# Relativity of Simultaneity

by Aniket1
Tags: relativity, simultaneity
 P: 45 I read some articles on relativity of simultaneity which said that the concept is a result of ONLY the finite speed of light and does not necessarily follow from the principle of relativity. I however was not convinced with the explanation. Could someone justify if it's true?
 Mentor P: 41,555 I'd say that it wasn't true. What is needed is not just that the speed of light is finite, but that it is invariant--the same in every inertial frame.
 Emeritus Sci Advisor PF Gold P: 5,598 If you want to say what's a consequence of what, you have to accept that there is more than one possible axiomatization of relativity: http://physicsforums.com/showthread.php?t=534862
PF Gold
P: 4,781
Relativity of Simultaneity

 Quote by Aniket1 I read some articles on relativity of simultaneity which said that the concept is a result of ONLY the finite speed of light and does not necessarily follow from the principle of relativity. I however was not convinced with the explanation. Could someone justify if it's true?
Relativity of simultaneity is the result of both the principal of relativity (Einstein's first postulate) and his second postulate, not just that the speed of light is finite, but that it propagates at that finite speed in any inertial frame, as Doc Al pointed out.

If it weren't for the fact that it takes so incredibly much energy to accelerate massive objects, like clocks, up to significant fractions of the speed of light, we would all be very much aware that they don't all tick at the same rate when moved around differently. We could take the approach, as did Lorentz, that clocks are not good instruments for measuring time, they are affected by their speed through the ether, the one inertial frame in which light actually propagates at a finite speed and in which stationary clocks tick at the correct and true absolute time of the universe. Note that this approach would be a denial of Einstein's second postulate. But this approach doesn't exempt you from all the affects of the relativity of simultaneity, it merely forces you to treat one inertial frame as the true one defining absolute time. The problem is, no one knows which one that is.

Einstein took a different approach. He said that clocks are good instruments for measuring time, even if they tick at different rates when moved differently. But this leads you to not be concerned about the universe having a single inertial ether frame that defines legitimate time, but rather, you can treat any inertial frame as defining legitimate time and in which light propagates at a finite speed just like it would in an ether frame.

And this leads to the relativity of simultaneity as being a legitimate process for relating the differing definitions of coordinate time in different inertial frames. But it also leads to a simple and consistent theory, as Einstein put it, his theory of Special Relativity.
 P: 45 Thanks a lot. This is one of those links I was refering to: http://www.fourmilab.ch/documents/Re...fSimultaneity/ I guess it's wrong.
Mentor
P: 3,920
 Quote by Aniket1 Thanks a lot. This is one of those links I was refering to: http://www.fourmilab.ch/documents/Re...fSimultaneity/ I guess it's wrong.
Your guess is right. That site is wrong.
Mentor
P: 17,526
 Quote by Nugatory Your guess is right. That site is wrong.
Yes, this site came up in a previous discussion also:
http://www.physicsforums.com/showpos...1&postcount=63

I believe that they have added the "technical note" since that time to sort of acknowledge the mistake.
 Mentor P: 11,862 Yes, he admits that when he talks about relativity of simultaneity, he's talking about something different from what "some physicists" mean by that term.
P: 4
 Quote by ghwellsjr Relativity of simultaneity is the result of both the principal of relativity (Einstein's first postulate) and his second postulate, that light propagates at speed c in any and all inertial frames. {quote paraphrased}
That 2nd postulate is giving me fits. Supposedly, it says that light's speed from point A to point B (in any inertial frame) is c, but I can't for the life of me see how this can happen. Would someone please provide an example using one or two inertial frames?
P: 848
 Quote by klyde That 2nd postulate is giving me fits. Supposedly, it says that light's speed from point A to point B (in any inertial frame) is c, but I can't for the life of me see how this can happen. Would someone please provide an example using one or two inertial frames?
klyde, one way of getting a handle on this is to consider the universe as 4-dimensional. Then, consider the different cross-sections of the 4-D universe that different observers live in. If you can follow the graphics below, some different 3-D worlds occupied by different observers moving at different speeds (with respect to the black reference frame) are shown. Notice that, because of the way each observer's X1 axis is rotated, the photon 4-dimensional worldline always bisects the angle between X4 (the time axis along which the observer moves in 4-D spacetime) and X1 (representing one axis of the 3-D world occupied by the observer).

This is the 4-dimensional representation of special relativity. Some people on the forum would not favor this as a correct representation of special relativity. Some would accept it as a mathematical representation, being careful not to take it as presenting the 4-dimensional universe as physical reality.

 P: 4 Goodness, Mr. Bobcat2, that's one heck of a reply! Apparently (but I am not a math whiz), the math has built-in the assumption of light speed invariance, but I still cannot see how this invariance can happen in real life, as in an experiment. Would you be so kind as to show an actual inertial observer getting c for the speed of light from point A to point B (in his own frame)? Thanks!
P: 181
 Quote by klyde ... but I still cannot see how this invariance can happen in real life, as in an experiment...
There are experiments that appear to prove this though - e.g. de Sitter double stars experiment (see: http://en.wikipedia.org/wiki/De_Sitt...tar_experiment). There is also the Alvager experiment. Such experiments show that the observer measures a constant velocity of light, regardless of the velocity of the source of the light.

What you are saying is that you find it hard to understand because it seems so obviously counter-intuitive and contrary to common sense. Relativity is counter-intuitive.

 Quote by klyde Would you be so kind as to show an actual inertial observer getting c for the speed of light from point A to point B (in his own frame)? Thanks!
I don't have the expertise to show this with a simple example - may be others can help. However, the constant c leads to the concept of time dilation, which is also a proven fact, counter-intuitive though it may appear at first glance.
P: 24
 Quote by bobc2 Each observer moves along his respective X4 axis at the speed of light.
I understand the different 3D worlds for different observers, and it seems to be a very useful concept, but I don't understand or see the benefit of the concept that an observer moves along his X4 (time) axis at the speed of light.
P: 4
 Quote by arindamsinha Such experiments show that the observer measures a constant velocity of light, regardless of the velocity of the source of the light. What you are saying is that you find it hard to understand because it seems so obviously counter-intuitive and contrary to common sense. Relativity is counter-intuitive.
Hello, arin, light's source-independency is not all that counter-intuitive because sound waves share this property; what I was actually trying to say is that it does not seem possible to me that light's one-way speed can be c for any and all inertial observers. But I see that you left this for others to solve, so I am not directing this to you at this time.

 Quote by arindamsinha I don't have the expertise to show this with a simple example - may be others can help. However, the constant c leads to the concept of time dilation, which is also a proven fact, counter-intuitive though it may appear at first glance.
Pardon me, but it seems rather odd that you would put off the simple one-way example but put forth time dilation (and the Twin Paradox), which is much more complicated.

Anyway, time dilation has nothing to do with the invariance of light's speed from point A to point B because this case involves two clocks and how they are related, so whether they are slowed or not is irrelevant.

May I humbly suggest that Mr. ghwellsjr himself provide an example? (He seems to have faded away for some reason!)

To emphasize exactly how simple this case is, here are the only tools needed:

Inertial Frame A
clock1-------------x axis--------------clock2 -->
S (light source)

Let's say that Frame A moves to the right relative to light source S. Let's further say that when clock 1 meets S in passing, S emits a light ray toward clock 2.

My problem is that I do not see how it is possible for light's one-way speed to be measured as c (relative to the Frame A observers).

Can anyone show me how this can happen, if only on paper??
Mentor
P: 17,526
 Quote by klyde Hello, arin, light's source-independency is not all that counter-intuitive because sound waves share this property; what I was actually trying to say is that it does not seem possible to me that light's one-way speed can be c for any and all inertial observers.
I would start here:
http://www.edu-observatory.org/physi...und-trip_tests

If the speed of light were frame variant, like sound, then we would expect to measure some isotropy which would single out the direction of the aether "wind". Once you have accepted the experimental fact that the speed of light is frame invariant then the "how" is shown by bobc2's image. Specifically notice the bottom blue box. The image inside shows geometrically how two different coordinate systems can get the same speed for a pulse of light.
Mentor
P: 11,862
 Quote by klyde That 2nd postulate is giving me fits. Supposedly, it says that light's speed from point A to point B (in any inertial frame) is c, but I can't for the life of me see how this can happen. Would someone please provide an example using one or two inertial frames?
Here's my attempt at an example. Units of time are seconds. Units of distance are light-seconds (the distance light travels in one second). Therefore c = 1 which simplifies calculations.

In frame S we have the Earth and space station Alpha at rest, at x = 0 and x = 10 respectively. A light signal leaves Earth at t = 0 and arrives at Alpha at t = 10. Its speed is c = dx/dt = 10/10 = 1.

On the Earth and Alpha I have fastened clocks which are synchronized in frame S, and therefore display "S-time".

Now consider this from the point of view of frame S' which moves at speed v = 0.6 to the right, relative to frame S. In S', both Earth and Alpha move to the left with speed 0.6.

Notice the following:

Length contraction - the distance between Earth and Alpha is reduced by a factor of ##\sqrt{1 - 0.6^2} = 0.8##.

Time dilation - while 5 seconds elapse in S', 4 seconds elapse on both the Earth and Alpha clocks (that is, they run slower by a factor of 0.8).

Relativity of simultaneity - the Earth and Alpha clocks are out of synchronization; their readings always differ by 6.

In both frames, the light signal leaves the Earth when the Earth-clock reads 0, and it arrives at Alpha when the Alpha-clock reads 10.

In frame S', the light pulse's speed is c' = dx'/dt' = 5/5 = 1 = c.
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Mentor
P: 11,862
 Quote by klyde If, as you say, the clocks are not synchronized (in the 2nd view), then why not? (How did they become asynchronous?) (Did they become asynchronous due to the given assumption of the invariance of light's one-way speed? If so, then you are merely assuming that which you are trying to prove.)
My example is not an attempt to prove that the speed of light is invariant, merely to give an example of how distance and time measurements turn out in the two frames, in such a way as to make the ratio Δx/Δt come out to be the same in both, for a light pulse. I mistakenly thought that's what you were asking for.

As you're probably aware, the invariance of the speed of light is a fundamental postulate of special relativity, and as such cannot be logically proved or disproved from first principles, at least not in the usual derivation of SR from Einstein's two postulates. It can only be verified or disconfirmed by experiment, either by measurements of the speed of light itself, or by other tests of the entire theory that has been built on that principle.

The theory as a whole has been extensively confirmed experimentally, as described here:

http://www.edu-observatory.org/physi...periments.html

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