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Thread: The Varying Speed of Light

  1. #1 The Varying Speed of Light 
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    Have a look on arXiv for papers with variable light speed or varying speed light or VSL in the title. There's a fair few. One of my favourites is Comments on "Note on varying speed of light theories" where Joao Magueijo and John Moffat were having a bit of a dispute with George Ellis. They said this:

    "The unit of time is defined by an oscillating system or the frequency of an atomic transition, and the unit of space is defined in terms of the distance travelled by light in the unit of time. We therefore have a situation akin to saying that the speed of light is ďone light-year per yearĒ, i.e. its constancy has become a tautology or a definition"

    It's true. And in truth, the speed of light is not constant at all. It's easy to appreciate this once you appreciate that time travel is a fantasy. Because clocks donít literally measure the flow of time. A clock isn't some kind of cosmic gas meter with time flowing through it. Instead a clock "clocks up" some kind of regular cyclical motion and gives a cumulative display that we call the time. It's a simple little observation, but it leads you places.

    Youíll know about gravitational time dilation: clocks go slower when theyíre lower. We allow for this in GPS, and itís even detectable in a lab. See this interview with David Wineland of NIST: "if one clock in one lab is 30cm higher than the clock in the other lab, we can see the difference in the rates they run at". The clocks he's talking about are optical clocks. And like other clocks, optical clocks go slower when they're lower. And when a clock goes slower itís because the regular cyclic motion inside that clock is going slower. So what sort of regular cyclic motion might you find inside an optical clock? The motion of cogs? The motion of a quartz crystal? No. The motion of light. I know that goes against the grain of what people say about relativity. People say things like "Einstein showed us that the speed of light is constant". He did in 1905, when he was doing special relativity. But check this out:

    Quote Originally Posted by Einstein
    1911: "If we call the velocity of light at the origin of coordinates c₀, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = c₀(1 + Φ/c≤)Ē.

    1912: "On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential".

    1913: "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis".

    1915: "the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned".

    1916: ďIn the second place our result shows that, 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 and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with positionĒ.
    Thatís Einstein talking about the speed of light varying in a gravitational field. If you ask around about all this, some will brush it off by pointing to the word velocity. Theyíll say "Itís a vector quantity. Itís speed and direction. The velocity changes because the direction changes". But they're wrong. Go back to the original German, and what Einstein actually said was that a curvature of rays of light can only take place when "die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert". That translates to "the propagation speed of the light with the place varies". The word "velocity" in the English translations was the common usage, as in "high velocity bullet". This is crystal clear because Einstein referred to c which is the speed of light, and to "one of the two fundamental assumptions". Thatís the special relativity postulate of the constant speed of light.

    Have a read of Ned Wrightís Deflection and Delay of Light and note this: "In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the lightĒ. Light doesnít curve because it curves, and it doesnít curve because spacetime is curved. Einstein never said that. It curves because the speed of light varies with position. Like sonar waves curve. Like this:

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    And to really appreciate this, we use that old favourite, the parallel-mirror light-clock. Itís employed in the simple inference of time dilation due to relative velocity, which relates to Pythagoras's theorem. Imagine we use two parallel-mirror light-clocks instead of the NIST optical clocks to demonstrate gravitational time dilation. Then imagine we exaggerate everything and let you see the light. What youíd see is something like this:


    Image credit: Brian McPherson

    Yes it's exaggerated, and yes the mirrors should be tilted back a little, and yes the light pulses should curve a little. But those two light pulses arenít going at the same speed. If they were, the clocks would stay synchronised. They'd run at the same rate, only they don't. The rate varies because the speed varies. There's a variance. But the thing that affects the clock affects you too. So there's a "covariance" and so you don't notice the variation. Not many people do. Check out the NIST caesium fountain clock. Itís used to define the second, like so:

    "Since 1967, the second has been defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom".

    See that mention of radiation? Thatís light. Some will say thereís a peak frequency which is found and measured by the detector. But note that frequency is defined as cycles per second, and the second isn't defined yet. So what the detector effectively does is count incoming microwaves. When it gets to 9,192,631,770, that's a second. After that, the frequency is 9,192,631,770 Hertz by definition. Then we use the second along with light to define the metre, like so:

    "Since 1983 the metre has been defined as the distance travelled by light in vacuum in 1⁄299,792,458th of a second".

    We use the motion of light to define the second and the metre. And what do we use them for? To measure the motion of light. Thatís why we always measure the speed of light to be 299,792,458 m/s. But it isn't constant. If it was, we wouldn't have a Shapiro delay. Those NIST optical clocks would run at the same rate. And they don't. Because the coordinate speed of light varies in a non-inertial reference frame. Like in a gravitational field. Like in the room you're in. And the coordinate speed of light is the speed of light. The measured speed of light isn't. Like Magueijo and Moffat said, that's just a tautology. And when you appreciate that, and look at the evidence and what Einstein said, it's as plain as day that the speed of light is not constant. As obvious as the nose in front of your face. As obvious as your blind spot. Once you know how to look. Once you see the light.
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    Could you please demonstrate where, in GR, one would use the variable speed of light in a toy example with some numbers?
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    Not easily. See Note on Varying Speed of Light Cosmologies where George Ellis said this:

    "Any proposed variation of the speed of light has major consequences for almost all physics, as it enters many physics equations in various ways, particularly because of the Lorentz invariance built into fundamental physics (see [4] for discussion). One needs to take cognisance of the effects of this variation on the rest of physics".

    It's as if General Relativity is presented from "your viewpoint" rather than "the God's eye view". Hence we see c in the expression below:

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    So, what you are saying is that the varying speed of light plays no role in GR as Einstein wrote it or as practiced in physics today?
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    This boils down to the exact same distinction between GLOBAL and LOCAL that I have been referring to on many previous occasions. For a far-away observer, if he sends a light signal past a massive body, he will determine the speed of light to be diminished GLOBALLY over its entire trajectory - a phenomenon well-known as the Shapiro delay. However, any observer placed along the trajectory will, in his/her own frame of reference, LOCALLY measure the light speed to be exactly c, everywhere and always.

    Distant measurements = coordinate measurements -> coordinate speed of light < c globally
    Local measurements = proper measurements -> proper speed of light = c everywhere locally

    This is not a contradiction, since the null geodesic that represents light does not have the same geometry around the massive body as a reference null geodesic in the absence of any source of energy-momentum does. In curved space-times, coordinate speed and proper speed are physically distinct concepts.
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    Quote Originally Posted by Physbang
    So, what you are saying is that the varying speed of light plays no role in GR as Einstein wrote it or as practiced in physics today?
    Almost. What I'm saying is the varying speed of light plays no role in GR as practiced in physics today. Even though Einstein referred to it repeatedly, and the hard scientific evidence demonstrates it.

    Quote Originally Posted by Markus Hanke
    This boils down to the exact same distinction between GLOBAL and LOCAL that I have been referring to on many previous occasions. For a far-away observer, if he sends a light signal past a massive body, he will determine the speed of light to be diminished GLOBALLY over its entire trajectory - a phenomenon well-known as the Shapiro delay. However, any observer placed along the trajectory will, in his/her own frame of reference, LOCALLY measure the light speed to be exactly c, everywhere and always.
    Exactly.

    Quote Originally Posted by Markus Hanke
    Distant measurements = coordinate measurements -> coordinate speed of light < c globally
    Local measurements = proper measurements -> proper speed of light = c everywhere locally
    No problem. The problem is that people say the speed of light is absolutely constant. When actually the locally measured speed of light is constant. Because wherever you go, you're in a place "where electromagnetic radiation and matter may be equally affected, since they are made of the same essence". Light slows down and so do you and your clocks, so you measure the same value.

    Quote Originally Posted by Markus Hanke
    This is not a contradiction, since the null geodesic that represents light does not have the same geometry around the massive body as a reference null geodesic in the absence of any source of energy-momentum does. In curved space-times, coordinate speed and proper speed are physically distinct concepts.
    There's no contradiction. But IMHO there is misunderstanding. Particularly when it comes to black holes. We'll come back to them at a future date. It's all tied in to why doesn't the light get out? And then like I was saying on another thread, there's are similarities between black holes and the early universe, so there's even more reason to get this stuff nailed down.
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    Quote Originally Posted by Farsight View Post
    Almost. What I'm saying is the varying speed of light plays no role in GR as practiced in physics today. Even though Einstein referred to it repeatedly, and the hard scientific evidence demonstrates it.
    Now what you are saying seems deceptive. I ask you for a simple example of where one can find this in GR, and you say it is too complicated to do. Yet now you claim not only that this is something in the original Einstein, but that there is hard scientific evidence.

    So, please, do a simple example in the original Einstein. Aster that we can begin looking at the supposed evidence. I would hate for it to appear that you are trying to deceive us.
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    There's no deception on my part. I've given you the Einstein quotes and the references to Magueijo and Moffat and Ellis. And we all know that the coordinate speed of light varies with gravitational potential. But like I said, General Relativity is presented from "your viewpoint" rather than "the God's eye view". The laws of nature are expressed by means of equations which are valid for all co-ordinate systems. They aren't expressed by means of equations that transcend co-ordinate systems.
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    So you are admitting that there is no evidence for your assertion that light "curves because the speed of light varies with position"? Thank you.
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    No. The evidence is patent. And it isn't my assertion. It's Einstein's.
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    Quote Originally Posted by Farsight View Post
    No. The evidence is patent. And it isn't my assertion. It's Einstein's.
    OK, so you should be able to do a simple GR problem, using Einstein's equations, that use the variable speed of light.

    You do have some reason, in physics, for making your claim, right?

    While the moderators have pointed out that there is a difference between lying and merely being mistaken, if you have been making claims to us about physics and evidence without having a reason, in physics, you are certainly more than mistaken.
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  13. #13  
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    Quote Originally Posted by Farsight View Post
    General Relativity is presented from "your viewpoint" rather than "the God's eye view".
    The covariant equations are not presented from any particular point of view. That is the whole point of covariance.


    Quote Originally Posted by Farsight View Post
    The laws of nature are expressed by means of equations which are valid for all co-ordinate systems. They aren't expressed by means of equations that transcend co-ordinate systems.
    Can you explain the distinction?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by PhysBang
    OK, so you should be able to do a simple GR problem, using Einstein's equations, that use the variable speed of light.
    I'm afraid not. Take for example which you can find as equation 75 in The Foundation of the General Theory of Relativity. It's got a c in it. Because the equations of motion are from "your viewpoint" rather than "the God's eye view".

    Quote Originally Posted by PhysBang
    You do have some reason, in physics, for making your claim, right?
    Yes. Once you understand what Einstein was saying you understand gravity, utterly. Then you understand something about black holes, then you understand something about the early universe.

    Quote Originally Posted by PhysBang
    While the moderators have pointed out that there is a difference between lying and merely being mistaken, if you have been making claims to us about physics and evidence without having a reason, in physics, you are certainly more than mistaken.
    Einstein said what he said. So did Magueijo and Moffat and Ellis and Wineland. Optical clocks run slower when they're lower. Parallel-mirror light clocks do too. And there isn't any literal time flowing through those clocks. A clock is not some kind of cosmic gas meter. It doesn't really measure the flow of time. And we do physics to gain understanding. That's reason enough.
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    Quote Originally Posted by KJW
    The covariant equations are not presented from any particular point of view. That is the whole point of covariance.
    I know. The idea is that they work for you wherever you are.

    Quote Originally Posted by KJW
    Can you explain the distinction?
    I quoted Einstein when I said the laws of nature are expressed by means of equations which are valid for all co-ordinate systems. Ask yourself this: what's a coordinate system? You can't point up to the clear night sky and say look, there's a coordinate system. Because a coordinate system is an abstract thing. To "transcend co-ordinate systems" your equations would be based on things that are actually there, instead of abstract things that are not. And what is there? Remember what I was saying on the other thread? At the fundamental level what you've got is energy stroke space and waves running through it. In a way, that's all that's there, because everything is made of this. Have a look at The Other Meaning of Special Relativity by Robert Close. He uses the wave nature of matter to explain why you always measure the speed of light to be the same. When you're made of waves, and your rods and clocks are made of waves too, it doesn't matter what you do. It doesn't matter how you move. It doesn't matter how fast those waves move. You always measure the local speed of waves to be the same. Because you calibrate your rods and clocks using the motion of waves, then use them to measure the motion of waves.

    But I don't know how to make the distinction by recasting GR into that God's eye view where c is the coordinate speed of light instead of the locally-measured speed of light.
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    Quote Originally Posted by Farsight View Post
    I'm afraid not. Take for example which you can find as equation 75 in The Foundation of the General Theory of Relativity. It's got a c in it. Because the equations of motion are from "your viewpoint" rather than "the God's eye view".
    This seems to be evidence that you have, in fact, deceived us in your original post.

    You wrote that, "Einstein never said that. It curves because the speed of light varies with position." You were here, and at other places, implying that Einstein's theory of gravity and spacetime works through a variable speed of light.

    So far, your only support from the physics of Einstein is physics that takes the speed of light to be constant; the opposite of your claim.

    Yes. Once you understand what Einstein was saying you understand gravity, utterly. Then you understand something about black holes, then you understand something about the early universe.
    This would seem, given what you have produced so far, to be untrue and that you must know this to be untrue. If there was a reason in the physics, then we would see the variable speed of light at work. Yet you are now seeming to claim that there is no role for the variable speed of light in any application in physics.
    Einstein said what he said.
    Indeed he did: he also wrote an entire theory of gravity using only the constant speed of light. It seems that despite your claims that Einstein used a variable speed of light in his physics of GR, you personally know of no physics done by Einstein with such light. I am curious as to how you justify making a claim to us that you know to be untrue.
    And we do physics to gain understanding. That's reason enough.
    Apparently, you post on message boards to stymie understanding: you have made a claim that you know to be false.

    Perhaps you meant to claim that Einstein wanted to make a variable speed of light theory and he failed?
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    Everyone, please remember that "speed" is a concept that is not as straightforward as it would initially seem, because we need to distinguish between coordinate speed and proper speed. In curved space-times, the coordinate speed of light does indeed vary, but proper speed does not. It is now crucial to understand that there isn't a contradiction between these.
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    There is no contradiction Markus, but there is something of an issue with "in curved space-times". It's a chicken-and-egg thing. And crucial. I'll try to bring this out in the next thread. NB: sorry I've been away for a couple of days.

    PhysBang: I refuse to conduct a conversation with somebody who is repeatedly accusing me of lying. Please desist. Instead please address the points of discussion with sincerity.
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    Quote Originally Posted by Farsight View Post
    PhysBang: I refuse to conduct a conversation with somebody who is repeatedly accusing me of lying. Please desist. Instead please address the points of discussion with sincerity.
    I am simpy confused as to why you seem unable to provide the most basic piece of evidence for your incredibly controversial claims. Indeed, you do not seem to be addressing the points of this discussion seriously.

    Can you please show us a GR example where the variable speed of light is used? If there are no such examples, then why do you claim that there are, contrary to every reputable source on GR?
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    Quote Originally Posted by Farsight View Post
    PhysBang: I refuse to conduct a conversation with somebody who is repeatedly accusing me of lying. Please desist. Instead please address the points of discussion with sincerity.
    I am simpy confused as to why you seem unable to provide the most basic piece of evidence for your incredibly controversial claims. Indeed, you do not seem to be addressing the points of this discussion seriously.

    Can you please show us a GR example where the variable speed of light is used? If there are no such examples, then why do you claim that there are, contrary to every reputable source on GR?


    Rich L. Comment: PhysBang, I'm not quite sure what special point Farsight is trying to make, but I think poor terminology is at the heart of this debate. In Special Relativity, which applies in flat space time everywhere, or in a local (spatially restricted) volume in a free falling frame in General Relativity, the speed of light is a constant. In General Relativity however, which applies to curved spacetimes, it is a little more complicated. Any observer measuring the speed of light locally (i.e. right where he is at, over a short distance) will ALWAYS measure the universal speed of light, "c". However if he sends a pulse of light into (or out of, or through) a gravitational field he will notice that the pulse of light actually traverses the space either faster or slower than "c".

    For example, consider someone orbiting a black hole. Suppose they lower a mirror on a cable 100km down towards the event horizon. If they send a pulse of light down to the mirror and then back up to the start, the pulse of light will take LONGER than 200km/c to return. On the other hand, if an experimenter with a timer was lowered down to that mirror, he would measure a SHORTER time for the pulse to go up to the start and then come back down again. Yet if this lower observer were to measure the speed of light at the lower mirror (using a much smaller optical path), he would measure the speed of light as "c".

    This can be understood in terms of the gravitational red shift. Consider two mirrors, one at the top of a tower and the other at the bottom. Send a pulse of light from the lower mirror to the upper, back down to the lower where it is reflected up again, etc. etc. The light bouncing up and down will have a specific frequency. Suppose it is f1 when measured at the bottom mirror. This could be done by making the mirror very slightly transparent and monitoring the pulses on a photo diode behind the mirror. At the upper mirror this frequency will be gravitationally red shifted just like light is, so if a photo diode was used to measure the pulse frequency at the upper mirror they would measure a frequency f2 < f1 at the upper mirror. The ratio of these frequencies is equal to the square root of the ratio of the g_00 metric components.

    But both experimenters, the one at the top and the one at the bottom, will agree about the distance between the mirrors. Therefore they will conclude that the speed of light is different when going between these two mirrors. The upper person will conclude that the speed of light was less than "c" during their experiment, while the lower person will conclude that the speed of light was greater than "c". Yet in both cases, if they were to measure the speed of light at each of their levels, they would get exactly "c". This is all standard GR and there is nothing mysterious about it.

    Rich L.
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    Quote Originally Posted by Rich L. View Post
    I'm not quite sure what special point Farsight is trying to make
    I believe he is trying to argue that coordinate measurements are physically privileged, and that proper measurements ( i.e. locally constant c ) are merely mathematical artefacts.
    Correct me if I am wrong, Farsight.
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    I'm not sure I'd use those words, Markus. But yes, it's something like that. We know that 1) we always measure the local speed of light to be the same. And that 2) the coordinate speed of light varies in a gravitational field. Like Rich says, this is all standard GR and there is nothing mysterious about it. But what's not standard is the idea that we should give some priority to 2. Because we use the local motion of light to calibrate our rods and clocks, which we then use to measure the local speed of light. So we will always measure the local speed of light to be the same. Even when it isn't.
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    Farsight,

    You said "So we will always measure the local speed of light to be the same. Even when it isn't."

    I would argue with the "when it isn't" part. I approach physics from a very physical point of view, and not so much mathematical. It is clear that different observers with different reference frames and thus different coordinates will describe phenomena differently. The key thing is that they are all "correct". There isn't one correct description of anything in GR unless you make it so abstract (i.e. tensor equations that apply to all coordinate systems) that it is difficult to relate back to what individual experimenters would measure or observe. Once you start to talk about the speed of light, you need to be very specific about who is measuring it and where they are located. The fact that their measurement differs from someone elses does not make either of those measurements incorrect. I disagree that the coordinate speed of light should be given priority because any coordinate system is to some degree arbitrary. There are other coordinates that could be used to map the space described by the Schwarzschild metric, and the resulting coordinate speeds of light would be different.

    I would agree, however, that it can be useful to translate all phenomena to a single coordinate system (or to a single observers point of view), solve some problem in that frame and then translate it back to a particular local observer. If that is what you are saying, I might agree with that. But I would still not call the coordinate speed of light more correct.
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    Is it a mistake to say that the foundation of the particular covariance in GR is that the speed of light is the same in all local regions? That is, doesn't the constant speed of light in local areas of the manifold of spacetime form the basis of the causal structure that allows one to create physically correct transformations between one system of coordinates and another?
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    Quote Originally Posted by Rich L.
    You said "So we will always measure the local speed of light to be the same. Even when it isn't."

    I would argue with the "when it isn't" part. I approach physics from a very physical point of view, and not so much mathematical.
    Me too. Look at the second post, and the parallel-mirror gif. At both elevations you will measure the local speed of light to be 299,792,458 m/s. The second at one elevation is not the same as the second at the other. So the two speeds are not the same. If they were, the clocks would stay in sync. The horizontal metre doesn't change by the way.



    Quote Originally Posted by Rich L.
    It is clear that different observers with different reference frames and thus different coordinates will describe phenomena differently. The key thing is that they are all "correct". There isn't one correct description of anything in GR unless you make it so abstract (i.e. tensor equations that apply to all coordinate systems) that it is difficult to relate back to what individual experimenters would measure or observe. Once you start to talk about the speed of light, you need to be very specific about who is measuring it and where they are located. The fact that their measurement differs from someone elses does not make either of those measurements incorrect. I disagree that the coordinate speed of light should be given priority because any coordinate system is to some degree arbitrary. There are other coordinates that could be used to map the space described by the Schwarzschild metric, and the resulting coordinate speeds of light would be different.
    The important point is that the various observers will agree that clocks go slower when they're lower. GR time dilation isn't like "the twins" SR time dilation. If you and I are moving fast past one another, I say your clock's going slower than mine, and you say my clock's slower than yours. It isn't like that for general relativity. The symmetry isn't there. If I'm lower than you, we both agree that it's my clock going slower than yours. And it's a light clock. You can fiddle around with fast-moving observers at different gravitational potentials, but it starts getting contrived. Also note that light moving through space is something real, but a coordinate system is just an abstract thing. I could point up to the clear night sky and show you some laser beam, but you can't do the same for a coordinate system.

    Quote Originally Posted by Rich L.
    I would agree, however, that it can be useful to translate all phenomena to a single coordinate system (or to a single observers point of view), solve some problem in that frame and then translate it back to a particular local observer. If that is what you are saying, I might agree with that. But I would still not call the coordinate speed of light more correct.
    I'm not sure that's how I'd put it. But nevermind, have a think about what a clock actually does, see this.
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    Quote Originally Posted by Farsight View Post
    The important point is that the various observers will agree that clocks go slower when they're lower. GR time dilation isn't like "the twins" SR time dilation. If you and I are moving fast past one another, I say your clock's going slower than mine, and you say my clock's slower than yours. It isn't like that for general relativity. The symmetry isn't there. If I'm lower than you, we both agree that it's my clock going slower than yours. And it's a light clock. You can fiddle around with fast-moving observers at different gravitational potentials, but it starts getting contrived. Also note that light moving through space is something real, but a coordinate system is just an abstract thing. I could point up to the clear night sky and show you some laser beam, but you can't do the same for a coordinate system.
    This discussion seems to be devoid of most of the physics that is actually going on;; one of the reasons I asked for an actual example with the physics worked out. While different systems of coordinates can agree on which clock moves slower, it is neither part of GR that a) one clock is moving the "true" rate or a "truer" rate, nor part of GR that b) the true reason for the difference is the slowing of light.

    I suspect that there is no case where one can use GR to describe a toy model where the slowing of the speed of light is a part of the translation from one set of coordinates to another or part of the calculation of the dynamics of the model.
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    Quote Originally Posted by Physbang
    ...it is neither part of GR that a) one clock is moving the "true" rate or a "truer" rate, nor part of GR that b) the true reason for the difference is the slowing of light.
    But gravitational time dilation is a part of GR. As is clocks go slower when they're lower. Only when you open up one of those clocks, you don't see time going slower. You don't see time going at all.

    Quote Originally Posted by Physbang
    I suspect that there is no case where one can use GR to describe a toy model where the slowing of the speed of light is a part of the translation from one set of coordinates to another or part of the calculation of the dynamics of the model.
    Maybe. Because when the light goes slower you go slower too, along with all electromagnetic and presumably other processes. So you don't see the light going slower. As for toy models, here's one: the God's eye global gist of general relativity. You can use this varying speed of light to gain an understanding of how gravity actually works. Imagine Einstein talking in his deep guttural voice: a curvature of rays of light can only take place when the propagation speed of light with the place varies. Then apply the wave nature of matter.
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    Quote Originally Posted by Farsight View Post
    But gravitational time dilation is a part of GR. As is clocks go slower when they're lower. Only when you open up one of those clocks, you don't see time going slower. You don't see time going at all.
    Yes, and the reason for this according to GR is that there is a local time and a local speed of light that determines the physics and the proper transformation from one system of coordinates to another. So far you have claimed that there is an alternative but offered no evidence of how one would go about using this alternative in physics.

    Maybe. Because when the light goes slower you go slower too, along with all electromagnetic and presumably other processes. So you don't see the light going slower. As for toy models, here's one: the God's eye global gist of general relativity.
    That fails as a toy model. Please show us some numbers.

    You can use this varying speed of light to gain an understanding of how gravity actually works.
    Only if one can do physics with it. So please demonstrate.
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    Quote Originally Posted by Farsight View Post
    But what's not standard is the idea that we should give some priority to 2.
    No, it's definitely not standard, because it violates the principle of general covariance. No frame of reference is somehow physically "privileged". This is why you can use a different way to label your events ( i.e. a different coordinate system ), and see the coordinate singularity at the event horizon disappear.

    But gravitational time dilation is a part of GR. As is clocks go slower when they're lower.
    Yes, we already agreed on these things long ago. The point is that a clock going slower is a coordinate measurement performed by an external observer ( refer to the animation I linked to ); someone falling together with the clock will never see it slow down at all. The important thing to understand is that both these observers are right.
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    So along these lines would it be correct to say that an observer might observe the speed of light to be slower as it passes though an area of stronger gravitational field?
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    Quote Originally Posted by Jilan View Post
    So along these lines would it be correct to say that an observer might observe the speed of light to be slower as it passes though an area of stronger gravitational field?
    Yes, if by "stronger" you mean deeper in the gravitational field than the observer. The key thing is the relative values of the g_00 metric components at the observer and where he is trying to measure the speed of light.

    BTW, you have to be a bit careful about what you mean by the speed of light (and many other things in GR) when talking about measuring a property at a location different from the observer. There is no unique direct way to relate your meter stick at your location to that at a different location, for example. You can take you meter stick to that location, but then you are there, not at your original location. Things get a bit more complicated when you consider something like electric currents and the magnetic fields they produce. What is the meaning of current at one location when it is being observed (i.e. the magnetic field being measured) at a different location. In flat space-time this is all easy, but in curved space-time it is a lot more complicated.
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    Quote Originally Posted by Markus Hanke
    No, it's definitely not standard, because it violates the principle of general covariance. No frame of reference is somehow physically "privileged".
    Tell yourself it's in line with the principle because it's taking a global "all frames" view.

    Quote Originally Posted by Markus Hanke
    This is why you can use a different way to label your events ( i.e. a different coordinate system ), and see the coordinate singularity at the event horizon disappear.
    No you can't. And the reason for that is a real Lulu. You'll kick yourself when you see it.

    Quote Originally Posted by Markus Hanke
    Yes, we already agreed on these things long ago. The point is that a clock going slower is a coordinate measurement performed by an external observer ( refer to the animation I linked to ); someone falling together with the clock will never see it slow down at all. The important thing to understand is that both these observers are right.
    And you never see yourself fall asleep. Think about the gedanken SR observer travelling at c. What does he see?
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    Quote Originally Posted by Farsight View Post
    No you can't. And the reason for that is a real Lulu. You'll kick yourself when you see it.
    It is fascinating for you to imply that you are smarter than anyone doing physics for most of the last century while at the same time refusing to do the most basic of physics calculations. Perhaps you would like to show us what mistake everyone has been making when attempting to use other coordinate systems?
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    Quote Originally Posted by Farsight View Post



    The second at one elevation is not the same as the second at the other. So the two speeds are not the same. If they were, the clocks would stay in sync.

    This is begging the question. In making the above statement, you are implicitly assuming that time is the same at both levels. By rejecting this assumption, your conclusion becomes invalidated.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    It isn't begging the question. The second is defined using the motion of light in a NIST clock. There is no time flowing in a clock.
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    Tell yourself it's in line with the principle because it's taking a global "all frames" view.
    But it doesn't, that's the point. The external observer uses a coordinate system that enables him to assign labels to events from the point of view of his particular frame of reference. The same holds true for every other observer. No observer is any more or less "global" than any other observer. In fact there is no inherent difference between observers at all, in the same way as there is no inherent difference between measuring your commute to work in miles or in kilometres. They are just different ways to label the same events. This is precisely the principle of general covariance, and it is precisely why you can't pick a specific coordinate system at random and claim that this is physically privileged over other coordinate systems - which seems to be what you are doing.

    So long as you agree that GR is a good model, and that you consider yourself a relativist and an adherent to Einstein, you cannot at the same time decide to abandoned general covariance - it is one of the fundamental building blocks of the model.

    No you can't.
    Farsight, the Einstein equations are manifestly covariant, so of course you can pick a different coordinate system without affecting the physics. That's kind of the whole point of the model, and is hardly subject to debate.

    Think about the gedanken SR observer travelling at c. What does he see?
    There are no observers that travel at c, so the question is moot. There are however observers that determine other observers to be travelling at c in a remote frame; such observers could in principle be "seen", but their speed in nonetheless inferred since it cannot be directly measured. For example, an observer who somehow manages to remain stationary at the event horizon will determine another observer freely falling past him at the speed of light, and then continue his plunge downwards. If that free-fall started at rest very far away such a free-fall frame is called a "rain frame", and the time it takes to get from radius (1) to radius (2) is



    in geometrised units. Crunching the numbers based on this, it takes



    to fall from rest at infinity into the centre of the black hole, and it takes



    to fall from rest at the event horizon into the centre, in terms of ratios between black hole mass and solar mass ( again, all in geometrised units ).

    This is all just more or less straightforward calculus; what you appear to be trying to do is declare this "unphysical", based on the fact that a far-away external observer disagrees with these determinations. However, the principle of general covariance immediately invalidates any such attempt, because going from a far-away rest frame into a local rain frame is a simple coordinate transformation from Schwarzschild to Gullstrand-Painleve coordinates; it represents the same geometry of space-time, just with a different way to assign labels to events. The same holds true for any other frame, whether stationary or in motion.
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    Quote Originally Posted by Farsight View Post
    It isn't begging the question.
    It is. You've chosen a criterion (the clocks would stay in sync) to satisfy your conclusion (different speeds of light).


    Quote Originally Posted by Farsight View Post
    The second is defined using the motion of light in a NIST clock.
    Since 1967, the second has been defined to be:

    the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom

    In 1997, the CIPM affirmed that the preceding definition refers to a caesium atom at rest at a temperature of 0 K.

    (from Wikipedia)

    There is no reference to any motion of light. You are apparently confusing this with the definition of the metre.


    Quote Originally Posted by Farsight View Post
    There is no time flowing in a clock.
    There is no space flowing in an odometer but this doesn't stop it from measuring distance.
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    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW
    It is. You've chosen a criterion (the clocks would stay in sync) to satisfy your conclusion (different speeds of light).
    Think of mechanical clocks. If one clock is going faster than the other, it's because its cogs are going faster. Then think of quartz wristwatches. If one watch is going faster than the other, it's because its crystal is vibrating faster. And so on. You do the same with light clocks. Whatever sort of clock you use, there's never any time flowing through it.

    Quote Originally Posted by KJW
    Since 1967, the second has been defined to be:

    the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom

    In 1997, the CIPM affirmed that the preceding definition refers to a caesium atom at rest at a temperature of 0 K.

    (from Wikipedia)

    There is no reference to any motion of light. You are apparently confusing this with the definition of the metre.
    I'm not confusing it. Imagine you're in a boat counting waves passing beneath you. Your boat bobs up then down: one, your boat bobs up then down: two, your boat bobs up then down: three. Now imagine you have electromagnetic waves coming at you rather than water waves. You count up to 9192631770 and then you declare that a second has elapsed. If the waves are coming at you slower your second is bigger.

    Quote Originally Posted by KJW
    There is no space flowing in an odometer but this doesn't stop it from measuring distance.
    Like a clock an odometer displays a cumulative measure of motion.
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    Quote Originally Posted by Markus Hanke
    But it doesn't, that's the point. The external observer uses a coordinate system that enables him to assign labels to events from the point of view of his particular frame of reference. The same holds true for every other observer. No observer is any more or less "global" than any other observer. In fact there is no inherent difference between observers at all, in the same way as there is no inherent difference between measuring your commute to work in miles or in kilometres. They are just different ways to label the same events. This is precisely the principle of general covariance, and it is precisely why you can't pick a specific coordinate system at random and claim that this is physically privileged over other coordinate systems - which seems to be what you are doing.
    I don't intend to do that. Instead I intend to look at multiple coordinate systems side by side. The parallel-mirror gif is a simple example of this. It's an idealisation of the NIST optical clocks that run at different rates when one is 30cm above the other.

    Quote Originally Posted by Markus Hanke
    So long as you agree that GR is a good model, and that you consider yourself a relativist and an adherent to Einstein, you cannot at the same time decide to abandoned general covariance - it is one of the fundamental building blocks of the model.
    I don't mean to. Instead I mean to adhere to what Einstein said about the speed of light varying with gravitational potential and bring it home to people like you.

    Quote Originally Posted by Markus Hanke
    Farsight, the Einstein equations are manifestly covariant, so of course you can pick a different coordinate system without affecting the physics. That's kind of the whole point of the model, and is hardly subject to debate.
    No problem.

    Quote Originally Posted by Markus Hanke
    There are no observers that travel at c, so the question is moot.
    It isn't moot, it's particularly relevant because we speak of infinitive SR time dilation and infinite GR time dilation, and you know we could contrive an SR observer who is travelling at some speed very close to c.

    Quote Originally Posted by Markus Hanke
    There are however observers that determine other observers to be travelling at c in a remote frame; such observers could in principle be "seen", but their speed in nonetheless inferred since it cannot be directly measured. For example, an observer who somehow manages to remain stationary at the event horizon will determine another observer freely falling past him at the speed of light...
    I believe this to be incorrect.

    Quote Originally Posted by Markus Hanke
    This is all just more or less straightforward calculus; what you appear to be trying to do is declare this "unphysical", based on the fact that a far-away external observer disagrees with these determinations...
    I'm trying to declare it unphysical based on an understanding of how gravity actually works.
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    Posting error.
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    Quote Originally Posted by Farsight View Post
    Think of mechanical clocks. If one clock is going faster than the other, it's because its cogs are going faster. Then think of quartz wristwatches. If one watch is going faster than the other, it's because its crystal is vibrating faster. And so on. You do the same with light clocks. Whatever sort of clock you use, there's never any time flowing through it.
    Yes, so the entire physics community since Newton has chosen to assume that there is some way to coordinate all physical operations according to time. You stick with Newton: you assume that there is a single coordinating feature of the universe that is a universal time against which all physical events may be compared. If you admit that it is an assumption of yours, then you are not begging the question. If you are claiming that it is a derivation, then you are begging the question.

    It's fine to assume an absolute time like you do, but it's not general relativity. Your specific Farsight Relativity hypothesis, the details that you have to work out in order to be more than idle speculation, disagrees with the fundamentals of General Relativity.

    I'm not confusing it. Imagine you're in a boat counting waves passing beneath you. Your boat bobs up then down: one, your boat bobs up then down: two, your boat bobs up then down: three. Now imagine you have electromagnetic waves coming at you rather than water waves. You count up to 9192631770 and then you declare that a second has elapsed. If the waves are coming at you slower your second is bigger.
    You are clearly confusing things, unless you are declaring a priori that all events are events that have moving photons. This also is a fine assumption, however, it is more of your idle speculation that needs work before it can be taken seriously as scientific speculation.
    Quote Originally Posted by Farsight View Post
    I don't intend to do that. Instead I intend to look at multiple coordinate systems side by side. The parallel-mirror gif is a simple example of this. It's an idealisation of the NIST optical clocks that run at different rates when one is 30cm above the other.
    This is an example of you ignoring General Relativity and pointing out how Farsight Relativity might work, if you bothered to work it out: you claim that there is a single standard of time that we can use to compare the operation of all events, regardless of where they occur. Please work out FR so that you can test it.
    Quote Originally Posted by Farsight View Post
    I don't mean to. Instead I mean to adhere to what Einstein said about the speed of light varying with gravitational potential and bring it home to people like you.
    Then, please, work out how your FR works so that we can see how your proposed textual reading of a few select statements of Einstein's statements works. You clearly disagree with GR as practiced and you disagree with GR as mathematically written by Einstein. If the world of physics is going to do better, you will have to demonstrate that FR is better than GR at doing the work of physics.
    It isn't moot, it's particularly relevant because we speak of infinitive SR time dilation and infinite GR time dilation, and you know we could contrive an SR observer who is travelling at some speed very close to c.
    There is clearly a difference between a reference frame moving at close to c relative to another frame and a reference frame that is impossible to construct. Perhaps you would like to explain how a reference frame that is possible to construct is like one that cannot be constructed?
    I believe this to be incorrect.
    Then the burden is on you to show us how FR is a better physics than GR. As I have suggested, you could start with some simple toy models to show that your system can capture basic results.

    I'm trying to declare it unphysical based on an understanding of how gravity actually works.
    You have yet to show that FR can match how gravity actually works. Without being able to match our observations of how things in the world actually move, your theory is not yet physics speculation, it is simply idle textual analysis.
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    Quote Originally Posted by Farsight View Post
    Think of mechanical clocks. If one clock is going faster than the other, it's because its cogs are going faster. Then think of quartz wristwatches. If one watch is going faster than the other, it's because its crystal is vibrating faster. And so on. You do the same with light clocks.
    The problem is that you have to explain why the cogs, the quartz crystals, the light, etc are going faster, and in particular why they are all going faster by the same amount. The notion that cogs, quartz crystals, light, etc are unchanged in rate in a gravitational field is the result of the principle of general relativity.


    Quote Originally Posted by Farsight View Post
    Whatever sort of clock you use, there's never any time flowing through it.
    What would you expect something with time flowing through it to look like? Putting it another way, how do you know no time flows through a clock?


    Quote Originally Posted by Farsight View Post
    I'm not confusing it. Imagine you're in a boat counting waves passing beneath you. Your boat bobs up then down: one, your boat bobs up then down: two, your boat bobs up then down: three. Now imagine you have electromagnetic waves coming at you rather than water waves. You count up to 9192631770 and then you declare that a second has elapsed. If the waves are coming at you slower your second is bigger.
    There is no mention of motion in the definition of the second. Your example introduced motion without justification. The definition of the second does not involve space in any way, hence speed is irrelevant.


    Quote Originally Posted by Farsight View Post
    Like a clock an odometer displays a cumulative measure of motion.
    That's not a denial that odometers measure distance even though no space flows through them, so why don't clocks measure time even if no time flows through them?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW
    The problem is that you have to explain why the cogs, the quartz crystals, the light, etc are going faster, and in particular why they are all going faster by the same amount.
    It's because they're all of "the same essence". See Wikipedia about that. It isn't something I've just made up. In pair production we can create light out of matter. The wave nature of matter is a definite. Bonds are electromagnetic. And so on.

    Quote Originally Posted by KJW
    What would you expect something with time flowing through it to look like? Putting it another way, how do you know no time flows through a clock?
    Because I understand time. Because I understand clocks. I understand that a clock clocks up some kind of regular cyclical motion. It's light moving in an optical clock, not time.

    Quote Originally Posted by KJW
    There is no mention of motion in the definition of the second. Your example introduced motion without justification. The definition of the second does not involve space in any way, hence speed is irrelevant.
    It's absolutely relevant. The second is defined to be the duration of 9192631770 periods of radiation. That radiation is light waves. Those light waves are moving.

    Quote Originally Posted by KJW
    That's not a denial that odometers measure distance even though no space flows through them, so why don't clocks measure time even if no time flows through them?
    Clocks measure the thing we call time, but they do this by clocking up some regular cyclical motion. They don't literally measure the flow of time like they're little cosmic gas-meters. The "flow of time" is just a figure of speech. In the real world things move, shit happens, and that's it.
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    Alright, you understand time. So please show us how to properly use time in at least a toy system.
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    You use it as you use it now, but you don't think of it as something that literally flows. It's just a cumulative measure of local motion.
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    Quote Originally Posted by Farsight View Post
    You use it as you use it now, but you don't think of it as something that literally flows. It's just a cumulative measure of local motion.
    I will accept this as an admission that you are offering nothing to physics.
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    So letís do this pulse experiment in GR again, but using the terms of SR. Let an inertial body be orbited by a non-inertial body.

    You emit a photon from an inertial position A across a distance d to an orbiting mirror B that is accelerating .

    Will the emitted photon still take LONGER than 2d/c to return? And if B sends the photon to A, will the emitted photon take LESS than 2d/c to return?
    If the answer is yes to both scenarios then surely it shows the equivalence principle in action.

    I have a view. Something happens when the photon that is sent by A strikes B- namely the photon is ďdelayedĒ by B. Conversely, when the photon that is sent by B strikes A, the photon is ďhurriedĒ by A. The ďdelayingĒ and ďhurryingĒ is due to the different worldlines in ďsystemĒ A and ďsystemĒ B respectively.

    You can always imagine a ďGodís viewĒ to explain the different feedback rates but then you could imagine a view of time presiding over that view too, and so on and so on.
    Last edited by Hal on Earth; 06-19-2014 at 01:18 PM.
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    You use it as you use it now, but you don't think of it as something that literally flows.
    I am not sure where you are getting this idea, but in GR time is most certainly not viewed as "something that flows". It's just a geometric dimension, like any of the spatial ones.
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    Quote Originally Posted by Farsight View Post
    It's absolutely relevant. The second is defined to be the duration of 9192631770 periods of radiation. That radiation is light waves. Those light waves are moving.
    The motion is not relevant. The light wave could be a standing wave in a cavity and one could still establish the duration of 9192631770 periods. In other words, just because the light waves are in motion doesn't mean that the motion is significant.
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    Quote Originally Posted by KJW View Post
    The motion is not relevant. The light wave could be a standing wave in a cavity and one could still establish the duration of 9192631770 periods. In other words, just because the light waves are in motion doesn't mean that the motion is significant.
    Don't be fooled by a standing wave. It might look like it isn't moving, but it is. If your cavity is an idealised mirror box and you open the box, your photon is off and away at c. It doesn't accelerate to c from a standing start. It was always moving at c.

    Quote Originally Posted by Markus Hanke
    I am not sure where you are getting this idea, but in GR time is most certainly not viewed as "something that flows". It's just a geometric dimension, like any of the spatial ones.
    It's a geometric dimension in a static mathematical model called spacetime. But Einstein gave us the equations of motion, the map is not the territory, and out of the space / time / motion trio, in our real world it's space and motion that are empirical.

    Quote Originally Posted by Hal on Earth
    You emit a photon from an inertial position A across a distance d to an orbiting mirror B that is accelerating. Will the emitted photon still take LONGER than 2d/c to return? And if B sends the photon to A, will the emitted photon take LESS than 2d/c to return?
    No and no. Light moves at the speed it does regardless of the motion of emitter.
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    Quote Originally Posted by Farsight View Post
    It's a geometric dimension in a static mathematical model called spacetime. But Einstein gave us the equations of motion, the map is not the territory, and out of the space / time / motion trio, in our real world it's space and motion that are empirical.
    Could you please demonstrate how one observes motion and distinguishes it from rest?
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    You emit a photon from an inertial position A across a distance d to an orbiting mirror B that is accelerating. Will the emitted photon still take LONGER than 2d/c to return? And if B sends the photon to A, will the emitted photon take LESS than 2d/c to return?

    Quote Originally Posted by Farsight View Post
    No and no. Light moves at the speed it does regardless of the motion of emitter.
    I think it's still yes. My sources are

    J West, "The differential aging of inertial and non-inertial observers: The Eyewitness observations of a relativistic polygon traveler" (see [0905.1859] )

    (He also proposed the FMEL- floor-mirrored Einstein-Langevin light clock)

    It is tricky to carry out calculations using an orbit scenario, so West uses a polygon as an approximating method. Says West-

    [QUOTE]In particular, the non-inertial traveler will observer a Lorentz-like contraction of distances measured perpendicular to the direction of relative motion. As a result, the traveler will obtain a value of for the ratio of circumference to diameter, in contradiction to recently published work that predicts a measured ratio less than and a non-Euclidean geometry for the polygon traveler. [QUOTE]

    This is consistent with my earlier thread 'do moving clocks always run slowly?' where you agreed with Don Koks. A non-inertial observer B that orbits A will see A's clock as running fast, while A will see B's clock running slow. These differences must obviously influence measurements.

    Now, if B and A shine lights at each other, it will take a SHORTER period of time in B's reference frame to see A, and a LONGER period of time in A's reference time to see B. In B's view, lengths have CONTRACTED. In A's view, lengths have EXPANDED. So the speed of light remains constant.

    There is another method to derive length contraction that I discovered heuristically, independent of the Lorentz transform. If you're interested I can start a new thread on how it works.
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    Quote Originally Posted by Hal on Earth View Post
    I think it's still yes. My sources are J West, "The differential aging of inertial and non-inertial observers: The Eyewitness observations of a relativistic polygon traveler" (see [0905.1859] )...
    I'd have to read it to be able to give a considered response. And it's 12 pages. And it looks like it isn't contentious. I searched on speed and only found this about the speed of light:

    "This does presume that Octo still considers the speed of light to be equal to c along the radial direction, a presumption that is not out of necessity true."

    Quote Originally Posted by Hal on Earth View Post
    This is consistent with my earlier thread 'do moving clocks always run slowly?' where you agreed with Don Koks. A non-inertial observer B that orbits A will see A's clock as running fast, while A will see B's clock running slow. These differences must obviously influence measurements.
    They will influence measurements, but they won't make light move faster through space. It's something like when you accelerate towards a photon. You measure an increased frequency and energy, but the photon didn't change one jot. Instead you did.

    Quote Originally Posted by Hal on Earth View Post
    Now, if B and A shine lights at each other, it will take a SHORTER period of time in B's reference frame to see A, and a LONGER period of time in A's reference time to see B. In B's view, lengths have CONTRACTED. In A's view, lengths have EXPANDED. So the speed of light remains constant.
    Yep. The speed of light is constant until you start looking at gravity. Sorry Hal, I think we've gotten into some kind of miscommunication here.

    Quote Originally Posted by Hal on Earth View Post
    There is another method to derive length contraction that I discovered heuristically, independent of the Lorentz transform. If you're interested I can start a new thread on how it works.
    Yes, please do. There's a little wrinkle when it comes to length contraction.
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    Before I present my heuristically derived length contraction method...I need to learn LaTeX. How do you use the symbols in the LaTeX Commands Quick-Menu?
    Do I need to download software? How long does it take to learn?
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    Quote Originally Posted by Farsight View Post
    Don't be fooled by a standing wave. It might look like it isn't moving, but it is.
    But it's a standing wave. It is not moving.


    Quote Originally Posted by Farsight View Post
    If your cavity is an idealised mirror box and you open the box, your photon is off and away at c.
    But if you don't open the box, it remains a standing wave... not moving.


    I should point out that even if you do demonstrate that the motion exists, you still have to demonstrate that the motion is relevant. I put it to you that your claim that the motion is relevant is metrologically invalid.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Hal on Earth View Post
    Before I present my heuristically derived length contraction method...I need to learn LaTeX. How do you use the symbols in the LaTeX Commands Quick-Menu? Do I need to download software? How long does it take to learn?
    It's fiddly, but all you really do is surround an expression with tex in square brackets and slash tex in square brackets. To practice, what you can do stripe an expression on say Wikipedia, then press control C to copy it. The press control V to paste it here. Like this:



    Quote Originally Posted by KJW
    But it's a standing wave. It is not moving.
    I know that's what they say. It doesn't look like it's moving, but it is. It's kinetic energy, even though it looks like potential energy. See wikipedia and note this: In the second case, for waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy. You've still got waves travelling in opposition directions. Or two parts of a single wave.

    Quote Originally Posted by KJW
    But if you don't open the box, it remains a standing wave... not moving.
    Half of it is moving this way ← at and c, and half of it is moving this way → at c.

    Quote Originally Posted by KJW
    I should point out that even if you do demonstrate that the motion exists, you still have to demonstrate that the motion is relevant. I put it to you that your claim that the motion is relevant is metrologically invalid.
    Light travels at c towards a mirror, and at c after it reflects. If you contrive two mirrors like this | | the light moves back and forth at c. When you move the mirrors towards another this this back and forth motion continues. It doesn't stop.
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    Quote Originally Posted by PhysBang View Post
    Could you please demonstrate where, in GR, one would use the variable speed of light in a toy example with some numbers?
    That's easy. Take the Schwarzschild metric and use if for an incremental section of a lightlike worldline on which light travels. This means setting the spacetime inteval ds^2 = 0. Then divide by dt and solve for dr/dt. Make it easy for yourself and let the beam of light travel radially so that d(phi) = d(theta) = 0. Then you'll get dr/dt = (1 - 2Gm/r)c which is the (coordinate) speed of light in a curved spacetime.

    So see where the varying speed of light must be taken into all one has to do is consider the Shapiro delay, I.e. the delay in the round trip time of a radar signal bounced off a planet. Nearly all general relativity textbooks will tell you that the speed of light varies in a gravitational field such as A Short Course in General Relativity - Second Edition by J. Foster & J.D. Nightingale, Springer Press, (1994). The authors explain on page 130, section 4.2 Radar Sounding
    Suppose that an observer is at a fixed point in space in the field of a massive object, at that directly between him and this object there is a small body. We can imagine the observer sending radar pulses in a radial direction towards the body, these pulses being reflected by it and subsequently received by the observer at some later time. Let us calculate the time lapse between transmission and subsequent reception of a radar pulse by the observer. If the spatial coordinates of the observer are (r_1, theta_0, phi_0), then those of the body are (r_2, theta_0, phi_0), with r_2 < r_1 (see Fig 4.3). The radar pulses travel in a radial direction with the speed of light, so putting d(tau) = 0 and d(theta) = d(phi) = 0 in the line element (4.1) we have


    (1 Ė 2m/r)c^2dt^2 = [1/(1 Ė 2m/r)]dr^2

    which gives

    dr/dt = +-(1 Ė 2m/r)c.

    This gives the coordinate speed of light in the radial direction.
    Experiments were done in the 60ís by a team at MIT Lincoln Lab led by Irwin Shapiro who verified the implications of this fact.

    From Fourth Test of General Relativity: Preliminary Results by Shapiro et al, Phys. Rev. Letters. Vol 13(26), Dec. 28, 1964
    Because, according to general relativity, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should be increased thereby be increased by almost 2x10^(-4)s when the radar pulses pass near the sun.
    From Fourth Test of General Relativity by, Shapiro et al, Phys. Rev. Letters, Vol 20(22), May 27, 1968
    The proposed experiment was designed to verify the prediction that the speed of propagation of a light ray decreases as it passes through a region of increasing gravitational potential.
    These facts are found in most textbooks on general relativity. In fact it's difficult to find a GR text which doesn't say that the speed of light changes in a gravitational field where the light moves through a varying gravitational potential.
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    Quote Originally Posted by Physicist
    So see where the varying speed of light must be taken into all one has to do is consider the Shapiro delay, I.e. the delay in the round trip time of a radar signal bounced off a planet. Nearly all general relativity textbooks will tell you that the speed of light varies in a gravitational field such as A Short Course in General Relativity - Second Edition by J. Foster & J.D. Nightingale, Springer Press, (1994). The authors explain on page 130, section 4.2 Radar Sounding
    The above is incorrect, the Shapiro delay is not a proof of "varying speed of light". The correct explanation of the Shapiro delay comes from the fact that the rays of light, by virtue of following geodesics, follow a longer path in the presence of gravitating bodies than in their absence. The Shapiro experiment compares the propagation time of light in the presence of gravitating bodies with the propagation time in the absence of such gravitating bodies and finds the former to be longer. Nothing to do with and "varying speed of light". Farsight has already been pushing crackpot ideas, no need to fuel his misconceptions.

    These facts are found in most textbooks on general relativity. In fact it's difficult to find a GR text which doesn't say that the speed of light changes in a gravitational field where the light moves through a varying gravitational potential.
    All the textbooks you are citing, refer to the COORDINATE speed of light. GR is operates in coordinate-FREE entities, precisely because coordinate - dependent entities are physically meaningless. So, is truly physically meaningless.
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    Quote Originally Posted by x0x View Post
    The above is incorrect, the Shapiro delay is not a proof of "varying speed of light". The correct explanation of the Shapiro delay comes from the fact that the rays of light, by virtue of following geodesics, follow a longer path in the presence of gravitating bodies than in their absence.
    I don't know who told you this, but it isn't true. Only one tenth of the Shapiro delay is caused by an increased path length.

    Quote Originally Posted by x0x View Post
    The Shapiro experiment compares the propagation time of light in the presence of gravitating bodies with the propagation time in the absence of such gravitating bodies and finds the former to be longer. Nothing to do with and "varying speed of light".
    It's exactly that. To satisfy yourself that it is, imagine a Shapiro delay where light passes between two gravitating bodies. It isn't deflected at all, the path length does not increase.

    Quote Originally Posted by x0x
    All the textbooks you are citing, refer to the COORDINATE speed of light. GR is operates in coordinate-FREE entities, precisely because coordinate - dependent entities are physically meaningless. So, is truly physically meaningless.
    Not when Einstein said a curvature of light can only occur because the speed of light varies with position. Not when an optical clock goes slower when it's lower. Have a read of this article on John Baez's website:

    Is The Speed of Light Everywhere the Same?

    "Given this situation, in the presence of more complicated frames and/or gravity, relativity generally relinquishes the whole concept of a distant object having a well-defined speed. As a result, it's often said in relativity that light always has speed c, because only when light is right next to an observer can he measure its speedóó which will then be c. When light is far away, its speed becomes ill-defined. But it's not a great idea to say that in this situation "light everywhere has speed c", because that phrase can give the impression that we can always make measurements of distant speeds, with those measurements yielding a value of c. But no, we generally can't make those measurements. And the stronger gravity is, the more ill-defined a continuum of observers becomes, and so the more ill-defined it becomes to have any good definition of speed. Still, we can say that light in the presence of gravity does have a position-dependent "pseudo speed". In that sense, we could say that the "ceiling" speed of light in the presence of gravity is higher than the "floor" speed of light.

    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."
    Read the OP and look at the gif in post #2. You'd have to be crazy to say that the speed of light doesn't vary.
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    Quote Originally Posted by Farsight
    It's exactly that. To satisfy yourself that it is, imagine a Shapiro delay where light passes between two gravitating bodies. It isn't deflected at all, the path length does not increase.
    ...and the speed does not "vary". So what is your point, Duffield?

    I don't know who told you this, but it isn't true. Only one tenth of the Shapiro delay is caused by an increased path length.
    Prove it, Duffield, let's see your calculations.

    Read the OP and look at the gif in post #2. You'd have to be crazy to say that the speed of light doesn't vary.
    KJW, Markus and Physbang already debunked your fringe claims. I am simply doing the same thing that they have already done: debunking your anti-science claims. You have been at this for years, when will you cease?
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    Quote Originally Posted by Physicist View Post
    Nearly all general relativity textbooks will tell you that the speed of light varies in a gravitational field such as A Short Course in General Relativity - Second Edition by J. Foster & J.D. Nightingale, Springer Press, (1994). The authors explain on page 130, section 4.2 Radar Sounding
    Thanks for the example. I have that text and it has a nice description of the metric.

    And it is an example of how we could expect certain events to happened based on the coordinate speed of light.

    It also indicate that we need to ask a more specific question to Farsight.

    In the Schwarzschild metric, the "speed of light" is clearly different when considered radially than it is perpendicular to a line to the center of mass. The "speed" is one considered over an appreciable difference. This is in contrast to the VSL theories that Farsight invokes in his original post.

    So the real question for Farsight is to see where in GR we see VSL of the type he invokes, VSL of not the vector form with directionality but VSL of the type he invokes where the speed is different regardless of direction.
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    Quote Originally Posted by PhysBang View Post
    So the real question for Farsight is to see where in GR we see VSL of the type he invokes, VSL of not the vector form with directionality but VSL of the type he invokes where the speed is different regardless of direction.
    In the gravitational time dilation. Go and read time travel is a fantasy and appreciate this: there is no time flowing in an optical clock. When that clock goes slower when it's lower, it's because light goes slower, not time. You might want to look again at the Einstein quotes in the OP and at A World without Time: The Forgotten Legacy of Godel and Einstein.
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    Quote Originally Posted by Farsight
    When that clock goes slower when it's lower, it's because light goes slower, not time.
    You have been making this fringe claim for years, Duffield. The reality is that the passage of time, INDEPENDENT of the type of clock being used (atomic, light, etc), is dependent of the gravitational potential, as derived from the metric. You need to learn how to deal with reality, Duffield.

    You can get the ratio of clock rates relatively easily by knowing GR.
    Start with the Schwarzschild solution to EFE:



    Use the fact that



    Then:



    produces, by division with :



    Write the above for two locations , at radial distances and and you get:





    Divide the two:



    where i=1,2. If the orbit is circular, then but this is not the usual case.

    The above equation relates the proper times of two clocks , located at different radial distances and moving at different angular speeds. It is the foundation of the calculations for setting up the frequencies of the GPS clocks (such that they are synched up).



    Since the above (exact) formula is rather complicated, the GPS calculations use a power series approximation, making use of the fact that . The formula encapsulates the effects in:

    1. gravitational potential difference , via the term in
    2. radial speed difference (if it exists), via the term in
    3. angular speed difference, via the term in

    In general, the formula is expressed in terms of ratios of frequencies, not clock rates:

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    Quote Originally Posted by Farsight View Post
    In the gravitational time dilation. Go and read time travel is a fantasy and appreciate this: there is no time flowing in an optical clock. When that clock goes slower when it's lower, it's because light goes slower, not time. You might want to look again at the Einstein quotes in the OP and at A World without Time: The Forgotten Legacy of Godel and Einstein.
    Lets see your derivation.

    In no place have you produced anything like we see in A Short Course in General Relativity where we see how we generate a coordinate difference in the speed of light and how to use it. You are claiming that there is a real difference in the speed of light, independent of coordinate. You have made claims, linked to sources that disagree with your claims, and generally avoided doing any work to justify your claims. Now show us some physics.
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    There is no derivation, merely the observation that there is no literal time flowing through a clock. Open up a clock and look at what it does. Can you see some river of time flowing through it? No. I've made claims and I've backed them up with evidence and Einstein. You're in denial, PhysBang. "A curvature of rays of light can only take place when the propagation speed of the light with the place varies". Hence gravity works because light "veers". See this thread: http://www.thephysicsforum.com/speci...elativity.html
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    Quote Originally Posted by Farsight View Post
    There is no derivation, merely the observation that there is no literal time flowing through a clock. Open up a clock and look at what it does. Can you see some river of time flowing through it? No.
    I also don't see oxygen flowing through it.

    Do you claim that oxygen doesn't exist?

    I follow the tradition of physics in recognizing that we identify time in the way that physical systems operate. We can be vary specific in the way that we identify time and the relationship between events.

    So far, you have shown nothing about how your supposed mystical revelation and dogmatic skepticism lead to doing any physics.

    I've made claims and I've backed them up with evidence and Einstein. You're in denial, PhysBang.
    I am in denial, since you cherry-pick Einstein and you refuse to show us how your ideas might gain empirical support.

    So, please, show us how we can describe a physical system using a) just motion and b) mass influencing just the variable speed of light, in a way independent of direction. Then show us how this does as good as a description using GR.
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    Quote Originally Posted by PhysBang View Post
    I also don't see oxygen flowing through it. Do you claim that oxygen doesn't exist?
    No. And nor do I claim that a clock measures the flow of oxygen. Your analogy is absurd.

    Quote Originally Posted by PhysBang View Post
    II follow the tradition of physics in recognizing that we identify time in the way that physical systems operate. We can be vary specific in the way that we identify time and the relationship between events.
    Well, your "tradition" is not in line with the empirical evidence. Get used to it.

    Quote Originally Posted by PhysBang View Post
    I am in denial, since you cherry-pick Einstein and you refuse to show us how your ideas might gain empirical support.
    I've shown you the empirical support. Go look inside a clock. Can you see time flowing? No. Can you see something moving? Yes. But you will of course ignore that in favour of your precious "tradition".

    Quote Originally Posted by PhysBang View Post
    So, please, show us how we can describe a physical system using a) just motion and b) mass influencing just the variable speed of light, in a way independent of direction. Then show us how this does as good as a description using GR.
    Duh! You've already got the GR description written by the guy who said this: "A curvature of rays of light can only take place when the propagation speed of the light with the place varies". And by the way, a concentration of energy causes gravity. A "mass" causes gravity because it is a concentration of energy.

    Strewth! Somebody please spare me from naysayer custodians of ignorance!
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    Quote Originally Posted by Farsight View Post
    Well, your "tradition" is not in line with the empirical evidence. Get used to it.
    I am used to it. Both Maxwell and Einstein explicitly address that their ideas of time are something that is required in order to do physics and as such it is pre-empirical. They are then able to go ahead and show how to do physics with their schema.

    You need to show us how to do physics with your scheme rather than beat around the bush and avoid doing science.
    I've shown you the empirical support.
    Again you lie rather than produce some work. Please show us how one can do physics with your no-time ideas.

    Duh! You've already got the GR description written by the guy who said this: "A curvature of rays of light can only take place when the propagation speed of the light with the place varies". And by the way, a concentration of energy causes gravity. A "mass" causes gravity because it is a concentration of energy.
    And yet you are unable to point out where in the science as written your ideas appear. Please do so.

    Strewth! Somebody please spare me from naysayer custodians of ignorance!
    I know that you want to be recognized as an expert, but people like me are going to refuse to recognize you as anything of the sort until you demonstrate that your ideas have anything to do with physics. You've given us a lot of promises of your abilities but you have also given us a lot of lies and misdirection.
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    MODERATOR WARNING:

    IF I SEE ONE MORE CASE OF ANYONE CALLING ANYONE ELSE A LIAR, IT WILL RESULT IN A BAN. YOU WILL ALL STOP THE AD-HOMINEMS HENCEFORTH, OR SUFFER THE CONSEQUENCES. THERE IS A DIFFERENCE BETWEEN SOMEONE BEING MISTAKEN AND THEM BEING A LIAR.

    You can say "you are mistaken", but you cannot say "you are telling lies".

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    Quote Originally Posted by PhysBang View Post
    I know that you want to be recognized as an expert, but people like me are going to refuse to recognize you as anything of the sort until you demonstrate that your ideas have anything to do with physics. You've given us a lot of promises of your abilities but you have also given us a lot of lies and misdirection.
    Physbang, did you read Farsight's story about the school teacher? If you did, did you understand what it meant? There are no experts!
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    Quote Originally Posted by Jilan View Post
    Physbang, did you read Farsight's story about the school teacher? If you did, did you understand what it meant? There are no experts!
    If this were true, then it would seem that Farsight is mistaken in a way that in no way stains his character, for he explicitly calls himself an expert on physics. E.g., JREF Forum - View Single Post - [Merged] Relativity+ / Farsight's thread
    Beer w/Straw likes this.
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    Lol, I guess that's where relativity comes into play!
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    Quote Originally Posted by x0x
    The above is incorrect, the Shapiro delay is not a proof of "varying speed of light".
    You are seriously mistaken. First off you made an error in logic here by referring to the results of an experiment constituting any sort of proof. Any decent physicist will tell you that just because the results of an experiment are consistent with the theory that predicted the results it cannot be taken as proof that the theory of prediction is correct. All it does is lend support to the theory. The more experiments done the more support a theory gains. But ďproofĒ never enters into it. Theories simply cannot be proven, period. And in the second place the results are very much consistent with the assertion that light slows down in a gravitational field.

    Quote Originally Posted by x0x
    The correct explanation of the Shapiro delay comes from the fact that the rays of light, by virtue of following geodesics, follow a longer path in the presence of gravitating bodies than in their absence.
    This too is wrong. Your explanation demonstrates a lack of understanding of the derivation. There are clearly two effects which alter the time delay. One these effects is the fact that the spatial geometry is altered by the gravitational field. This is due to the coefficient of dr^2 in the spacetime metric. This accounts for how radial distances are altered by the gravitational field. The spatial geometry is no longer flat but curved. The distance is now increased which is part of the reason for the greater delay in time. That increase in distance cannot be correctly interpreted as a slowing of the speed of light. However there is another effect in play here which does account for the slowing of light in the gravitational field and thatís the gravitational time delay which is taken into account by the coefficient of dt^2 in the spacetime metric. Now that is why light slows down in a gravitational field.

    Quote Originally Posted by x0x
    The Shapiro experiment compares the propagation time of light in the presence of gravitating bodies with the propagation time in the absence of such gravitating bodies and finds the former to be longer. Nothing to do with and "varying speed of light".
    You are clearly wrong for the reasons I stated above and the reasons given in any textbook which describes the effect. The ALL state in no uncertain tersm ďLight slows down in a gravitational field.Ē I fail to understand what part of that very simple statement, which all GR experts agree on, confuses you. Itís not as if thereís any debate in the general relativity community about the interpretation of the Shapiro time delay being beause light slows down. You yourself just read how Irwin Shapiro himself interpreted his own results of his experiment, i.e. in one article he wrote
    Öthe speed of a light wave depends on the strength of the gravitational potentialalong its path,Ö
    and in another article he wrote
    Quote Originally Posted by x0x
    Öthe speed of a light wave depends on the strength of the gravitational potential along its path,Ö
    (underscores are mine). If you believe that Shapiro didnít assert that light slows down in a gravitational field and that had to be taken into account in order to predict the time delay then you clearly are unable to understand what youíre reading and are in serious need of help. You just might have a learning disability.

    Quote Originally Posted by x0x
    Farsight has already been pushing crackpot ideas, no need to fuel his misconceptions.
    Hey! Thatís not very nice. Be a good boy and play nice. Itís rude of you to act like that. Please stop. There is no need of it. Just because you think heís a crackpot thereís no need to speak it out loud and hurt his feelings. Donít forget, these are real people here who have real feelings and can be hurt by insults. Farsight is a nice guy and thereís no reason to treat him like this. If you think heís a crackpot then simply ignore his posts. Itís not as if Iím getting a good impression of you but I donít say it out loud.

    Quote Originally Posted by x0x
    All the textbooks you are citing, refer to the COORDINATE speed of light. GR is operates in coordinate-FREE entities, precisely because coordinate - dependent entities are physically meaningless. So, c_coord = c(1-2m/r) is truly physically meaningless.
    Youíre quite wrong, again. First off, with light there is no other speed than the coordinate speed of light, period. You didnít know that? Itís impossible to define a coordinate free speed of light for light. In inertial frame in flat spacetime the speed of light is the coordinate speed/velocity of light. However with light the magnitude is a Lorentz scalar and thus invariant. And itís wrong to assert that GR operates in coordinate-free entities. Coordinate dependent entities are very real because thatís what youíre actually measuring. You donít seem to understand that simple fact.

    You should have paid closer to the following post by Marcus. I donít know who he(she?) is but he certainly understands it. Recall what he wrote
    This boils down to the exact same distinction between GLOBAL and LOCAL that I have been referring to on many previous occasions. For a far-away observer, if he sends a light signal past a massive body, he will determine the speed of light to be diminished GLOBALLY over its entire trajectory - a phenomenon well-known as the Shapiro delay. However, any observer placed along the trajectory will, in his/her own frame of reference, LOCALLY measure the light speed to be exactly c, everywhere and always.
    If you knew GR then youíd know who John Wheeler was. Recall what he wrote in his textbook Exploring Black Holes by Edwing F. Taylor & John Archibald Wheeler, (2000), pages 5-2 to 5-4 where the section on this is found, i.e. Alternative Speeds of Light I Ė When does light move slower than speed unity? Then turn to Project E entitled Light Slowed Near Sun. Then, instead of making ignorant (by which I mean without knowledge, not ďstupidĒ) you should read this text and actually learn what the experts are trying to teach you rather than simply assume that youíre right and everyone else in the world is incredibly ignorant. I simply donít have the time nor the will to continue on with all these baseless assertions made without any proof, justification or citation to the physics literature whatsoever. Case in point. You made this terribly aweful claim that GR is coordinate free. Thatís terribly wrong. Youíre confusing that with the fact that you can use any coordinate system that you want. NOT that youíre not using any coordinate system, which is blatantly wrong since all calculations and all measurements are made using coordinates.

    Go to the library and pick up the text Gravitation and Spacetime Ė Third Edition by Hans C. Ohanian and Remo Ruffini, (2014). Turn to page 223 and read the section entitled 6.1 General coordinates and tensors

    But this is not about coordinates because the time delay would have been the same regardless of what coordinate system you chose to use. You could just as well have used Cartesian spatial coordinates instead. Itíd just be very messy and very difficult to do.

    I wonít be responding to this thread again since the only one who has a problem here is you and I donít care what you think or whether you understand it or not. Iím delighted to let you think that youíre right and all the genius experts that Iíve read and know personally are wrong. Especially when you donít make any attempt to publish your claims or contact all these experts and tell them why theyíre wrong. If theyíre wrong and youíre right, donít you think that theyíd want to know? Donít you think the entire GR community would like to see you publish your claim? Then why not try? Or are you all talk and canít actually talk your way through an argument with the worlds leading experts on GR and what they explain in their texts?


    Once more
    Quote Originally Posted by x0x
    GR is operates in coordinate-FREE entities, precisely because coordinate - dependent entities are physically meaningless
    I canít believe you really said this. In physics it has a lot of physical meaning when it comes to the physical meaning of spacetime coordinates. A Lorentz boost changes results in a change in kinetic energy, strength of the components of the electric and magnetic fields, etc.

    This is from page 69 of Waldís GR text. It can also be found in most GR texts. Consider the following example from SR: most people, such as yourself Iím sure, donít realize that the observer is represented by a 4-vector, ususally labeled U_obs. When that 4-vecotor is used one can get the energy measured by that observer and thatís from taking the inner product of two 4-vectors which yields a Lorentz scalar. For example, if you take the inner product of U_obs with the 4-momentum of a particle you get a Lorentz scalar which is proportional to the energy of the particle. Another example, one Iím sure youíll claim I donít know what Iím taking about so please look it up first in Waldís GR text on page 64.

    Let O = U_obs, F = Faraday tensor. Then E_a = F_ab O^b is interpreted to as the electric field measured by the observer whose 4-velocity is O = U_obs. A similar result is on that page for the magnetic field.

    Then thereís the gravitational field of a beam of light. Think of a beam of light coincident with the x-axis whose energy density is so large that it generates a measurable gravitational field strong enough to gravitationally attract particles. That it does generate a gravitation field was demonstrated in the following places

    Relativity, Thermodynamics and Cosmology, Richard C. Tolman, Dover Pub, Sections 112-115.

    On The Gravitational Field Produced by Light, Tolman, Ehrenfest and Podolsky, Physical Review, Vol. (37), March 1, 1931, pg 602-615.

    There is a coordinate system for each frame of reference at rest near the beam. If you change to another frame which is moving parallel to the beam relative to the original frame then he too can think of himself at rest but in this frame the strength of the field is different. Each frame has a different strength of the field. And each frame corresponds to a different coordinate system.

    Youíre confusing the different coordinates we use in classical mechanics such as Cartesian, spherical or polar coordinates where the measured results donít mean a lot other than the components measured along an axis with the actual physical differences that one gets in relativity where clocks deep in a field run slower, moving clocks run slower, moving rods are shorter, etc.

    You have some serious misconceptions about relativity but you think that youíre right and the entire physics community is wrong. I have neither the time nor the patience to help you understand all of this, especially since you donít think youíre wrong. When that happens then such people arenít willing to learn. So I see no reason to respond to anymore of your incorrect assertions. Please feel free to make any assertions you wish such as everyone is wrong and only you are right.
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    Quote Originally Posted by PhysBang
    Thanks for the example. I have that text and it has a nice description of the metric.
    Youíre quite welcome Sir. My pleasure. Itís such a relief to help someone who appreciates it rather than someone making false assertions which they refuse to back up with a derivation or reference, huh?

    Quote Originally Posted by PhysBang
    And it is an example of how we could expect certain events to happened based on the coordinate speed of light.
    Exactly. The important thing here is the fact that Shapiro actually showed that by choosing his physical coordinate system, i.e. Schwarzschild coordinates, he got a result which was different than had he used another physically different coordinate system such as a local coordinate systeml. I think we simply canít get that through to x0x.

    Quote Originally Posted by PhysBang
    It also indicate that we need to ask a more specific question to Farsight.
    Actually up to now Iíve been ignoring him. I learned last year that he canít be gotten through to. Iím getting too old to try to get people to learn when they donít have what it takes in the first place. It took me a long time to learn this.

    Quote Originally Posted by PhysBang
    In the Schwarzschild metric, the "speed of light" is clearly different when considered radially than it is perpendicular to a line to the center of mass. The "speed" is one considered over an appreciable difference. This is in contrast to the VSL theories that Farsight invokes in his original post.
    Iím in agreement with his quotes of Einstein since I read some of those papers.

    Quote Originally Posted by PhysBang
    So the real question for Farsight is to see where in GR we see VSL of the type he invokes, VSL of not the vector form with directionality but VSL of the type he invokes where the speed is different regardless of direction.
    Let me read some and get back to you.

    Iím new here so I want to say that itís nice to meet you Sir/Maddam. Donít let the handle give you the wrong impression. If I saw someone with the title ďPhyscistĒ Iíd think that they were very arrogant. ROTLF!! However I was at a total loss and for once I wanted a hanle that reflected who I am rather than a simple name so I put down my profession instead. I wanted to make that clear so people donít get the wrong idea of me.

    Best wishes
    Physicist
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    Quote Originally Posted by Physicist
    You are seriously mistaken.
    Contrary to your claims, the extra delay in the Shapiro experiment is not caused by any "variable speed of light". First of all, the speed doesn't vary at all in the Shapiro explanation. second off, it is the extra length due to the fact the light follows geodesics and these geodesics are curved, they deviate from the straight lines. The geodesics are longer than the straight lines, causing the extra delay.

    I canít believe you really said this. In physics it has a lot of physical meaning when it comes to the physical meaning of spacetime coordinates. A Lorentz boost changes results in a change in kinetic energy, strength of the components of the electric and magnetic fields, etc.
    Well, this is tough. The language of GR is combination of tensor algebra and differential geometry, both fields of math being coordinate-free.

    If you knew GR then youíd know who John Wheeler was. Recall what he wrote in his textbook Exploring Black Holes by Edwing F. Taylor & John Archibald Wheeler, (2000), pages 5-2 to 5-4 where the section on this is found, i.e. Alternative Speeds of Light I Ė When does light move slower than speed unity? Then turn to Project E entitled Light Slowed Near Sun.
    I know GR quite well. You are trying to make your point by appeal to authority. Even worse, you are cherrypicking quotes from a pop-science book.

    Here is the deal, the extra delay in the Shapiro experiment is described rigorously in Rindler: "Relativity, Special , General and Cosmological" , page 237. The deviation from the straight time roundtrip is :



    where:

    is the predicted time along the geodesic
    is the Schwarzschild radius of the gravitating body that "bends" the light
    is the straight line distance observer-emitter
    is the "radius of closest approach", i.e. the closest distance between the photons following the geodesic and the center of the gravitating body that "bends" the light

    The term simply encapsulates the fact that light follows a longer path*, deviating from the straight path. Very simple. Quite the contrary, you can see "c", the invariant speed of light in the extra term , right?

    Nothing to do with any "variable speed of light".

    *Chapter 3.4.2 in "Living Reviews"
    Last edited by x0x; 07-03-2014 at 12:09 AM.
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    Quote Originally Posted by Markus Hanke
    Everyone, please remember that "speed" is a concept that is not as straightforward as it would initially seem, because we need to distinguish between coordinate speed and proper speed. In curved space-times, the coordinate speed of light does indeed vary, but proper speed does not. It is now crucial to understand that there isn't a contradiction between these.
    Iíd like to point out something crucial here. When it comes to the speed of light itís assumed that weíre 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. Thatís the reason I assumed that everyone knows that Iím talking about the coordinate speed of light.
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    Quote Originally Posted by Physicist
    Iíd like to point out something crucial here. When it comes to the speed of light itís assumed that weíre talking about the coordinate speed
    Yes, we all know that, it isn't "crucial", it is rather trivial, light follows null geodesics in GR, so . Divide by and you get the formula for the coordinate speed of light. This part is correct in your posts. The incorrect part is the one where you try to explain the Shapiro delay using "variable speed of light " (i.e. the coordinate speed of light). The (varying) coordinate speed of light does not intervene in the explanation of the Shapiro delay. See references to modern explanation in post 75.

    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.
    This is also incorrect, local (proper) speed of light , aka "c", appears all over GR, so it is clearly a well defined entity, not "undefined" at all.
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    Quote Originally Posted by Physicist
    Actually up to now Iíve been ignoring him. I learned last year that he canít be gotten through to. Iím getting too old to try to get people to learn when they donít have what it takes in the first place. It took me a long time to learn this.
    I can be gotten through to. Just show me the evidence. By the way, I don't recall having spoken to you previously. Many physicists have an excrutiatingly poor understanding of relativity, but you stand out as a relativist who knows his stuff. Oh, and do note that you're siding with what I've said here.
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    Quote Originally Posted by Farsight
    and do note that you're siding with what I've said here.
    It is amusing to see that you two guys agree. Doesn't mean you are right, you are both equally wrong.

    Many physicists have an excrutiatingly poor understanding of relativity
    LOL
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    Quote Originally Posted by Farsight View Post
    I can be gotten through to. Just show me the evidence. By the way, I don't recall having spoken to you previously. Many physicists have an excrutiatingly poor understanding of relativity, but you stand out as a relativist who knows his stuff. Oh, and do note that you're siding with what I've said here.
    I think you are mistaken in a way that does nto stain your character: you speak of VSL at the level of the elements of the manifold in scalar form, whereas the example we were discussing with details has, of necessity, a coordinate VSL in vector form. If you bother to work out the details of your theory to the extent that it approaches physics, then you might be able to learn this.
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    It isn't my theory. And Einstein genuinely referred to the speed of light varying with position. Again, read the OP.
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    Quote Originally Posted by Duffield
    Again, read the OP.
    Your OP is wrong. You have been wrong for years, John. Come to grips with it.
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    Quote Originally Posted by Farsight View Post
    It isn't my theory. And Einstein genuinely referred to the speed of light varying with position. Again, read the OP.
    Perhaps you need to read the OP. Please do not continue to be mistaken in a way that does not stain your character: your OP relied on references to VSL in the form of a scalar, your OP explicitly relies on VSL in the form of a scalar, so far, there seems to be no extant example of VSL in GR except in the vector for that everyone but you expects. This means that you have a particular theory about GR that you have not justified and that, for whatever reason that does not stain your character, you refuse to attempt to justify.
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    The "no stain on your character" thing is pretty annoying. Why bother mentioning anything about character at all?

    Why can't you guys just discuss the issues at hand without all the sniping? Just explain exactly what is wrong about what someone else said and leave it at that.
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    Many physicists have an excrutiatingly poor understanding of relativity, but you stand out as a relativist who knows his stuff.
    Thanks. Iíve been studying relativity for well over two decades and know if very well. I also know how to costruct a solid argument with no holes in it and I rarely make mistakes. When I do make a mistake I correct it as soon as its pointed out to me (real mistakes, not the delusions some people we know). I donít make mistakes because Iím flawless but because I never post in subjects Iím not fairly fluent in, such as this one.

    I always provide proof of what I assert, unlike x0x

    Oh, and do note that you're siding with what I've said here.
    On this point, yes. Thatís quite correct. I never said nor implied that youíre always wrong, John. I just got tired with some of the ways that you argue so I stopped trying.

    I was glad to see that you too recognize the nature of x0xís invalid claim regarding why there is a time delay. I, like you, explained precisely why heís wrong but, as usual, he ignored that fact and repeated his flawed claim all over againwithout blinking an eye. The worst part about all this is that heís claiming that every GR expert that exists is wrong and merely repeats himself giving no proof whatsoever. I define that behavior to be crank behavior.

    Even worse he has consistently ignored the demonstratable fact that Shapiro himself stated that light slows down in a gravitational field. ROTFL!!!

    When people behave light that I ignore them. I suggest you do the same thing. Heís certainly not worth talking to. All Iíve seen him do is post errors and his misconceptions and watched him ignore all proof of his claims to the contrary. So why would you want to converse with someone like x0x?
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    Quote Originally Posted by Physicist
    I always provide proof of what I assert, unlike x0x
    Actually,I disproved your claims, with math, rigorously. See this post.

    I was glad to see that you too recognize the nature of x0xís invalid claim regarding why there is a time delay. I, like you, explained precisely why heís wrong but, as usual, he ignored that fact and repeated his flawed claim all over againwithout blinking an eye. The worst part about all this is that heís claiming that every GR expert that exists is wrong and merely repeats himself giving no proof whatsoever. I define that behavior to be crank behavior.
    I find it really entertaining that you and Farsight are in agreement so often.
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    PhysBang Ė Since you didnít say that there were flaws in it and only complained about the author I read the paper. Normally I donít read articles that are unpublished but sometimes I make exceptions in hopes of finding interesting references. It was a poorly written article but I found the premises to be correct and the logic sound. All the author did was to say the same things weíve been talking about so it was really a waste of time. I wish you had pointed that fact out to me. Please do so the next time. Try not to let personalities get in your way. I donít want to read papers that I wonít gain any insight from and that was the case here since most of what is in that article has been discussed in this forum.

    As far as x0x goes, why waste your time with him? He clearly ignores every proof that heís wrong just like he ignored the fact that Irwin Shapiro himself interpreted the results of his own experiment as being consistent with the slowing of light in a gravitational field. As you know, if I read along, I explained why he was mistaken and he ignored it and repeated his false claims all over again. I.e. the portion of the time delay due to an altered spatial geometry and thus an increase in the spatial path length comes from the coefficient of dr^2 (i.e. from ). If we ignored the change in the spatial path increase by setting = 1 then weíd still get a decrease in the speed of light. This is due to the fact that is not equal to one. That this is so easy to see is evident in Einsteinís derivation of this result in his paper On the Influence of Gravitation on the Propagation of Light by Albert Einstein, Annalen der Physik, 35 (1911). In that article he derives the expression for a uniformly accelerating frame of reference in flat spacetime. Therefore the spatial geometry is remains unchanged (no increase in the distance that the light travels). According to Einsteinís argument, based on the equivalence principle, this is the same as a uniform gravitational field. Einstein then derived the expression for an observer whose frame of reference has its origin at z = 0 in the uniform field. Einstein concludes
    It we call the velocity of light at the origin of coordinates , then the velocity of light c at a place with the gravitational potential will be

    So here too x0xís argument once again falls apart.

    One sign of a crank is to assign criticism of a scientific fact they disagree with to the person stating it. When they agree with the scientific fact they assign credit to the person who published it. This is something x0x keeps doing every time he claims I made an error since Iím not the one responsible for these theories or their interpretation.
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    These are the same questions I asked Farsight:

    Farsight, do we measure the speed of light locally in vacuum to be the c?

    Would it matter if our location differs when we measure the speed of light locally in vacuum?
    Will you answer?
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    Quote Originally Posted by Beer w/Straw
    Ödo we measure the speed of light locally in vacuum to be the c?

    Would it matter if our location differs when we measure the speed of light locally in vacuum?
    Ö
    Will you answer?
    I donít understand? Who are you asking this to? If itís me then sure, Iíll answer it. Yes. Of course. The speed of light (SOL) depends on the gravitational potential. When you measure the SOL locally what youíre effectively doing is changing your frame of reference to one where the gravitational potential where the light is to be zero. When that happens
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    Quote Originally Posted by Physicist
    I donít understand? Who are you asking this to? If itís me then sure, Iíll answer it. Yes. Of course. The speed of light (SOL) depends on the gravitational potential.
    Repeating the same falsity ad nauseaum doesn't make it true, the coordinate speed of light depends on the gravitational potential, more correctly said, on the Schwarzschild radial coordinate, r:


    Local speed of light DOES not. At least, this is the view of mainstream physics. The fact that your posts disagree with it is a problem that can be addressed through educating you. Which is exactly what I am trying (albeit not very successfully) to do.

    When you measure the SOL locally what youíre effectively doing is changing your frame of reference to one where the gravitational potential where the light is to be zero
    The above is not even a coherent sentence.
    Last edited by x0x; 07-03-2014 at 05:45 PM.
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    Quote Originally Posted by Physicist View Post
    PhysBang Ė Since you didnít say that there were flaws in it and only complained about the author I read the paper. Normally I donít read articles that are unpublished but sometimes I make exceptions in hopes of finding interesting references. It was a poorly written article but I found the premises to be correct and the logic sound. All the author did was to say the same things weíve been talking about so it was really a waste of time. I wish you had pointed that fact out to me. Please do so the next time. Try not to let personalities get in your way. I donít want to read papers that I wonít gain any insight from and that was the case here since most of what is in that article has been discussed in this forum.
    Sorry, I got distracted in the middle of that post and came back to it hours later. I didn't even think I posted what I had written so far.

    As far as x0x goes, why waste your time with him?
    x0x does seem to be sticking to some very strict points that do not seem relevant.
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    Quote Originally Posted by Physicist View Post
    I donít understand? Who are you asking this to? If itís me then sure, Iíll answer it. Yes. Of course. The speed of light (SOL) depends on the gravitational potential. When you measure the SOL locally what youíre effectively doing is changing your frame of reference to one where the gravitational potential where the light is to be zero. When that happens
    I see what you are saying. If I move the same gravitational potential as the object there is no longer a difference in the potential, so it is as if there is no potential at all. I am local to the object so
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    Quote Originally Posted by Jilan
    If I move the same gravitational potential as the object there is no longer a difference in the potential, so it is as if there is no potential at all. I am local to the object so c=c0
    This is a very bad way of phrasing it, it has nothing to do with any "object". In addition, the variability of coordinate light speed has nothing to do with "difference in the potential".
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    x 0h x, thanks for the feedback. Would you be able to offer an improved wording as I am new to all this GR business.
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    Quote Originally Posted by Jilan
    x 0h x, thanks for the feedback. Would you be able to offer an improved wording as I am new to all this GR business
    Sure: in any inertial frame . Free-falling frames are inertial. Hence, in a free-falling frame .
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    But To be in the same inertial frame as the object I would need to be at the same gravitational potential wouldn't I else our frames would be accelerating wrt the big mass as different rates?
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    Quote Originally Posted by Jilan
    But To be in the same inertial frame as the object I would need to be at the same gravitational potential wouldn't I else our frames would be accelerating wrt the big mass as different rates?
    I am sorry, this is the second time you are posting this and it makes no sense to me. There is no "object" involved. There is only one frame, so there is no "our frames".
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    I'm sorry but I thought relativity always required an object and an observer, else what is relative to what?
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    No, it doesn't. You have a (fee-falling) frame and you measure the speed of light. The result of your measurement is
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    But isn't that just the trivial case?
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