How can two ships pass each other twice at the same moment?

[O Great One]

TL;DR Summary

How can someone be in 2 different places simultaneously?

Ship1 at rest at top.

          T--------------------N
<-----    N----------T

Ship2 at rest at bottom.

T----------N ----->
N--------------------T

The moment when T of ship1 is lined up with N of ship2 must be the same moment in both frames of reference because there is only 1 moment when this occurs. At this moment, for someone at N of ship1 to see T of ship2 they have to look in 2 different directions simultaneously. This is impossible. N of ship1 is simultaneously both passed and not passed T of ship2. This is impossible.

 

[Dale]

Summary:: How can someone be in 2 different places simultaneously?

At this moment, for someone at N of ship1 to see T of ship2 they have to look in 2 different directions simultaneously.

This is not correct. Please show your work.

 

[FactChecker]

Summary:: How can someone be in 2 different places simultaneously?
The moment when T of ship1 is lined up with N of ship2 must be the same moment in both frames of reference because there is only 1 moment when this occurs. At this moment,

Stop right here. There is no way for the two reference frames to agree on "at this moment" at separated locations. As @Orodruin , says "You did not take relativity of simultaneity into account. - The answer to 99% of all paradox threads in the relativity forum". The two directions that you say he must look is at two different times -- each time is what one of the reference frames thinks is "at this moment". But they are not the same time at separated locations.

 

[Ibix]

This is just the train and embankment scenario covered in every treatment of relativity since Einstein's 1905 paper. Keep repeating to yourself the words "simultaneity is relative, simultaneity is frame dependent" until the meaning sinks in.

I guarantee that failing to understand this is the cause of the problem here.

 

[Nugatory]

You will continue to be confused by these problems until you understand the relativity of simultaneity.
I would really strongly recommend that you first understand the train/lightning thought experiment (google for "Einstein train simultaneity" and don't move on until you understand) and then try working through your setup here using the Lorentz transformations.

You are saying that N of ship1 looks out at the same time that T of ship1 and N of ship2 are lined up. A wise physics instructor (who coincidentally happens to be my daughter) once remarked that the key to all paradoxes in special relativity is to find out where those words are hiding - that's where the mistake will be.

 

[Ibix]

OP - I note that you have been posting threads on PF phrased as if there were some contradiction in SR (as distinct from the reality, that you fail to take into account one or other or both of the Doppler effect or the relativity of simultaneity) for seventeen years.

Understand that this is all well-tested well-understood ground. You may find it easier to learn if you think of your scenarios in terms of where the failure in your logic is, rather than framing it as if there were a failure in our logic.

 

[MikeeMiracle]

Coming up with different scenario's for the same question repeatedly will not get you a different answer to the one you have already been given multiple times...why are you asking the questions if you do not accept the answers?

 

[O Great One]

The moment when T of ship1 is lined up with N of ship2 must be the same moment in both frames of reference. If there is a certain moment when I'm looking at you and you are directly across from me and you are also looking at me and directly across from me it is impossible for you or I to be located somewhere else at that moment. If this isn't the same moment it also means that T of ship1 passes N of ship2 twice. Therefore, this is the same moment in both frames of reference.

 

[Ibix]

The nose and tail passing is an event, yes. It's the rest where you go wrong. As Dale says, present your maths.

 

[PeterDonis]

If there is a certain moment when I'm looking at you and you are directly across from me and you are also looking at me

If you and I are moving relative to each other, there is no "moment" that is common to both of us; our definitions of simultaneity--what events on each of our worldlines are happening at the same "moment"--are different.

You have been told this multiple times now in multiple threads. We are approaching the point where further repetition of the same thing will be pointless and your threads will simply be closed.

 

[Dale]

The moment when T of ship1 is lined up with N of ship2 must be the same moment in both frames of reference.

No. The event when the tail of ship 1 is lined up with the nose of ship 2 is the same event in both frames of reference. That does not mean that the moment is the same. Do you understand the distinction?

In spacetime an event is a point, but a moment is a plane. It is the same point in both frames, but not the same plane. The point is in both planes but they are not the same plane.

 

[Mister T]

The moment when T of ship1 is lined up with N of ship2 must be the same moment in both frames of reference because there is only 1 moment when this occurs.

This is an event. The two ships could agree to set their clocks to the same time for this event.

Moreover, someone at rest in Ship 1 can carefully synchronize the clocks located at the T and N of their ship. But someone at rest in Ship 2 will claim that the synchronization was not done correctly. They will observe the clocks at the T and N of Ship 1 to be out of sync.

Likewise, someone at rest in Ship 2 can carefully synchronize the clocks located at the T and N of their ship. But someone at rest in Ship 1 will claim that the synchronization was not done correctly. They will observe the clocks at the T and N of Ship 2 to be out of sync.

This is really the only way that each ship will observe the clocks on the the other ship to be running slow.

As others have pointed out, this is called the relativity of simultaneity.

 

[Sagittarius A-Star]

Ship1 at rest at top.

1          10:00                10:00
1            T--------------------N
2    <---    N----------T
2          10:00      10:02

Ship2 at rest at bottom.

1  10:00      09:58
1    T----------N   --->
2    N--------------------T
2  10:00                10:00

I gave all 4 persons watches.

At this moment (= 10:00 according to his watch), for someone at N of ship1 to see T of ship2 ...

 

[phinds]

We are approaching the point where further repetition of the same thing will be pointless and your threads will simply be closed.

I have read a number of his threads and I think we are not approaching that point, we have long passed it. Peter, I've always admired your patience but I think you might be carrying it too far in this case.

 

[O Great One]

How is it possible for T of ship1 to pass N of ship 2 twice?
That's what your diagram shows.
It passes once when the time at N of ship1 is 9:58.
It passes again when the time at N of ship1 is 10:00.

 

[PeterDonis]

How is it possible for T of ship1 to pass N of ship 2 twice?
That's what your diagram shows.

No, it's not. It shows single events occurring once, and that "once" is at different times in different frames, because of relativity of simultaneity. Again, you have been told this repeatedly in multiple threads.

We have now reached the point I said we were approaching in my previous post. You have been repeatedly told the resolution of the issue you are having. There is no point in further repetition. This thread is closed.