# Relativity of Simultaneity

by mangaroosh
Tags: relativity, simultaneity
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P: 17,540
 Quote by mangaroosh My interpretation of it would be that, if the clocks which give the time co-ordinates all ran at the same rate, then absolute simultaneity should prevail; and in order for RoS to prevail clocks would have to give different times (co-ordinates).
This interpretation is incorrect. dt'/dt=1 so all of the clocks run at the same rate.

 Quote by mangaroosh That would be another thing that I don't understand, namely how, or why, the time co-ordinate would include a spatial term.
If the transform is linear (I.e. Both frames are inertial) then the transform in general includes a spatial term. It may be that the coefficient is zero, but that is an additional assumption.
P: 5,632
 That would be another thing that I don't understand, namely how, or why, the time co-ordinate would include a spatial term.
in some sense, it makes no sense. But this may offer a way to begin to think about it:

A simple minded thought experiment: picture an x,y plot....as two particles move around there in different paths, they experience different rates of x and y distances covered,,,right? we don't normally think much about that......each would observe the
other moving differenty through space [distance] than themselves....

now consider a plot of time versus,say, x distance: observe two particles moving differently.... say straight lines with different slopes as an example....one moves faster thru time and another faster thru distance [space]. We observe the particles and each observe's the other moving differently through time and the x direction than themselves....all the
observations are 'correct' but they are also 'different'.
P: 359
 Quote by DaleSpam No, I explicitly showed that to be incorrect above, and I have stated it clearly multiple times.
Hi Dalespam, are you referring to another thread, because I only saw your response on the first page of this one and had a few questions about it?

 Quote by DaleSpam This interpretation is incorrect. dt'/dt=1 so all of the clocks run at the same rate. If the transform is linear (I.e. Both frames are inertial) then the transform in general includes a spatial term. It may be that the coefficient is zero, but that is an additional assumption.
I'm sorry, I don't really understand what dt'/dt=1; I am familiar with the notation from high school maths but I'm not sure how to interpret it in this context.

Where I am not clear is why there is absolute simultaneity according to Lorentzian relativity but RoS according to Einsteinian. Do both not use the same transformations?
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Quote by mangaroosh
 Quote by DaleSpam No, I explicitly showed that to be incorrect above, and I have stated it clearly multiple times.
Hi Dalespam, are you referring to another thread, because I only saw your response on the first page of this one and had a few questions about it?
I explicitly showed it to be incorrect here:
http://www.physicsforums.com/showpos...22&postcount=2

And I stated it clearly here:
http://www.physicsforums.com/showpos...5&postcount=57
http://www.physicsforums.com/showpos...9&postcount=59
http://www.physicsforums.com/showpos...7&postcount=11

 Quote by mangaroosh I'm sorry, I don't really understand what dt'/dt=1; I am familiar with the notation from high school maths but I'm not sure how to interpret it in this context.
It means that the ratio of the time in one frame to the time in the other frame is 1, i.e. time is not dilated.
P: 359
 Quote by DaleSpam I explicitly showed it to be incorrect here: http://www.physicsforums.com/showpos...22&postcount=2 And I stated it clearly here: http://www.physicsforums.com/showpos...5&postcount=57 http://www.physicsforums.com/showpos...9&postcount=59 http://www.physicsforums.com/showpos...7&postcount=11

I do appreciate your taking the time to entertain my questions, and I'm sure you're probably addressing countless other [perhaps equally naiive] questions, so it will hopefully reduce any frustration you might be feeling by highlighting why I still haven't got my head around the issue, despite your generous attempts to clarify it.

 Quote by DaleSpam It means that the ratio of the time in one frame to the time in the other frame is 1, i.e. time is not dilated.
Thanks for the clarification.

My trouble with "getting it" lies in the difference, or lack thereof, between Einsteinian relativity and Lorentzian relativity; do I understand correctly that there is essentially no difference between the mathematics of both interpretations?

If so, the trouble I have is understanding how one interpretation includes RoS while the other includes absolute simultaneity. George suggested that it is down to the different assumptions about the propagation of light, but I don't see how that would lead to RoS without some intermediary step(s).

If my understanding is correct, and the mathematics is the same for both theories, then I'm not sure a mathematical explanation will address the issue; I would imagine it has to be more of a theoretical consideration of what the maths represents.
P: 67
Hello Mangaroosh,

May I suggest yet another way of answering your two questions about Relativity of Simultaneity [RoS]? You might find it simpler to understand, and I am confident that DaleSpam, Ghwellsir, and other posters who have been answering your questions so tirelessly will vouch for its correctness:

 Quote by mangaroosh this might seem like yet another basic question, but I was wondering about RoS. The impression that I got from reading about relativity was that relativity of simultaneity was a consequence of Lorentz contractions, primarily time dilation.
And your latest post question is (with [SR] & [LET] inserted for clarity):

 Quote by mangaroosh ... the trouble I have is understanding how one interpretation [SR] includes RoS while the other [LET] includes absolute simultaneity. George suggested that it is down to the different assumptions about the propagation of light, but I don't see how that would lead to RoS without some intermediary step(s).
Fortunately in this case, both questions can be addressed without Lorentz transforms, clocks or rulers. The price of using this approach is that we cannot quantify RoS, but we can demonstrate its existence.

Relativity of Simultaneity means simply that two events, separated by a distance from one another, and simultaneous according to one competent observer are not (generally) simultaneous according to another moving relative to the first at some constant speed.

The simultaneity of two events can be established using a shuttered lamp on a track between two distant mirrors positioned on the track to reflect any light pulses from the lamp back to it and yourself, the observer. The mirrors need not be at rest and may move independently at arbitrary speeds along the track. Suppose that you are very quick with the shutter and send an extremely brief pulse of light towards both mirrors. If the reflected pulses from both mirrors happen to return simultaneously, what can you legitimately infer? Since by Einstein's postulate, light moves at one speed only, you know these two things:
1. the mirrors were equidistant from the lamp at the time of the reflection, and
2. the two reflections occurred simultaneously.

Now suppose that a second observer happens to be moving along the track just as you send your light pulse from the lamp. Will he agree that the reflections were simultaneous? No. By the time the two reflected pulses meet at your lamp, observer #2 has moved some distance along the track, and correctly notes that the two pulses did not "return" simultaneously to his "here", and for that reason, by Einstein's postulate he must infer that the two reflections did not occur simultaneously.

The LET interpretation predicts exactly the same phenomena, but differs from SR only in that it insists that light depends upon a hypothetical medium, or aether, Therefore the method of "simultaneous arrival" for determining simultaneity is valid only for an observer who is motionless in the aether, and there is only one "true" definition of simultaneity -- that of the motionless observer. Einstein's great insight was that the aether hypothesis was completely superfluous.

- Regards
P: 3,188
 Quote by mangaroosh [..] Where I am not clear is why there is absolute simultaneity according to Lorentzian relativity but RoS according to Einsteinian. Do both not use the same transformations?
Hi I answered that in post #28 and also, indirectly, in post #31. RoS corresponds to the "local time" concept as interpreted by Poincare but Einstein interpreted it differently. Did you study the references? Is there something unclear about it?
P: 3,188
 Quote by mangaroosh [..] My trouble with "getting it" lies in the difference, or lack thereof, between Einsteinian relativity and Lorentzian relativity; do I understand correctly that there is essentially no difference between the mathematics of both interpretations? [..]
Apparently you missed my post here, in which I explained this in detail and with a lot of precision:
http://physicsforums.com/showpost.ph...3&postcount=54

Harald
P: 612
 Quote by mangaroosh My trouble with "getting it" lies in the difference, or lack thereof, between Einsteinian relativity and Lorentzian relativity; do I understand correctly that there is essentially no difference between the mathematics of both interpretations?
It would probably be fair and correct to say that the mathematics going into and coming out of the Lorentz Transformation and their usage is very different comparing Einstein-Minkowski and Lorentz-Poincare relativity. While the Lorentz Transformation itself is obviously common. For the most part, Lorentz worked with vectors, differential equations and their initial and boundary conditions. Einstein and Minkowski built a platform where those things were abstracted away in which tensors and 4-vectors are preferred.
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http://en.wikipedia.org/wiki/Relativity_of_simultaneity

From wikipedia:

 "A popular picture for understanding this idea is provided by a thought experiment consisting of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past. It is similar to thought experiments suggested by Daniel Frost Comstock in 1910[1] and Einstein in 1917.[2][3] A flash of light is given off at the center of the traincar just as the two observers pass each other. The observer onboard the train sees the front and back of the traincar at fixed distances from the source of light and as such, according to this observer, the light will reach the front and back of the traincar at the same time. The observer standing on the platform, on the other hand, sees the rear of the traincar moving (catching up) toward the point at which the flash was given off and the front of the traincar moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times."
Is this helpful? According to SR the speed of light on earth is not c in relation to the gravitational field of the earth but relative to "any inertial frame". Thus the observer on the platform sees the front- and the backside of the wagon lit up at different times but the guy on the train will think that the front and the backside of the train are lit up simultanesously, because the light coming back from the rear and the front end of the wagon walls will hit him simultaneously.

I think this type of thought experiments are always what is meant when someone talks about "relativity of simultaneity", but I might be wrong...
P: 359
 Quote by James_Harford Hello Mangaroosh, May I suggest yet another way of answering your two questions about Relativity of Simultaneity [RoS]? You might find it simpler to understand, and I am confident that DaleSpam, Ghwellsir, and other posters who have been answering your questions so tirelessly will vouch for its correctness: Your OP question is, And your latest post question is (with [SR] & [LET] inserted for clarity): Fortunately in this case, both questions can be addressed without Lorentz transforms, clocks or rulers. The price of using this approach is that we cannot quantify RoS, but we can demonstrate its existence. Relativity of Simultaneity means simply that two events, separated by a distance from one another, and simultaneous according to one competent observer are not (generally) simultaneous according to another moving relative to the first at some constant speed. The simultaneity of two events can be established using a shuttered lamp on a track between two distant mirrors positioned on the track to reflect any light pulses from the lamp back to it and yourself, the observer. The mirrors need not be at rest and may move independently at arbitrary speeds along the track. Suppose that you are very quick with the shutter and send an extremely brief pulse of light towards both mirrors. If the reflected pulses from both mirrors happen to return simultaneously, what can you legitimately infer? Since by Einstein's postulate, light moves at one speed only, you know these two things: 1. the mirrors were equidistant from the lamp at the time of the reflection, and 2. the two reflections occurred simultaneously. Now suppose that a second observer happens to be moving along the track just as you send your light pulse from the lamp. Will he agree that the reflections were simultaneous? No. By the time the two reflected pulses meet at your lamp, observer #2 has moved some distance along the track, and correctly notes that the two pulses did not "return" simultaneously to his "here", and for that reason, by Einstein's postulate he must infer that the two reflections did not occur simultaneously. The LET interpretation predicts exactly the same phenomena, but differs from SR only in that it insists that light depends upon a hypothetical medium, or aether, Therefore the method of "simultaneous arrival" for determining simultaneity is valid only for an observer who is motionless in the aether, and there is only one "true" definition of simultaneity -- that of the motionless observer. Einstein's great insight was that the aether hypothesis was completely superfluous. - Regards
Hi James, thanks a million for taking the time to reply.

I hope I'm using the right phraseology here when I say that, under Galilean transformations we would expect the moving observer to measure a different speed of light to the pulse operator, but under Lorentz transformations this isn't the case; is that accurate?

Lorentzian relativity maintains absolute simultaneity, while Einsteinian relativity incorporates RoS. I don't think we're too concerned with Lorentzian relativity in this particular instance, what we're looking for, or rather, what I'm trying to understand, is what phenomena must occur in order for the speed of light to remain constant for all observers, regardless of their motion realtive to the source of the light; which appears to be the reason given, why RoS prevails. That was essentially the point made by George, so I presume he would agree with your statement to a similar effect.

One thing he might disagree on is that Lorentzian relativity necessarily includes the superfluous concept of an aether.
 Quote by ghwellsjr nowadays, when we speak of LET, we have striped it of everything except the idea of a preferred rest frame.
P: 359
 Quote by harrylin Hi I answered that in post #28 and also, indirectly, in post #31. RoS corresponds to the "local time" concept as interpreted by Poincare but Einstein interpreted it differently. Did you study the references? Is there something unclear about it?
Hi Harry, the conversation with DaleSpam is in reference to mathematical transformations, while your reply in post #28 was with respect to clocks; unfortunately I don't have the nous to make the connection between the two, so I find it more beneficial to engage with the point that is raised and see where it goes.

I had a quick glance at the reference in post #31, but statement immediately following the link was something you had mentioned before, with respect to detecting absolute simultaneity (or the time on a distant clock) and which I had addressed in #18; so that affected my judgement of the necessity to go through it in detail. Is there a specific part that I can jump to that would address the issue?

Just reading back over the exchange I realise that I didn't address reply in #20 directly. I tried reformulating the question, which lead to your reply in #28, which appears to just be a reformulation of the same reply that was questioned previously.

Post #20:
 Quote by harrylin We understood your intention, which appears to be based on an unfounded assumption. Clocks are man-made and when you put a battery in it you can set it at any time you want. Thus, in order to have two clocks tell the same time, you have to do that. You seem to have already a difficulty with getting two distant clocks synchronized according to yourself, despite your suggestion that all clocks will be automatically synchronized with all other clocks according to everyone. Nevertheless it was only an introduction to the next question: how can you do that in such a way that everyone will agree?
The issue being raised appears to be the idea of detecting absolute simultaneity; but that isn't necessarily an issue that needs to be addressed. We don't need to figure out how to synchronise clocks to say that if all clocks remained synchronised then there would be absolute simultaneity; it's somewhat of a tautology. If any clock falls out of sync, and the change isn't due to mechanical processes, then RoS prevails; if the change is down to mechanical processes then absolute simultaneity prevails - that is assuming that a clock measures time, because if a clock doesn't measure time, then we have no way of measuring time, and it wouldn't necessarily be something that could be dealt with in physics - as someone mentioned in another thread on here a while ago, pertaining to the MMX.

This is #28, which, as mentioned, appears to just reformulate the issue of detecting absolute simultaneity.
 Quote by harrylin In Lorentzian relativity there is absolute simultaneity that cannot be measured, as well as "local time". Poincare pointed out that clocks measure local time. This local time already had the characteristic of relativity of simultaneity before relativity, but until 1904 it was only approximate. Einsteinian relativity considers only what can be measured; consequently he calls "local time" simply "time". A similar thing happened earlier in classical mechanics: Newtonian mechanics distinguishes absolute velocity that cannot be measured as well as relative velocity that can be measured. Classical mechanics only deals with relative velocity.
P: 359
 Quote by harrylin Apparently you missed my post here, in which I explained this in detail and with a lot of precision: http://physicsforums.com/showpost.ph...3&postcount=54 Harald
I didn't miss it, my reply was deleted because I used an invalid reference; although I didn't intend for it to be a reference per se, rather as a means of explaining a point that was made more eloquently than I could have done.

I'll PM you the reply, but I'd prefer to continue the discussion in an open thread. Perhaps if I PM you, you might be able to paraphrase the quote in your reply, for the posterity of the thread - that is if you deem it worthy of reply, of course.
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P: 17,540
 Quote by mangaroosh I replied to that explaining that I didn't fully understand the logic as represented by the maths
That is fine. If you don't understand then ask new questions that will help me get at your root concern. But if you merely repeat the same incorrect claim that I answered already then all I can do is as I did above and refer back to my previous answers.

You are correct, I was travelling for about two weeks with reduced time and access. However, I did find it frustrating to come back and find you repeating the same mistake that I already addressed weeks ago.

 Quote by mangaroosh My trouble with "getting it" lies in the difference, or lack thereof, between Einsteinian relativity and Lorentzian relativity; do I understand correctly that there is essentially no difference between the mathematics of both interpretations?
I don't think that anything productive will come from a discussion of Lorentzian relativity. It is a defunct interpretation which asserts the reality of undetectable entities. All of the confusion with LET comes from the simple fact that the aether is undetectable, so in LET you continually have to make careful distinctions between measurements and what is happening in (undetectable) reality. It is a rabbit hole not worth going down.
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P: 17,540
 Quote by mangaroosh my reply was deleted because I used an invalid reference
Try the reply without the invalid reference. Btw, I saw the reference, and if that is the kind of material that you are trying to learn relativity by reading then it is no wonder that you are confused.
P: 359
 Quote by Agerhell http://en.wikipedia.org/wiki/Relativity_of_simultaneity From wikipedia: Is this helpful? According to SR the speed of light on earth is not c in relation to the gravitational field of the earth but relative to "any inertial frame". Thus the observer on the platform sees the front- and the backside of the wagon lit up at different times but the guy on the train will think that the front and the backside of the train are lit up simultanesously, because the light coming back from the rear and the front end of the wagon walls will hit him simultaneously. I think this type of thought experiments are always what is meant when someone talks about "relativity of simultaneity", but I might be wrong...
Thanks Agerhall, I am familiat with the thought experiment alright, and it is essentially the same one that James posted, I think.

What phenomena occur that means the speed of light is c "in any inertial frame"? We would, ordinarily, expect the moving observer to measure a different speed of light - why is this not the case?
P: 3,188
 Quote by mangaroosh I didn't miss it, my reply was deleted because I used an invalid reference; although I didn't intend for it to be a reference per se, rather as a means of explaining a point that was made more eloquently than I could have done. [...]
Then, evidently, you did not understand it. As Dalespam suggests, you can simply re-post the reformulation of your question without including a link to a crank(?) site.
P: 152
 Quote by mangaroosh Thanks Agerhall, I am familiat with the thought experiment alright, and it is essentially the same one that James posted, I think. What phenomena occur that means the speed of light is c "in any inertial frame"? We would, ordinarily, expect the moving observer to measure a different speed of light - why is this not the case?
If you first assume that the speed of light is c in relation to the guy standing on the platform. The guy on the platform would classically expect that it takes longer time for the light from the guy on the train to reach the back and front wall and bounce back towards the guy on the train than if the train had not been moving. You can do the math, it is simple.

However, in Special Relativity the Time Dilation formula kicks in and it so happens that if the guy on the platform would expect it to take a factor k longer for the light to reach the back and front wall and get back to the guy on the train again, then the time for the guy on the train slows down with the same factor k so he thinks the two way speed of light has the same value, c, no matter what the velocity of the train relative to the ground is...

In this way the "two-way speed of light is the same in all inertial frames".

I belive this is how it is always explained...

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