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Are laws of nature really the same in all reference frames? 
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#73
Oct811, 02:43 PM

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All what we can be 100 % sure about is;
I see no reason to complicate that more than this. I believe we first at all only need to look at this purely / simple mathematical. Speed multiplied with time = distance,  this must be true both for A as well for B,  since there is no reason to believe that only our ( or A’s) reality is more true like others. This leaves us with 2 simple mathematical options; Option 1. The orbit speed for the 2 clocks (and the Sun) must seen from the perspective of observer B be faster as for observer A.  (I don’t believe in that option,  since A and B do not change distance between them). Option 2 B's meter stick is longer and therefore distances shorter.  This is the only explanation I can accept so far. As I understand relativity;  there are no certain reality (also not ours), since time (and probably also “size / distance”) not is comparable the same. I think before accelerating the speculation into too much complexity we should try to look at the must simple level, as just shown, and finish here first. 


#74
Oct811, 03:17 PM

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#75
Oct911, 02:28 AM

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According to the example the 2 clock counteracts gravity from the Sun,  (they have small racket engine on board). All other observers (in the Universe) will observe that the Sun and the 2 clocks are completing 1 orbit of the Milkyway in the exact same period of (their) time. This will not affect the motion (or timerate) of the 2 clocks.. 


#76
Oct911, 03:19 AM

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I think that aberration can be factored out if both observers translate their observations to rest frame of MW mass center. After they do that they should point in the same direction as where is MW mass center. 


#77
Oct911, 05:44 AM

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So it might be good to check out about Shapiro delay 


#78
Oct911, 06:11 AM

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#79
Oct911, 08:04 AM

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#80
Oct911, 08:12 AM

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Be that as it may, there is straightforward way the two can observers agree on their speed relative to the milky way center. Suppose each adopts as their distance standard (converting other ways of measuring distance to far away object to match this standard) c times light round trip time to object as they measure it. Then the closer to sun observer thinks the MW center is closer (less time for the round trip). They then figure a smaller circumference for the orbit. They divide the smaller circumference by the shorter time, and come up with the same speed as the 'further from sun' observer. 


#81
Oct911, 10:55 AM

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This concretely explains the idea that, within GR, there is no objective meaning to an SR effect versus a GR effect. Almost always, you can validly treat some effect as different mix of SR vs. gravitation effect by choosing different observers or coordinates. There is yet another way to choose to treat gravitational time dilation as kinematic rather than gravitational (involving parallel transport of 4vectors). However, I don't think you have the background for that. 


#82
Oct1011, 03:23 AM

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To make some statements about time delay in context of Shapiro delay you have to make some assumption about distance measurements. And this assumption is that distances stay the same. When you assume this then Shapiro delay agrees with expected time delay. Or looking at this from another side. From Shapiro delay we find out that coordinate speed of light is different at different gravitational potentials. Now if local speed standard (c) is different for two observers then speed measurements for the same (global) physical situation should be different for two observers. Just like it is with time. You can try to make prediction for coordinate speed of light using your Option 2 (B's meter stick is longer and therefore distances shorter). What it will be? 


#83
Oct1011, 05:04 AM

P: 344

[QUOTE=PAllen;3548070]Actually, along with gravitational time dilation, there is also gravitational length contraction. According to the 'further from sun' observer, the closer observer's rulers are slightly short, rather than long. The meter stick cannot be the same comparable lenght both places,  can it ? http://www.physicsforums.com/showpos...4&postcount=64 C is; “a third observer who is falling freely directly towards the Sun”. Off course C is then accelerating, due to acceleration due to gravity. A and B is not affected due to the fact that C can have the illusion that it is A and B that is moving opposite. I don’t understand the point. C’s reality and the illusion that A and B is moving opposite, is not real for anyone else than C. Why make a big point out of what only is an illusion. ? Let us now say that B’s clock tick half so fast like A’s (for simplicity reasons)  (still according to the example above) . A and B would send a light beam to the same planet . The light beam would reflect and return. After the exact same period of time (seen by any external third observer “EX”) the light beam would return to both A and B. Observer A would now say it took 1 (earth)year, (31536000 s.) But B would say it took half so much time. Seen from observer EX perspective the distance the light was travelling to A and B is the exactly same. The ONLY way both A and B can agree that the light was travelling with the “same” speed, is when B’s meterstick is comparable double so long as A’s meterstick. So simple is that. This mean that speed is really “c” (300,000 km/h) seen from both the perspective of observer A , as well as from B’s reality. BUT when you would compare the speed it would be a different history. The only solution to that (as I can see) is that we cannot mix realities, but are forces to separate these. And as I wrote this must mean a different comparable meter stick – that’s all, and the only simple mathematical solution. Why not keep things simple, when they are simple? 


#84
Oct1011, 07:18 AM

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The only problem is that if we would make prediction for Shapiro time delay it would be zero because coordinate speed of light does not change in your case. And yet we observe slowing down of coordinate speed of light when signal passes gravitating object at close distance. So your model does not agree with observations. So what we do next? 


#85
Oct1011, 12:46 PM

P: 344

Now we assume the meter stick always is comparable the exact same for both A and B. Observer A and B will now in a certain period measure a photon traveling a certain distance (300,000 km). Both observers agrees that this is what really happen. Based on this observer A would say that the speed of light is exactly 300,000 km in one (of his) second. But observer B would say OK I agree the distance the photon was travelling is 300,000 km ... BUT I do not agree it took one second,  my clock shows it only took ½ second, so here the speed of light is 600,00km/s Do you prefer that solution? Hmmm… So what we do next? What do you think the answer is (except that distances / the meter stick always are comparable the same lenght) ? 


#86
Oct1011, 12:55 PM

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There truly is no unique, preferred answer to large distances in GR (short of choosing a preferred global coordinate system). Actually, there isn't in SR either  distances are observer dependent. 


#87
Oct1111, 01:23 AM

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There is only one observer who is sending radar signals so that sometimes they are passing close to the Sun and sometimes far from the Sun. When you make a correction for time delay depending on signal's closest passing distance from the Sun you can consistently describe orbit of observed object (Venus). In your case speed of light is always the same because proportion "m/s" does not change. "The time delay effect was first noticed in 1964, by Irwin I. Shapiro. Shapiro proposed an observational test of his prediction: bounce radar beams off the surface of Venus and Mercury, and measure the round trip travel time. When the Earth, Sun, and Venus are most favorably aligned, Shapiro showed that the expected time delay, due to the presence of the Sun, of a radar signal traveling from the Earth to Venus and back, would be about 200 microseconds,[1] well within the limitations of 1960s era technology. The first tests, performed in 1966 and 1967 using the MIT Haystack radar antenna, were successful, matching the predicted amount of time delay.[2] The experiments have been repeated many times since then, with increasing accuracy." Statement that "laws of physics are the same in all inertial reference frames" means that local experiments will give the same results. But global observations can be different. 


#88
Oct1111, 06:28 PM

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None of this is relates at all to the issue I was presenting (measuring distance over tens of thousands of light years using radar ranging distance as your definition, with other measuring methods calibrated to match). Especially because your own scenario had these measurements being done from lab held stationary (by thrust) with respect to the sun. Also, of course, there are no astronomic measurement that could be made at a precision where it mattered whether they were done at your head or your feet. 


#89
Oct1111, 07:10 PM

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What I can show you mathematically is that both the volume and radial distance between two shells is more than we would suspect if we would calculate it based on their areas. And the discrepancy increases for lower rvalues closer to the EH. 


#90
Oct1111, 09:44 PM

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I've only seen this contraction discussed radially. Two references validating its existence (but not deriving it) are (search for contraction on of these pages): http://www.upscale.utoronto.ca/PVB/H...el/GenRel.html http://www.mathpages.com/rr/s601/601.htm 


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