I thought I was beginning to understand relativity (as much as one can without doing the math) but I'm having trouble with simultaneity. I've gone to thinking that two observers should never agree that any event happened simultaneously even if both observers are at rest. If this is not the case, please show me what I'm misunderstanding. Lets say we had 3 observers (A,B,C) and a train at rest. Person A is at the back of the train, B is in the middle, C is in the front. The distance between A,B is the same as between B,C. Person B sees lightning hit the front and back of the train at the same time. Since the light has distance to travel, then Person A should see lightning hit the back first, then the front and vice versa for Person C. http://www.youtube.com/watch?v=wteiuxyqtoM The depiction is easy to understand, but what if the person on the platform was standing a few feet to his right when the lightening struck? Following the example above, I'd imagine the light from the front of the train would reach him before the light from the back of the train. Would they then agree on what they saw? Would they then disagree on the delay between lightening strikes? ----------------------------------------- Here's where my thought is going...Simultaneity only occurs between two events where the light from those events intersect each other and that simultaneity changes its position in space over time. If that's the case, it would seem like simultaneity can occur between two events separated by any amount of time if an observer is in the right position in space. S But honestly this just seems like an optical illusion, so my question is, what is the difference at high speeds?
Relativity says that positions can be known (that is, you know where you are, and you know where another observer, say on the train, is), but different observers will not agree on the time an event occurs, because of relative motion. It says that time, for an observed event, is relative to position and momentum of the observer and the event. You only "set" your own position, or frame of reference, to "the origin" in a logical sense, because you can't determine your absolute motion, but you can determine relative motion (because the speed of light is constant in all reference frames). Therefore the problem of simultaneity is "resolved" only when two observers agree on times and locations of events. Since light is the method used to agree this, its speed (of communication) is critical.
Come to think about it, taking the example from the link I provided it would seem like they only disagree because of the woman's position, not her speed. Lets say lightening hit nearby poles instead. The man is standing about 10 feet from each pole. Wouldn't they agree on the simultaneity if the woman was able to reach a position where she was also 10 feet from each pole at the moment the man sees the lightening strike?
I understand that, but in the example I provided the 3 observers and the train were at rest relative to each each other. They are only separated by space, but none are in motion relative to each other.
For the third time, yes the train is at rest. Is the lightning relevant? Any kind of light source will do, I just used lightning because of the video I included.
There are three observers in your initial scenario, A B and C. B sees lightning hit the front and back simultaneously, but A and C see something different. The times for the lightning hitting the front and back are displaced for A and C, because of the time it takes light to travel (at finite speed). An observer on a platform outside the train, will see the lightning strikes hit depending on their own relative location to the train, and to the lightning (events). So an observer on the platform will see what B sees, only if they are at the same relative location, or halfway between the lightning strikes. IOW the platform observer has to be located halfway between the light sources, to see them occur simultaneously, as B does.
Disclaimer - I'm an amateur at this stuff. Check my replies against a reliable source. Hi AJRelic, A, B, and C will all agree that the lighting strikes were simultaneous. They don't agree about whether they saw the strikes at the same time, but when they measure how far the light travelled and work out the corresponding delay between when each strike happened and when they saw it, they will all agree that the strikes occurred simultaneously. Don't be confused by when an observer sees the events - what matters is when the events actually happened. If an observer sees an event, they can't tell when it occured unless they know how far away it was.
The woman will see the strikes at the same time, but think carefully about how this scenario pans out in the woman's rest frame. In her rest frame, the poles are moving. At the instant that she sees the lightning strikes, the poles are the same distance away from her. But before then, one pole was closer than the other, right? So, for her to see the strikes at the same time, the strike from the further pole must have happened before the strike from the closer pole.
AJRelic: As Pete said, you're confusing the time that events are seen with when they actually occurred. The relativity of simultaneity is not an effect due to the finite time it takes light to travel from where an event occurs to the location of some observer. The loss of simultaneity occurs even after the light travel time has been factored out. More accurately, the light from the front and back of the train reaches B at the same time. Light from the front of the train reaches C before A, and light from the back reaches A before C (obviously). But ALL three of them agree that the lightning hit the two ends of the train simultaneously. To come to that conclusion experimentally they need to know the distance the light had to travel, so that they can factor out the time delay due to the finite speed of light. The equations of relativity, such as the Lorentz transformations, already assume that the observers have factored out any travel time for light - i.e. they deal with where and when the events actually happened, not where and when the light from them was seen.
Ahh that's what I figured. It wasn't obvious at first but it makes sense when every relativity problem I've come across begins with the observers at equal distances from where the event occurs. I thought that was added for simplicity, not convenience. Fair enough...this is just evidence that I need to stop being lazy and learn the math behind relativity. It's not that I don't want to...I just don't know where to start :scratchin: Thanks for the help guys
