# Relativity of simultaneity

• B
• Andrew1955

#### Andrew1955

Hi, I read through einsteins popular book on relativity translated into english around 1922 and subsequently read the original 1905 paper on the electrodynamics of moving bodies.

So we have a fixed observer seeing flashes happening at the same time and we have a moving observer seeing one flash after the other. However we know the reason the moving observer sees one flash before the other is because he is moving towards the first flash. By einsteins definition of his experiment the two flashes occur at the same time.

So how do we then get to the conclusion of time passing at different rates?

Yes we can say the observers are confused by their experience due to the motion of the train and the finite speed of light, but it seems clear to me it is a fact the flashes happen at the same time on the train/moving line.

Am i missing something or am I reading too much into the proposed thought experiment which in fact is not so very good at introducing the idea?

You can't analyse it from only one point of view.

Both observers consider themselves as at rest, and between the location of the two strikes *. If one see the flashes at the same time, the strikes were simultaneous for them, if the flashes are not seen at the same time, the strikes were not simultaneous for them. The experiment goes on to show the two observers can't both see the flashes at the same time, so their judgement of the simultaneity of the strikes can't be the same. Neither is wrong, though they don't agree.

(Note that two other strikes could occur, that the train observer considers simultaneous and the embankment observer doesn't. There's nothing special about either observer.)

It's easy to get misled into thinking the train is "really" the thing moving, because we think of the ground as not moving and trains are moving, so we can think the ground observers view is the "real" view, but that's missing the point.

(* the train observer is at rest relative to the train, and as far as they are concerned it's the tracks and the embankment observer who is moving. Also note that the strikes are clearly said to be hitting across the tracks and the ends of the carriages.)

Vitro
I realize the observers do not both see simultaneous flashes. The issue i am raising is why it matters? how does einstein then leap from observer experience to time itself having changed? Sure the two observers might be confused but we can see the cause of their confusion, ie one observer is moving more rapidly towards one of the light flashes.

I realize the observers do not both see simultaneous flashes. The issue i am raising is why it matters? how does einstein then leap from observer experience to time itself having changed? Sure the two observers might be confused by we can see the cause of their confusion.

Neither is "confused". They are both correct in their view. The strikes were simultaneous for one, they were not for the other.

Overall, the thing is we tend to see distance and time as fixed, but they are not, they wiggle as it's the speed of light that's actually fixed.

A lot of that comes down to the relativity of simultaneity. One way to visualise it would be the ticks of clocks. Say two people in relative motion (each thinks they are at rest and the other is moving) are holding clocks. Since simultaneity is not absolute, they end up not being able to say that their clocks tick each second (or minute or hour) at the "same time". So they can't measure the same time.

Each observer is correct in what he observes. Only one correctly detects reality using his vision. One observer does not see a simultaneous flash. However on the moving object there were two simultaneous flashes. We can explain to the observer on the moving platform why he has not seen a simultaneous flash when in fact it did in reality happen simultaneously. In reality he did not experience it simultaneously even though in reality it did happen simultaneously.

Again the point i am making here is how does Einstein make the enormous leap to time being different due to relative motion? How did he go from observer experience of time being different to saying time passed at a different rate?

Last edited:
Each observer is correct in what he observes. Only one correctly detects reality using his vision.

You seem to contradict yourself, but, why is only one correct?

One observer does not see a simultaneous flash. However on the moving object there were two simultaneous flashes.

I think you've mixed up the scenario.

We can explain to the observer on the moving platform why he has not seen a simultaneous flash when in fact it did in reality happen simultaneously. In reality he did not experience it simultaneously even though in reality it did happen simultaneously.

No, as soon as you say "in reality" here you're asserting absolute simultaenity, and missing the whole point of what the experiment shows us.

There's nothing special about the embankment observer. Again, it could be that two strikes are simultaneous for the train observer and not the embankment observer.

Again the point i am making here is how does Einstein make the enormous leap to time being different due to relative motion? How did he go from observer experience of time being different to saying time passed at a different rate?

It's not an enourmous leap, and it's covered above.

Maybe you can quote the exact passage that concerns you, but I do think you should get the relativity of simultaenity straight before worrying about what it leads to.

https://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf

Page 25

Einstein says "
Lightning has struck the rails on our railway embankment at two places A
and B far
distant from each other. I make the additional assertion that these two lightning flashes
occurred simultaneously."

He supplies a diagram to show the points of the train A and B are exactly alongside the embankment points A and B at the moment of the simultaneous lighting strikes.

Einstein then says "every event which takes place along the line also takes place at a particular point of the train."

and

"
the events A and
B also correspond to positions A
and B on the train"

Last edited:
Again the point i am making here is how does Einstein make the enormous leap to time being different due to relative motion? How did he go from observer experience of time being different to saying time passed at a different rate?

A light pulse inside a moving train takes a little bit of extra time to travel from rear to front, as observed from the platform. Returning to the rear cancels that out almost perfectly at slow speeds, but not at high speeds.

Check out yourself that the above is true, no relativity is required.

When the train moves at relativistic speed, it takes a long time for a light pulse to travel from the rear to the front and then back to the rear, as observed from the platform. A passenger on the train does not notice that, so he must have a slow wristwatch or a slow atomic clock, as observed from the platform.

https://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf

Page 25

Einstein says "
Lightning has struck the rails on our railway embankment at two places A
and B far
distant from each other. I make the additional assertion that these two lightning flashes
occurred simultaneously."

He supplies a diagram to show the points of the train A and B are exactly alongside the embankment points A and B at the moment of the simultaneous lighting strikes.

Einstein then says "every event which takes place along the line also takes place at a particular point of the train."

It's rather dishonest to have that quote and omit the following words "If I ask you whether there is sense in this statement, you will answer my question with a decided "Yes." But if I now approach you with the request to explain to me the sense of the statement more precisely, you find after some consideration that the answer to this question is not so easy as it appears at first sight."

In any case, study the next chapter, then come back to this one. It's what clearly explains the relativity of simultaneity. https://www.marxists.org/reference/archive/einstein/works/1910s/relative/ch09.htm

It's rather dishonest to have that quote and omit the following words "If I ask you whether there is sense in this statement, you will answer my question with a decided "Yes." But if I now approach you with the request to explain to me the sense of the statement more precisely, you find after some consideration that the answer to this question is not so easy as it appears at first sight."

I am sorry to hear you find me dishonest.

From my point of view i am trying to understand why einsteins concludes what he concludes.

A light pulse inside a moving train takes a little bit of extra time to travel from rear to front, as observed from the platform. Returning to the rear cancels that out almost perfectly at slow speeds, but not at high speeds.

Check out yourself that the above is true, no relativity is required.

When the train moves at relativistic speed, it takes a long time for a light pulse to travel from the rear to the front and then back to the rear, as observed from the platform. A passenger on the train does not notice that, so he must have a slow wristwatch or a slow atomic clock, as observed from the platform.

I am not sure what you are wanting to say to me.

Einstein tells us the train observer does not see simultaneity because he is moving towards the light rays coming from B.

...

Einstein tells us the train observer does not see simultaneity because he is moving towards the light rays coming from B.

That's from the point of view of the embankment observer.

From the point of view of the train observer, they are exactly between the two strikes, and they are at rest, so if the strikes were simultaneous they'd see the flashes at the same time. They don't, so according to them, the strikes were not simultaneous. It's no bother to them that the embankment observer saw the flashes at the same time, it makes perfect sense because according to the train observer the embankment observer was moving towards one strike and away from the other.

Both views are correct, even though the two observers don't agree on simultaneity.

-----

Maybe forget relativity of simultaneity for a moment, as you're stuck on thinking it's absolute.

Consider some (ambidextrous!) person holding a ball in each hand, we'll consider them as at rest. They throw the two balls forward at 20 km/h at two other people.

Those two other people are running towards the ball thrower; one at 5 km/h and one at 10 km/h.

The one running at 5 km/h finds it easier to catch their ball, than the one running at 10 km/h; as their speed relative to the ball is 25 km/h compared to the other person for whom the ball is 30 km/h.

OK so far? That's our regular non-relativistic World, as we see it every day.

It's wrong.

What if it's not balls but light? Two people are moving towards a light source. At different speeds.

The trick is, light will always be measured to be moving at the same speed (in a vacuum ...). How can the two people moving towards the light source at different speeds, both measure that light to be moving at the same speed? Because distance and time are not the same for both of them.

Einstein tells us the train observer does not see simultaneity because he is moving towards the light rays coming from B.
So you agree that the flashes of light are not simultaneous from the point of view of the train observer? What's the problem, then?

This is going to be easier if you just stick with einsteins text.

Are you saying the timing of the two events on the embankment are not directly related to the timing of the two events on the train where both events are known as A and B?

So I am asking you how are you interpreting his text and diagram which i drew your attention to earlier? You strongly appear to be saying the events are not corresponding to each other. That seems to require an explanation by you.

Einstein talks about events and uses the same letters for Event A on the embankment and the A event on the train.
-----------------

He supplies a diagram to show the points of the train A and B are exactly alongside the embankment points A and B at the moment of the simultaneous lighting strikes.

Einstein then says "every event which takes place along the line also takes place at a particular point of the train."

and

"
the events A and
B also correspond to positions A
and B on the train"

Its a consequence of the constancy of the speed of light which means that light travels at the same speed, c, to all observers (in flat spacetime/inertial frames).

Your situation is essentially identical to the traincar problem.

First, imagine you are inside a moving traincar, directly in the center, and you fire two beams of light in either direction. The invariance of the speed of light in your frame of reference means they will hit the train walls at the same time.

Now imagine there is another person sitting on the station witnessing the events happening in the train as it moves by. The invariance of the speed of light in their reference frame means that it will hit the back first and the front later.

Neither frame is more valid than the other, because how could you determine that?

This isn't like throwing two balls to either end of the traincar, because the light doesn't have the additional velocity of the train. Think about it: imagine the person standing in the middle of the train threw two balls to either end of the traincar and they hit the walls simultaneously. Because the balls have the initial velocity of the train, they would also contact the walls simultaneously in the outside observer's frame too. This isn't the case with light.

Because of this relativity of simultaneity, Einstein thought that maybe it was time that was changing. He concluded that time may be flexible and went on to make an incredible theory around that.

#### Attachments

• 9pZgg.png
2.8 KB · Views: 991
• cWMr1.png
2.6 KB · Views: 1,048
Last edited by a moderator:
Vitro
>>So you agree that the flashes of light are not simultaneous from the point of view of the train observer? What's the problem, then?

Einstein appears to be saying the reason for the flash not being simultaneous for the train observer is because he is moving towards the light rays coming from B and moving away from the light rays coming from A. According to Einstein the A events are linked as are the B events. event A on the embankment is an event A on the train. Einstein gives no indication event A on the embankment is not happening at the same time as event A on the train.

If in advance of his words he is saying A on the embankment is at a different epoque as event A on the train the whole wording just becomes very odd.

All he is saying is the two observers cannot agree on simultaneity using the method he has chosen. He then leaps into time being different for each observer.

...
Einstein appears to be saying the reason for the flash not being simultaneous for the train observer is because he is moving towards the light rays coming from B and moving away from the light rays coming from A. According to Einstein the A events are linked as are the B events. event A on the embankment is an event A on the train. Einstein gives no indication event A on the embankment is not happening at the same time as event A on the train.

If in advance of his words he is saying A on the embankment is at a different epoque as event A on the train the whole wording just becomes very odd.

All he is saying is the two observers cannot agree on simultaneity using the method he has chosen. He then leaps into time being different for each observer.

I don't know why you make this more complicated than it is.

He stipulates that A and B are simultaneous for the embankment observer, then asks if they (A and B) are simultaneous for the train observer. Turns out the answer is no.

Yes, A is on the tracks and train, yes, B is on the tracks and train. But that doesn't mean the two observers in relative motion must agree whether A and B were simultaneous.

#### Attachments

• train.png
5.8 KB · Views: 614
Einstein appears to be saying the reason for the flash not being simultaneous for the train observer is because he is moving towards the light rays coming from B and moving away from the light rays coming from A.
Yes, that's from the point of view of the ground observer. From the point of view the train observer he's not moving at all, so the flashes of light ARE non-simultaneous.

Alfredo Tifi
A lazy Shizno

Thanks. It seems I was not understanding what Einstein was saying and getting confused by what is meant by the invariance of the speed of light.

I will have to think about the text but it seems to be sorted out.

Cheers

Andrew

So how do we then get to the conclusion of time passing at different rates?

This is a highly counter-intuitive conclusion for me, and I think for most people.

The highly counter-intuitive axiom that leads to this conclusion is that all observers measure the speed of light to be the same speed in all frames. If one takes that as a starting point and follows it, one arrives at the conclusion that all observers may not then agree on the rate of passage of time.

It is experimentally verified beyond any room for reasonable doubt that the speed of light is constant in all frames - this isn't a derived conclusion from more fundamental axioms, it is itself a starting point for subsequent reasoning.

It might help you to consider two moving objects on the train - one of them a normal baseball that an observer on the platform sees moving at the speed of the train plus whatever velocity the train passenger see the ball moving at, and one photon baseball that moves at the same speed according to both the platform observer and the train observer regardless of how fast the train is moving. You should be able to see that constraining both observers to always agree on the speed of the photon baseball forces you to change some of the other things that it seems natural for the observers to agree on, like the rate of passing time.

Alfredo Tifi
I am still finding this hard. If it is agreed the A events are one and the same then the only thing left to discuss is what each observer experiences.

I am not getting it.

You guys appear to be saying the A events happen at a different time. If so the whole thought experiment seems to be a waste of time as no meaning can be found from it.

I am still finding this hard...
Have you understood A Lazy Shisno's example? I too prefer the scenario with a single flash of light originating in the middle of the train instead of Einstein's two flashes starting at the ends, but they are both equally valid and illustrate the exact same thing.

In A Lazy Shisno's example define events A = "light hits left wall" and B = "light hits right wall". Do you agree and understand that these events happen at the same time for the observer on the train? Do you understand and agree that these same two events do not happen at the same time for the observer on the platform?

That's all there is to it, and the reason is because the speed of light is finite and the same for both observers, they both measure it to propagate at ##c## to the left and to the right in their own coordinate system.

A Lazy Shisno
I understand a lazy shisnos example alright. I am still not clear why peculiarities about the speed of light must mean time and length must also change.

If light causes us to perceive weird stuff does this mean that weird stuff is really happening? If we see wave lengths of light as red is red really out there or is there just colourless energy which we interpret and imagine as being red? Do you think the sky is actually blue? The grass is green? These things are only illusions created by the human visual system.

We use light to help us perceive reality. If light tells us time has changed, should be believe that just because 'light says its true'.?

I understand a lazy shisnos example alright. I am still not clear why peculiarities about the speed of light must mean time and length must also change.
For that you have to move beyond the relativity of simultaneity thought experiment: google for "light clock time dilation" to find the simplest thought experiment that demonstrates time dilation.

Hi, I read through einsteins popular book on relativity translated into english around 1922 and subsequently read the original 1905 paper on the electrodynamics of moving bodies.

So we have a fixed observer seeing flashes happening at the same time and we have a moving observer seeing one flash after the other. However we know the reason the moving observer sees one flash before the other is because he is moving towards the first flash. By einsteins definition of his experiment the two flashes occur at the same time.

So how do we then get to the conclusion of time passing at different rates?

Yes we can say the observers are confused by their experience due to the motion of the train and the finite speed of light, but it seems clear to me it is a fact the flashes happen at the same time on the train/moving line.

Am i missing something or am I reading too much into the proposed thought experiment which in fact is not so very good at introducing the idea?

To understand Einstein's coordinate system (which is considered the conventional system) the half-hour video YouTube instructor/animation listed below does a remarkable job at simplifying the relationships you describe in SR:

Episode 42. The Lorentz Transformation

It is a short 30 minute Caltech college classroom lecture and animation with Professor David Goodstein.
Prof. Goodstein was a student of Feynman who was noted for his uncanny ability to make physics understandable to the neophyte and Goodstein is no slouch himself. I was able to obtain a DVD set just before the series sales were discontinued, but it is still relevant today, perhaps only a bit incomplete due to new discoveries. I'm glad it is still available on YouTube because I thought it would be lost forever.

Wes

"Episode 42. The Lorentz Transformation: If the speed of light is to be the same for all observers, then the length of a meter stick, or the rate of a ticking clock, depends on who measures it.

“The Mechanical Universe,” is a critically-acclaimed series of 52 thirty-minute videos covering the basic topics of an introductory university physics course.

Each program in the series opens and closes with Caltech Professor David Goodstein providing philosophical, historical and often humorous insight into the subject at hand while lecturing to his freshman physics class. The series contains hundreds of computer animation segments, created by Dr. James F. Blinn, as the primary tool of instruction. Dynamic location footage and historical re-creations are also used to stress the fact that science is a human endeavor.

The series was originally produced as a broadcast telecourse in 1985 by Caltech and Intelecom, Inc. with program funding from the Annenberg/CPB Project.

The online version of the series is sponsored by the Information Science and Technology initiative at Caltech. http://ist.caltech.edu

©1985 California Institute of Technology, The Corporation for Community College Television, and The Annenberg/CPB Project"
...

Its a consequence of the constancy of the speed of light which means that light travels at the same speed, c, to all observers (in flat spacetime/inertial frames).

Your situation is essentially identical to the traincar problem.

First, imagine you are inside a moving traincar, directly in the center, and you fire two beams of light in either direction. The invariance of the speed of light in your frame of reference means they will hit the train walls at the same time.

View attachment 213851

Now imagine there is another person sitting on the station witnessing the events happening in the train as it moves by. The invariance of the speed of light in their reference frame means that it will hit the back first and the front later.

View attachment 213852

Neither frame is more valid than the other, because how could you determine that?

This isn't like throwing two balls to either end of the traincar, because the light doesn't have the additional velocity of the train. Think about it: imagine the person standing in the middle of the train threw two balls to either end of the traincar and they hit the walls simultaneously. Because the balls have the initial velocity of the train, they would also contact the walls simultaneously in the outside observer's frame too. This isn't the case with light.

Because of this relativity of simultaneity, Einstein thought that maybe it was time that was changing. He concluded that time may be flexible and went on to make an incredible theory around that.

This post does a nice job introducing the traincar problem and the relativity of simultaneity, but the paragraph I put in bold needs qualification: In Newtonian mechanics, yes, the balls hit the walls simultaneously in all frames; but in special relativity, they do not.

If light causes us to perceive weird stuff does this mean that weird stuff is really happening?

No. But light is not causing us to perceive weird behavior in this case. Rather, light is being used to demonstrate that weird stuff is actually happening. The weird stuff can be demonstrated in other ways that don't involve light. For example, engineers who orchestrate the various clocks used in the GPS must take this weird behavior into account otherwise the GPS receiver you use to find your location wouldn't be precise enough to locate the city you're in, let alone the street corner you're on. The weird stuff really happens.

I recommend that before you try to understand Einstein's relativity you try to understand this example from the relativity we had before Einstein gave us his.

You toss a ball directly upward and then catch it when it comes back down, about 0.5 s later. To you it travels along a vertical line. If you do it while seated in an airplane traveling at 200 m/s you know in that 0.5 s the plane moves a distance of 100 m, so the ball doesn't move in a vertical line, it follows a curved path. So, what is the true path of the ball? Is the path really curved or is it really straight?

SiennaTheGr8
... You guys appear to be saying the A events happen at a different time. ...

No, it's about whether A happens at the same time as B, and more interestingly, if two observers in relative motion can agree on that.

#### Attachments

• train2.png
31.7 KB · Views: 455
This isn't like throwing two balls to either end of the traincar, because the light doesn't have the additional velocity of the train. Think about it: imagine the person standing in the middle of the train threw two balls to either end of the traincar and they hit the walls simultaneously. Because the balls have the initial velocity of the train, they would also contact the walls simultaneously in the outside observer's frame too. This isn't the case with light.

The relativity of simultaneity should hold between the two frames no matter if a ball or light is used. I think to show this you would have to use the relativistic addition of velocities whereas you are assuming classical addition.

This isn't like throwing two balls to either end of the traincar, because the light doesn't have the additional velocity of the train.

@pixel has a good point. The ball doesn't have the additional velocity of the train, either. There's nothing special about the light itself in this context, the thing that's special is the speed of the light. I realize that everybody knows this, but it might be worth making explicit because sometimes learners are confused by it.

You guys appear to be saying the A events happen at a different time.
There is more than one "time". Each reference frame judges the time that events occur by its own set of clocks synchronized within its reference frame. But if two frames in relative motion try to synchronize between the two at one point, they are forced to be unsynchronized at other points in the direction of relative motion. So they can never agree on whether two events which are separated in the direction of relative motion are simultaneous. If one reference frame thinks that they are simultaneous, then the other can not agree.
If so the whole thought experiment seems to be a waste of time as no meaning can be found from it.
I couldn't disagree more. It helps one understand how it all fits together. It helps one to understand how each reference frame can think that the other's clocks are running too slow. -- Because each reference frame is moving toward the other reference frame's trailing clocks, which people in the first frame thinks were synchronized incorrectly.

Last edited:
I think @SiennaTheGr8 likewise had a good point in #26.

@pixel missed your post #26 and would have otherwise referenced it.

SiennaTheGr8
The question I would add to this discussion is what is time? I would stress that it is not a thing itself but rather a measurement or snapshot of the state of the relationship of things (atoms) at a particular moment. Personally I think Einstein treats time too much as a thing.

@pixel has a good point. The ball doesn't have the additional velocity of the train, either. There's nothing special about the light itself in this context, the thing that's special is the speed of the light. I realize that everybody knows this, but it might be worth making explicit because sometimes learners are confused by it.

Sorry, I'm still trying to learn some of the finer details of SR, but why doesn't the ball have the initial velocity of the train? If I'm on a train and I have a ball in my hand, it has the same velocity as the train. So when I throw it in the direction of the train's motion, it has the velocity of the train plus the velocity I imparted on it (from the perspective of an outside observer). I thought the special thing about light is that its speed doesn't depend on the velocity of the thing it's being emitted from?

Last edited by a moderator: