# Relativity of Simultaneity Gendankin

Discussion in 'Physics & Math' started by MacM, Feb 3, 2006.

1. ### DaleSpamTANSTAAFLRegistered Senior Member

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True.

From our previous conversations I understand that you do not accept the fundamental postulate of relativity and instead believe in some sort of prefered reference frames. Given that you reject the postulates of relativity it makes sense that you reject the conclusions of relativity. If you do accept prefered reference frames then it should be quite possible to work up a self-consistent theory and mathematical framework that would not include time dilation. In such a theory your pulsar clock could work as you suggest. And I am sure it could all be done self-consistently. Logical consistency is about the limit of what a gedanken can show.

However, the idea that a potential non-relativistic theory could be self-consistent hardly makes SR any less self-consistent.

This is a silly criticism of SR. I have to neglect gravity because I lack the math to follow GR. That doesn't mean that gravity is not a part of relativity. IMO, to criticise SR for not addressing gravity without recognizing that its generalization does address it is just like criticising Newton's 1st law for not handling accelerations without recognizing that its generalization does address them.

In my comments I specifically stated that, according to SR, the time dilation effect exists even after you take into account the Doppler effect. It does matter, because it is an effect that cannot be explained purely by the relative velocity (Doppler) but can be explained by the pulsar or lighthouse or hydrogen actually rotating or emitting slower (time dilation).

Yes. I posted it earlier, but here it is again: http://en.wikipedia.org/wiki/Transverse_Doppler_effect

Again, I understand that you reject the primary postulate of relativity so it is reasonable for you to also reject the conclusions of relativity. You could potentially develop a self-consistent theory with no time dilation. However, the idea that other theories could also be logical in no way diminishes the self-consistency of SR.

-Dale

3. ### CANGASRegistered Senior Member

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Cheese.

There is no question that Special Relativity, in its circular logic squared, is a marvel of internal consistency. The issue is: does Special Relativity accurately represent reality?

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Correct.

7. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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It is too late for me to go thru all your ideas but I again recomend the "Is time universal? -No (and its proof)" thread as it makes clear that frame A's simultanity is not the same as frame B's simultanity.
Lets imagine that all clocks in my frame A, JUST NOW, show 12:00 noon AND at that same time in frame B there is a moving clock adjacent to each of mine. I am king of the universe and by earlier royal order I required that all clocks in frame B must be set to 12:00 in agreement with the clock of my frame A adjacent to them when my frame A clocks shows 12:00. Thus for that instant, all clocks in both frames are showing the same 12:00 on their dials.

My second royal decree is that at 2:00, my time of course, I have 1000 photographers in many separate location in my realm take photos of the Frame B clocks passing very close to the cameras. When the film is developed what do you know - they all show 1:00, not 2:00. They are keeping perfect time for people of frame B, but no longer sychronized with the royal clocks of frame A and I am mad, so Royal degree 3 is:

All clocks in frame B will have new gears installed so that the hands rotate twice as fast. Now they are all again reset to 12:00 when passing mine showing 12:00 and the photographs are taken again at 2:00. I am happy with the results. They are now sychronized with the Royal frame A clocks.

My communication page is telling me the people in frame B have lots of busness men complaining that the the workers are now only producing half as much in the "new" 40 hour week. Lot of othe complaints are starting to come in also. (Farmers go to milk the frame B cows every 12 hours but the cows are still in the field eating, not back at the barn, etc.) They all boil down to the fact that the frame B clock do not measure time in frame B correctly with the new "double speed" gears installled.

Do you see why now? Answer: Time in B is slow, by the Royal clocks of frame A.
Even me, the royal king of the universe, can not have both (1)all clocks of the universe sychronized and (2) yet all keep time correctly in their frames. SRT wins another one.

Last edited by a moderator: Feb 25, 2006
8. ### CANGASRegistered Senior Member

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BillyT slyly throws before us the famous RED HERRING twin paradox in new clothing so that nobody discerns it until it is too late and we are arguing about TIME instead of anything else that is genuinely important.

Sorry, Charlie, I mean, Billy, not good enough.

I mean, not good enough for me. Anyone else that is dumb enough can be dragged into Twin Paradox Argument # one Gillian and one.

9. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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by DaleSpam:
"However, the idea that a potential non-relativistic theory could be self-consistent hardly makes SR any less self-consistent."
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I agree with you DaleSpam. I am not attempting to 'create' an alternative theory, I fully recognize that is far beyond my very limited abilities. I just see Special Theory as LOGICALLY inconsistent, and things keep popping up in my mind to illustrate what I, personally, see as the logical inconsistencies. I cannot claim to be 'correct' and Special Theory to be 'wrong'. I certainly don't know all the answers, I just like to discuss what 'seems to me' to be logical inconsistencies. I know it is a heck of a lot easier to find assumed logical weakness in a theory than it is to formulate a new theory without any weaknesses. The brightest minds in science are at this minute trying to formulate new theories to address the shortcommings of established theories, a better model of reality in other words.
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by DaleSpam:
"This is a silly criticism of SR. I have to neglect gravity because I lack the math to follow GR. That doesn't mean that gravity is not a part of relativity. IMO, to criticise SR for not addressing gravity without recognizing that its generalization does address it is just like criticising Newton's 1st law for not handling accelerations without recognizing that its generalization does address them."
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Sorry, I guess I didn't state my critism of SPECIAL THEORY'S lack of addressing gravitational influencies clearly. I believe gravitational fields and their effects on spacetime are of primary importance in any theory dealing with the vacuum of space. Gravity is intimently connected with spacetime, light is just a method of transferring information and it is AFFECTED by gravitational potential. Special Theory ignores gravity, and I admittedly took a cheap shot at STR by inferring we couldn't use the example of gravitational collapse of a galaxy rotating too slowly to critize Special Theory.
I conceeded I don't have the answers, but consider this unsupported thought for a moment. Remember when I stated what I have read concerning inertial frames as used in General Gelativity? Special Theory uses GLOBAL inertial frames, GR uses LOCAL inertial frames. Tell me if I am way off base here, but my understanding of the difference is that STR's global frames extend throughout the universe from a coordinate point, GR's local inertial frame extends only in the immediate vicinity of the observer. The local observer is isolated in his spacetime in a local frame. With that interpretation, time could possibly beat more slowly ONLY in the moving spacecraft. The rest of the universe would not have to slow because the spacecraft is travelling at a high rate of speed, only the time within the spacecraft would slow relative to the rest of the universe. Sound stupid?

10. ### DaleSpamTANSTAAFLRegistered Senior Member

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What circular logic? Start with two postulates, they lead logically to time dilation, length contraction, and the relativity of simultaneity, then package it up into the Lorentz transform operating on Minkowski spacetime. That's all there is to SR. Seems purely linear to me.

-Dale

11. ### DaleSpamTANSTAAFLRegistered Senior Member

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I agree with the idea that there probably could exist a better model of reality, it just hasn't been developed yet. At some point I am sure that relativity will be supplanted in much the same way that Newtonian physics was when relativity was developed. It is the best that we have now, but hardly the uber-theory to end all theories.

However, SR simply does not have any logical inconsistencies. The whole point of developing a rigorous mathematical framework for any theory is to discover and eliminate logical inconsistencies (in addition to allowing quantitative predictions). That is why the math behind a theory is so important, math is a language you can use to describe a theory where only logically consistent statements are gramatically correct.

I think you are right, gravitational fields and their effects on spacetime are incredibly important. That is why there was such a prolonged effort to develop GR. Again with the analogy between SR and GR and Newton's 1st and 2nd law. SR is only valid in regions completely without gravity (regions of perfectly flat spacetime), Newton's 1st law is only valid when all forces are perfectly balanced. Do such situations really exist? No. But situations often exist where they are each close enough (within a given experiment's measurement error). And they both provide useful means of analysis and prediction. But they have known limitations, and that is why their generalizations (GR and the 2nd law) are so important.

Your global v local inertial frames sounds approximately right to me. I don't know if the "official" idea is for local frames where the frames are individually straight but curved wrt each other or for global frames where the whole frame itself is curved and only approximately straight in sufficiently small local regions. I am really not trying to duck the issue here, I just never feel that I understand a theory until I understand its math, and I don't understand GR's math.

-Dale

12. ### kevinalmRegistered Senior Member

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993
Keeping in mind that tensor calc in 4D curved spactime is _way_ over my head, I beleive that the "official" idea is something like this:

To predict what an observer at a particular point in spacetime will observe, construct a local lorentz frame at that point. Strictly speaking, that view is only true at that point. As I remember from my mostly failed attempt to read M,T and W's "Gravitation", a lot of the math involved over how large a region this veiw could be said to hold and to what precision, and characterizing how the veiw diverged from curved spavetime.

13. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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OK, yes you are. SR is a subset of GR. (DaleSpan has already said this, but perhaps not so bluntly.) I.e. If you take GR and set all gravity fields to zero and disallow any acceleration, then you have SR*. The range of the coordinates of GR must therefore be at least as large as those of SR subset.
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*fortunately the math required to work / think about SR is very much simpler when this is done. That is why "I don't do GR." - GR's tensor math is too rough for me.

14. ### CANGASRegistered Senior Member

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To be historically correct, as if that means anything to some of us, GR is an outgrowth of SR. SR came first.

GR can be construed to be a rather desperate attempt to resucitate SR after the disasterous reaction to the infamous twin paradox indiginous to SR, and the fatal blow, not properly recognized, delivered by Sagnac 1914.

The coordinates of GR are specifically designed to LIMIT, not enlarge, the space analyzed. The concern of GR is to develope a LOCAL METRIC, not a universal metric. The LOCAL METRIC is then related to the entire universe.

SR, being nondefined in the sense of its universality, implying universality, gave embarrassing conclusions which were attempted to be reined in by the limiting local metric of GR.

Last edited: Feb 26, 2006
15. ### CANGASRegistered Senior Member

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I am tempted to expostulate a new theory of physics. It will have two postulates.

1. Everything in the theory is perfectly true.

2. Nothing else can be true.

16. ### DaleSpamTANSTAAFLRegistered Senior Member

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I don't remember who on this forum proposed it, but there was recently a rather elegant SR-only formulation of the twin paradox in terms of spacetime intervals in a single inertial frame. Since spacetime intervals are invariant under the Lorentz transform both twins' perspectives can be derived quite easily using SR alone.

As far as Sagnac goes, I have read two or three articles on the Sagnac effect that seem to indicate nothing fatal to SR. Are you refering to some less famous experiment than his ring interferometry experiment?

Of course, you are free to construe as you choose.

-Dale

17. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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What the Sagnac does is to prove the speed of light is a constant in a non-moving local inertial frame. If another frame is moving relative to the non-moving (rest) frame, the speed of light is different for an observer in that moving frame. The speed of the rotating frame can be determined by the difference in the speed of light in the two frames, the change in the interference pattern. Yes, the speed of light is a constant in all 'at rest' inertial frames, but it is NOT invariant to all observers. The observer in the rotating frame will see the speed of light as c +v, or c - v, depending on that observer's speed (v). A light beam that is split to propagate in different paths around a triangle will take the same time to complete both legs if the triangle is not rotating with respect to the local vacuum. When this same triangle is rotating with respect to the local vacuum, the time for the light to complete the two paths will differ according to the rotational speed of the triangle. A laser which generates a beam that counterpropagates around the triangle will generate a monochromatic beam when the triangle is not rotating, and beams that propagate at different frequencies when the triangle is rotating wrt the local inertial frame.

18. ### DaleSpamTANSTAAFLRegistered Senior Member

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Yes, but none of that is counter to SR. The famous Sagnac effect is predicted by SR. So its verification certainly cannot constitute evidence against SR. But its existence is not really evidence for SR either since it is also predicted by Galilean relativity.

CANGAS must be talking about some other less-famous experiment by Sagnac.

-Dale

19. ### funkstarratsknufValued Senior Member

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1,390
That would be me:

The proper time along a worldline is the path length wrt. the Minkowski metric:

ds<sup>2</sup> = dx<sup>2</sup> - c<sup>2</sup> dt<sup>2</sup>

Now, the spacetime interval is

s<sup>2</sup> = &Delta;x<sup>2</sup> - c<sup>2</sup> &Delta;t<sup>2</sup>

i.e. the path length along a (Euclidian) geodesic between two events. A straight line, in other words.

In his own frame, the stay at home twin's worldline obviously has exactly length equal to the spacetime interval between the start and endpoints and is the geodesic between them. Now, every other worldline than the geodesic between those points has a shorter path length wrt. the above metric, as can easily be seen:

Such a worldline will be strictly monotonically rising in the time dimension (as a function of proper time). Hence, the contribution from the time part of the path to its length will be the same as for the geodesic. But, unlike the geodesic, there will be a non-zero spacial contribution to the differential, which will therefore end up with a smaller (closer to zero) value, which means less proper time. I.e., the spacetime interval is the highest amount of proper time possible for a worldline between two (timelike) spacetime events.

So, the travelling twin, moving along a different worldline between the two events, simply by virtue of not travelling along the geodesic, must have a shorter path length, and therefore shorter proper time. And since path lengths are Lorentz invariant, we have that the travelling twin absolutely is younger than the stay-at-home twin.

20. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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You might show me how the Sagnac effect is PREDICTED by SR. All Sagnac experiments I am aware of have been conducted with the rotation of the Sagnac device at non-relativistic velocities. An observer located at one of the points of the rotating triangle will measure the time it takes light to travel around the device to be anisotropic.

21. ### DaleSpamTANSTAAFLRegistered Senior Member

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Yes, as I mentioned previously it is also predicted by Galilean relativity, so it shouldn't be surprising that relativistic velocities are not necessary.

If you have a ring interferometer with three points (A,B,C) then when the ring is not rotating the distance A-B-C-A is equal to the distance A-C-B-A in any inertial frame. Since, according to the postulates of SR, c is constant the times are also equal and there is no interference. When it is rotating the two distances are not equal in any inertial frame. Since c is constant the times are not equal and there is interference.

-Dale

Last edited: Feb 26, 2006
22. ### Physics MonkeySnow Monkey and PhysicistRegistered Senior Member

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Just to reiterate what has been said, the special theory relativity remains perfectly valid locally in the greater context of the general of relativity. Spacetime is a Lorentzian manifold according to the general theory. If spacetime is flat then no matter how things move about, special relativity is sufficient to handle the job (at least so long as gravitational radiation is unimportant). Special relativity can do even more since it remains valid in sufficiently limited regions of curved spacetime. Just how limited a region one must consider depends on the nature of the curvature. True gravitational effects are manifest in the geodesic separation of initially parallel trajectories i.e. tidal forces.

Also, the twin paradox and the Sagnac effect are perfectly explainable with the confines of special relativity. In fact, as has been noted, the explanation of the Sagnac effect doesn't even really need the special theory of relativity so long as the speeds concerned are small.

23. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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by DaleSpam:
"When it is rotating the two distances are not equal in any inertial frame."
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That is the point. The distances ARE equal according to an observer INSIDE or located at one of the points making up the triangle. According to that observer, there is NO DIFFERENCE in the length measured wether the light travels to the right or the left of his location. If the mirrors making up the triangle are 100 kilometers apart, the distance around the triangle is 300 kilometers either way it is measured. But the laser beam still takes longer in one direction than it does in the other. I have given a link previously concerning NASA's upcomming LISA experiment were the laser interferometer will have to take into consideration this anisotropic light speed travel.

You are using the reference frame of an inertial observer OUTSIDE the triangle to imply a greater distance travelled by the light in one direction. In that reference frame, the emitting device has changed locations by the time the light has completed the circuit. In the Sagnac interferometer's REST frame, the emitter/reciever has not changed locations. Special Theory cannot accurately deal with a rest frame that is rotating wrt the rest of the universe. You cannot use the Lorentz transforms to transform into the rotating frame.