# Relativity of Simultaneity

by Aniket1
Tags: relativity, simultaneity
 P: 41 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: 40,227 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.
 PF Patron Sci Advisor Emeritus P: 5,302 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
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P: 4,153

## 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: 41 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.
P: 2,350
 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: 15,553
 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: 10,677 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: 846
 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??
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P: 15,553
 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.
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P: 10,677
 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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 P: 4 Mr. jtbell, I appreciate your answer, but I do have a few questions re your diagrams. [Please note that you really do not have to spend much time reading my questions since they will soon be superseded by a diagram from a relativity text that purports to show observers in different frames both getting c for light's one-way speed.) What is your basis for the time t=10 in frame S? (If the source for the light ray was not attached to S, and S happened to move relative to the source, then S may also move relative to the ray. You need to take this into account. You cannot just assume that S has no motion either toward or away from the ray.) Why did you show times t=0 and t=0 in the first view of S, and then change the times to t=0 and t=6 in the 2nd view? 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.) And if the clocks of any observer are asynchronous, then how can they correctly measure time spans, including light's one-way travel time? What has the relativistic length contraction got to do with each frame's observers independently measuring light's speed? (All that matters is the distance in each frame, not the distance per S observers of another frame.) Are asynchronous clocks the cause of said length contraction? (If so, then said contraction is bogus.) Are asynchronous clocks the cause of time dilation? (If so, then said dilation is bogus.) Why bring Alpha into the equation? Why not use just Earth and its x axis? If the observers' rulers actually contract, then how can they make correct measurements? Why has no actual experiment ever shown the invariance of light's one-way speed? I will now present the example that I mentioned above which purports to do that which you were also purporting to do, i.e., to show observers in different frames both getting c for the one-way light speed. The following example of observers in different frames "getting the same one-way speed for light" is from _introduction to the theory of relativity_ by Sears & Brehme, Addison-Wesley, p. 16 (clocks are shown as (t), and the trains are moving at approx. .5c wrt each other): Train A -------------(0)----------90m----------(?)--> -------------->light ray ----------<--(0)----------150m------------------(?) Train B Train A ---------------(?)----------90m---------(300ns)--> ------------------------------------------->light ray ---<--(?)----------150m-----------------(500ns) Train B According to the diagrams given by Sears & Brehme, Light's one-way speed per A = 90m/300ns = .3m/ns Light's one-way speed per B = 150m/500ns = .3m/ns The problem with this example is the trivial experimental fact that a light ray will hit two adjacent clocks at absolutely the same time. (An equivalent fact is the fact that two touching clocks can be absolutely synchronized, and this fact is the basis of the start of the slow-clock-transport scenario.) Why, then, did Sears show the two right-hand clocks reading different times even though they were hit truly simultaneously by the light ray? As Sears freely admits, this happens because the clocks in each frame were forced to get the value "c" for light's one-way speed *prior* to the above "measurement." As he said on page 33, each clock in each frame was set (or forced) to read the time x/c whenever it is started by a light ray that was emitted at the origin clock at time zero. And as he later says on page 87, this forced "clock synchronization" actually causes the clocks in each frame to NOT be absolutely or truly synchronous. Of course, we all have long known that Einstein's clocks are not absolutely synchronous, but we never thought about the fact that such clocks cannot correctly measure time spans. Therefore, no one ever saw any problem with Sears' diagrams. As noted above, this problem is having two clocks at the same place reading two different times. It's funny that if anyone saw such clocks sitting on a table in their house, then they would immediately complain that one or both clocks are wrong. Whether he did it intentionally or not, Sears used the case that is easier to slip by even the most careful reader. Had Sears used the "opposite" case, then he might have been caught. Here is the "opposite" case (i.e., the case where the light ray starts each frame's right-hand clocks at different times): Frame A origin clocks start but right-hand clocks unstarted [0]------------------x------------------[x/c]--> S~>light emitted [0]------------------x------------------[x/c]---> Frame B Note: A moves to the right relative to S, and B moves to the right relative to A. Note: It is not critical that the two distant clocks be perfectly aligned as shown; all that matters is that the observers in each frame have separately measured their own distance between their own clocks to be x, as was given. (For example, x in each frame could be 1 light-year.) Related note: In no case does any observer in either frame measure any distance that is not in his own frame. (No "cross-measurements" are involved.) Note: Even though there is zero justification for Einstein's placement of the time x/c on A's distant clock, we will let this slide. Frame A right-hand clock starts --------[?]------------------x------------------[x/c]--> S------------------------------------------------>light --------------------[?]------------------x------------------[x/c]---> Frame B right-hand still clock unstarted From the above, we see that Einstein's forced "c-invariance" directly conflicts with experiment by improperly forcing clocks to read the same start time when they were really started at different times. (We know that they were started at absolutely different times because the two clock-starting events are light-like, and such events have an absolute before and after.) The reason for this conflict with experiment is simply the use of asynchronous clocks, i.e., clocks that cannot possibly correctly measure time spans or agree with experiment, as was noted above. Now we can clearly see why no experiment has shown one-way light speed invariance. It simply cannot happen experimentally because light's one-way speed actually varies with frame velocity, as would readily be seen if absolutely synchronous clocks were used.
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 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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