Possible Exits Simultaneously in Two Positions: Explained

[bgq]

Hi,

Consider two fixed points A and B in a frame S. In this frame a person P moves towards the point A and does an event EA. After that, this person moves to the point B and does an event EB.

Based on Lorentz's transformations, it is very easy to find a frame S' where events EA and EB occur simultaneously. The problem is that this leads to that the person P exists in both positions A and B simultaneously! (according to S').

How is this possible?

 

[ghwellsjr]

Hi,

Consider two fixed points A and B in a frame S. In this frame a person P moves towards the point A and does an event EA. After that, this person moves to the point B and does an event EB.

Based on Lorentz's transformations, it is very easy to find a frame S' where events EA and EB occur simultaneously.

Oh, really? Can you give an example?

The problem is that this leads to that the person P exists in both positions A and B simultaneously! (according to S').

How is this possible?

It's not possible.

 

[Dale]

In this frame a person P moves towards the point A and does an event EA. After that, this person moves to the point B and does an event EB.

ghwellsjr is correct. When you calculate it out, be sure to figure out how fast P moves when going from A to B.

 

[PAllen]

Put another way, EA and EB are separated by a timelike interval (unless P was moving FTL, which SR prohibits). The magnitude of a timelike interval is invariant under Lorentz transform. Thus there will be nor frame in which these events become either simultaneous or reverse their order. There are frames in which the coordinate time between these events is as small as you like, but never zero or reversed.

 

[ghwellsjr]

Put another way, EA and EB are separated by a timelike interval (unless P was moving FTL, which SR prohibits). The magnitude of a timelike interval is invariant under Lorentz transform. Thus there will be nor frame in which these events become either simultaneous or reverse their order. There are frames in which the coordinate time between these events is as small as you like, but never zero or reversed.

It can't be as small as you like. The Spacetime Interval indicates the smallest value it can be.

 

[bgq]

Put another way, EA and EB are separated by a timelike interval (unless P was moving FTL, which SR prohibits). The magnitude of a timelike interval is invariant under Lorentz transform. Thus there will be nor frame in which these events become either simultaneous or reverse their order. There are frames in which the coordinate time between these events is as small as you like, but never zero or reversed.

What is FTL?

 

[Nugatory]

What is FTL?

"Faster Than Light"

 

[bgq]

Actually I thought I can choose any numerical values making Δt' = 0. When I tried to find an example as ghwellsjr asked me to do so, I found this is impossible unless both the person and the frame S' both move at a speed c which is impossible.

I am sorry if this thread is annoying anyway. Thanks for your generosity.

 

[PAllen]

It can't be as small as you like. The Spacetime Interval indicates the smallest value it can be.

Right, I was thinking of the interval maximizing the proper time between two events among all paths. But, yes, for given events with timelike interval, all (inertial) frames will see coordinate time greater than or equal to the interval.