
#1
Nov2812, 05:35 AM

P: 344

The speed of light is measured to 299 792 458 m / s and 1 meter defined to 1/299 792 458 of the speed of light.
Let us assume that A live at the top of a skyscraper and B in the cellar the past 10 billion years. After 10 billion years B’s clock have “lost” 10 second due to different gravitational influence, compared to A’s clock. 10 billion years ago 2 photons was leaving a star 10 billion light years away and hit A and B at the same moment 10 billion year after. B would now say that he measured the time it took for the photon to reach earth, to 10 second less than A measured. B would therefore claim that either the speed of light must have been traveling faster than 299 792 458 m / s, or local distance (where B is) must be stretching or contracting proportional with the stretch of time. Which option is correct, and what proves it ? 



#2
Nov2812, 05:39 AM

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Length contraction.
Proof? It can't be proven with that experiment, each would have to locally measure the speed of light and measure that it is C. Then they would know the distance has to be different. Please don't make this about the recursiveness of the definitions. That is not a confounding factor. 



#3
Nov2812, 08:33 AM

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To completely understand their observations, they must both measure the local speed of light; they'll both get the same result. Then they can assume that that value is also the speed of the light traveling from the distant galaxy, see whether that assumption leads to an internally consistent theory that also matches experimental evidence. Only then can they accept the explanation that A and B experienced different amounts of gravitational time dilation. (And you are still free to try to construct a completely different theory if you want to... but given the experience of the past century with relativity, this is unlikely to be a good use of your time). 



#4
Nov2812, 09:16 AM

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Is the speed of light always 299 792 458 m / sA different simultaneity convention Different paths of the photons through spacetime Different paths of A and B through spacetime A's clock is wrong B's clock is wrong Etc. The math can be interpreted many ways, but the important thing is that GR makes correct predictions about experimentally measured results. 



#5
Nov2912, 07:49 AM

P: 344

I guess that according to GR this must mean that 1 local meter by B (in the cellar) is longer, compared to 1 meter at the top of the skyscraper. And this is why the distance B would measure is shorter (contracted). I mean in reality the distance to the source (10 billion km away) is not changing,  it would be illogical if it was,  but what instead happens is that B experience some kind of optical change due to change of space time ( deformation of space).. Or how can we be more specific to understand “length contraction” in this case? 



#6
Nov2912, 08:06 AM

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Saying "optical change" implies to me that you think it is an illusion. It isn't. Length is just different for different observers, just like time and speed....and even color.




#7
Nov2912, 09:03 AM

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#8
Nov2912, 10:36 AM

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Depends how you do the comparison. This is something that you didn't clearly specify in your previous thread either.




#9
Nov2912, 11:44 AM

P: 344

We know speed of light is the "same" for both A and B. We also know speed for both A and B Speed * Time = Distance. The result is that the time it took the 2 photons to reach the skyscraper is 10 less second seen from B’s perspective compared to A’s observation.. The first simple mathematical conclusion is therefore that length cannot be the same. But the most logical conclusion must be the 2 photons must be assumed to have hit the same skyscraper “in the same moment” – I mean if both A and B would see the same supernova 10 billion LY away,  the light B would receive would not be delayed 10 seconds compared to A. So fare I believe we are on safe ground. Furthermore the most logical conclusion must also be that the “real distance” (doesn’t matter how it is measured and by who) – is NOT changing. I mean if I would take the elevator to the top of a building,  this is not changing the “real distance” to the Sun etc... Based on such simple logical conclusions, the only way left, whereby distances in this case possible can be different,  is if the way they are measured,  which off course must mean 1 meter is not comparable the same,  for both A and B. (or ?) 



#10
Nov2912, 12:05 PM

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Btw, the whole discussion about the light from the star has little to do with the comparison of meters local at A and meters local at B since the bulk of the path of the light is not local to either A or B. It is a "red herring". 



#11
Nov2912, 02:32 PM

P: 344

Regarding whether a deeper understanding of the “length contraction phenomena”  possible could be caused due to that 1 meter not is the comparable same for A and B (at the top of the skyscraper compared and at the cellar) ?  I cannot see any method to either confirm or reject this. Can you (really) ? I think it is impossible to measure / prove, since the device to measure it cannot be in 2 different spacetime realities at the same time, and this is as I see it necessary. SR was overlapping GR , and I was more confused after the discussion as before. The thought experiment in this threat is far more simple,  at least to my opinion.
Sorry, by in my ears none of these sounds,  like the most logical conclusion. Option 1  A different simultaneity convention. If you mean this should be responsible for the whole timedifference between A and B (?) If so that would also mean that B would see photons from a supernova (billion LY away) several seconds true delayed compared to A. Will A and B see see the 2 photon's in the same moment?,  I believe so. Disagreement must be relative insignificant compared to the measured time difference (by A and B).. So, to a certain degree I guess YES,  but insignificant compared to the relative large time difference measured by A and B during a period of 10 billion years. Option 2.  Different paths of the photons through spacetime To a certain degree YES, but insignificant compared to the relative large time difference measured by A and B during a period of 10 billion years. I mean imagine a supernova not only was 10 billion LY away but for example 1.000.000.000LY (and the Universe is 'bit' older than now) . 2 photons leaving a supernova that long distance away, would not only cause few second difference but cause many hours’ time measurement difference (seen from A and B's perspective) . I assume such 2 photons anyways would hit the skyscraper (top and cellar) at the same moment . We are not only talking about split second differences,  but much more than that. I cannot imagine that A can see the supernova from first floor, after that go to the top and here have to wait 1 hour before he can see it here too,  due to something serious had happen to the photon's path. Option 3  Different paths of A and B through spacetime To a certain degree YES, but insignificant compared to the relative large time difference measured by A and B. It is the same kind of problem as option 2,  we are dealing with a relative large time difference, increasing during billions of years.  This should make it possible to ignore all insignificant factors. Option 4+5 Wrong Clock’s ? This aspect of GR / SR have past plenty test / GPS etc.. We can even simplify the thoughtexperiment further Imagine one neutrino, travelling the same distance, first hitting the skyscraper from right above, (and detected at the upper floor,) and a split second later detected in the cellar. Now relative motion of A and B,  or – “traveling by different paths”  cannot be significant options or at least very insignificant. And still A and B would far from agree about the distance the neutrino had traveled since it started 10 (or 100.000.000) billion LY away. So we are back where we started;  is it possible to reach a logical and deeper difination of ; what is length contraction ? How many true options are there? I mean several options must be possible,  logical – to shut out. 



#12
Nov2912, 03:41 PM

P: 1,098

A meter stick as measured by you (comparably at rest) rockets off a boomerang trajectory at a significant chunk of c. on it's return towards you in impales your body; sorry just trying to bring these separate physical realities together. how much length passes through you; a full meter? 



#13
Nov2912, 04:13 PM

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#14
Nov2912, 04:47 PM

P: 181

Would it be valid to explain it in this way?




#15
Nov2912, 05:33 PM

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Spacetime is locally Minkowskian at every point. The local speed of light is the same everywhere. The diameter of a hydrogen atom is the same, and the frequency of its spectral lines are the same. So from B's local point of view, nothing has contracted, neither time nor space. And c is c.
The only question then is how A views B's experiments. He does so using his own Schwarzschild coordinates, r, t, θ and φ. A interprets the velocity of a light ray moving in the radial direction to be its coordinate velocity, dr/dt. In the azimuthal direction he interprets it as r dφ/dt. Neither of these is equal to c. Furthermore they are not equal to each other. A believes the speed of light down in the well is not c, and not isotropic either. 



#16
Nov2912, 09:57 PM

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Again, the light from the star is irrelevant to the comparison of the meters at A and B. 



#17
Nov3012, 04:19 AM

P: 344

I was just trying to explain that seen from any overall perspective  "the distance"  "it self"  (between the Earth and the distant star) is not changing,  (regardless which overall observer that would measure it),  the disagreement between A and B, is rather due to a "local" different space time deformation / reality perception. But still the point is what happens to 1 meter,  I guess the same thing. Let say A would use a lot of effort putting a measurement tape between the Sun and the Earth. Everybody could now see that the distance was exactly 1,5E11 meter, so as A predicted. But B is skeptical, he would say, seen from his cellar perspective,  (due to length contraction),  the distance must be 10 meter less. Something very basic must be wrong with A’s measurement tape. It must be crystal clear that B never would be able accept that A's total measurement to the Sun is correct. If A's total measurement not is correct (seen from B's perspective),  he must most likely also have failed to measure 10% of the path to the Sun,  and also failed to measure 1% of the path. In the end of the day it comes down to that B would say to A,  I don't trust your ruler is exactly 1 meter. Prove it to me. A's definition of 1 meter is the time interval of 1/299,792,458 of a second,  So what is exactly wrong with that? I think the definition of one meter is always correct = 1/299,792,458 of a second BUT it must be relative to the local timedilation. Which mean a short second = a short meter,  and a relative longer second = a proportional longer meter. That would be the most simple and logical way to exactly settle the disagreement. Such conclution should not come as a surprise, because space is curving,  illustrated by the stretching rubber sheet. So when space is ‘stretching’ towards a field of gravity, and time also,  I cannot see what prevent such logical conclusion,  There should as I see it not be any conflict to that 



#18
Nov3012, 06:41 AM

P: 1,098

I appreciate the perspective that the interval is the same, and stands as a "true" measure of spacetime, in turn one physical reality. But i don't think that is your point with calling different measures of length time of the same physical reality. To reword my point of view, the Twins are different ages, at one point they experienced different physical realities...comparably. 


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