# Relativity of Simultaneity

1. Oct 16, 2004

### timetraveldude

The classic example of demonstrating the relativity of simultaneity uses bolts of lightning striking two places "simultaneously". When you do the same experiment with sound then all observers can determine which event occured first because sound does not follow the 2nd postulate of SR.

2. Oct 16, 2004

### Fredrik

Staff Emeritus
I have no idea what you're talking about.

What experiment?

What do you mean "determine which event occured first"? In SR, the only events that all observers agree happened in a certain order, are the ones that are timelike separated. This means that

$$-c^2t^2+x^2<0$$

where t is the time between the events (in some inertial frame) and x is the spatial distance between the events (in the same inertial frame).

3. Oct 16, 2004

### jcsd

Yep I know the experiment, but timetrvaeldud your wrong as in relativty, the order in which an observer sees or even hears two events it not necessarily the order that they occur in his frame.

4. Oct 16, 2004

### timetraveldude

You need to read what I wrote

I know what SR says. What I am saying is that if you do the same experiemnt with sound all observers will agree on which occured first. What you are doing is taking what I am disputing and using it as evidence to refute my position.

5. Oct 16, 2004

### Hurkyl

Staff Emeritus
No they wouldn't.

6. Oct 16, 2004

### Janus

Staff Emeritus
Which is wrong. If you did the experiment with sound you would get the same results as you would with light. The speed of sound may not be invarient, but it is subject to the addition of velocities theorem.

7. Oct 16, 2004

### Fredrik

Staff Emeritus
Timetraveldude, I take it you know SR pretty well, but it didn't seem that way to me when I read your first post in this thread. Jcsd and I both thought you meant something you didn't. Perhaps you should have told us more about that experiment, and explained your thoughts more carefully.

I think I understand (roughly) what you were trying to say, because I can imagine a thought experiment that uses light to define what events are simultaneous (to a certain observer) with a specified event. That would work with sound too. What you can't do with sound (in the same way) is determine what events are simultaneous to another observer.

8. Oct 16, 2004

### timetraveldude

Exactly, sound is subject to the addtion of velocities formula which light is not. I suggest you either do the though experiment or a proof.

9. Oct 16, 2004

### Janus

Staff Emeritus
Actually light and sound are subject to the same addition of velocities formula, namely:

$$w= \frac{u+v}{1+\frac{uv}{c^2}}$$

10. Oct 16, 2004

### timetraveldude

You are wrong again.

If you want I can suggest some good books on basic relativity. This addition of velocity formula that you are stating is based on the fact that two intertial observers will never agree on events being simultaneous if they are moving relative to one another. Again you are taking the assumption that is under question and using its results to justify the assumption itself.

You need to stop regurgitating and start thinking.

11. Oct 16, 2004

### timetraveldude

Here is a very simple thought experiment. Stand at the midpoint between two machines A and B that launch tennis balls horizontally at the same speed. You begin moving towards machine B and the ball from B arrives before the ball from A. Since the speed of the balls are not the same in all interal reference frames you can determine that ball A must have traveled farther and at a slower speed. Working backwards you could determine that the balls were launched at the same time.

This is the same result that someone standing at the mid point would determine. Therefore, there is no relativity of simultaneity.

You need to be open to the possibility that what you think my be wrong.

12. Oct 16, 2004

### Hurkyl

Staff Emeritus
We are. Are you?

13. Oct 16, 2004

### timetraveldude

Obviously I am open to it. What I am waiting for is someone to address the question. I have shot down all your comments. None of them have a made a dent in my contention.

Refute my thought experiment. Prove me wrong that is all you have to do.

14. Oct 16, 2004

### Hurkyl

Staff Emeritus
If you've already made the assumption that special relativity is wrong and Gallilean relativity is right, it's fairly easy to disprove special relativity.

The trick is to do it without making the assumption, or equivalently, assume special relativity is right, and derive a contradiction.

Last edited: Oct 16, 2004
15. Oct 16, 2004

### anti_crank

This statement is extremely surprising from someone who understands relativity. The relativity of simultaneity is a mathematical consequence of the Lorentz tf. or the constancy of the speed of light principle; if that fails, so does all of SR. Thankfully, it does not.
Here's something that should settle this issue. Consider the following setup: observer A sits at the midpoint of a platform of length 2L, observer B sits somewhere else on the platform, and observer C moves at a constant speed u wrt the platform. Primed coordinates will correspond to C, unprimed to A. Choose the origin s.t. C passes by A when t=t'=0.

Now suppose that at t=0, *something* happens at both ends of the platform. It does not matter whether a light pulse is emitted, a sound wave is emitted, or a ball is sent towards A.

A will receive the two light pulses/sound waves/balls simultaneously at t=L/v. He knows where the events originated, and he assigns them spacetime coordinates (L,0) and (-L,0)

B will not receive the two light pulses/sound waves/balls simultaneously. To him, they arrive at t1=L1/v and t2=L2/v. However, once he accounts for the distance travelled, he concludes that they were emitted simultaneously and assigns them coordinates (L1, 0) and (-L2,0)

C is in a state of motion wrt A (his speed may be 1cm/s or 299000km/s, the principle still applies) so we can use the Lorentz tf. on the measurements of A. In particular, we are interested in the time components:
$$t{^'}_1 = \gamma t_1 - \frac{x_1 u}{c^2} = -\frac{Lu}{c^2}$$
Similarly $$t{^'}_2 = +Lu/c^2$$

I may have the signs inverted, but it should be clear that the times are different. This is not a distinction of whether the two light pulses/sound waves/balls *arrive* at C's position simultaneously; they obviously do not. However, unlike observer B, C still has a difference in the *emission* times after he accounts for their motion. To prevent misunderstandings, he is not allowed to explicitly refer to A or B when he makes his calculations, or to consider himself in any state of motion.

16. Oct 16, 2004

### pervect

Staff Emeritus
You seem to me to be a bit confused. The fact that there is an atmosphere does appear at first glance to set up a specific coordinate system (it's not quite a frame because of various effects such as the rotation of the earth) that's at rest relative to the atmosphere.

In this coordinate system, it's possible to synchronize clocks. Unfortunately, the details of how this clock synchronization process works are going to depend on a large number of factors, including how the winds are blowing at that moment, because when you look closely, the atmosphere isn't at rest relative to itself.

So you haven't really defined a very useful or practical coordinate system at all so far.

If you manage to "fix up" your proposal to solve the problems of winds affecting how clocks are synchronized, you will still not have disproven relativity.

In fact, people already have a well defined system for synchronizing clocks on the Earth's surface. It's called, TAI time, which is a coordinate time. It's called a coordinate time because it sets up a coordinate system on the Earth's surface.

Now the next question is why you think that setting up a specific coodinate system with non-Einstenian clock synchronization somehow disproves relativity

A lot of people make the mistake (and I would guess that this is your error) that because they have set up some particular coordinate system, or used an existing system such as TAI time, Newton's laws must work in that coordinate system.

So the problem in these cases are not in relativity - it is in the assumption that Newton's laws must work in their coordiante system. This is a bad assumption.

Relativity points out otherwise - if you do not synchronize clocks according to Einstein's conventions, you will not have a coordinate system where you can apply Newton's laws, even at low velocities.

The "velocities" that one measures in a coordinate system that is not based on Einsteinian clock synchronization have an inherent spatial bias, a "preferred direction". They are not isotropic.

This means specifically that a mass m moving in one direction with a "coordinate velocity" v will not have the same momentum as a mass m moving in the opposite direction with a "coordinate velocity" v.

Another way of putting this is that if you were running an automobile race, automobiles would run faster in one direction than another.

The Einsteinan condition of using light to synchronize clocks is the same convention that's needed to run "fair" automobile races, ones in which no automobile has an advantage going in any particular direction - to use the technical term, an isotropic coordinate system.

Usually this gets simplified to the point of view of telling people that they "have to" use Einstein's method of synchronizing clocks. This is not a bad approach, however it's slightly over simplified. A more complete discussion includes the "or else", which is, as I described, the fact that your coordinate system won't be isotropic if you don't use Einstein's clock synchronization method.

I'd like to post some web references, but unfortunately I only have one which isn't very helpful - other than Einstein's original papers, I haven't seen much discussion about isotropy. Google finds a few crank pages, but nothing potentially useful, other than an abstract from a Physical review D paper by Clifford Will (and that's not very useful in abstract form, and I can't answer to how useful even the original would be not having seen it).

17. Oct 16, 2004

### Fredrik

Staff Emeritus
Timetraveldude, don't you think the problem with the discussion in these two threads is that you haven't expressed yourself clearly enough? I read your thought experiment with the tennis balls, and unfortunately I must place it in the "not even wrong" category. You haven't stated what your postulates are, it's impossible to follow your reasoning, and even your conclusion is difficult to understand.

I can see that you're saying that "there is no relativity of simultaneity" (which is clearly in contradiction with SR), but what are you really saying? Are you saying that your conclusion is not in contradiction with SR, or that your thought experiment proves that SR is wrong?

18. Oct 16, 2004

### so-crates

Let me see if you have your setup right:

Code (Text):
A  -->o                      O                           o<--- B
O'  -->

O is an observer at rest with respect to A and B, at the midpoint between A and B.
A and B are launching projectiles with a certain speed, lets call it v.
O' is moving toward B at some speed v'.

Last edited: Oct 16, 2004
19. Oct 16, 2004

### timetraveldude

Again you have failed to see my motionvation for this post. It is clear from the Lorentz transformations that if one observer says two events we simultaneous another inertial observer moving relative to them will not say they were simultaneous. This is obvious.

The point I am making is that if the relativity of simultaneity is invalidated using material objects then there is something wrong with SR. This requires a new method of deriving the Lorentz transformations since the argument based on the constantcy of light in all inertial reference frames is the basis for the original derivation.

20. Oct 16, 2004

### timetraveldude

You inability to understand me is your problem.