# Simultaneity in Special relativity

## Main Question or Discussion Point

I really think i'm not understanding this correctly and I haven't had a chance to think it through, but i'm confused about the issue of simultaneity in special relativity.

As I understand it, a simultaneous event happens at exactly the same time in some reference frame. Special relativity says that a simultaneous does not have to be simultaneous in other reference frames.

I think my issue is that I'm not sure how an observer determines when an event occurs. For example. consider two light bulbs on a line 100 meters apart, with observer A exactly half way between them, and observer B 1000 meters away from one bulb, and 1100 meters away from the other. Both are at rest, relative to the bulbs, and each other obviously. As I understand it, the flashing of the bulbs is a valid event, so suppose the bulbs are flashed so that observer A detects the flash at the same time. Then to observer A, the events are simultaneous. But to observer B, the events are then obviously not simultaneous, since there is a difference in distance from each bulb. Is it then valid to say that simultaneity is lost? even though A and B are in the same frame?

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This is why a distinction is made between what you 'see' and what you 'observe'. For instance, you may see two stars at the same time, but the light from those stars was emited at very different times. An observation involves knowing both when and where an event occured in the time and space of your own frame. The events that occur at a given time in a given frame are simultaneous in that frame regardless of what anyone sees.

That's what I thought would be the case. Thanks for clarifying that up.

robphy
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asdf60 said:
I really think i'm not understanding this correctly and I haven't had a chance to think it through, but i'm confused about the issue of simultaneity in special relativity.
As I understand it, a simultaneous event happens at exactly the same time in some reference frame. Special relativity says that a simultaneous does not have to be simultaneous in other reference frames.
I think my issue is that I'm not sure how an observer determines when an event occurs. For example. consider two light bulbs on a line 100 meters apart, with observer A exactly half way between them, and observer B 1000 meters away from one bulb, and 1100 meters away from the other. Both are at rest, relative to the bulbs, and each other obviously. As I understand it, the flashing of the bulbs is a valid event, so suppose the bulbs are flashed so that observer A detects the flash at the same time. Then to observer A, the events are simultaneous. But to observer B, the events are then obviously not simultaneous, since there is a difference in distance from each bulb. Is it then valid to say that simultaneity is lost? even though A and B are in the same frame?
As pointed out by jimmysnyder, it is insufficient to assign the [apparent] time of a distant event by using only the reception of light rays.

Here is a method, called the radar method [assuming SR applies, at least in a local region], that I learned from the books by Geroch and by Ellis-Williams (see my other post https://www.physicsforums.com/showpost.php?p=809230&postcount=78 ). While noting the time read off your wristwatch, emit a light ray (arranged to meet the event in question... i.e., arrange for the light ray to reach the target position at the target time), then wait for its reflection (i.e. echo) to be received. Note the wristwatch time of the reception. Assign the time-coordinate of the distant event to be the average-wristwatch-time (t_1+t_2)/2 and the space-coordinate to be half-of-the-round-trip-time times the speed of light c(t_2-t_1)/2. When A assigns times to events that are at rest according to A and equidistant from A's worldline, he can do so by sending out the light rays at one event (and will receive the reflections at a common event). For B, who is also at rest in this frame but not equidistant from those same events, the analogous set of light rays must be emitted in sequence and will be received in reverse sequence. [The method above can be applied to compute apparent temporal and spatial displacements of distant events from an event on the observer's worldline. This requires three wristwatch time-readings. The invariant interval takes a simple form in terms of these three time-readings.]

You might want to take a peek at some of the animations on this page
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/ [Broken].

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