# Relativity of Simultaneity

by mangaroosh
Tags: relativity, simultaneity
 P: 1,068 Thanks for the reply Dalespam. Maybe if I pose my question differently it will become more apparent where my confusion is. In what scenario would two observers have the same measure of length / time, but not agree on simultinaity? To your point in the last comment, when I think of relative motion, I immediatly consider their measure of length / time to not be equal "parts/units" comparatively. If RoS includes relative motion, how can length / time measure the same (comparatively) for each observer? Lastly, sure you know now that I don't know math, can this demonstration of RoS without LC / TD be concluded with thought?
Mentor
P: 15,617
 Quote by nitsuj In what scenario would two observers have the same measure of length / time, but not agree on simultinaity?
If you are assuming special relativity then there is no such scenario since SR implies all three (LC, TD, and RoS). If you are not assuming SR then the last transform of post 2 is an example.

 Quote by nitsuj To your point in the last comment, when I think of relative motion, I immediatly consider their measure of length / time to not be equal "parts/units" comparatively.
If you assume SR that is correct.
 P: 1,068 Ah okay and phew!
P: 3,179
 Quote by nitsuj From reading some of this thread I realize that I don't have a good understand ing of RoS. I would have assumed that time dilation / length contraction would account for RoS, invariance of c ect.
I think that it was mentioned in this thread that "RoS" has slightly different meanings.
RoS in the sense that we can't determine absolute simultaneity relates to the PoR, and the basic features that enable the PoR despite constant c are TD and LC.
Note that Einstein's constant c (independent of the motion of the source) should not be confused with invariance of c (relativity principle for light propagation).

 Is / was RoS an issue or noticed pre-SR / LET? Why not if it's exclusive of time dilation / length contraction?
What's your meaning of RoS in that sentence?
 Even in post #42, there is relative motion involved. I can't think of a scenario (visual) demonstrating RoS, where there is no relative motion. (amongst the event, and the two observers)
RoS refers to measurements in reference systems that are in relative motion. It is always possible to apply Galilean simultaneity based on a Master reference system - as is common practice.
 P: 1,068 Ah okay, I didn't (nor have I ever) seen that mentioned. There is always something new in SR from my perspective, this one is particularly suprising given what I do know of SR concepts. I can't make the distinction you mention with "Note that Einstein's constant c (independent of the motion of the source) should not be confused with invariance of c (relativity principle for light propagation)." Is there a simply way to make that distinction more clear (for me)? Maybe I should just consider scenarios of each, maybe that's where my confusion is. If so wow, good eye Harrylin! I only have the one understanding of RoS, where two events seperated spatialy could be measured as occuring simultaniously depending on relative motion.
P: 3,179
 Quote by nitsuj Ah okay, I didn't (nor have I ever) seen that mentioned. There is always something new in SR from my perspective, this one is particularly suprising given what I do know of SR concepts.
Yes, and in this thread: see post #105.
 I can't make the distinction you mention with "Note that Einstein's constant c (independent of the motion of the source) should not be confused with invariance of c (relativity principle for light propagation)." Is there a simply way to make that distinction more clear (for me)? Maybe I should just consider scenarios of each, maybe that's where my confusion is. If so wow, good eye Harrylin!
Sure.

1. Just look up "invariant" on Wikipedia:
http://en.wikipedia.org/wiki/Invariant Note that (at least today!) the word "constant" doesn't appear on that page. In the context of SR, people mean with "invariant" that a frame transformation doesn't change it.

Then look up "physical constants" on Wikipedia:
http://en.wikipedia.org/wiki/Physical_constant Note that (at least today!) the word "frame" doesn't appear on that page.

According to SR, such physical constants are not affected by a frame transformation; and that may be the reason that the distinction is often blurred. However, in classical physics it was assumed that the speed of light is a constant that is independent of the motion of the source ("the speed of light is a constant c"). Maxwell assumed that the speed of light could only be exactly c relative to a light medium - just like the speed c of sound in air. Consequently, in classical optics it was though that the speed of light is a constant but not invariant.

Similarly, Einstein's second postulate of SR refers to a single inertial frame. The speed of light is assumed to be a constant c: the same in all directions, and independent of the motion of the source. That postulate seemed incompatible with the relativity principle according to which all physical constants should be invariant (the speed of sound is variant, so how can the speed of light be invariant?).

Is that clearer?
 I only have the one understanding of RoS, where two events seperated spatialy could be measured as occuring simultaniously depending on relative motion.
"depending on relative motion" sounds like it merely involves the standard synchronization procedure. That was already applied before SR, but it was thought (because of the above) that the laws of physics only worked in good approximation in moving frames.
P: 359
 Quote by dalespam your language here is a little confused, so i am concerned that your thoughts are also a little confused. When we are talking about the different postulates and conclusions in relativity we are not talking about a "cause and effect" effect relationship, but rather a "logical implication" relationship. A cause and effect relationship involves more than a logical implication relationship, specifically it also implies a temporal ordering where the cause preceeds the effect. There is no such temporal ordering between lc, td, ros, the principle of relativity (por) and the invariance of c (c), so you cannot speak of causes or effects amongst them.
This is one thing that I have trouble with, and it might be down to my lack of understanding of the nuances of the concepts; but my understanding is that that light is physical, and when the speed of light is measured a physical effect is being measured; I'm also of the understanding that LC & TD are physical effects. For that reason I don't understand how we can't speak in terms of cause and effect.

I have not trouble with the idea that the postulates of relativity allow us to reason what should be the case, if the postulates are assumed to be true; and what effects must occur, in order for the assumptions to hold true; but insofar as they relate to the physical world, then I think we have to be able to discuss cause and effect at some point; reasoning alone, as far as I am aware, doesn't cause physical effects (of the sort we are talking about).

 Quote by dalespam So, what we have is properly "implies" and not "causes". The proper way to express this formally is: $(\text{PoR} \cap \text{C})\leftrightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})$ This whole conversation began when you correctly pointed out that $(\text{lc} \cap \text{td})\rightarrow \text{c}$ is false. I responded by correctly pointing out that $(\text{lc} \cap \text{td} \cap \text{ros})\rightarrow \text{c}$ is true and you had neglected ros which is an essential part of sr. You then followed up with the incorrect assertion that $(\text{lc} \cap \text{td})\rightarrow \text{ros}$ to which i gave a counter-exmaple. The rest of the conversation has basically been follow-up to that. I hope this clarifies things.
Apologies, I'm not overly familiar with the formal notation, although I think I understand the above; I just can't write a full response using the correct operators.

It might be worth drawing the distinction, again, between an invariant measurement of c $\text{(mC)}$ and an invariant actual c $\text{(aC)}$; where
$\text{mC}$ does not necessarily imply $\text{aC}$ ; as per the example where two reference frames measure the speed of light to be c, but because the instruments used are of different lengths, the actual speed represented by the measurements is different.

You mentioned that I had neglected RoS, and so had drawn the wrong conclusion; however, RoS is a consequence of the actual speed of light (c) remaining invariant, not necessarily of an invariant measurement of ca 300/000 km/s.

$(\text{PoR} \cap \text{mC})$ does not necessarily imply $(\text{LC} \cap \text{TD} \cap \text{RoS})$

but
$(\text{PoR} \cap \text{mC})\leftrightarrow (\text{LC} \cap \text{TD})$

If we consider, that we can only ever, really, speak about the measurement of c, and not the actual speed", then:
$(\text{PoR} \cap \text{mC} \cap \text{RoS})\leftrightarrow (\text{aC})$

Which leaves us with the formulation:
$(\text{PoR} \cap \text{mC} \cap \text{RoS})\leftrightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})$

which appears to be circular.

 Quote by dalespam No, it is merely a counter example to your claim of post 121 that "lc & td must occur in order for c to be invariant" i.e. $\text{c}\rightarrow (\text{lc} \cap \text{td})$
OK; again, I'm not 100% sure of the relevance of an unrelated transformation. It might be best to just assume that the context is Einseinian relativity.
Mentor
P: 15,617
 Quote by mangaroosh I'm also of the understanding that LC & TD are physical effects. For that reason I don't understand how we can't speak in terms of cause and effect.
Physicalness is neither a necessary nor sufficient condition for causality. Indeed, you can speak of psychological effects in terms of causality, e.g. his delusions of grandure caused his risk-taking behavior. But there must be a temporal ordering, the cause always comes chronologically before the effect. That is not the case here.

 Quote by mangaroosh It might be worth drawing the distinction, again, between an invariant measurement of c $\text{(mC)}$ and an invariant actual c $\text{(aC)}$;
I don't think it is worth drawing the distinction; consider all of my previous statements to refer to measurements. Scientifically, all that matters is the measurements. If there is a hidden actuality that cannot be measured then it is irrelevant to physics.

 Quote by mangaroosh OK; again, I'm not 100% sure of the relevance of an unrelated transformation. It might be best to just assume that the context is Einseinian relativity.
I am fine with that. Then the whole discussion goes away since in Einsteinian relativity there is C and PoR and LC and TD and RoS. We are left with only my original response that you had forgotten about RoS.
P: 3,179
 Quote by mangaroosh [..] I'm also of the understanding that LC & TD are physical effects. [..]
I agree, insofar as those effects are independent of clock synchronization (in fact they are, but the description isn't!).
 [..] RoS is a consequence of the actual speed of light (c) remaining invariant [..]
Perhaps you mean that no absolute simultaneity can be measured because of how the universe works, as expressed by the relativity principle. I agree with that.

Harald
P: 359
 Quote by DaleSpam Physicalness is neither a necessary nor sufficient condition for causality. Indeed, you can speak of psychological effects in terms of causality, e.g. his delusions of grandure caused his risk-taking behavior. But there must be a temporal ordering, the cause always comes chronologically before the effect. That is not the case here.
But psychological effects have a physical manifestation.

As for the temporal separation, that would probably be a more philosophical discussion on the nature of "cause" and "effect".

 Quote by DaleSpam I don't think it is worth drawing the distinction; consider all of my previous statements to refer to measurements. Scientifically, all that matters is the measurements. If there is a hidden actuality that cannot be measured then it is irrelevant to physics.
I think it is worth making the distinction, because, as mentioned above, an invariant measurement of c does not imply RoS; it is an invariant measurement of c plus RoS which results in RoS; with the latter being circular in nature.

 Quote by DaleSpam I am fine with that. Then the whole discussion goes away since in Einsteinian relativity there is C and PoR and LC and TD and RoS. We are left with only my original response that you had forgotten about RoS.
I should, more precisely, have said, I don't see the relevance of using a transformation that is not the Lorentz transformation. As there are two interpretations of the Lorentz transformation, one which incorporates RoS and one which doesn't; with one of those being, arguably, circular in nature.
P: 359
 Quote by harrylin I agree, insofar as those effects are independent of clock synchronization (in fact they are, but the description isn't!).
Apologies har, I don't fully understand the point being made.

 Quote by harrylin Perhaps you mean that no absolute simultaneity can be measured because of how the universe works, as expressed by the relativity principle. I agree with that. Harald
That's not really what I was trying to get at. As outlined above, an invariant measurement of c does not necessarily imply RoS; RoS is a consequence of the actual speed of light remaining unchanged. This requires us to assume RoS, which is the conclusion being drawn.

I think that saying that no absolute simultaneity can be measured is somewhat of a category mistake, because absolute simultaneity is not a physical object. However, a consequence of RoS, I believe, is that for each individual observer, their "past" state continues to exist in some reference frame, and their "future" state also "exists" in some reference frame; this requires each observer to make unverifiable assumptions about the existence of "past" and "future"; absolute simultaneity, however, doesn't require such assumptions, it simply requires us to accept the empirical evidence that an ever changing present moment is all that exists - this is because, I'm pretty sure, no observation of "past" or "future" can be made by an observer.
P: 3,179
 Quote by mangaroosh Apologies har, I don't fully understand the point being made.
For example a change of clock rate in a train due to a change of velocity can be detected with clocks along the railway, but depending on clock synchronisation one can measure an increase or a decrease. Thus that the detection of the effect is independent of synchronisation, but not the description of the effect.
 That's not really what I was trying to get at. As outlined above, an invariant measurement of c does not necessarily imply RoS; RoS is a consequence of the actual speed of light remaining unchanged. This requires us to assume RoS, which is the conclusion being drawn.
Sorry, I don't know what you mean with "the actual speed of light": what do you mean with "actual", and do you mean the 2-way speed of light?
 I think that saying that no absolute simultaneity can be measured is somewhat of a category mistake, because absolute simultaneity is not a physical object.
Time is not a physical object, but it can be measured. Do you have a problem with that?
 However, a consequence of RoS, I believe, is that for each individual observer, their "past" state continues to exist in some reference frame, and their "future" state also "exists" in some reference frame [..]
?? Not at all! As measured with every inertial reference system, everyone's present corresponds to a certain present event (x, t) in that system...
Perhaps you mean that an observer who is using a certain reference system can attribute certain distant events that he/she has not yet seen, to the past or future while using another reference system, the contrary would be attributed to those events.
 P: 251 The best way to understand SR is geometrically. Take a sheet of paper and draw a simple spacetime diagram: put two dots on the sheet horizontally aligned to represent two events which are simultaneous in the frame of the drawing and spatially separated. Now get some transparent film, draw graph lines on it and place it over the paper so one grid line passes though the two events. Rotate the film a few degrees to represent a different frame and the events can no longer lie on the same gridline, they are not simultaneous in the new frame. What special relativity says is that there is no intrinsically preferred frame in reality, any choices of frame is equally valid. Note that this is jut an analogy, to get an accurate picture you have to rotate the vertical and horizontal lines in opposite directions (e.g clockwise and anti-clockwise). Length contraction and time dilation are just names for the effect of changing coordinate separations resulting from frame rotation.
P: 3,179
 Quote by mangaroosh [..] As there are two interpretations of the Lorentz transformation, one which incorporates RoS and one which doesn't. [..]
The Lorentz transformation incorporates RoS and no interpretation can alter that. Perhaps that's the cause of the confusion?
Mentor
P: 15,617
 Quote by mangaroosh I think it is worth making the distinction, because, as mentioned above, an invariant measurement of c does not imply RoS; it is an invariant measurement of c plus RoS which results in RoS; with the latter being circular in nature.
Well, then you should find someone else who thinks it is a distinction worth making if you wish to pursue that topic further, that person isn't me. However, I should point out, that if you do make the distinction between measured and actual values of one thing (e.g. c) then you can make a similar distinction between measured and actual values of something else (e.g. RoS) and thereby un-circularize anything you run into, even if you consider the measured/actual distinction worthwhile.

 Quote by mangaroosh I should, more precisely, have said, I don't see the relevance of using a transformation that is not the Lorentz transformation.
Consider the attached Venn diagram representing the set of all linear transformations on spacetime. The Lorentz transformation has $\text{LC} \cap \text{TD} \cap \text{RoS}$ so it is in subset 4. When you make a statement like $(\text{LC} \cap \text{TD}) \rightarrow \text{RoS}$ you are saying that subset 1 is empty. You cannot determine the emptiness of subset 1 by considering only transforms in subset 4.

If you assume the Lorentz transform then all you can say is $\text{LT} \rightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})$ and you cannot make any claims about whether or not any of them are implied by any of the others. I am certainly happy to do that, but it basically ends the entire discussion after my original point that you had neglected RoS.
Attached Thumbnails

P: 359
 Quote by harrylin For example a change of clock rate in a train due to a change of velocity can be detected with clocks along the railway, but depending on clock synchronisation one can measure an increase or a decrease. Thus that the detection of the effect is independent of synchronisation, but not the description of the effect.
You'll have to forgive me for being very slow on the uptake, but I'm having trouble tying this into the context of the discussion.

 Quote by harrylin Sorry, I don't know what you mean with "the actual speed of light": what do you mean with "actual", and do you mean the 2-way speed of light?
The distinction being drawn is between the measurement of the speed of light and the actual speed of the light.

For example, let's say that you measure the speed of light to be ca. 300,000 km/s, using your instruments; then I measure the speed of light to be ca. 300,000 km/s using my instruments, but my metre stick is contracted such that "my meter" is shorter than "your metre", and "my second" (measured by my slower clock) is longer than "your second", then it means that the actual speeds represented by those measurements are different.

In reality, the light in my reference frame took a little longer than a second to travel a distance shorter than 300,000 km/s - although our units of measurement are the same, the actual speeds represented by those measurements are different.

 Quote by harrylin Time is not a physical object, but it can be measured. Do you have a problem with that?
I do have trouble with how time is actually measured. I just can't seem to see how it is possible to measure what is supposed to be a physical property, even if it isn't considered an object.

 Quote by harrylin ?? Not at all! As measured with every inertial reference system, everyone's present corresponds to a certain present event (x, t) in that system... Perhaps you mean that an observer who is using a certain reference system can attribute certain distant events that he/she has not yet seen, to the past or future while using another reference system, the contrary would be attributed to those events.
If we take two relatively moving observers for example, where the relative velocity is something like 0.6c; there will be events in the present of one observers reference frame, that are in the past of the other (and vice versa). This suggests that the events which are in the past for one observer continue to exist.

To accept this as true, however, would require that observer to assume that, not only the past events continue to exist, but also their "past self"; the same can be said of "future" events and "future self"; each and every observer would have to make this assumption, despite the fact that this would be contrary to the empirical evidence (with regard to "past" and "future").
P: 359
 Quote by GeorgeDishman The best way to understand SR is geometrically. Take a sheet of paper and draw a simple spacetime diagram: put two dots on the sheet horizontally aligned to represent two events which are simultaneous in the frame of the drawing and spatially separated. Now get some transparent film, draw graph lines on it and place it over the paper so one grid line passes though the two events. Rotate the film a few degrees to represent a different frame and the events can no longer lie on the same gridline, they are not simultaneous in the new frame. What special relativity says is that there is no intrinsically preferred frame in reality, any choices of frame is equally valid. Note that this is jut an analogy, to get an accurate picture you have to rotate the vertical and horizontal lines in opposite directions (e.g clockwise and anti-clockwise). Length contraction and time dilation are just names for the effect of changing coordinate separations resulting from frame rotation.
Thanks George; the issue isn't so much understanding what Einsteinian relativity says about RoS, it is more understanding the assumptions which such an interpretation requires.
P: 359
 Quote by harrylin The Lorentz transformation incorporates RoS and no interpretation can alter that. Perhaps that's the cause of the confusion?
Not necessarily though, do they? Lorentzian relativity uses the same transform, but doesn't incorporate RoS, no?

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