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Are laws of nature really the same in all reference frames? 
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#91
Oct1111, 09:52 PM

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2. If so, how do you conclude that the observer at infinity has the ultimate saying about what the real length is? r simply represents the, so called, reduced circumference and directly relates to the circumference and area of resp. a circle and sphere. Are you perhaps saying that the increase in radius and volume between shells of lower rvalues over the expected Euclidean values is not due to the fact that space is no longer Euclidean but due to the fact that rulers shrink? wrt the first reference, I am sorry I must be slow but I do not see where it states anything that is relevant to what you said, could you tell me exactly what you think shows the reference that rulers shrink. wrt to the second reference I am also at a loss, where exactly is this pointed out that rulers shrink? 


#92
Oct1111, 10:32 PM

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"Gravitational Length Contraction Lengths of objects in gravitational fields are contracted according to the theory. The prediction has never been tested. For the keen, you may wish to derive this prediction using the same techniques used in the previous subsection to derive gravitational time dilation. " With regard to the second reference, there is the following: "The factor of 2 relative to the equation of 1911 arises because in the full theory there is gravitational length contraction as well as time dilation. Of course, the length contraction doesn’t affect the gravitational redshift, which is purely a function of the time dilation, so the redshift prediction of 1911 remains valid" Here is another discussion, but it is not at all rigorous: http://www.relativity.li/en/epstein2/read/g0_en/g4_en/ "The smaller r is, the longer a segment in the radial direction will be when measured with local yardsticks. As seen from OFF: yardsticks shorten in the radial direction with increasing strength of the gravitational field! Thus, for the thickness of a spherical shell around M, a local surveyor determines a larger value than an observer in OFF. " [EDIT: found better discussion of this: http://www.mathpages.com/rr/s703/703.htm ] 


#93
Oct1211, 01:25 AM

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#94
Oct1211, 02:20 AM

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I agree (and "disagree"). Notice Observer “Ex” (external) will not see any length contraction. Seen from the perspective of "Ex" the distance of the Milkyway would be the same for both A and B. B is deeper inside the gravitionel field of the Sun. He will complete 1 orbit in less time as A. If B shall have the right to claim that the orbit of the MW is shorter (length contraction), it is only possible if B’s ruler is comparable longer than A’s. Do you understand that point? – It seems like a contradiction but it is not, but rather a mathematical necessity that B’s meter stick must be longer than A’s. (You must also respect the mathematical reality of observer Ex,  Observer Ex must also have the possibility to understand other realities  relative to his own ) B and A’s perception of speed can also not possible be the same, simply because B’s clock is ticking slower. We should not be allowed to mix realities, hence also not to force our (A’s) perception of speed into B’s reality. So since B’s timerate is ticking slower,  that alone should mean that B moves FASTER than A,  but because B’s ruler (seen from a mathematical point of view) must be longer the speed is the “same” – but not comparable the same. Notice A and B will agree to complete the orbit of the MW in the exact same period, but they can impossible agree about distance / circumstance / time / rulers. I appreciate your contribution to the thread and I understand most of what you have explained, but still I wish there was a simpler way to understand and compare how B's reality really is, as well as understand how would B’s ruler would be compared to A’s. I think there still is more to discover to make that simpler, straight and logical. 


#95
Oct1211, 05:48 AM

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#96
Oct1211, 08:24 AM

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 The space in not Euclidean, so rulers measure more radius than expected based on the circumference, so the rulers appear to be shrunk when compared to identical rulers placed around the circumference. This is equivalent to:  The spacetime in not Euclidean, so clocks measure less time than expected, so the clocks appear to be slowed down when compared to identical clocks placed around the circumference. 


#97
Oct1211, 09:20 AM

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Totally independent of the issue of local rulers perceived from a distant free fall observer, I proposed a different, simple convention for astronomic distances (radar ranging, using local time, and assumption speed of light is isotropically c. It is only using this convention (rather than local rulers) that you end up with shorter distances to distant objects, and thus the same speed measured by A and B. Note that whatever definitions are used, some measurements by A and B will differ (assuming each uses the same definitions). This is not unexpected or inconsistent with invariance of laws of physics. Let's state what is really claimed by different relativity principles: 1) Galilean relativity: All laws take the same, simplest, form in any inertial frame. Note, this never meant that measurements are the same, only laws (equations) relating measurments. The main thing wrong with this was that its law for velocity transformation between inertial observers turned out to be experimentally incorrect. Between observers with relative acceleration, there is no simple relativity, and laws take more complex form. 2) Special relativity: Same principle as above, except the transformation law between different frames is different and consistent with experiment. In particular, there is no 'relativity' between observers undergoing relative acceleration. 3) General relativity gives you both less and more. The laws of special relativity only apply locally, for inertial observers, defined as those in free fall. There is no unique answer at all to such things as long distances or velocity of a distant object (whether for inertial observers or noninertial observers). Instead there are only useful conventions you may choose, and procedures for making valid physical predictions based on whatever conventions you choose. There is a general formulation of laws such that whatever conventions are used by any observer, the laws in this form apply (but measurements are not the same). However, the same conventionality of coordinates means, in practice, you use transformation rules to convert your measurements to the most convenient coordinates for calculation. Based on (3), your A and B observes each know they are noninertial; they know the magnitude of their acceleration. Seeing the sun, and making measurements, they can determine the qualilocal structure of spacetime. What each does, in practice, is convert their local measurements, using the predictions of GR to accomplish this, to milkyway center coordinates (each able to determine a different required clock adjustment, for example). They compute distances, speeds, etc. in this frame. Each one doing this ends up with the same predictions and values. This is all that is expected, and found to be true. 


#98
Oct1611, 06:56 AM

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Well I have come to a new simpler conclusion. When I would jump from A’s to B’s reality, I would see the exact same Universe. The distance between the earth and the Moon, or any other distance would be exact the same everywhere. But if we compare these 2 realities,  B’s reality would be a bit smaller.  Everything would be a bit smaller, also the ruler. That could then also explain the cause of the Shapiro delay http://en.wikipedia.org/wiki/Shapiro_delay Because speed of light must then be measured in the local surroundings. Edit No I change my mind This can't be true because then there would be no Shapiro delay, but rather opposite PS Any idea what is causing the Shapiro delay ? 


#99
Feb1212, 01:11 AM

P: 344

Let's say the International Space station (ISS) was orbiting the Sun in the exact same orbit as the Earth.
A clock on board the ISS and the Earth would now tick different due to different gravity. This mean that the laws of orbit gravity can't be the same these 2 places, simply because the time consumption to complete one orbit for both objects,  is larger for the ISS So what is wrong? I mean the law of nature must be the same everywhere, or ? Is the answer that;  the length of one second not is the same both places ,  or in other words that one second is "stretching" on board the Earth (compared to one second on board the ISS) and therefore longer compared to one second at the ISS ? I mean the time to complete one orbit must be the same on board at both objects, but a clock on board the 2 objects would not show this. There must be a simple way, basic to explain which factor(s) is (are) changing 


#100
Feb1212, 02:18 AM

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But what is important is that they both measure the same value for the speed of light and in order to do that, they must use the time from their local clock, not some other time such as from GPS which gives the same time for every point on earth. 


#101
Feb1212, 06:49 AM

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#102
Feb1212, 04:06 PM

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But the example of the ISS and the Earth orbiting the exact same orbit is at least for me easier to handle, because both such observers (these places) must be right, which mean the time one orbit takes can't be the same. Hence there is a problem since the gravityorbitequations a ISS inhabitant and a Earth inhabitant will use,  will not give the same result. For exsample to determinate their speed or orbit size. So whos calculation will be wrong? The Earth observer or the ISS observer? Option 1 is the definition of 1 second cannot be universal. Option 2,  this is what wrote about above, ( but now I have change my mind) and believe option 1 must be correct. So what is wrong,  which simple factor(s) must be flexible? Is it the definition of how long 1 second is from place to place,  or is it distances or/and speed that not are the same in such 2 observer realities. ? As I wrote I believe it is “one second” that cannot have a universal definition. If that should be wrong WHAT is hen the correct answer? The answer must as I see it be simple, logical and understandable  since we are discussion simple math, >> time multiplied with speed must = distance ( and not for exsample distances) 


#103
Feb1212, 05:07 PM

P: 344

Let say one (atomic) clock is on board at the ISS and another on board of the Earth, both objects orbit the Sun in the exact same orbit. Let’s say the clock on board the ISS ticks double so fast compared to a clock at the Earth (due to different gravity) And exactly this is the problem,  because time is different these 2 places. Hence many laws / equations cannot give the same result. 1 orbit of the Sun cannot at the same time be both 500 million km and also 250 million km. This should be pretty simple, at least so long time multiplied with speed must = distance. Due to time is not the same even in the same orbit, we have such principle problem (just not so exaggerated as the example shows,). This means that either equationconstants, distances and/or speed,  or the definition of 1 second cannot be the same in different spacetime realities. Does the stable nailed definition of one second mean that we are mixing ingredients of different spacetime realities? As I see the difination of "onesecond" cannot be universal, and if it really should be how can we know it is so? It seems that “our definition” of 1 second simple cannot be used in other spacetime realities.. I know this will confuse you,  but the point is that yes a process in a different space time reality can be either faster or slower as here at the planet. How can equation and laws of gravity be exactly the same everywhere, something must give and take. Why doesn’t it seem to be answer to these questions? Shortly spoken, let say 1 second is the same length everywhere,  but the process responsible for the definition of 1 second is not the same. Is that possible? 


#104
Feb1212, 05:15 PM

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#105
Feb1212, 05:18 PM

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Simply because two different observers measure something different does not mean that the law governing the measurement is different. For example, due to Doppler shift two different observers will measure different frequencies for a given light source, but that by itself does not imply that Maxwell's equations are different. 


#106
Feb1212, 05:34 PM

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Right? So you can sit on the Earth and calculate the orbit of the Earth and you will get a certain result. – You will believe this is 100 % true. A ISS inhabitant can do the same from his perspective,  and from the exact same orbit, he also will believe his result is absolute right about the circumstance just calculated. But since time is not the same, (and I assume we agree speed is the same) – we have now 2 different circumstances,  these can’t be the same. So who is wrong and who is right? I mean do you believe the orbit of the Earth can be both 250 billion km and also 500 billion km ? It doesn’t sound logical  and hence hard to buy. 


#107
Feb1212, 07:17 PM

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Using their odometers they each measure the length of 100 billion laps around the same track. One obtains a length of 250 billion km and the other 500 billion km. So who is wrong and who is right? I mean, do you believe that the track can be both 250 billion km and also 500 billion km? It doesn't sound logical  and hence hard to buy. Therefore, the laws of physics must clearly be different on the inside of the track and the outside. 


#108
Feb1312, 02:42 AM

P: 344

According to this example there are no logical problems, except when you mean that the radius to the Sun is different measured from the Earth to the sun compared to measured from the ISS and to the sun,  even though both objects,  ( the Earth and the ISS) both would obit the Sun in the exact same orbit (and with the exact same speed). Is that what you mean? 


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