What determines when events are simultaneous?

[idea2000]

Hi,

I was wondering, in the einstein train example, the observer who is on the ground and not moving sees both lightning bolts strike the train at the same time, while the observer who is on the train sees one bolt strike before the other. However, if there is another observer on the ground who is NOT standing right in between the two lightning strikes, what would he see? Would he see the two lightning strikes as being simultaneous? Does what is simultaneous depend on where you are standing? Or only depend on whether you are moving?

 

[Orodruin]

This is a common misconception. When we say that events are simultaneous we take travel time into account. The reason to place the observer in the middle is to make this easier - same distance implies same travel time. Another ground obsrever will not see the flashes simultaneously, but can conclude they occurred simultaneously by taking travel time into account.

 

[idea2000]

So, what you're saying is that I need to reverse calculate how far the light actually traveled to get into my eyes? Is this correct? I actually thought of an analogy that might partially answer my question. So, when I notice two photons coming from two different galaxies coming into my eyes, I have to take into account how far they traveled. I cannot just simply note that they came into my eyes at th same time, because one of them might have come from a galaxy that is a million light years away, while the other might have come from a galaxy that is a billion light years away.

But, I have another question that is related to this one. When I read about the twin paradox, the explanation said that events travel outward at the speed of light. And this leads to something that sort of looks like a doppler effect when one of the frames is accelerated. But, if events do in fact travel outward at the speed of light, then, how come the observer who is closer to one bolt of lightning doesn't conclude that that one bolt happened before the other? Why does this only depend on whether the frame is moving or not?

 

[Orodruin]

So, what you're saying is that I need to reverse calculate how far the light actually traveled to get into my eyes? Is this correct? I actually thought of an analogy that might partially answer my question. So, when I notice two photons coming from two different galaxies coming into my eyes, I have to take into account how far they traveled. I cannot just simply note that they came into my eyes at th same time, because one of them might have come from a galaxy that is a million light years away, while the other might have come from a galaxy that is a billion light years away.

Right (apart from the fact that you will not see individual photons and it is better to talk about light signals or light pulses in relativity). If you see two supernovae, one in a galaxy which is relatively close and another in a galaxy which is twice as far away, then the supernova that occurred a long time a go was in the galaxy far, far away.

But, I have another question that is related to this one. When I read about the twin paradox, the explanation said that events travel outward at the speed of light.

It most certainly is not. Events do not travel, they are points in space-time corresponding to a particular place at a particular time. What might expand is the light cone from an event.

 

[idea2000]

Thanks for your responses. I really appreciate them. =)

I'm somewhat confused. I understand that events don't travel outward at the speed of light, now. But, why do I suddenly experience a whole ton of events coming from the side I am accelerating towards in the twin paradox?

 

[Ibix]

I think your understanding is fine - it's just your terminology.

"Events" are points in spacetime - a point in space at a particular time. For example, lightning striking the nose of the train is an event - it is a place (the front of the train) at a particular time (when it got struck by lightning). Information about the events spreads out at the speed of light, and this leads to the "bunching up" of your discovery of the events in the twin paradox. The surface along which the information spreads is called a "light cone".

 

[idea2000]

Hi,

My confusion comes from the information about the event spreading out at the speed of light. If this is the case, then, how come a stationary observer standing next to one of the bolts of lightning wouldn't see that bolt as happening first, while seeing the bolt that is farther away as happening second?

The stationary observer on the ground that is right in between the two bolts would see them both happening at the same time if information about the two events did in fact spread out at the speed of light, but what about the observer who is standing next to one of the bolts? What would he see?

 

[Orodruin]

Hi,

My confusion comes from the information about the event spreading out at the speed of light. If this is the case, then, how come a stationary observer standing next to one of the bolts of lightning wouldn't see that bolt as happening first, while seeing the bolt that is farther away as happening second?

The stationary observer on the ground that is right in between the two bolts would see them both happening at the same time if information about the two events did in fact spread out at the speed of light, but what about the observer who is standing next to one of the bolts? What would he see?

He would see the flashes at different times, but he would still conclude that they were simultaneous because the one coming from further away had to travel for a longer time. The relativity of simultaneity is not about what an observer sees, it is what different observers can conclude.

 

[idea2000]

Many thanks for your patience, I really appreciate the help. =)

I can see how the observers in the train example can separate what they see from what they conclude. But, in the twin paradox case, or more specifically, the "doppler effect" explanation of the twin paradox, when the rocket frame turns around and heads back towards earth, he suddenly sees his twin's heart beats on Earth occurring far faster than usual because of his acceleration. My question here is, how can he separate what he sees from what he can conclude in this case? Can he separate the two just like the stationary observer could in the train example? Can he do the math and conclude that his twin's heartbeats shouldn't have occurred so quickly? How do we know what we are seeing and what we are concluding?

 

[jbriggs444]

Many thanks for your patience, I really appreciate the help. =)

I can see how the observers in the train example can separate what they see from what they conclude. But, in the twin paradox case, or more specifically, the "doppler effect" explanation of the twin paradox, when the rocket frame turns around and heads back towards earth, he suddenly sees his twin's heart beats on Earth occurring far faster than usual because of his acceleration. My question here is, how can he separate what he sees from what he can conclude in this case?

[emphasis mine]

What he sees is the relativistic Doppler effect. Only relative velocity figures into this effect. The traveler sees his twins heart beating fast because he is moving toward his twin. Acceleration does not enter in (at least not directly).

What he concludes is based on factoring in the relativity of simultaneity. In the frame of reference in which the traveler is momentarily at rest, he judges how many times his twin's heart has beaten up to "now". What time it is "now" for the stay-at-home twin depends on what frame of reference the traveler uses to judge simultaneity. As the traveler accelerates, the inertial frame in which he is momentarily at rest keeps changing. That affects the traveler's judgment of what time it is "now" for the stay-at-home twin. Acceleration is crucial since it determines how rapidly the sequence of inertial frames in which the traveler is momentarily at rest are changing.