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Are laws of nature really the same in all reference frames? 
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#55
Oct511, 04:24 PM

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So how was it done then ? 


#56
Oct511, 04:29 PM

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Both the example in the link is about Special relativity. That confusion is not necessary. General relativity alone is enough. Don’t make it more complicated as it is. 


#57
Oct511, 05:28 PM

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#58
Oct611, 02:05 AM

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#59
Oct611, 04:06 AM

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Only clocks tick at different rate. Measuring rods are of the same length. 


#60
Oct611, 08:46 AM

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Next, you should be aware that for both SR and GR it is wrong believe there is equivalence between inertial and noninertial frames, or between two noninertial frames (which is what you really have). Acceleration (deviation from inertial path) is an invariant feature, not a relative feature (it is characterized by proper acceleration). In a nutshell, every aspect of your scenario is ill conceived. The only thing you can actually expect from your scenario is that if all laws are expressed in their general tensor form, then each observer can build a coordinate system in which they are at rest, and use said coordinate system and laws in tensor form to make valid physical predictions. 


#61
Oct611, 12:26 PM

P: 140

How it was measured has no bearing on what I was talking about. I am trying to figure out what you mean to say or what you are thinking. Here are a couple questions for you. Does it matter what frame of reference you are talking about when you say earth is moving at 250km/s? Or are we simply moving at that velocity no matter what frame of reference we take? 


#62
Oct611, 12:51 PM

P: 344

We can say A is you and B have a slower ticking clock, due to gravity, we could say that A live in a skyscraper, and B in a cellar etc. Or we can use the example above. Hence it doesn’t matter 


#63
Oct611, 01:29 PM

P: 344

The scenarios I have shown SR do not apply since speed of both observers is the same. Both clocks orbit the MW in the same radius. The cause of time difference between the 2 observers is in this case is only caused due to gravity (GR) (General Relativity). We can assume that A’s reality is exact the same as ours. Hence we know everything about A’s reality, as well how A has come to all his conclusions,  for example the circumstance of the Milkyway etc.. But when a clock is ticking slower due to the gravity of the Sun, for another observer (we call that observer B,)  then it is simple calculation that A’s reality cannot be valid for B. The answer must be that A‘s reality must be exactly so real as B’s, and therefore we also must know how is comparable distances speed etc or B. For example; How is speed for B ? How is comparable speed between A and B ? What is the distance of the MWorbit for B ? How is the comparable distance between of the MW orbit for A and B ? Is B's meter stick comparable smaller than A's – or longer – or the same length ? Is a meter stick comparable smaller – or longer – or the same length, at the surface of the Sun compared to 100 billion km away,  du to gravity (GR) ? seen from B’s reality Hence 2 clocks orbit the Milkyway exactly as the Sun does. The difference is that one clock (B) is closer to the sun and therefore ticking slower than the other clock (A). This certainly , logically and mathematical MUST have SIMPLE consequence(s), since 1 complete orbit round the Milkyway take less time for B as it does for A. Time multiplied with speed = distance. Try instead exactly to answer some or all the questions. There must certainly be “consequences” of time dilation. There are no reasons to make the simple scenario more difficult or impossible as necessary. “If you can't explain it simply, you don't understand it well enough”. Albert Einstein 


#64
Oct611, 02:20 PM

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Asking for an answer in terms of GRwithoutSR is meaningless. No such theory exists. The only theories available are either SR alone (without gravity), or else GR+SR (with gravity).
According to each of your two observers, the velocity of the other observer is zero. But according to a third observer who is falling freely directly towards the Sun, the two observers are not a fixed distance apart. According to this third observer, who within GR is an inertial observer (and the other two are not inertial), Lorentz contraction causes their distance to keep changing, i.e. they are not both moving at the same speed according to the third observer. According to this 3rd observer, this relative motion is the cause of the time dilation between the first two observers. 


#65
Oct611, 03:00 PM

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You are asking about analyzing the motion of the MW center from A or B point of view. This requires two global coordinate systems. Each of these coordinate systems is built from a noninertial frame because thrust would be required to hold A and B in position against the Sun's gravity. They are different noninertial frames because each would require a different amount of thrust. Further, from A and B point of view the laws to be applied would be determining the elliptical motion of MW center around each of them. For each, this would be a complex application of GR field equations in a rather complex coordinate system. They would still find that their application GR would be successful. You can pretend the problem is simple only by ignoring its essential features, and misapplying relativity. Einstein also said: be as simple as possible, but no simpler. 


#66
Oct611, 03:30 PM

P: 344

Right,  I remember We will call the third observer C The problem that C also cannot agree how "comparable distances" (between A and B) is doesn’t make the problem smaller, does it? Still we have time rate difference, that must mean 2 (real) and different realities. The many questions (concerning A and B) mentioned above is still unanswered. Answering these must be possible also even though SR and GR are "connected" 


#67
Oct611, 04:04 PM

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Well, the reality is roughly as follows.
We don't have to verify physical predictions in A coordinates and B coordinates would come out the same because this follows purely from mathematical definitions and theorems. However, doing physical computations in these coordinates would be a bummer (the metric tensor would have a very complex form). So, confident of pure math, A and B would each translate their local measurements to a convenient coordinate system (MW central frame, presumably). This translation would be based on relativity. They would have to translate locally measured times, distances, angles, and red/blueshift. Once they translated their local measurements, they would compute in the MW center frame. And no, I have no interest in carrying this out with your numbers. [Addendum: A and B can determine how to transform their local measurements with local measurements plus GR. They measure their proper acceleration with an accelerometer. This along with a bunch of local redshift and other astronomic measurements give enough information. ] 


#68
Oct711, 02:21 AM

P: 344

We will call the third observer C. When C is falling towards the sun and first passing A and next B he would off course accelerate faster (due to acceleration of the Sun) when passing B as he would when passing A. So for C it would look like B is moving faster away from C than A. But in fact C is moving relative to A and B,  and not A and B relative to C. I mean any other observer as C (on the Earth or other places in the Universe) would not see that A or B is moving away from the sun, (or away from each other) but only that C is moving towards the sun. How can the reality (an illusion) of the third observer C have anything to do with the timerate for A and B ? 


#69
Oct711, 04:57 AM

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Orbital speed can be calculated by simple formula when ellipticity is zero (circular orbit). 


#70
Oct711, 08:01 AM

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#71
Oct811, 03:57 AM

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First, the setup for consideration is such that we can investigate gravitational time dilation with other things unchanged. Yes we can do that in physically meaningful way exactly as Bjarne described. And that's the right approach to understand something. Isolate that one factor as much as possible. That is exactly the thing that you do in real experiments. Second, observers make astronomical observations about their movement relative to the center of MW and the distance to the center of MW. Again, yes we can do that and we don't have to factor out anything related to our gravitational acceleration. Astronomers on surface of Earth (gravitationally accelerated frame) perform observations all the time and the only thing they factor out is aberration but that's velocity not acceleration effect. Third, we compare results for two observers. So far question (actually background for question) is formulated in physically meaningful way. Do you agree with that? 


#72
Oct811, 07:07 AM

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I wanted to focus on this being a false expectation. That it is expected that different observer's measurements may differ. And that for arbitrary observer's, the only form 'laws being the same' that you can expect is if they are expressed in general tensor form. 


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