What other case would you want?

Say one where an object is approaching the event horizon of a black hole and I am a few light years away?
You can find the length of a null geodesic by using an affine parameter as opposed to the more restrictive parametrisation using proper time. Proper time between two neighbouring points on such a geodesic being zero does not imply that a null geodesic has no proper length  if that were the case, light would propagate at infinite speed, i.e. it would have to be everywhere at once. The reason why this does not work is that "light" is not a valid frame of reference.When it comes to the speed of light it’s assumed that we’re talking about the coordinate speed since the proper speed is undefined for light because the proper time between all closely spaced events along a null geodesic is zero and, of course, division by zero is undefined.
Remember also the general definition of what a geodesic is  it's a curve that paralleltransports its own tangent vector. This does not require the notion of a metric, nor is there a concept of nullity.
So, you want to calculate the coordinate speed of that object? Is this the question?Say one where an object is approaching the event horizon of a black hole and I am a few light years away?
I try to be similar.
I guess sometimes my patience gets short and I don't live up to my own ideals. Apologies for anything I've said that you didn't like.
I don't. I find people like him really irritating. They spoil discussions. And thence forums. But on the other hand if I totally ignore him it might look like I couldn't deal with objections.Originally Posted by Physicist
It is refreshing to see you and Physicist in agreement again. maybe you could put your ideas together into a "paper"?Originally Posted by Farsight
No. You asked why would I be interested in the non trivial case. I was just making the point that most cases are non trivial. The observer in GR is rarely in the same frame as the object, else we wouldn't need relativity! The ? was more of a question as to whether you were thinking the same way.
Well, your question:
Originally Posted by Jilan
makes no sense, cannot be even parsed, so you will need to learn the basics. Have you considered taking an intro class to GR?
Wrt = with respect to! sorry if that wasn't clear.
I know what "wrt" means, your whole question makes no sense.
OK x0x you cannot help me, I understand.
Try to phrase the question in a correct way, then I will be able to help you. The way it is know, it is garbled.
Ok, try post # 102 , is that garbled also?
Ok, so you have an object falling (radially?) towards the EH. What is the question? You haven't formulated one.
Actually, I never asked a question. You asked a question in post # 101 and I was just responding to that. I am quite happy with what I have learned so far from the learned forum members and online resources and am not confused at this point. My question more related to whether you would consider the more general situation to be nontrivial.
PhysBang – I thought that you might appreciate what follows – I gave a description somewhere as to why light slows down in a gravitational field, i.e., it’s due to gravitational time dilation. I wanted to look into the historical background for this so I read it coming from a wellknown GR source, i.e. Hans C. Ohanian. He wrote a book called Einstein’s Mistakes, which I’m sure you could find online if you wanted to, in which he describes a great deal of Einstein’s successes and some of his mistakes. In the chapter entitled ”Suddenly, I had an idea” in which Ohanian describes Einstein’s creation of general relativity and its predictions the author writes at the bottom of page 189
Ohanian derives all of this in his and Ruffini’s text Gravitation and Spacetime – Third Edition and also explains that the light slows down and that it can still be thought of as bending through a space with variant refractive index. If you’d like I can email that section of his text to you.He assumed that when the speed of light is measured at some location in a gravitational field with the local clock slowed, the speed still has its standard value, 300,000 klicks per second. But since the clock is running slow, the actual speed must be slowed by as much as the clock is slowed – in a gravitational field, light propagates more slowly than outside the field. This means that in regard to the propagation of light, the neighborhood of the Sun behaves like a large glassfilled globe encasing the sun, so this glass slows the propagation of light. The glass is most dense near the Sun, less dense farther out, and it gradually fades away into empty space at large distances (where the speed of light resumes its standard value.).
Einstein recognized that such a slowing of the speed of light would bend rays of light in the same way that a globe of glass bends rays of light – it bends rays of light that strikes the left half toward the right, that is, it always bends the rays if light towards the center line.
Yes, it is funny you can't form a coherent question.
Like said before, I have no question other than can you see what you posted was trivial? yawn.
When I took GR, we stole parts and exercises from a number of different textbooks. O'hanion and Ruffini were a source for a good chunk of the course and I have the text somewhere. (Edit: I even have a scan of the first edition!) I didn't know about the Mistakes book, though. Thanks for the reference.
Last edited by PhysBang; 07052014 at 12:37 PM.
Ohanian and Ruffini are awesome physicists and authors, wouldn’t you agree? By the way, they just published a new version of their text Gravitation and Spacetime. Precisely it’s referred to as Gravitation and Spacetime – Third Edition by Ohanian and Ruffini, Cambridge University Press (2014). They treat the uniform gravitational field, gravitational time dilation and the equivalence principle on page 136. On pages 147148 they discuss the slowing of light in a gravitational field of the Sun. They also discuss on page 148 the deceleration of light on page 148 too. It’s a weird effect. You should check it out if you can.Originally Posted by PhysBang
If you're interested on what the authors have to say about the slowing of light in a gravitational field then read section 4.4. That's the part which is relevant to this thread is the beginning of that section which is on page 142. The section is entitled 4.4 The Time Delay of Light which reads
Another observable effect that we can obtain from the linear approximation is the time delay suffered by a radar signal sent from Earth to a planet and reflected back to Earth. As was first observed by Shapiro (1964), the gravitational field of the Sun contributes to a measureable increment to this time delay, because it reduces the speed of propagation of light signals.
This is what you get when you "do physics" by quote cherrypicking . Ohanian and Ruffini calculate the the Shapiro delay by using the COORDINATE speed of light. What you conveniently forgot to cite, is what they say at the end of the derivation:Originally Posted by physicist
By contrast, D'Inverno (and Rindler, as I have shown earlier) do a much cleaner job, never resorting to the variability of COORDINATE light speed. See here, for the D'Inverno elegant proof.Originally Posted by Ruffini&Ohanian
PhysBang – Richard A. Mould says all this nicely in his text Basic Relativity, [I]Springer Press[I], (1994). On page 239 he writes
And in addition to all those other sources let's look at Pauli's text. Wolfgang Pauli also said the same thing in Theory of Relativity, on page 143 where he wroteIt may be stated in a general way that local measurements made at any point in space will find the velocity of light equal t 1. It is the nonlocal or global determinations of light velocity that normally violates Einstein’s special postulate.
A further result was that the velocity of light is not constant in a gravitational field, ...
Last edited by Physicist; 07052014 at 08:17 PM.
No one claimed that velocity doesn't vary. The point that you keep failing to grasp is that speed does not. Velocity and speed are two different things, you know.Originally Posted by physicist
Everyone agrees that if you are floating through space and a photon passes you, you will measure it's speed with local clocks and rulers as (I will stick to using to denote this particular physical constant).
Everyone also agrees (I hope) that if we bounce a radar signal off Venus, the roundtrip time as judged by Earth will be strictly greater than times the distance from Earth to Venus as measured across a hyperplane of constant Schwarzschild time. Let me just emphasise that; not only is the travel time greater than you'd expect based on a naive Euclidean calculation of the distance travelled, it is also greater than you'd expect based on the distance measured across the constanttime surface with metric .
Everyone agrees on the precise value of the roundtrip time, and the mathematics used to arrive at that conclusion.
Everyone also presumably agrees that there are different ways of defining the distance travelled by the signal, and that the ratio "distance divided by time" is dependent on which is chosen. For example, although a definition similar to the one I mentioned above works and is reasonably natural for a geometry which is invariant under time translation (like Schwarzschild), it probably wouldn't be satisfactory for a geometry lacking such a symmetry.
If those statements are an accurate summary of everyone's positions, it's hard to see what is left to argue about.
I don't really understand why there is an argument to start with. Locally we can never ever measure anything else but exactly c for the speed of light, and no one can dispute that; GR now teaches us that local frames are globally related in a nontrivial manner ( that's the whole point of the theory ! ), so the average velocity along some spatially extended region that contains sources of energymomentum cannot be exactly c, or else we would just be dealing with trivial Minkowski spacetime. This is once again about that very crucial distinction between local and global, which lies at the very heart of GR  there is no argument and no contradiction, it's just what it means to have a curved spacetime as opposed to a flat one. It's a manifestation of gravity.If those statements are an accurate summary of everyone's positions, it's hard to see what is left to argue about.
The situation is very simple  locally the speed is always exactly c, and that includes places like the event horizon too. Globally ( along an extended region ) it is not. That is all there is to it !
The argument was about whether the notion of "varying speed of light" is confirmed by the Shapiro delay experiment. The answer from an earlier post stands: no.
No, it doesn't.Originally Posted by btr
Right on cue, "physicist" just proves that.
I think that some people have a hard time admitting that they were wrong so they have to change definitions and choose what to call "physically meaningful" differently than the authorities (and physics dictionaries) so that they can give the appearance to themselves as being right. Although they're really only fooling themselves, nobody else. That’s why he actually believes that the answer is no, ignores all the proof and the correct definitions and derivations given to him time and again, ignores all the work and statements by countless experts quote here so far, claims that he’s right and the world is wrong and expects everyone to buy into it. I’m so sorry that he has such a low opinion of everyone here. But that’s what happens when a person thinks they’re right and the entire relativity community is wrong. The fact remains and has been proven time and again – light slows down in a gravitational field and no delusions can prove otherwise.
Given a choice whom would you accept as knowing the correct answer? Einstein + Taylor & Wheeler + Ohanian & Ruffini + Foster and Nightingale + Pauli + Gron + Don Koks + etc etc etc or x0x who refuses to provide any proof other than changing the definition of “speed of light”?
Shapiro’s physical measurements had to mean that the physical speed of light slowed down. Shapiro and his team didn’t have spaceships in which they could travel to the planets and back to take measurements so they had to use Schwarzchild coordinates.
Please correct me if I’m wrong, but I thought that the purpose of this forum was to help people and students learn mainstream physics, defined as that found in undergraduate and graduate textbooks and not someone’s offshoot of it derived by changing definitions? Do you gentleman/ladies argue about definitions every time someone comes here and asks a question merely to win an argument, confusing the OP in the process?
Repeating the same misconception over and over doesn't make it true.Originally Posted by physicist
BTW, none of the names you have been dropping agrees with your claim. For example, you quote Pauli as supporting your claim but Pauli talks about velocity while you make claims about speed (see redline above).
Huh, so in the same post as denying that other people are using different definitions, you link me to a post where you actually point out that different definitions are in play.
I think earlier you said that the delay could be explained purely in terms of the extra distance travelled due to spacetime curvature. I'd like to explore that idea a bit further, so here are a couple of simple exercises for you. They concern the Schwarzschild solution in the usual spherical polar coordinates:
Now, consider two stationary observers () with radial coordinates (the first observer) and (the second observer), with . Assume they have the same angular coordinates, so that the second observer is in inferior conjunction from the point of view of the first. Given that setup:
 What is the proper length of the radial spacelike geodesic lying within a hypersurface of constant and going from the first observer to the second?
 If the first observer sends a light pulse to the second, who immediately reflects it back to the first, what is the roundtrip time of the pulse as judged by the first observer?
If you can't do them, just say. I'll post the answers if you want (if noone else does first).
Last edited by btr; 07052014 at 09:43 PM. Reason: Tidied up typesetting of metric and fixed a typo.
I linked you the post that corrects "physicist"'s misconceptions.Originally Posted by btr
I not only said that, I cited Rindler's solution. Page 237, his second edition book. I highly recommend it.I think earlier you said that the delay could be explained purely in terms of the extra distance travelled due to spacetime curvature.
. You , of all people, are in no position to give me "exercises". You need to take care of your own errors.I'd like to explore that idea a bit further, so here are a couple of simple exercises for you
1. What is the proper length of the radial spacelike geodesic lying within a hypersurface of constant and going from the first observer to the second?
Looked to me like you recognised that "coordinate speed" was something different from "locally measured speed", and thus acknowledged that there are different notions of "speed" in use in the discussions going on here.
You are referring to section 11.7, Isotropic metric and Shapiro time delay, right? Well, nowhere in that section does Rindler claim that the Shapiro delay can be accounted for by increased path length alone. He in fact obtains the travel time by approximating the pulse's path as a straight line along the direction in isotropic coordinates , and integrating an approximation of the following (first order in ) along the path:
Rindler (just like everyone else) is calculating the travel time by integrating the reciprocal of the spatially varying coordinate speed along the pulse's path, a speed which depends on both the spatial and temporal parts of the metric (as you can see from the above equation, and as he explicitly highlights towards the end of the section).
Perhaps you have a "special" version of the 2nd edition, in which case please do quote the relevant part here (it would count as fair use, I'm sure). Otherwise I have to conclude that you misread him as supporting your view of the Shapiro delay being purely due to extra distance being travelled.
That aside, I agree that the book is good and would also recommend it.
Is that a tacit admission that you are unable to answer the questions? Do you want me to walk you through the calculations?
Yes, I am, I just showed you. You are in no position to give me "exercises" , take care of your errors first.Ah, you edited your post after I replied (again). OK, that's the correct answer to one of my questions (kind of  you didn't actually evaluate the integral, but never mind). Are you able to answer the other?
I just showed you, now it is time for you to drop the arrogant attitude and take care of your errors.
Err, nowhere in the calculation does Rindler use "varying light speed". This is the point I made and this is the point that you keep missing. You are either missing it or you are just trolling.Well, nowhere in that section does Rindler claim that the Shapiro delay can be accounted for by increased path length alone.
You only answered one of the questions. I have a pretty good idea why, but let's see how things pan out.
I said, specifically, that he integrated the reciprocal of a spatially varying coordinate speed along the pulse's path.
Lo! In section 11.7 we see the following:
Unless you are arguing that is constant along the path, I think that should suffice.
Anyway, do you ever intend to back up your claim that Rindler computed the Shapiro delay by considering it to be purely an increase in travelled distance? Because there's still nothing from you on that front, I notice.
Rindler integrates dt as a variable of x along the geodesic path. This is what basic calculus says. You can stop trolling now and go take care of your earlier errors. You have no standing to give me "exercises".Originally Posted by btr
Frankly, based on your earlier errors, I don't think you have a clue:I have a pretty good idea why, but let's see how things pan out.
btr – This comment makes x0x a hypocrite because it was just recently he challenged me to provide the relationship between the magnitude of a uniform magnetic field, the proper mass of a charged particle, its charge and the radius that a charged particle moves in. So please feel free to give him “exercises” since he has no qualms about giving people who know the physics better than he does a test.Originally Posted by x0x
Btr – This comment about Rindler not specifically stating in the exact words that light slows down when moving through a gravitational potential is neither here nor there. It doesn’t matter to him whether he said it or not. After all he ignores what all the authorities on the subject have to say on it. For some bizarre reason that I’ve been unable to figure out, he expects everyone to ignore all the experts and authorities in mainstream GR/physics, ignore what the physics and calculations show and blindly accept what he tells us, hook, line and sinker. Why would anybody do that? Don’t forget that although Rindler didn’t speak of the varying speed of light to account for the Shapiro time delay, Shapiro himself stated so in no uncertain terms in both papers his team published on the experimental results.
x0x keeps insisting that the Shapiro time delay is due solely due to the increase in the spatial distance due to the presence of the sun, even though I proved to him that part of the change in dr/dt is due to gravitational time delay. As I’m sure we all know by now, x0x will ignore everything that proves him wrong in a heartbeat just as if it was never said whatsoever. That’s the reason he’s now in my ignore list. I won’t have anything to do with a member who has that habit. However let’s consider his claim in more detail. Farsight already pointed out to x0x that the portion of the time due to the increased spatial distance is very small compared to the entire time delay. However, as usual, x0x ignored him. However I did not.
Recall post 57 about where I quoted Shapiro’s paper Fourth Test of General Relativity: Preliminary Results by Shapiro et al, Phys. Rev. Letters. Vol 13(26), Dec. 28, 1964
In that article shortly below that comment the authors write the expression for the time delay in Eq. (1) which is defined as the difference between the propertime delay predicted in general relativity and the corresponding flat spacetime value. In the paragraph which follows the authors writeBecause, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby increase by almost sec when the radar pulses pass near the sun.
My prediction: I’m sure he’ll ignore this too, either he’ll claim that Shapiro himself doesn’t know what he’s talking about, we don’t understand what he means and only he does, or something else equally bizzare.The righthand of Eq. (1) is due primarily to the variable speed of the light ray; the contribution from the change in path, being second order in , is neglegible.
Actually, you did not. As a matter of fact, you did not post any math to support your claim.Originally Posted by physicist
It is very refreshing to see you and Farsight on the same page again.Farsight already pointed out to x0x that the portion of the time due to the increased spatial distance is very small compared to the entire time delay. However, as usual, x0x ignored him. However I did not.
The purpose of the exercise was to show that, contrary to your claims, particle physicists do know how to use relativity (and use it routinely). You promptly botched the answer to the very simple exercise pretty badly.This comment makes x0x a hypocrite because it was just recently he challenged me to provide the relationship between the magnitude of a uniform magnetic field, the proper mass of a charged particle, its charge and the radius that a charged particle moves in..... he has no qualms about giving people who know the physics better than he does a test.
Of course not, Rindler knows physics. So does d'Inverno. Unlike you they know the difference between velocity and speed. I tried to explain to you that the Shapiro delay is due to varying velocity of light and not, as you keep claiming, due to varying speed of light, just like Farsight.Originally Posted by physicist
Now, one could use the varying coordinate speed of light to do the calculations, just like Ruffini, this doesn't mean that the Shapiro experiment validates the notion of "varying speed of light". It is unfortunate that Shapiro wrote what he wrote but that was due to being sloppy.
Actually, it's neither. The Shapiro delay is due to the fact that null geodesics in a spacetime containing sources of energymomentum have a geometry that differs from a reference null geodesic in completely flat ( i.e. empty ) spacetime. No concept of speed or velocity is required to explain this. The increase in global coordinate speed as determined by far away observers is a result of the Shapiro effect, not its cause. This again comes down to how small local coordinate patches are related in a global chart; it's all just simple geometry. There is really no need to turn this into a big argument.the Shapiro delay is due to varying velocity of light and not, as you keep claiming, due to varying speed of light
Apologies, of course I meant to say decrease in coordinate speed. The edit button is not working for me at the moment.
Hi Marcus,the Shapiro delay is due to varying velocity of light and not, as you keep claiming, due to varying speed of light
You didn’t note who you quoted but it can only have been x0x. He’s in my ignore list because I got very tired of his inability to understand and accept the correct physics. Even given the fact that he’s clearly wrong about his claim that the Shapiro time delay is due to an increase in speed – as stated by Shapiro himself – he is unable to get it. Unless he’s confused between the difference between velocity and speed. It’s the speed that varies where the speed is the magnitude of velocity. If it was just the velocity that changed (i.e. direction) then nobody would care. Even in SR the velocity of light can change, i.e. it’s not invariant in SR. Only speed is invariant. However in GR it’s not invariant and changes when it moves into a region of space where there’s a gravitational potential. Nobody wouls say that light slows down in a gravitational field otherwise. Either he’s still unable to admit is mistake or he’s still unable to understand the physics. That's why I gave up on him. He only appears to want to agrue and make people think he's right about something. He doesn't seem all that interested in the correct physics because he's always ignoring derivations (but tosses out so wrong ones of his own.
Marcus – I obviously disagree with you as well for all the reasons I stated in this thread and for all the reasons given in the GR literature.
Your interpretation
is misguided. The Shapiro delay is due to the slowing of the speed of light. I’m sorry,. Marcus, but there’s just not talking your way around it. All you did here is given a description of why the light slows in terms of altered spacetime geometry. Please don’t tell me that you too believe that all the GR experts are unable to understand the difference between what you just said and what they teach in the textbooks they publish?Actually, it's neither. The Shapiro delay is due to the fact that null geodesics in a spacetime containing sources of energymomentum have a geometry that differs from a reference null geodesic in completely flat ( i.e. empty ) spacetime. No concept of speed or velocity is required to explain this. The increase in global coordinate speed as determined by far away observers is a result of the Shapiro effect, not its cause. This again comes down to how small local coordinate patches are related in a global chart; it's all just simple geometry. There is really no need to turn this into a big argument.
You either point out where I claimed that or you admit that you are just fabricating.Originally Posted by physicist
LOL. You are digging yourself deeper and deeper into your morass of misconceptions.Keep at it, you sound eerily like your buddy, Farsight.Marcus – I obviously disagree with you as well for all the reasons I stated in this thread and for all the reasons given in the GR literature.
Your interpretation
is misguided. The Shapiro delay is due to the slowing of the speed of light. I’m sorry,. Marcus, but there’s just not talking your way around it.Actually, it's neither. The Shapiro delay is due to the fact that null geodesics in a spacetime containing sources of energymomentum have a geometry that differs from a reference null geodesic in completely flat ( i.e. empty ) spacetime. No concept of speed or velocity is required to explain this. The increase in global coordinate speed as determined by far away observers is a result of the Shapiro effect, not its cause. This again comes down to how small local coordinate patches are related in a global chart; it's all just simple geometry. There is really no need to turn this into a big argument.
Agreed. This is what I have been telling the "physicist" for quite a while. It all started a few days ago, with post 58. Based on my experience, I don't think you'll get through though. Good luck trying!Originally Posted by Marcus Hanke
Hi Marcus,the Shapiro delay is due to varying velocity of light and not, as you keep claiming, due to varying speed of light
You didn’t note whom you quoted but it can only have been x0x. I forgot that I might see more of his erroneous comments when other people quote them. He’s in my ignore list because I got tired of his repetition of the same things when overwhelming proof was given to him to the contrary. E.g. even given the fact that he’s clearly wrong about his claim that the Shapiro time delay is due to an increase in speed – as stated by Shapiro himself – he is unable to admit that he’s wrong, unless, of course, he’s confused between the difference between velocity and speed. It’s the speed that varies and is what’s being measured where the speed is the magnitude of velocity. The speed is a function of the direction too. That could be what’s confusing him. After all that’s why all the experts, such as John Wheeler, make this point and describe this effect as the slowing of light in a gravitational field. The subject is so important that it’s called the Fourth Test of General Relativity and in his and Taylor’s book on GR they have an entire chapter on it entitled Light Slowed Near Sun. So, Marcus, if even Taylor and Wheeler think it’s important enough to write an entire chapter called Light Slowed Near Sun. Are you familiar with Schwarzschild coordinates? I assume you are since from your posts you seem very knowledgeable on the subject of GR and differential geometry. Am I correct on that too?
If it was just the velocity that changed (i.e. direction) then nobody would care. Even in SR the velocity of light can change, i.e. it’s not invariant in SR. Only speed is invariant. However in GR it’s not invariant and changes when it moves into a region of space where there’s a gravitational potential. Nobody would say that light slows down in a gravitational field otherwise. Either he’s still unable to admit is mistake or he’s still unable to understand the physics. That's why I gave up on him. He only appears to want to argue and make people think he's right about something. He doesn't seem all that interested in the correct physics because he's always ignoring derivations (but tosses out so wrong ones of his own.
Marcus – I disagree with your interpretation for all the reasons I stated in this thread and for all the reasons given in the GR literature. The Shapiro delay is due to the slowing of the speed of light. There’s just no talking around it. All you did was to provide the description of why the light slows in terms of the altered spacetime geometry. That’s a big difference in what you concluded. I don’t think you believe that all the GR experts are unable to understand the difference between what you just said and what they teach in the textbooks and journal articles they publish, do you?
Hi Marcus,the Shapiro delay is due to varying velocity of light and not, as you keep claiming, due to varying speed of light
You didn’t note whom you quoted but it can only have been x0x. I forgot that I might see more of his erroneous comments when other people quote them. He’s in my ignore list because I got tired of his repetition of the same things when overwhelming proof was given to him to the contrary. E.g. even given the fact that he’s clearly wrong about his claim that the Shapiro time delay is due to an increase in speed – as stated by Shapiro himself – he is unable to admit that he’s wrong, unless, of course, he’s confused between the difference between velocity and speed. It’s the speed that varies and is what’s being measured where the speed is the magnitude of velocity. The speed is a function of the direction too. That could be what’s confusing him. After all that’s why all the experts, such as John Wheeler, make this point and describe this effect as the slowing of light in a gravitational field. The subject is so important that it’s called the Fourth Test of General Relativity and in his and Taylor’s book on GR they have an entire chapter on it entitled Light Slowed Near Sun. So, Marcus, if even Taylor and Wheeler think it’s important enough to write an entire chapter called Light Slowed Near Sun. Are you familiar with Schwarzschild coordinates? I assume you are since from your posts you seem very knowledgeable on the subject of GR and differential geometry. Am I correct on that too?
If it was just the velocity that changed (i.e. direction) then nobody would care. Even in SR the velocity of light can change, i.e. it’s not invariant in SR. Only speed is invariant. However in GR it’s not invariant and changes when it moves into a region of space where there’s a gravitational potential. Nobody would say that light slows down in a gravitational field otherwise. Either he’s still unable to admit is mistake or he’s still unable to understand the physics. That's why I gave up on him. He only appears to want to argue and make people think he's right about something. He doesn't seem all that interested in the correct physics because he's always ignoring derivations (but tosses out so wrong ones of his own.
Marcus – I disagree with your interpretation for all the reasons I stated in this thread and for all the reasons given in the GR literature. The Shapiro delay is due to the slowing of the speed of light. There’s just no talking around it. All you did was to provide the description of why the light slows in terms of the altered spacetime geometry. That’s a big difference in what you concluded. I don’t think you believe that all the GR experts are unable to understand the difference between what you just said and what they teach in the textbooks and journal articles they publish, do you?
Hi Marcus,the Shapiro delay is due to varying velocity of light and not, as you keep claiming, due to varying speed of light
You didn’t note whom you quoted but it can only have been x0x. I forgot that I might see more of his erroneous comments when other people quote them. He’s in my ignore list because I got tired of his repetition of the same things when overwhelming proof was given to him to the contrary. E.g. even given the fact that he’s clearly wrong about his claim that the Shapiro time delay is due to an increase in speed – as stated by Shapiro himself – he is unable to admit that he’s wrong, unless, of course, he’s confused between the difference between velocity and speed. It’s the speed that varies and is what’s being measured where the speed is the magnitude of velocity. The speed is a function of the direction too. That could be what’s confusing him. After all that’s why all the experts, such as John Wheeler, make this point and describe this effect as the slowing of light in a gravitational field. The subject is so important that it’s called the Fourth Test of General Relativity and in his and Taylor’s book on GR they have an entire chapter on it entitled Light Slowed Near Sun. So, Marcus, if even Taylor and Wheeler think it’s important enough to write an entire chapter called Light Slowed Near Sun. Are you familiar with Schwarzschild coordinates? I assume you are since from your posts you seem very knowledgeable on the subject of GR and differential geometry. Am I correct on that too?
If it was just the velocity that changed (i.e. direction) then nobody would care. Even in SR the velocity of light can change, i.e. it’s not invariant in SR. Only speed is invariant. However in GR it’s not invariant and changes when it moves into a region of space where there’s a gravitational potential. Nobody would say that light slows down in a gravitational field otherwise. Either he’s still unable to admit is mistake or he’s still unable to understand the physics. That's why I gave up on him. He only appears to want to argue and make people think he's right about something. He doesn't seem all that interested in the correct physics because he's always ignoring derivations (but tosses out so wrong ones of his own.
Marcus – I disagree with your interpretation for all the reasons I stated in this thread and for all the reasons given in the GR literature. The Shapiro delay is due to the slowing of the speed of light. There’s just no talking around it. All you did was to provide the description of why the light slows in terms of the altered spacetime geometry. That’s a big difference in what you concluded. I don’t think you believe that all the GR experts are unable to understand the difference between what you just said and what they teach in the textbooks and journal articles they publish, do you?
The second time that you post this fabrication. You should retract and apologize.Originally Posted by physicist
You sound eerily like Farsight. Repeating the same misconceptions over and over doesn't make them right.Originally Posted by physicist
I disagree with this comment. I believe that you’re confusing spatial distances along a geodesic (which depends on your choice of coordinates) with the affine parameter (which isn’t coordinate dependant). Usually the affine parameter doesn’t have a physical meaning.Originally Posted by Markus Hanke
I have a question for those who claim that the speed of light varies in a gravitational field: Does the speed of light vary in an accelerated frame of reference in flat spacetime?
True, but neither does the fact that the line element between neighbouring points along a null geodesic is zero imply that the geodesic itself is of zero length between two distant events. It clearly isn't, since light evidently propagates at finite speed. All it really means is that we cannot use proper time to parametrise such null geodesics, since, as you correctly pointed out, proper time is not defined for light, only for the external observer who measures its speed.Usually the affine parameter doesn’t have a physical meaning.
No.
What we call "flat spacetime" relates to a region of space where the speed of light really is constant. So even if you were to measure the speed of light varying, it isn't really varying. It's the same general idea as measuring frequency. If you accelerate towards a light source, you'll measure the frequency increasing. But it hasn't actually increased.
Markus: it isn't just geometry. Like physicist has been saying, the speed of light varies. Read the OP again.
Physicist: light doesn't slow down because of gravitational time dilation. It's the other way round.
I suggest you and your buddy (the "physicist") pool your discoveries and write a paper together. For the time being, I move that the administrators move your thread into the "Personal Theories" forum, where it belongs. "Trash" would also be appropriate.Originally Posted by Farsight
That's fine, I wasn't looking for your agreement. I simply contributed my own take on the subject matter.Marcus – I disagree with your interpretation for all the reasons I stated in this thread and for all the reasons given in the GR literature.
I won't comment, since I prefer to let others be the judge of that. I find that people disagree on this  some think I am knowledgeable and insightful, others take me to be a mindless robot who just recites textbook dogma. Each one to his/her own. I consider myself to be an interested amateur with a certain level of knowledge that is nonetheless far from where I would like it to be.I assume you are since from your posts you seem very knowledgeable on the subject of GR and differential geometry.
This is true for global coordinate speed across an extended region, but not true for local proper speed in a small patch, so it depends which one it is you are considering. Note that instruments can only directly measure proper speed in a small region; such a notion as "coordinate speed" can be abstractly defined, but is not physically meaningful since there is no global notion of time that is valid everywhere. If you have two spatially separated emitters/receivers in a curved spacetime, what they record is an average speed calculated from their own local time measurements, which is not globally valid everywhere along the null geodesic  hence the variation in coordinate speeds. In my mind there is nothing wrong with considering this concept ( which is why people like Taylor/Wheeler use it on occasion ), so long as you understand its physical meaning, or rather its lack thereof. It's a bookkeeping device, nothing more.However in GR it’s not invariant and changes when it moves into a region of space where there’s a gravitational potential.
What I am suggesting is to do away with meaningless arguments over speed altogether, and simply consider the geometry of the null geodesic itself instead. Fix two distant reference points in flat Minkowski spacetime, and calculate the null geodesic intercepting both ( the embedding of which is just a straight line ). Now place a source of energymomentum anywhere in between, use the Einstein equations to derive a corresponding metric, and recalculate the null geodesic between the same two reference points. Compare the two geodesics, and take note of how they differ. You will find that this difference corresponds exactly to what is known as the Shapiro delay.
The crucial point in all of this is that the proper speed physically measured in a small region is always exactly c everywhere along the null geodesic, whereas the global geometry of the geodesic itself varies with sources of energymomentum as per the Einstein equations. Coordinate speed is not physically meaningful, simply because there is no such thing as global time in a curved spacetime, so how do you define such a notion as "speed" across an extended region ? It does not make physical sense; time  and thus speed  is always a purely local notion. Taking averages across extended regions is a nice little exercise in maths, but it does not have the same meaning as "speed" in the Newtonian sense. Have you ever wondered why Taylor and Wheeler call Schwarzschild coordinates "bookkeeper coordinates" ? It's precisely for this reason  they are a convenient mathematical device, but have no direct physical meaning. I quote from Taylor/Wheeler Exploring Black Holes, page 236 :
I fail to see why this needs to be such a bone of contention  all of this seems intuitively obvious, but then maybe that's just meThe strength of bookkeeper coordinates in universality; their weakness is isolation of most data entries from direct experience.
I meant to say they have no direct physical meaning in a global sense. Apologies, the edit button is still not working for me.
You are obviously aware that I know that, right? That kind of comment is intended as a leadin to what followed.Originally Posted by Markus Hanke
I’m sorry to see that you’ve had to face people who say things like that. It’s never called for. I see this kind of thing happen to all the physicists that I’ve met and know well. Usually it comes from people who aren’t trained in math or science and don’t understand the relationship between the two. Too many amateurs who haven’t had formal training in math and science don’t understand what it consists of and they erroneously think that we’re just required to absorb statements that our professors want us to believe whereas in reality they require us to be able to defend such statements from all angles and challenge those assertions. Since amateurs haven’t been through that grueling process for what seems like unending years, they’re unable to grasp it.Originally Posted by Markus Hanke
Anyway, sorry to hear that. I don’t think that of you or anybody else here, save one.
Plenty of themI’m sorry to see that you’ve had to face people who say things like that.
True. I should reiterate though that I am not formally trained in maths and physics myself either.Usually it comes from people who aren’t trained in math or science
But it is. The NIST optical clocks are in a small patch. One is 30cm below the other, and it runs slower. The same would be true of the gedanken parallelmirror light clocks. And there is no light flowing in these clocks, just light moving. If the local proper speed at light was constant in that patch the clocks would stay synchronised and your pencil wouldn't fall down.
It absolutely is. What isn't physically meaningful is using the motion of light to define your second and your metre and then using them to measure the speed of light. And saying it's always the same when it isn't. Like Magueijo and Moffat said, it's a tautology.
It doesn't matter. You don't need a global notion of time to see that the lower optical clock is going slower than the upper clock.Originally Posted by Markus Hanke
I think you're putting abstraction ahead of reality here. Spacetime is static, curved spacetime is a geometrical model. Your emitters/receivers are located in space. Light moves through that space, but there is no motion in spacetime. If the speed of light is uniform in that space, you'd talk of flat spacetime. If it isn't you'd talk of curved spacetime.Originally Posted by Markus Hanke
It does. But the light doesn't move through spacetime along a null geodesic. It moves through space. And it is delayed because it goes slower near the source of energymomentum.Originally Posted by Markus Hanke
This is a restatement of the above.Originally Posted by Markus Hanke
It's crucial for understanding gravity and black holes and other things too.Originally Posted by Markus Hanke
OK, show us an example. You keep making these claims without a) a detailed description of what you actually mean and b) without a way to test your interpretation.
Oddly, I have to agree with Farsight on this point: if one merely uses a tautology, then one is not going to introduce something physically meaningful. I also agree that one can measure the coordinate speed of light (indeed, all one can ever measure are coordinate times and coordinate distances!) but that these coordinates are best understood together with physics that accounts for differences in coordinate systems. Contemporary science does not simply use a tautology to describe the speed of light, it uses an operational definition that is amenable to revision. It follows the GR assumption about proper time that Farsight rejects.It absolutely is. What isn't physically meaningful is using the motion of light to define your second and your metre and then using them to measure the speed of light. And saying it's always the same when it isn't. Like Magueijo and Moffat said, it's a tautology.
Indeed. However, one needs a gross misunderstanding of GR to think that the time coordinates of every system of coordinates directly govern the behavior of optical clocks.It doesn't matter. You don't need a global notion of time to see that the lower optical clock is going slower than the upper clock.
This is clearly untrue: spacetime is the only means that we have of representing physical events. Without describing things using spacetime of some sort, there is no physics and there never has been. Perhaps one day FarsightRelativity will go beyond the fantasy stage and then we will see a physics without spacetime, but there is little reason to suspect this.I think you're putting abstraction ahead of reality here. Spacetime is static, curved spacetime is a geometrical model.
This too is a gross misunderstanding of GR and a flatout rejection of it.Your emitters/receivers are located in space. Light moves through that space, but there is no motion in spacetime.
Please show us the details.If the speed of light is uniform in that space, you'd talk of flat spacetime. If it isn't you'd talk of curved spacetime.
Again, a strange plea for an absolute reference frame that Farsight has never fully explained.It does. But the light doesn't move through spacetime along a null geodesic. It moves through space. And it is delayed because it goes slower near the source of energymomentum.
I've surely given enough with the Einstein quotes and the NIST optical clock reference and the gravity thread. A curvature of light can only occur when the speed of light varies with position. Light "veers" like a car veers when it encounters mud at the side of the road. Hence Ned Wright’s Deflection and Delay of Light: "the delay experienced by light passing a massive object is responsible for the deflection of the light”.
No, it simply uses a tautology. An amazing breathtaking cargocult tautologyOriginally Posted by PhysBang
Assume nothing. Go and look at what a clock really measures. There ain't no proper time flowing through it.Originally Posted by PhysBang
Nobody thinks that, surely. A concentration of energy usually in the form of a massive star "conditions" the surrounding space altering its properties. So light goes slower when it's lower, so light clocks go slower when they're lower, and we use rods and clocks to define our coordinate system. When lightclocks don't tick at the same rate we talk of curved spacetime.Originally Posted by PhysBang
Does not parse. Spacetime is just a static mathematical model, and the model works. But light doesn't move through spacetime, it moves through space.Originally Posted by PhysBang
No it isn't. Spacetime models space at all times. Think "block universe". It is totally devoid of all motion.Originally Posted by PhysBang
We've referred to this previously: Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime and to Einstein's Leyden address where he said space was inhomogeneous where a gravitational field is.Originally Posted by PhysBang
It isn't an absolute reference frame in the relativity sense.Originally Posted by PhysBang
You have never, ever posted a link that details your, friankly crazy, VSL theory. Certainly none that agrees with your claim that, "If the local proper speed at light was constant in that patch the clocks would stay synchronised and your pencil wouldn't fall down." It is a mistake that is not a stain on your character for you to say otherwise.
A reasonable basis to believe your claims about pencils would be to see that you can use your claims about VSL to describe the motion of a pencil.
However, given that you have displayed nothing but your own personal dogma and no coherent physics, I am betting that you have no reasonable basis for your belief and you cannot show even the beginnings of a reasonable basis to others.
That response is merely a non sequitor that avoids the issue. Not surprising.Assume nothing. Go and look at what a clock really measures. There ain't no proper time flowing through it.
You do: you claim that the time coordinates of the Schwarchild solution directly set the behavior of optical clocks.Nobody thinks that, surely.
In GR one does not always use rods and clocks to define coordinate systems.A concentration of energy usually in the form of a massive star "conditions" the surrounding space altering its properties. So light goes slower when it's lower, so light clocks go slower when they're lower, and we use rods and clocks to define our coordinate system. When lightclocks don't tick at the same rate we talk of curved spacetime.
You are ignoring all of physics. Spacetime is and has always been a requirement for the description of physical systems and events.Does not parse. Spacetime is just a static mathematical model, and the model works. But light doesn't move through spacetime, it moves through space.
You are mistaking the map for the territory.No it isn't. Spacetime models space at all times. Think "block universe". It is totally devoid of all motion.
It is not a stain in your character to offer this poor citation again: You need to show us directly how, "If the speed of light is uniform in that space, you'd talk of flat spacetime. If it isn't you'd talk of curved spacetime."We've referred to this previously: Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime and to Einstein's Leyden address where he said space was inhomogeneous where a gravitational field is.
You say this only because you do not understand.It isn't an absolute reference frame in the relativity sense.
That surprises me, and not much surprises me. It's so rare to see someone train themseleves like that. My compliments my good man!Originally Posted by Markus Hanke
Or very tall woman with short hair!
Hmmm...I can at this point now only suggest that you take a very careful look at your own statement above, and consider what is wrong with this. I can't really help you over and above this, given the rest of the comments.It doesn't matter. You don't need a global notion of time to see that the lower optical clock is going slower than the upper clock.
I'm looking at it. You have two NIST optical clocks in front of you, one 30cm below the other. They started off synchronised, but they don't stay synchronised. The lower clock reading starts to lag the upper clock reading. The lower clock goes slower.
Can we have some moderation here please? It was Einstein who said a curvature of rays of light can only occurs when the speed of light varies with position.Originally Posted by PhysBang
That would be good, maybe t would finally cut short your nonending stream of antiscience posts.Originally Posted by Farsight
Physics is not a collection of cherrypicked sound bites. The light rays "curve" because light rays follow (null) geodesics. These geodesics are not straight lines, they curve in the presence of gravitating fields. After all these years, you should have learned that much, Duffield.It was Einstein who said a curvature of rays of light can only occurs when the speed of light varies with position.
And it was you who, in the OP, claims that this means a scalar VSL like the citation you link to, despite Einstein never, ever using such a theory as you admit.
The moderators have stepped in and said that your constant presentation of first one thing and then another that directly contradicts your earlier claim is not a stain on your character.
I don't understand you comment here, PhysBang. Can you please clarify it for me please? Are you saying that Einstein never said that light slows down in a gravitational field or he didn't say if when his theory was competed in 1915?Originally Posted by PhysBang
PhysBang, you might want to pay attention to this:
This is utterly wrong. A null geodesic is an abstract line drawn in a static mathematical model called spacetime. Light doesn't move along a geodesic, and it doesn't move through spacetime. Instead it moves through space. And it curves because the speed of light varies with position. That's what Einstein said. That's what Ned Wright said too. See the OP. He's a physics/astronomy professor at UCLA. In his Deflection and Delay of Light he said this: "In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light”. Light doesn’t curve because it "follows a geodesic", and it doesn’t curve because spacetime is curved. Einstein never said that. One more time: it curves because the speed of light varies with position. Like sonar waves curve. Like this:
Also see what Don Koks said on the Baez website:
"Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers."
I'm saying that there is a significant difference between the changing of the speed of light in GR (as a coordinate speed) and the changing of the speed of light in the VSL theories discussed in Farsight's references and indeed by Farsight himself. I suspect this renders impossible the idea that Farsight's fantasies can even hope to produce something that might be called physics that matches the available evidence.
Seriously , Duffield?Originally Posted by Farsight
LOLLight doesn’t curve because it "follows a geodesic", and it doesn’t curve because spacetime is curved. Einstein never said that. One more time: it curves because the speed of light varies with position. Like sonar waves curve.
Hi PhysBang – I still don’t understand. Are you saying that you don’t accept that Einstein or modern mainstream physicists don’t accept the notion that light is refracted by the slowing of light in the gravitational field? Don’t make the obvious error that I expected x0x to make and assume that the bending is due to spacetime curvature and not to refraction (I gave up trying to get through to her). After all she’s once again making the same mistake that she always made. I.e. she keeps neglecting all the facts that demonstrate that her ideas are wrong. In this case her claim about light being bent by gravity being caused by spacetime curvature cannot work in general. If she tried that line of reasoning using the same situation used when he analyzed this then she’d use a uniform gravitational field and when that’s done you can’t blame the bending of light on either spacetime curvature or spatial curvature because a uniform gravitational field has no such curvature. It’s the same old thing with her. She’ll never learn.
Anyway, back to the problem – refraction of spacetime curvature  They aren’t different phenomena, they’re the same phenomena. I.e. two perfectly correct but different ways of describing exactly the same thing.
The deflection of light rays by the Sun due to null geodesics in a curved spacetime and light rays being due to refraction of the wavefront cannot be said to be different phenomena or different reasons for different phenomena. They are two equivalent ways of describing exactly the same thing. This was explained by Einstein and others in the GR literature since GR was created and is still described alternatively this way in GR texts today too.
Consider one of my favorite texts that you see me quote so often, i.e. Gravitation and Spacetime – Third Edition by Ohanian and Ruffini, (2014). On pages 133144 the authors write
Remember, this text wasn’t written for the amateur but with someone with some education in physics. That’s why the authors don’t explain why the deflection of light can be regarded as a refraction of the wavefront. That’s something you learned a long time before this.Originally Posted by Ohanian & Ruffini
Let’s trace Einstein’s thoughts on this: From On The Influence of Gravitation on the Propagation of Light, Albert Einstein, Annalen Der Physik, 35, 1911.
Einstein: "On the Influence of Gravitation on the Propagation of Light"
Einstein got the wrong value because at that time he didn’t know that radial distances would be altered by gravity, i.e. that space itself was curved by the sun. In his 1915 GR paper that was corrected.Originally Posted by Albert Einstein
From The Foundation of the General Theory of Relativity by Albert Einstein, Annalen der Physik, 49, 1916
The Foundation of the General Theory ... (1 to 3, of 22, 1916)
If everyone wants to get to the heart of this then I recommend stop using the gravitational field of the sun and earth because you won’t be able to narrow down the cause. Just like x0x did, you too can become confused as to the reason why light bends in a gravitational field. Once you analyze a uniform gravitational field, which has no spacetime curvature and you thus can’t blame the deflection on spacetime curvature, you’ll have to find the real reason. It’d be good for all of you to follow Einstein’s derivation from his 1911 paper.Originally Posted by Albert Einstein
Peter,Originally Posted by physicist
Repeating the same misconceptions, as you always do, doesn't make them right, you are just as wrong in this post as in the previous ones.
The gravitational field of the Sun is NOT uniform. The curvature of spacetime in the vicinity of the Sun is what produces the interesting effects (light bending, Shapiro delay). These effects do not exist in flat spacetime , therefore they do not exist in a uniform gravitational field. Please stop pushing your fringe misconceptions.If everyone wants to get to the heart of this then I recommend stop using the gravitational field of the sun and earth because you won’t be able to narrow down the cause. Just like x0x did, you too can become confused as to the reason why light bends in a gravitational field. Once you analyze a uniform gravitational field, which has no spacetime curvature and you thus can’t blame the deflection on spacetime curvature, you’ll have to find the real reason.
Well said Physicist. It's refreshing to bump into somebody who doesn't fall for the popscience nonexplanations that are trotted out in lieu of physics.
You will doubtless be aware that Einstein referred to Huygen's principle in the Foundation of the General Theory of Relativity. One can search the wikisource version, and copy and paste chunks of it fairly easily, putting tex brackets around the expressions and img brackets around an image:
Originally Posted by Einstein
Duffield,Originally Posted by Farsight
It is refreshing to see you and Peter M. Brown agree. Unfortunately, you agree on misconceptions.
I am still waiting for a description of how light moves through space.
If you really want to go on acting as though is somehow not the reciprocal of the pulse's coordinate speed, , by all means go for it.
Ray D'Inverno's derivation in section 15.6 of Introducing Einstein's Relativity would have been a far better example of how to do the calculation without explicitly using the coordinate speed of the signal. Working entirely in the Schwarzschild spherical polar coordinates, he eliminates the azimuthal degree of freedom by assuming a straightline path for the pulse, and thus obtains an ordinary differential equation of the form , which he then integrates. I think it is very much open to debate whether he does a "much cleaner job" than authors such as Rindler, who simply integrated the reciprocal of the coordinate speed of the pulse between the start and end points. For my money, Rindler's integral was far easier to perform.Originally Posted by x0x
That's incorrect, I'm afraid (which is quite amusing in light of your tone here). Could you walk us through how you arrived at that answer? I'm actually quite curious; it's almost like you were answering a question different from the one I asked.
To recap, the two questions I asked you (back in this post) were:
 What is the proper length of the radial spacelike geodesic lying within a hypersurface of constant and going from the first observer to the second?
 If the first observer sends a light pulse to the second, who immediately reflects it back to the first, what is the roundtrip time of the pulse as judged by the first observer?
You answered the first question with , which is almost correct (I'll let you off for the sign error caused by forgetting that , even though I know you despise "sloppiness"). For the benefit of anyone who wants to know where that comes from, you basically just set in the metric and integrate (given my sign convention) from to . I'll denote the correct answer to this question by :
The second question you answered incorrectly as , which is obviously wrong (consider what happens as ). We can get the correct answer like so: first, set in the metric, and deduce that the total coordinate time for the round trip is
bearing in mind again that . Next, to find the proper time elapsed in the first observer's frame (which is the quantity the question called for), we note that, since the observer is stationary, . Therefore,
which you can easily evaluate if you feel motivated to do so.
Now here's an interesting thing, which is actually the point I wanted to get to when I first asked you those questions. If you believe that the Shapiro time delay is "really" just due to the extra distance being travelled by the pulse, you are confronted here with having to explain why (in natural units). I discussed some issues with this earlier, but I wonder what your take on it will be.
You are downright trolling now, please feel free to put the integral within bars .Originally Posted by btr
Your integral blows up.The second question you answered incorrectly as , which is obviously wrong (consider what happens as ).
Like I said, given the gross errors that you made in this forum, there is little to no credibility to your claims.
My post 75 explains it quite well. In case you have difficulties, . Let me know if you have other difficulties understanding, I'll be happy to explain. I am quite puzzled by your inability to understand how the Shapiro delay is being calculated. Hint: you start with and integrate with respect to x. NB: the "t" in LHS is coordinate time, not clear why you were so preoccupied with proper time.If you believe that the Shapiro time delay is "really" just due to the extra distance being travelled by the pulse, you are confronted here with having to explain why (in natural units). I discussed some issues with this earlier, but I wonder what your take on it will be.
What puzzles me is that Rindler's text was simply a terrible example for someone to choose, if they hoped to illustrate that the Shapiro delay could be computed without using the variable coordinate speed explicitly. It is actually an excellent demonstration of precisely the opposite point: Rindler's calculation is quite transparently an integral of the reciprocal coordinate speed along the path!
So does C.M. Will in "Theory and Experiment in Gravitational Physics". Neither Rindler nor Will are crackpots that would appeal to the "varying (coordinate) speed of light" in their explanations. To wit, the term NEVER appears in either text (nor does it appear in the d'Inverno book). So, I am puzzled by your insisting along these fringe lines of argumentation.Originally Posted by btr
No worries  I already fixed your error for you.
Yes, expressing the physical fact that if you try to bounce a radar pulse off something on the event horizon, you'll be waiting a long time for it to return. You're equation predicts that the time doesn't blow up, which is wrong.
Nnnnnnnnnnnno I don't. Where on Earth did you get that idea from? I guess I'll have to spell it out a bit more explicitly:
Step 1: Set and in the metric to obtain
along the radial null geodesics. Rearrange and take the square root to obtain
which is justified since in the region of interest.
Step 2: Integrate the previous equation along both legs of the pulse's journey, to obtain
for the elapsed coordinate time. From here you can compute the elapsed proper time for observer 1 as before.
Now, where on Earth did you get your equation from? Where you thinking of a different problem?
I can't see anything in post #75 which explains why the roundtrip time judged by the first observer is not equal to twice the proper distance between the observers that we just computed. Post #75 doesn't even touch on the issue. Did you mean some other post? Could you quote the relevant bit that explains  specifically  why the roundtrip time judged by the first observer is not equal to twice the proper distance between the observers that we just computed?
Originally Posted by btr
Yes, your integral blows up, rendering your approach meaningless. At this point, I would suggest an introductory class in calculus.
It isn't a "physical fact", it is an artifact of you using a deficient mathematical approach.Yes, expressing the physical fact that if you try to bounce a radar pulse off something on the event horizon, you'll be waiting a long time for it to return. You're equation predicts that the time doesn't blow up, which is wrong.
At the start of section 11.7, Rindler points out that in isotropic coordinates "the coordinate speed of light [is] directionindependent", and uses this fact to simplify his derivation of the time delay. Note that he does not say "constant", but "directionindependent" (that's where the name "isotropic coordinates" comes from, just so you know). Are you seriously entertaining the idea that he believes that the coordinate speed of light is constant in isotropic coordinates? Even though he actually computed it's reciprocal further on in the same section as (plus higherorder corrections)?
Actually, let's take a step back. Do you understand what "coordinate speed of light" actually means?
What gives you this bright idea?Originally Posted by btr
(See the correction to my earlier post, due to misreading your claim slightly.)
Blowing up is the correct answer. If a photon is emitted from an object which is exactly on the event horizon (at the time of emission), that photon will never reach an observer in the region . So, in the limit as the time taken for the photon to return has to blow up. Your prediction, which you apparently came up with by applying a randomlychosen equation to the problem, is incorrect.
In any case, I spelled out the derivation of the correct answer for you, so you don't need to take my word for it; you just need to study the derivation until you appreciate how it works. If you insist on ignoring it, there's nothing I can do to help you.
You said neither Rindler nor Will are crackpots that would appeal to the "varying (coordinate) speed of light" in their explanations. Since Rindler quite clearly refers to the notion of the coordinate speed of light in his derivation of the Shapiro time delay, and since you have read that explanation and are aware of that fact, you must somehow believe that he is appealing to a constant coordinate speed of light. Or did you misspeak? You must have misspoke.
Given your gross errors in this forum, I see no reason to "study" anything that you post.Originally Posted by btr
Rindler does not appeal to any speed of light, coordinate or local in his derivation. You are arguing in the style of Farsight now , using cherry picked soundbites truncated to "prove" your misconceptions.At the start of section 11.7, Rindler points out that in isotropic coordinates "the coordinate speed of light [is] directionindependent", and uses this fact to simplify his derivation of the time delay.
The complete, untruncated quote is: "By a simple change of the radial coordinate (cf. exercise 11.3) we can recast the Schwarzschild metric (11.13) into the following so called isotropic form (which makes the coordinate speed of light direction independent):
"
Note that he never uses the speed of light (coordinate or local), he simply uses the metric in order to derive dt as a function of x.
I'm still waiting for your explanation on this point, x0x:
You do realise that it's wrong, surely? I mean, the fact that it predicts a finite return time for a signal bouncing off an object on the horizon should have been a dead giveaway, as should the fact that it doesn't even have the right asymptotic form at large radii.Originally Posted by btr
Edited to add:
To look at it yet another way, consider the limit as . Your formula blows up for all radii, while mine (which is to say, GR) predicts that the delay becomes proportional to the difference in radii, as we'd expect.
Or maybe you really do think the Shapiro time delay would be much greater if the Sun only had the mass of a proton?
You are getting really desperate in order to suggest such nonsense, m cannot be 0. You are piling up the errors.Originally Posted by btr
I start to see your new error, you are comingling the proper proper time for a light ray bouncing radially with the coordinate time in the Shapiro delay for a ray of light that follows a geodesic. Two very different things. Where did you go to school?Or maybe you really do think the Shapiro time delay would be much greater if the Sun only had the mass of a proton?
Unfortunately, to continue discussion with you, I'd have to at least believe that you believed in your claims. However, as erroneous as some of your previous posts have been, I still cannot bring myself to accept that you truly hold to the quite patently ludicrous position you attempt to defend here with this travesty of an argument.
Your formula, which you pulled out of thin air by the way, clearly predicts a time delay which increases without bound as the mass of the gravitating source goes to zero. I don't think for one minute you fail to see how wrong that is.
Here's your chance to prove me wrong. Let's see you actually use your formula to calculate the travel time for some values of the parameters. Let's say, for Earth and Venus at inferior conjunction, but with the Sun mass set to 1 kg. That should be enough to make the point.
Given the enormities that you have posted so far, I take your above post as meaningless trolling.
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