. Quite the opposite, it is variable.

In the launcher frame, the speeds are $v_i=\frac{a_i}{\sqrt{1+(a_it/c)^2}}$, i.e. they are all different (and they do not depend in any fashion of the initial positions $x_{0i}$).

In the frame co-moving with any particle, the calculation is a little more complicated but the conclusion is the same, there is relative motion between the particles because, their speeds, as calculated from any such frames are variable and not equal. Indeed, the proper speed of the particle i=1 is $v_1=c * tanh (a_1 \tau/c)$. The proper speed of particle i=2 is $v_2=c * tanh (a_2 \tau'/c)$. $\tau'$ and $\tau$ are connected by the coordinate time $t$:

$t=\frac{c}{a_1} sinh (a_1 \tau/c)$

so:

$\tau'=\frac{c}{a_2}arcsinh(a_2t/c)=\frac{c}{a_2}arcsinh(a_2/a_1 sinh (a_1 \tau/c)$

Substitute in the formula for $v_2=c* tanh (arcsinh(a_2/a_1 sinh (a_1 \tau/c))$

Obviously, $v_2 \ne v_1$, so, contrary to your claims, the motion is not Born rigid and the particles keep getting spread apart or bunched together depending to their proper accelerations. It doesn't matter how the accelerations were set up wrt the the initial positions. I would appreciate if you responded with your own calculations rather than referring to some drawings that JVNY made. Thank you.

Exactly. Shapiro delay confirms it. Light passing a mass is slowed on approach and slowed likewise on departure. yep yep

Edited by xyzt
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Xyzt, I will have to leave it to someone else to do the mathematical proof you request. Hopefully Iggy has time.

Separately, though, I think that two of your posts are inconsistent.

In post 81 above, you say the following about two particles accelerated the way that we call Born rigid: "the only correct claim he makes is a trivial one 'A and B agree at all times on their common velocity'. Yes, this is obvious, so what?" This seems to say that the two particles share a "common velocity," which is to say that they have the same velocity.

In post 94 above you say that we "are dealing with three particles that all have different speeds in any frame you consider". This implies that the no two of the particles share a common velocity.

Do the particles have a common velocity, or not, in your view?

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The motion is not Born rigid and this problem has nothing to do with Born rigidity, you are dealing with three particles that all have different speeds in any frame you consider, so, there is relative motion between them. As such, their relative distances, contrary to your claims, cannot be constant. Quite the opposite, it is variable.

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Xyzt, I will have to leave it to someone else to do the mathematical proof you request. Hopefully Iggy has time.

Separately, though, I think that two of your posts are inconsistent.

In post 81 above, you say the following about two particles accelerated the way that we call Born rigid: "the only correct claim he makes is a trivial one 'A and B agree at all times on their common velocity'. Yes, this is obvious, so what?" This seems to say that the two particles share a "common velocity," which is to say that they have the same velocity.

In post 94 above you say that we "are dealing with three particles that all have different speeds in any frame you consider". This implies that the no two of the particles share a common velocity.

Do the particles have a common velocity, or not, in your view?

No , they don't, I have shown this repeatedly. The posts aren't inconsistent since the particles in YOUR example DO NOT have the same speed, contrary to your drawings they are not accelerated in a Born rigid fashion. Math contradicts your drawings (and drawings never form a valid form of proof).

Besides, your exercise is just a sideshow, the main show is the incorrect claim that Shapiro delay somehow proves light "slowing down". I would like you and Iggy to retract this false claim.

Nothing to do with any length contraction. The speeds are unequal, each rocket moves at a different speed as I have demonstrated several times.

Edited by xyzt
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No , they don't, I have shown this repeatedly. The posts aren't inconsistent since the particles in YOUR example DO NOT have the same speed. Besides, your exercise is just a sideshow, the main show is the incorrect claim that Shapiro delay somehow proves light "slowing down". I would like you and Iggy to retract this false claim.

I thought everyone agreed that that claim was speaking of the coordinate speed of light.

Nothing to do with any length contraction. The speeds are unequal, each rocket moves at a different speed as I have demonstrated several times.

That's why you must consider length contraction.
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I thought everyone agreed that that claim was speaking of the coordinate speed of light.

The coordinate speed of light does not intervene in the explanation of the Shapiro delay, so, not. Shapiro delay is an exercise in the calculation of the total elapsed time done in the context of assuming light speed constancy, not variability.

That's why you must consider length contraction.

Perhaps you can do the math and post it, the way I did it? I would be very interested in your proof. Frankly, I would prefer you, JVNY and Iggy opened a different thread , this exercise is just a sideshow to the false claim made by Iggy who got this all started. Let's concentrate on the main show, the false claim about the Shapiro delay confirming the slowing of light speed.

Edited by xyzt
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Frankly, I would prefer you, JVNY and Iggy opened a different thread , this exercise is just a sideshow to the false claim made by Iggy who got this all started. Let's concentrate on the main show, the false claim about the Shapiro delay confirming the slowing of light speed.

I missed the post where the thread was officially redefined. No one claimed that the local speed of light is slowed, only the coordinate speed. Why make false accusations? Let's get back on topic of JVNY's question.

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