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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 [math]v_i=\frac{a_i}{\sqrt{1+(a_it/c)^2}}[/math], i.e. they are all different (and they do not depend in any fashion of the initial positions [math]x_{0i}[/math]). 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 [math]v_1=c * tanh (a_1 \tau/c)[/math]. The proper speed of particle i=2 is [math]v_2=c * tanh (a_2 \tau'/c)[/math]. [math]\tau'[/math] and [math]\tau[/math] are connected by the coordinate time [math]t[/math]: [math]t=\frac{c}{a_1} sinh (a_1 \tau/c)[/math] so: [math]\tau'=\frac{c}{a_2}arcsinh(a_2t/c)=\frac{c}{a_2}arcsinh(a_2/a_1 sinh (a_1 \tau/c) [/math] Substitute in the formula for [math]v_2=c* tanh (arcsinh(a_2/a_1 sinh (a_1 \tau/c)) [/math] Obviously, [math]v_2 \ne v_1[/math], 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. I am more interested in your answering my question about your above statement, do you still maintain that it is correct and that it reflects the physical reality? Please answer, I answered all your questions, I would expect you to do the same.

Neither. Read here

Read here. There is no change in medium for light propagating in vacuum.

The gravitational lensing is not refraction, it is a different effect.

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"). 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?

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. It is all explained in post #3. In the Schwarzschild coordinate system, the expression [math]\frac{dr}{dt}[/math] 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 [math]\frac{dr}{dt}[/math] obtained through the cancellation of the LHS of the metric, [math]ds=0[/math] represents the coordinate-dependent speed of light (because light follows null geodesics). It is not measurable because.....you can fill in the blanks now.

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

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). Thank you, I will try to do that. It was difficult for me to deal with the barging in claiming that I'll take Iggy aside next time he does that.

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 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 [math]\tau[/math]. As such, it obviously varies with [math]\tau[/math]. What you are calculating is not the proper distance between the ships. You are calculating something else, I'll let you think about it.

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?

Despite of your repeated claims, there is no "variable speed of light" and Shapiro delay doesn't "verify" any such thing, the Shapiro delay mainstream explanation (you can try MTW, Rindler, Moller, to name just afew), shows that the delay is due to the deviation of the geodesic from a straight line. I gave the mainstream explanation in this post, the one that you chose to ignore. For further information, there is no light approaching the event horizon in the Shapiro delay. Err, what did you do with [math]\tau[/math]? How did it "disappear" from the formulas? [math]v=v(\tau)[/math] , remember? You just calculated the value of the speed at a particular instant in time , yet you extended the claims to the whole trajectory. This is clearly incorrect. ....because that is the proper distance between the two ships. And you claimed that that distance is constant for ant value [math]\tau[/math]. So, I would like to see your calculations. Please refrain from plugging in numbers and from pointing to colored lines on drawings. You appear to be thinking that the proper distance between ships is to be measured at the points (in time) where the three ships have the same proper distance, this means different values of the proper time [math]\tau[/math] for each of them (due to the differences in proper acceleration, the ships do not achieve the same speed at the same proper time). Proper distance is measured by marking the points at the same time, this is why your approach is incorrect.

Nope. Also nope.

False, the photons travel at c wrt to ANY observer. Try again. In English , please.

You are playing word games, so what would velocity/speed "slowdown" mean in your post on the explanation of the Shapiro delay be? Contrary to your claims, there is no "speed slowdown" in the mainstream explanation of the Shapiro delay. I'd like you to answer the challenge to your claim that : Or you may want to retract it. But your attempt at proving that the "distance is constant" used length contraction, so you are contradicting yourself or you do not realize that you have actually (as you admitted at the end of your post) actually calculated the length in the lab frame.See your [math]L=L_0 \sqrt {1-v^2}[/math]? As an aside, how did you get [math]v=0.6c[/math] in the above? The rockets have different proper accelerations, they have different speeds, so how did you get the value you plugged in? Yes, it was a typo, I corrected it. Doesn't change the fact that your "proof" failed. Try proving that [math]\frac{c^2}{a_3} (cosh(\frac{a_3T}{c}) - 1)-\frac{c^2}{a_2}(cosh(\frac{a_2T}{c}) - 1)=constant[/math], please. One last thing, at [math]t=0[/math], [math]T=0[/math] so [math]x_{i0}=X_{i0}[/math] because the rockets are at rest, so their instantaneous frames of reference coincide with the launcher frame of reference. Therefore, contrary to your objection, [math]x_i(T)=x_{i0}+\frac{c^2}{a_i} (cosh(\frac{a_iT}{c}) - 1)[/math] is the correct general formula since [math]x_i(T=0)=x_i(t=0)=x_{i0}[/math]. But this is just a set of secondary issues, a sideshow to our MAIN disagreement. I'd like you to answer the challenge to your claim that : Or you may want to retract it. Either way, I'd like you to stop evading the main topic of our disagreement and address it. Mainstream view is that there is no such thing as a "light slowdown".

No. This is not correct, you cannot attach frames of reference to photons. Therefore you cannot say "two photons travelling together would be stationary to an other".

I asked IVNY to explain how he arrived to his conclusions, I asked you to justify your claims that velocity and speed are interchangeable and that "light speed slowdown explains the Shapiro delay". You are trying to answer the question posed to IVNY but your approach using length contraction is incorrect. Let's try again: the trajectories of the three rockets are [math]x_i(\tau)=x_{i0}+\frac{c^2}{a_i}(ch \frac{a_i \tau}{c}-1)[/math] with [math]i=1,3[/math] and [math]x_{i0}=0.5, 0.75,1.0[/math]. It is obvious that for any given [math]\tau >0[/math] [math]x_2(\tau)-x_1(\tau) \ne x_3(\tau)-x_2(\tau)[/math], so a naive solution based on length contraction fails miserably. You may not realize that what you tried to prove is that [math]x_2(t)-x_1(t) = x_3(t)-x_2(t)[/math], i.e. the distance between the rockets stays constant in the frame of the launch pad. The lab frame cannot "calculate that the proper distance between the front and rear rockets remains...", this is a contradiction of terms. The proper distance between the rockets is [math]x_2(\tau)-x_1(\tau) , x_3(\tau)-x_2(\tau)[/math] . What the "lab frame calculates..." is the coordinate , not the proper distance. Do you know the difference?

You are trying to turn the attention from your crank claims into a debate over terminology. There are no "multiple interpretations", Iggy has been very proactive in pushing his fringe ideas. I see the errors that other (Iggy, JVNY ) are posting, I do not see any valid calculations. The one that is the most glaring is the claim that Shapiro delay is a result of "light speed slowing down".

Frankly, I do not understand why you persist in this embarrassing charade. Roger Anderton is a well known antirelativistic crackpot, thank you for revealing your source of information. Now, it all becomes clear. Yes, so what? The point is that what causes the delay is the change in velocity direction , not magnitude, as you and Iggy incorrectly claim. I don't see anything supporting your claim, why don't you explain, with math, in your own words , your claim. Please do so.

The modern, mainstream view is quite clear on this issue, end of story. Did you read the explanation I wrote for you on the Shapiro delay? What did you understand from it? I also twice questioned your claim about the three rockets maintaining equal distances, can you answer those questions for me, please?

Velocity is a vector, so it cannot "be c". The redlined sentence shows that you do not know the difference. I explained to you several times that while the velocity (a vector) changes (as in the Shapiro delay, gravitational lensing, etc), the speed of light (i.e. the scalar) does NOT vary. If you want to keep pushing your fringe ideas, you should try an anti-relativity forum, that is where cranks routinely use the quote from Einstein (1920) to support their claims that the "speed of light" (in vacuum) varies. I asked you before and I am asking you again: prove that the speed of light varies in the Shapiro delay, If you cannot prove that, have the integrity to admit that you were wrong all along and stop pushing fringe misconceptions as if they were mainstream concepts. The above claim is not only grossly incorrect but you repeated it several times. Contrary to these repeated claims, textbooks teach you that "light passing a mass is NOT slowed on approach and slowed likewise on departure". It is the velocity that changes, more exactly the direction of the vector, not the scalar (the speed). The speed stays the same,c. For your education , I am including a diagram that explains the Shapiro delay correctly, just to debunk your fringe "explanation". You can see that the velocity is what changes, this is what Einstein tried to teach you , so what I have been telling you is exactly what Einstein has been telling you, no disagreement. The only disagreement is between your claims and mainstream GR.

Yes, the Lorentz transforms work. Yes, you just got banned for the same exact type of ant-mainstream trolling on the ScienceForums, chinglu. Why do you feel compelled to spam all the physics forums with this type of garbage?

yes, Shapiro Delay is another good one.

Neither of them "calculated" any such thing. For a basic answer, see here.

Yes, it is. And no, gravity does not "slow down the speed of light".

But the math of hyperbolic motion does not support your claim, it actually contradicts your claim. How do you explain that? The difference in elapsed time is due to closing speeds, as I already explained to you in a couple of posts, not due to ANY variability in the speed of light, as the title of the thread claims. There is no analogy with gravity. I explained that as well. You are mixing up closing speeds in an accelerated frame with the calculation of the coordinate speed of light in the presence of a gravitational field. There is no "deeper" meaning, this is what closing speeds to, the travel time is bigger when you chase something going away from you. Gravity does NOT "slow" light.