Relativity of Simultaneity: Proving Lightning Strikes A & B Same Time?

[Sullivan Stockwell]

My question is based around the popular thought experiment regarding Einstein's relativity of simultaneity. That is, the one regarding two lightning strikes and two observers. Observer 1 is stationary relative to the ground, and is located equidistant between lightning strikes A and B. Observer 2 is moving on a train parallel to the lightning strikes and observer 1. It is said that observer 2 will judge the lighting strikes to happen at different times, and observer 1 will say they happen at the same time. This is true. But often times the explanation goes beyond addressing that the perceptions will indeed view the lighting strikes as happening at different times and claim that the lighting actually happens at different times. If you had a sensor under lighting strikes A and B, could you not prove that they do happen at the same time? The perceptions are different, but the events themselves can be proven as to their time. Maybe I just don't fully understand the interpretations people give regarding it. Thanks.

 

[Ibix]

How will you compare the readings on your sensors? You need to bring the readings together somehow to see if they happened at the same time or not.

Work through that and you'll find there's no way to do it that doesn't have a different result in the platform and train frames.

 

[Nugatory]

The events really are simultaneous in one frame but not the other - it's not a matter of perception.

Let's say lightning hits a tree one light-second away from me, and the light from that event reaches my eyes at time T. Because I know it took one second for the light to travel from the tree to my eyes, I know that the lightning really hit the tree at time T-1 and that's not a matter of perception. (It would be more precise to say that "the lightning hit the tree at the same time that my wristwatch read T-1; the light from that event reached my eyes at the same time that my wristwatch read T").

The point of Einstein's train thought experiment is that after we have properly corrected for the light travel time to remove the issues of perception, the events that are simultaneous for one observer are not simultaneous for the other, and there's no reason (except for our long-standing habit of thinking that there's something special about the surface of the Earth because we live on it) why one of them should be any more right than the other.

 

[Dale]

Observer 1 is stationary relative to the ground, and is located equidistant between lightning strikes A and B. Observer 2 is moving on a train parallel to the lightning strikes and observer 1.

Note that observer 2 is also equidistant from the lightning strikes. That is important.

 

[Janus]

My question is based around the popular thought experiment regarding Einstein's relativity of simultaneity. That is, the one regarding two lightning strikes and two observers. Observer 1 is stationary relative to the ground, and is located equidistant between lightning strikes A and B. Observer 2 is moving on a train parallel to the lightning strikes and observer 1. It is said that observer 2 will judge the lighting strikes to happen at different times, and observer 1 will say they happen at the same time. This is true. But often times the explanation goes beyond addressing that the perceptions will indeed view the lighting strikes as happening at different times and claim that the lighting actually happens at different times. If you had a sensor under lighting strikes A and B, could you not prove that they do happen at the same time? The perceptions are different, but the events themselves can be proven as to their time. Maybe I just don't fully understand the interpretations people give regarding it. Thanks.

Here's a pair of animations I created a while back to help to visualize what is happening.
We start in with the ground observers frame:

He is halfway between the red dots and when each end of train aligns with a dot, the lightning strikes both the dot and end of the train. The flashes expand outward from the strikes reaching the ground observer simultaneously, as the started simultaneously and traveled at the same speed relative to the ground observer. They reach the train observer at different times (and when he is adjacent to different points of the tracks).

Now we switch to the train observer's frame. One thing to note first is that in the last animation the train was moving relative to the observer's frame, Thus the train will be measured to be length contracted: Thus is is this contracted length for the train that just fits between the red dots. When we switch to the train's frame, the train will measure as having its normal proper length. Now it is the ground that is moving and is length contracted. Thus from the train we would measure our train length as being greater than the distance between the two red dots and can never fit between them;

Here, the right end of the train reaches the right dot before the left end reaches the left dot. The strikes still occur when the dots and ends of the trains align. (an observer at the right end of the train and an observer at the right dot both will agree that they were hit by a lightning strike simultaneously. The same can be said for observers at the other end of the train and other dot.) The flashes expand outward from the ends of the train. Each have to travel an equal distance to reach the train observer at the train midpoint. The rightmost flash reaches him first, then the leftmost flash. Since they traveled the same distance at the same speed, they only could have left at different times.
Also note that in this second animation the two flashes still reach the ground observer simultaneously.
In fact, any observer anywhere on the train or by the the tracks would have to agree as to what part of the train was next to what part of the track at the moment either of the flashes reached that point. In other words, no matter how many observers or sensors you put on the train or the ground, all the ground sensors would conclude that the strikes occurred simultaneously and all the train mounted ones would say that they did not.

 

[Sullivan Stockwell]

The events really are simultaneous in one frame but not the other - it's not a matter of perception.

Let's say lightning hits a tree one light-second away from me, and the light from that event reaches my eyes at time T. Because I know it took one second for the light to travel from the tree to my eyes, I know that the lightning really hit the tree at time T-1 and that's not a matter of perception. (It would be more precise to say that "the lightning hit the tree at the same time that my wristwatch read T-1; the light from that event reached my eyes at the same time that my wristwatch read T").

The point of Einstein's train thought experiment is that after we have properly corrected for the light travel time to remove the issues of perception, the events that are simultaneous for one observer are not simultaneous for the other, and there's no reason (except for our long-standing habit of thinking that there's something special about the surface of the Earth because we live on it) why one of them should be any more right than the other.

Is it not perception to acknowledge that the event being observed is relative? After all, it would be assumed that, in reality, one of the observers is correct, but we just have no way of knowing or figuring out which one is.

 

[Sullivan Stockwell]

How will you compare the readings on your sensors? You need to bring the readings together somehow to see if they happened at the same time or not.

Work through that and you'll find there's no way to do it that doesn't have a different result in the platform and train frames.

I did consider this, as the sensors are practically just more observers. But it would seem that there would truly be a correct "reality" under it all, regarding the lightning, but that it's just impossible to find out which. Making it that everything appears like it actually happens a certain way to each observer, but that there is an underlying true reality to it that just isn't possible to find out.

 

[Dale]

it would be assumed that, in reality, one of the observers is correct,

That is exactly contrary to the assumption. The assumption, or postulate, is that every inertial reference frame is equally correct, not just one.

 

[Chestermiller]

Is it not perception to acknowledge that the event being observed is relative? After all, it would be assumed that, in reality, one of the observers is correct, but we just have no way of knowing or figuring out which one is.

No. Both observers are correct. Neither one is wrong. Events that are simultaneous in one inertial frame are not simultaneous in another inertial frame in relative motion. As Nugatory said, it is not perception.

 

[Ibix]

I did consider this, as the sensors are practically just more observers. But it would seem that there would truly be a correct "reality" under it all, regarding the lightning, but that it's just impossible to find out which. Making it that everything appears like it actually happens a certain way to each observer, but that there is an underlying true reality to it that just isn't possible to find out.

I think you can assume that if you want. But it's an additional assumption on top of the ones you need for relativity, and raises the question of why the universe behaves like a four dimensional manifold when it's not.

Imagine that there are two boxes on the floor, and I say they're both exactly in front of me but someone else says one is in front of her but the other is off to the left. You can figure that out, I presume - we're both looking at the same boxes but from slightly different angles. You would not insist that the boxes were in front of each other in some absolute sense and my friend was somehow wrong to say that one wasn't in front of her. Or vice versa.

All relativity does is put time on a similar footing to the three spatial dimensions. Just as there's no absolute sense of "in front", there's no absolute sense of "at the same time". It depends on your choice of coordinate system.

I strongly recommend that you look up Minkowski diagrams. That's the tool that made it all click together for me.

 

[FactChecker]

If you had a sensor under lighting strikes A and B, could you not prove that they do happen at the same time?

It's not just perceptions that are different -- it's the times they record. Suppose observer 1 has two devices, one at each strike location, that record the exact strike time in his observer 1 time system. Also suppose observer 2 has the same thing recording strike times in his observer 2 time system. Observer 2's clocks, separated in the direction of his motion, can not agree with observer 1's clocks. If observer 1 says that the strikes were at the same time, then observer 2 must disagree. How do we know that the observer's clocks disagree? Because every time they measure the relative speed of light, they get the same constant number, c, even though observer 2 is moving relative to observer 1. They can even be measuring the same light flash and they will both record the relative light speed of c. It must be their clocks.

Note. The two observers can agree on simultaneous events that are not separated in the direction of motion.