# Hi! This is the definition of simultaneity I was taught: Two

1. Sep 28, 2011

### blueberrynerd

Hi! This is the definition of simultaneity I was taught:

Two events that are simultaneous in one frame of reference need not be simultaneous in a frame moving relative to the first frame.

I'm wondering if this concept only applies to relativistic phenomenon, and if not, would you happen to know any examples of nonrelativistic simultaneity?

2. Sep 28, 2011

### ghwellsjr

Re: Simultaneity

Well, the concept is usually known as "the relativity of simultaneity". I never heard of "the non-relativity of simultaneity".

Your definition is very good, by the way.

3. Sep 28, 2011

### pervect

Staff Emeritus
Re: Simultaneity

Your statement is correct, but it seems to me that it's not a definition of simultaneity, but a consequence of the definition.

The usual special relativistic definition is based on the speed of light being constant, and simply says that if you have a pair of clocks with zero relatiave velocity (so that they define a frame), a signal emitted at the midpoint in said frame will arrive at both clocks simultaneously.

You might extend this into a non-relativstic defintion by using carrier pigeons rather than light, i suppose, but you'll find a lot of experimental issues in keeping the speed of the carrier pigeons constant. (For instance, they'd be affected by wind, so you'll need to specify that the air in your frame is still).

The really important thing here is isotropy. If you demand that two objects with the same velocity going in opposite directions have equal and opposite momentum, (so that if they collide there won't be any residual motion), and you use the usual "two clock" definition to measure the speed, you will find that the zero momentum condition is only obtained when the clocks are synchronized isotropically, and that this is equivalent to the Einstein "midpoint" syncrhonization.

4. Sep 28, 2011

### ghwellsjr

Re: Simultaneity

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A pair of clocks with zero relative velocity do not define a frame, until and unless you synchronize the times on them so that a signal emitted at the midpoint arrives at both clocks simultaneously.

Merely saying that the speed of light is a constant is ambiguous because that is already covered under the first postulate and is not enough to establish Special Relativity. The first postulate is the principle of relativity. But SR needs the second postulate which states that the one-way speed of light from any source is defined to be that same constant for all frames covered by the first postulate. And Einstein's clock synchronization convention is the way that postulate is realized.

5. Sep 29, 2011

### harrylin

Re: Simultaneity

Hi! As Pervect already mentioned, in special relativity two clocks are defined to be simultaneous if the time for a light (or radio) signal from one clock to the other is the same as from the other to the one (if they are in rest in your reference system; else you must correct for their speeds). And that is in fact still how clocks typically are synchronized.
See the first section of:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Harald

6. Sep 29, 2011

### harrylin

Re: Simultaneity

Precision: the second postulate states that it is possible to synchronize clocks such that the speed of light becomes c in all directions.

PS in addition, I see that in fact the question has not yet been answered.
As a matter of fact the relative simultaneity definition already existed before the theory of relativity, see:
http://en.wikisource.org/wiki/The_Measure_of_Time

However, with classical physics it wasn't perfectly self-consistent: it only works to good (first order) approximation. But as it anyway involved only a small correction compared to completely ignoring the speed of light, the consequences were usually negligible.

Last edited: Sep 29, 2011
7. Sep 29, 2011

### ghwellsjr

Re: Simultaneity

Where in that paper is relative simultaneity defined like Einstein defined it? Poincare is using a lot of the same words used by Einstein but his bottom line is, "No general rule, no rigorous rule, a multitude of little rules applicable to each particular case." What a waste of time that paper is, except to show that Poincare should never share Einstein's glory, if that is the best he can do.

The second postulate is what separates LET from SR. LET's second postulate is: light is only propagated in a single absolute imovable state with a definite velocity c which is independent of the state of motion of the emitting body.

8. Sep 30, 2011

### harrylin

Re: Simultaneity

Blueberrynerd asked if we know any nonrelativistic examples of the concept that two events that are simultaneous in one frame of reference need not be simultaneous in a frame moving relative to the first frame.

As that 1898 paper points out, astronomers made events simultaneous by assuming, as a postulate, that the speed of light is the same in all directions (that is, wrt the reference frame that they used: the earth or, I suppose that in fact they used the ECI frame; see also next).

But indeed, this particular paper does not mention that as a necessary consequence of this approach simultaneity is different in reference systems that are moving relative to each other - for example the Earth at different times of the year. But I think that it's still a good introduction for his follow-up paper of 1900*, in which he does elaborate on that issue by relating those time measurements to the non-relativitstic Lorentz frame transformations of those days.

The time transformation was, with t' "local time":
t' = t − vx/c2
and he explained that clocks are synchronized as function of the velocity v of the Earth (the used reference frame).

BTW he already mentions the relativity principle there: "the principle of relativity of motion has been verified only imperfectly". His 1900 commentary was still "non-relativistic" in the sense that at that time relativity wasn't yet established as fully valid, with full precision.

So Blueberrynerd, if you work it out (the math is not difficult) you will quickly see that it only works approximately: with the theory as given there, the two-way time of light is not exactly the same for different observers. The Lorentz contraction (which was by then already assumed) only makes the speed of light equal in different directions. Nevertheless, two events that were simultaneous in one frame of reference were not simultaneous in a frame moving relative to the first frame.

* La theorie de Lorentz et le principe de reaction, you can find it on physicsinsights; as I don't know for sure if that is considered by physicsforums to be a non-crank site, here's the link to the Wikipedia relativity portal:
http://en.wikisource.org/wiki/Portal:Relativity

Last edited: Sep 30, 2011
9. Oct 8, 2011

### ghwellsjr

Re: Simultaneity

But when Poincare points out that the astronomers posutate the speed of light is the same in all directions, he's not applauding them, he's castigating them. Look at the context of his statement:
And if you go on to read the rest of the paper in context, you will see that Poincare does not like postulates, definitions and assumptions, he wants measurements, hence the title of his paper, although he still doesn't know how to make satisfying measurements.
Yes, t' is local time whereas t is true time, according to Poincare. He also contrasts relative motion with absolute motion and apparent energy with real energy. There is no reason to believe that Poincare had any concepts that were on a par with what Einstein later came up with or that Poincare could ever have come up with them on his own.
I get the impression that you think Einstein invented his first postulate, the principle of relativity, or that you think that is what I'm saying, which he did not and I am not. The principle of relativity came long before Einstein but it is not his Theory of Special Relativity. That takes the combination of both his postulates.
The two-way time of light is not exactly the same for different observers? Are you talking about a theory that includes only length contraction and not time dilation? What do you mean by this?

10. Oct 9, 2011

### harrylin

Re: Simultaneity

I see* nearly the contrary and I don't share your conclusions; however, that discussion as well as arguing which scientist was "greater" is off topic here.
No, none of that - nothing to do with you, me or Einstein. See next.
When Poincare explained that the principle of relativity of motion was verified, he obviously implied to MMX and other EM experiments. He critized Lorentz's Electron Theory because it did not achieve a perfect invariance of natural phenomena. However, the theory did include length contraction. Apparently the equations did not yet include the effect of motion on resonance frequencies on "local time", despite the fact that Lorentz had already derived the correct factor by then - in contrast with Poincare, Lorentz had not yet realised the relationship between resonance frequencies and local time!

I think that in modern form, the transformation equations were as follows (please correct me if that's wrong):

t' = t − vx/c2
x' = γ(x - vt)
y' = y
z' = z

Harald

* For example (empahasis mine):
He has begun by supposing that light has a constant velocity, and in particular that its velocity is the same in all directions. That is a postulate without which no measurement of this velocity could be attempted. This postulate could never be verified directly by experiment; it might be contradicted by it if the results of different measurements were not concordant. We should think ourselves fortunate that this contradiction has not happened and that the slight discordances which may happen can be readily explained.
The postulate, at all events, resembling the principle of sufficient reason, has been accepted by everybody; what I wish to emphasize is that it furnishes us with a new rule for the investigation of simultaneity, entirely different from that which we have enunciated above.[..] We therefore choose these rules, not because they are true, but because they are the most convenient