# Possible Exits Simultaneously in Two Positions: Explained

• bgq
In summary, based on Lorentz's transformations, it is possible to find a frame S' where events EA and EB occur simultaneously. However, this leads to the person P existing in both positions A and B simultaneously, which is not possible in special relativity. The spacetime interval between EA and EB remains constant in all frames, and it is not possible for the coordinate time between these events to be zero or reversed. This also means that it is not possible for the person P to move faster than the speed of light.

#### 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?

bgq said:
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?

bgq said:
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.

bgq said:
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.

1 person
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.

1 person
PAllen said:
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.

1 person
PAllen said:
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?

bgq said:
What is FTL?

"Faster Than Light"

1 person
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.

ghwellsjr said:
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.