Two Laser Emissions: Resolving Contradiction

[Whatifitaint]

I can't figure this out.

Say 2 frames are in relative motion. When the origins at at the same place, 2 lasers shoot up the positive x-axis and negative x axis. Let's call the 2 frames F and F'. F says the lasers will always hit simultaneous events along the x-axis. Then by the relativity of simultaneity F says the lasers for F' will never cause simultaneous events. But, F. says the lasers always cause simultaneous events along its x axis.

So, how is this resolved that special relativity says F' will never see simultaneous events by F but F' says it always see simultaneous events?

 

[PeterDonis]

Say 2 frames are in relative motion. When the origins at at the same place, 2 lasers shoot up the positive x-axis and negative x axis.

So, just to be clear, the lasers only fire once each, and the event at which they both fire is the event at which the origins of both frames are co-located? I'll assume that this is correct in what follows.

F says the lasers will always hit simultaneous events along the x-axis.

Yes.

Then by the relativity of simultaneity F says the lasers for F' will never cause simultaneous events.

No, that's not quite correct. What F can say, by relativity of simultaneity, is that the pairs of events on the x-axis that he considers simultaneous are not simultaneous for F'. However, there will be *other* pairs of events on the x' axis (which is spatially the same as the x axis) that are simultaneous for F' but not for F.

If the above still isn't clear, I recommend drawing a spacetime diagram of the scenario.

 

[ghwellsjr]

I can't figure this out.

Say 2 frames are in relative motion. When the origins at at the same place, 2 lasers shoot up the positive x-axis and negative x axis. Let's call the 2 frames F and F'. F says the lasers will always hit simultaneous events along the x-axis. Then by the relativity of simultaneity F says the lasers for F' will never cause simultaneous events. But, F. says the lasers always cause simultaneous events along its x axis.

So, how is this resolved that special relativity says F' will never see simultaneous events by F but F' says it always see simultaneous events?

Here's a spacetime diagram depicting your scenario for frame F. Note the pairs of events with the same color:

Now I transform the coordinates of the events to frame F' moving at 0.6c with respect to frame F:

​

Now you can see that none of the pairs of same-colored simultaneous events from frame F are simultaneous in frame F' but there are other pairs of events that are simultaneous in frame F' but they won't be simultaneous if frame F.

For example, in frame F' (the bottom diagram), the green event on the left beam is simultaneous with the black event on the right beam but these two events are not simultaneous in frame F.

Does that help?

 

[Whatifitaint]

So, just to be clear, the lasers only fire once each, and the event at which they both fire is the event at which the origins of both frames are co-located? I'll assume that this is correct in what follows.



Yes.



No, that's not quite correct. What F can say, by relativity of simultaneity, is that the pairs of events on the x-axis that he considers simultaneous are not simultaneous for F'. However, there will be *other* pairs of events on the x' axis (which is spatially the same as the x axis) that are simultaneous for F' but not for F.

If the above still isn't clear, I recommend drawing a spacetime diagram of the scenario.

Oh, so F says his pairs of simultaneous events will not be simultaneous for F', but F' will be seeing its own simultaneous pairs of events at any given time. I think that is what both you and ghwellsjr are saying.

Say then that we put F and F' frame observers at A1 and A2 , |A1|=|A2| F frame coordinates.

F observers say these events are simultaneous and the F' observers say they are not.

Is this all correct?

 

[ghwellsjr]

Oh, so F says his pairs of simultaneous events will not be simultaneous for F', but F' will be seeing its own simultaneous pairs of events at any given time. I think that is what both you and ghwellsjr are saying.

Say then that we put F and F' frame observers at A1 and A2 , |A1|=|A2| F frame coordinates.

F observers say these events are simultaneous and the F' observers say they are not.

Is this all correct?

I don't know what you are asking. F and F' are frames, not observers. the coordinates of frames determine simultaneity. Observers are unaware of the coordinates unless they do a lot of work.