Possible Exits Simultaneously in Two Positions: Explained

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Discussion Overview

The discussion revolves around the implications of Lorentz transformations in special relativity, particularly concerning the simultaneity of events EA and EB as experienced by a moving observer P. Participants explore the concept of timelike intervals and the conditions under which events can be perceived as simultaneous in different reference frames.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that Lorentz transformations allow for a frame S' where events EA and EB occur simultaneously, raising questions about the implications of this scenario.
  • Others argue that if events EA and EB are separated by a timelike interval, there cannot be a frame in which these events are simultaneous or reversed, as the magnitude of a timelike interval is invariant under Lorentz transformations.
  • One participant emphasizes the need to calculate the speed of person P when moving from A to B to understand the situation better.
  • Another participant points out that while one can approach a situation where the coordinate time between events is minimized, it cannot reach zero or reverse the order of events.
  • There is a discussion about the concept of FTL (Faster Than Light) travel and its implications for the simultaneity of events.
  • A participant expresses confusion about the possibility of choosing numerical values that would make the time interval between events zero, ultimately concluding that it is impossible unless both the observer and the frame are moving at the speed of light.

Areas of Agreement / Disagreement

Participants express differing views on the implications of Lorentz transformations and the nature of timelike intervals. While some agree on the invariance of the timelike interval, there is no consensus on the possibility of simultaneity in different frames.

Contextual Notes

Limitations include the dependence on the definitions of simultaneity and timelike intervals, as well as unresolved mathematical steps regarding the conditions under which events can be perceived as simultaneous.

bgq
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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?
 
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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.
 
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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.
 
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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.
 
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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"
 
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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.
 

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