# Relativity of Simultaneity concept

1. Dec 25, 2012

### 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?

2. Dec 25, 2012

### Staff: Mentor

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.

3. Dec 25, 2012

### bcrowell

Staff Emeritus
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: https://www.physicsforums.com/showthread.php?t=534862 [Broken]

Last edited by a moderator: May 6, 2017
4. Dec 25, 2012

### ghwellsjr

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.

5. Dec 26, 2012

### Aniket1

6. Dec 26, 2012

### Staff: Mentor

7. Dec 26, 2012

### Staff: Mentor

Last edited: Dec 26, 2012
8. Dec 26, 2012

### Staff: Mentor

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.

9. Dec 29, 2012

### 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?

10. Dec 29, 2012

### bobc2

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.

11. Dec 29, 2012

### klyde

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!

12. Dec 29, 2012

### arindamsinha

There are experiments that appear to prove this though - e.g. de Sitter double stars experiment (see: http://en.wikipedia.org/wiki/De_Sitter_double_star_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.

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.

13. Dec 30, 2012

### Alain2.7183

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.

14. Dec 30, 2012

### 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. But I see that you left this for others to solve, so I am not directing this to you at this time.

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??

15. Dec 30, 2012

### Staff: Mentor

I would start here:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#round-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.

16. Dec 30, 2012

### Staff: Mentor

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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17. Dec 30, 2012

### klyde

[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.

Last edited: Dec 30, 2012
18. Dec 30, 2012

### Staff: Mentor

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/physics-faq/Relativity/SR/experiments.html

19. Dec 31, 2012

### Austin0

They don't correctly measure light's one-way time . This is fundamentally unmeasurable.
And as you correctly noted above this is simply a convention.The implementation of an unproved assumption.
They correctly measure time spans because those time intervals as indicated by those conventionally "unsynchronous"clocks correctly correspond to the spacetime at the given velocity and correspond to the physical values of mechanics and electrodynamics etc in that frame.

I will give you my take which may not reflect the consensus but may still be helpful.
Length contraction has two separate causal sources.
1) A mechanical source due to the lightspeed interactions of atomic tensile and nuclear forces within the atomic structure of bodies. AN"actual" physical contraction.
2) Purely kinematic contraction due to clock desynchronization.
Individually both these concepts are asserted by different people and different circumstances. My feeling is that both are operative to varying indeterminate degrees in virtually all cases. But like so much in our relative universe there is no way to quantify or evaluate in any real sense which is the cause and to what extent in any particular case.
In neither case is it bogus.

Likewise for dilation. Clearly there is actual dilation which has nothing to do with clock synch EG. The returning twin.
But in a case of a single inertial clock traveling between two points and clocks in another frame then the ratio of this clocks proper time to the the coordinate delta t of those two clocks does involve consideration of relative synchronization between those clocks.

If everything contracts equally why wouldn't they make accurate measurements??

FOr the mentioned reasons. It is unmeasurable.
The 2nd postulate does not actually state that the measured one-way speed of light is invariant. It says that the speed of light is independe3nt of the motion of the source and is everywhere constant in vacuum.
It is measured as invariant by convention which is no real measurement at all.

yes that is obviously true. This is an implicit axiom of SR, that system clocks are only operationally synchronous with no implication of actuality or absoluteness.. The only absolute or actual simultaneity is in the case of co-located occurrence of events.

Of course all experiments I.e.actual one way measurements of light speed do show invariance so your first statement here is not really correct but I would certainly agree that the actual one-way speed of light does vary with the velocity (unknown) of the frame. so those measurements have no real meaning . And so the actual relative velocity of the light or velocity of the measuring frame is also completely indeterminable.

Last edited: Dec 31, 2012
20. Dec 31, 2012

### pervect

Staff Emeritus
I haven't seen the point I'm about to make in the literature, (at least not very directly) but I think it's a good one.

There is one, and only one, way of synchronzing clocks that will make Newton's laws work correctly.

To see this, just imagine having two equal masses with two equal velocities collide and then come to a complete stop - perfectly standard, and routine.

Now, tweak the clock synchronization you used to measure the velocities and repeat.

The velocities you measure are no longer equal. But the colliding masses still stop. They don't care how you synchronize your clocks.

Thus, there is one and only one clock synchronization that will make Newton's laws work. One way of viewing relativity is to say that this method is always equivalent to Einstein's much simpler method, using light signals.