Einstein's Train and Lightning Bolt Simultaneity Situation

[highschoolkid]

I have seemed to confuse myself after watching this video:
Everything makes sense except for the bit where the video says the passenger sees the bolts at different times. How can this be justified and how do we know the passenger doesn't see them at the same time from his frame of reference?

 

[K^2]

Simultaneous events are the ones that have exactly the same time coordinate. However, for moving and stationary observers, the time axis points in different "directions", so two events which have the same time coordinate for one observer actually have different coordinates for the other.

Simultaneity is a relative concept. "At the same time" has meaning only in a specific coordinate system. Once you accept that, the video does good job of explaining where it all comes from.

 

[highschoolkid]

So you can use that idea to justify that lightning strikes simultaneously for the ground observer and that it doesn't strike simultaneously for the train observer. can't you use that to justify that for two given observers within their own inertial frame of reference traveling at different speeds, every event which happens occurs simultaneously for one and not simultaneous for the other?

 

[Superstring]

So you can use that idea to justify that lightning strikes simultaneously for the ground observer and that it doesn't strike simultaneously for the train observer. can't you use that to justify that for two given observers within their own inertial frame of reference traveling at different speeds, every event which happens occurs simultaneously for one and not simultaneous for the other?

Yes, except in the trivial case where the two events occur at the same space coordinate.

 

[ghwellsjr]

So you can use that idea to justify that lightning strikes simultaneously for the ground observer and that it doesn't strike simultaneously for the train observer. can't you use that to justify that for two given observers within their own inertial frame of reference traveling at different speeds, every event which happens occurs simultaneously for one and not simultaneous for the other?

In Special Relativity, an event is defined as a single point in space at a particular time as defined by a Frame of Reference, in other words, a point in space-time. So it doesn't make sense to say "every event which happens occurs simultanteously". You need two or more events in the same FoR (whether or not something is "happening" there or not). If they have the same value for their time coordinate, (and they are at different locations in space) then thay are simultanteous in that FoR.

So, in general, events that are simultaneous in one FoR will not be simultaneous in another FoR moving with respect to the first one.

 

[Janus]

I have seemed to confuse myself after watching this video:
Everything makes sense except for the bit where the video says the passenger sees the bolts at different times. How can this be justified and how do we know the passenger doesn't see them at the same time from his frame of reference?

The simple answer is that otherwise you would have a physical contradiction. Both observers must agree to events that happen at a single point, like the fact that the lightning strikes a particular point of the track and an end of train while they are adjacent or that the flash of the strike reaches the train observer when he is adjacent to a particular point of the track.
Since, according to the embankment, the train observer is at two different points of the track when the flashes reach him, the train observer is forced to agree, and he cannot be adjacent to two different points at the same time.