What is the relativity of simultaneity measuring?

[DAC]

Hello PF.
Prior to the train/embankment thought experiment, Einstein argues that in order to determine if events are simultaneous, an equidistant observer is required.
The embankment observer is equidistant, and when the light from the two flashes reaches him he sees them as simultaneous.
The train observer is not equidistant as he is moving relative to the flashes. Therefore whilst he sees the two flashes as separate. he has no way of knowing what originally happened, because to do so requires him to be equidistant, as stated by Einstein.

 

[Dale]

See section 1 here:
https://www.fourmilab.ch/etexts/einstein/specrel/www/

There is no equidistant requirement.

 

[Nugatory]

As DaleSpam says, there is no equidistance requirement. The train thought experiment is easier to explain if both flashes are equidistant from an observer, so it's usually explained that way - but it's not necessary.

The underlying logic is fairly straightforward. First, if light from some event reaches your eyes, when did that event happen? That's easy - you take the time the light reached your eyes, subtract the light travel time, and that's when it happened.

Second. what does it mean to say that two events are simultaneous? That might be even easier - they are simultaneous if they happened at the same time.There's no reason that the light from both needed to reach me at the same time or that the two events be equidistant. If light from an event five light-minutes away reaches my eyes at noon I'll say that it happened at 11:55 AM; if light from another event ten light-minutes away reaches my eyes at 12:05 PM, I'll say that it also happened at 11:55 AM and therefore the two events were simultaneous.

The train experiment shows that if you are moving relative to me, then when you do the same calculation of subtracting the light travel time from the time the light reached your eyes, you will not find that they both happened at the same time. That's relativity of simultaneity.

 

[DAC]

Thanks ,
Part one, On The Idea of Time in Physics. Special&General, gives a fairly lengthy argument as to the need for an observer who is equidistant in order to determine simultaneity. So both methods are correct?

What if flashes are staggered , with the later flash closer to the observer. The light travel times will be different, but the flashes will arrive simultaneously. Whereas an equidistant observer would see the flashes had different starts.

 

[Orodruin]

You can take non-equidistance into account to compute the different travel times and therefore the times when the flashes occured.

 

[Dale]

Part one, On The Idea of Time in Physics. Special&General, gives a fairly lengthy argument as to the need for an observer who is equidistant in order to determine simultaneity.

Equidistance is not a requirement for simultaneity. It is a conveniently simplified scenario for teaching. The definition is given in section 1 of the reference I provided, and in the reference you mention he never claims that the simplified example is a general case.

 

[Dale]

The train observer is not equidistant as he is moving relative to the flashes.

Also, even though equidistance is not a requirement, the train observer is equidistant between the flashes in the train frame. So the simplified analysis applies to the train observer also.

 

[Janus]

Thanks ,
Part one, On The Idea of Time in Physics. Special&General, gives a fairly lengthy argument as to the need for an observer who is equidistant in order to determine simultaneity. So both methods are correct?

What if flashes are staggered , with the later flash closer to the observer. The light travel times will be different, but the flashes will arrive simultaneously. Whereas an equidistant observer would see the flashes had different starts.

Let's use an example:
Say observer 1 is 2 light min from flash 1, and 1 light min from flash 2, while observer 2 is 1.5 light min from both. Flash 1 occurs 1 min before Flash 2. Observer 1 sees both flashes at the same time, but knowing the distance to each flash, and the speed of light, he can determine that the flashes happened 1 min apart. Observer 2 seeing the flashes one minute apart and knowing that he is halfway between the flashes knows that they occurred 1 min apart.

The main difference between the two observers is that in order for the observers to determine when the flashes occurred, observer1 has to know the speed of light, while observer 2 doesn't. The equidistant observer only has to know that the speed of light is the same from both flashes.

This is why we use equidistant observers in the train example; it simplifies things.

With that in mind, let's look at the train example.

We start in the embankment frame:
The lightning strikes occur at equal distances from him, at the moment the train observer is passing him, and leave burn marks on both the embankment and train. ( thus he remains halfway between the burn marks on the embankment, while the train observer remains halfway between the burn marks on the train.)
The light from each flash expands outward from the burn marks on the embankment. (meanwhile, the burn marks on the train move away from the center of each expanding flash.)
The train observer is moving towards on burn mark on the embankment and away from the other, so he meets up with the light from one flash before the other catches up with it. This also means that his relative position with respect to the burn marks on the embankment is different when he sees each flash.
The light from the strikes meet up at the embankment observer sometime between when the train observer see one strike and when he sees the other.

Now consider the train frame.
First we establish the events that he agrees with the embankment observer about:
The lightning strikes leave burns an equal distance from him on the train and an equal distance from the embankment observer on the embankment.
The lights from each strike meet at the embankment observer.
Thus he is closer to one burn mark on the embankment than the other when he sees the flashes, and his relative position with respect to the flashes is different when he sees each flash. (in fact, both observer agree exactly on his relative position with respect to the embankment when he sees each flash.)
This means he sees each flash at different times.

Now to what he determines is different.
After the lightning strikes, the light from each strikes expands out in a circle from the burn mark on the train. In other words, in his frame, Burn marks on the train stay in the centers of the expanding lights while the burn marks on the embankment move away from the centers. This a result of the second postulate. The speed of light is a constant in any inertial frame as measured relative to that frame. This means that light will expand outward at an equal speed relative to the train as measured by anyone at rest with respect to the train.

Since the train observer is halfway between the burn marks on the train, and he knows that the light leaving these burn marks are coming at him at equal speeds from both directions, the fact that each light arrives at a different time means that the lightning strikes that created the light happened at different times.
Anyone on the train will come to the same conclusion, it is just that for them, they would have to know their exact distance from the burn marks and the speed of light to make the exact determination of when the strikes occurred.

 

[DAC]

Thank you again for your replies.
A further question.
An observer, equidistant from two simultaneous flashes, is moving towards them, whilst remaining equidistant to them. A second observer who is stationary relative to the flashes is also equidistant from them. Both observers see the flashes as simultaneous, yet their reference frames are different. How is this explained?

 

[Orodruin]

You have not even specified a valid situation. You cannot just say that two events are simultaneous, you need to specify which frame they are simultaneous in. Furthermore, events do not move, they are points in spacetime.

 

[DAC]

They are simultaneous in both frames, that is the issue.
The observer moves. I did not say the events moved.
Thank you.

 

[Orodruin]

They are simultaneous in both frames, that is the issue.

No they are not. You cannot impose this by wishing it is so. I suggest you try to draw a Minkowski diagram of what is happening.

A second observer who is stationary relative to the flashes

The observer moves. I did not say the events moved.
Thank you.

You did so in the part quoted above. You cannot be stationary relative to an event because an event has no velocity to be compared with.

 

[Nugatory]

Thank you again for your replies.
A further question.
An observer, equidistant from two simultaneous flashes, is moving towards them, whilst remaining equidistant to them. A second observer who is stationary relative to the flashes is also equidistant from them.

it's hard to visualize the setup you're describing because your description is very unclear: you've said the two flashes are simultaneous without specifying a frame; and the phrase "stationary relative to the flashes" makes no sense at all. But I think you're trying to describe a situation in which two observers not at rest relative to one another are moving in such a way that for both the distance to the spot where the first flash struck is equal to the distance to the spot where the second flash struck at all times.

We can't arrange a setup like this if the lightning strikes along the railroad tracks, but we can if the lightning strikes away from the tracks. If the tracks run east-west, and one flash strikes a given distance north of the tracks, and the second flash lands the same distance south of the tracks and due south of where the first flash hit...
Then if the two flashes were simultaneous for anyone observer moving along the tracks (including the platform observer who is moving along the tracks at speed zero), they will be simultaneous for all observers moving along the tracks at any speed.

Both observers see the flashes as simultaneous, yet their reference frames are different. How is this explained?

What's to explain? We've carefully constructed the setup so that it would come out this way. Note that although both observers will say "the flashes struck at the same time", if you ask them what time that was, they will give different answers.

 

[DAC]

Einstein said, what is simultaneous in the embankment frame is not with respect to the train frame. How does the Relativity of Simultaneity apply when, as in this configuration, the moving and stationary observers agree on simultaneity? ( and thank you again for your reply.).

 

[SlowThinker]

Einstein said, what is simultaneous in the embankment frame is not with respect to the train frame.

That only applied to his setup. Your setup is different.

 

[Nugatory]

Einstein said, what is simultaneous in the embankment frame is not with respect to the train frame. How does the Relativity of Simultaneity apply when, as in this configuration, the moving and stationary observers agree on simultaneity?

They don't agree on simultaneity - for that they'd need to agree about the time-ordering of all events, not just a few that have been carefully selected to not show relativity of simultaneity. You've just discovered that there are some pairs of events that will not be good examples of the why they disagree about simultaneity as long as both observers only move in a particular way.

 

[DAC]

You said" They don't agree on simultaneity"
and
" they will be simultaneous for all observers".?

What do you mean by agreeing " about the time ordering of all events."

I don't see how two observers who are equidistant from an event don't agree on the event's simultaneity.

Thanks.

 

[Dale]

@DAC let's use the standard train/platform scenario. Tom is standing in the middle of the train, and Paul is standing in the middle of the platform. As Tom passes Paul lightning flashes hitting the ends of the train and leaving char marks both on the train and on the platform. The lightning flashes are simultaneous for Paul. Do you understand this set-up?

Now, let's determine what Tom and Paul observe. Paul observes that he is standing exactly in the middle of the char marks on the platform, so the two flashes were equidistant. Tom observes that he is standing exactly in the middle of the char marks on the train, so the two flashes were equidistant. Because the flashes were simultaneous for Paul, the light reaches his eyes at the same time. Accounting for the finite travel time of light, Paul can determine exactly when they both happened. Tom sees the flash from the front of the train first. When Tom accounts for the finite travel time of light and the known distance, he determines that the two flashes occurred at different times.

Therefore, two observers who are each equidistant (with respect to their individual rest frames) from a pair of events don't agree on the simultaneity of the two events.

 

[DAC]

Thanks. No problem with the set up.

Let the flashes strike the tracks in front of the train, front left and front right. Tom stands anywhere along the moving trains central long axis.
He will therefore be an equal distance to both flashes, and is moving towards them equally. Meanwhile Paul who drew the short straw is standing in the middle of the track. He is therefore equidistant from the flashes.
Both the moving and stationary observers agree on simultaneity

 

[Nugatory]

Let the flashes strike the tracks in front of the train, front left and front right. Tom stands anywhere along the moving trains central long axis.
He will therefore be an equal distance to both flashes, and is moving towards them equally. Meanwhile Paul who drew the short straw is standing in the middle of the track. He is therefore equidistant from the flashes.
Both the moving and stationary observers agree on simultaneity

The do not agree on simultaneity. They do agree that these two particular flashes happened at the same time.

To agree on simultaneity they must agree for all pairs of possible flashes, not just two particular flashes. The point of Einstein's train thought experiment is not that observers in motion relative to one another will always disagree, it is that (unlike in classical Galilean relativity) they will not always agree.

 

[Dale]

No problem with the set up.

Let the flashes strike the tracks in front of the train, front left and front right.

That is not the standard setup. Tom and Paul disagree about the simultaneity of events spatially separated along the track, not perpendicular to it.