Can Velocity Reversal Alter Temporal Order in Special Relativity?

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SUMMARY

The discussion centers on the conditions required for the temporal order of two spacelike-separated events to be reversed in special relativity. Event A precedes Event B in the original inertial frame, and the transformation to another inertial system O', moving at velocity vi, must satisfy the condition t'(B) ≤ t'(A). The nature of the interval between these events is confirmed as "spacelike," indicating that they can be separated by a sufficient relative velocity to alter their temporal order. The transformation involves understanding how the coordinates change between the two frames based on the relative velocity.

PREREQUISITES
  • Understanding of spacetime intervals in special relativity
  • Familiarity with Lorentz transformations
  • Knowledge of inertial frames and relative motion
  • Basic concepts of velocity in the context of special relativity
NEXT STEPS
  • Study Lorentz transformations in detail
  • Research the implications of spacelike intervals in special relativity
  • Explore the concept of simultaneity in different inertial frames
  • Learn about velocity addition formulas in special relativity
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This discussion is beneficial for physics students, educators, and anyone interested in the principles of special relativity, particularly those exploring the effects of relative motion on the temporal order of events.

Ayame17
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Homework Statement


a) Event A = [ct(A)=1, x(A)=5, y(A)=0, z(A)=0] precedes event B = [ct(B)=2, x(B)=1, y(B)=0, z(B)=0]. What is the nature of the interval (HAVE DONE THIS). Then, it is desired to transform to another inertial sysyem O', moving at velocity, vi, relative to O, where the temporal order of the two events are reversed ie t'(B)[tex]\leq[/tex]t'(A). What condition on v does this requirement impose?


Homework Equations


N/A for second part I assume!


The Attempt at a Solution


Have worked out that the nature of the interval is "Spacelike". Also I know that to transform to another inertial system, the velocity normally becomes -vi. However, I don't know if the temporal order will mean that something different happens, and it just being negative seems too easy an answer! Any help would be appreciated.
 
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Ayame17 said:

The Attempt at a Solution


Have worked out that the nature of the interval is "Spacelike". Also I know that to transform to another inertial system, the velocity normally becomes -vi.

If an object stands still in one inertial frame, then from an inertial frame moving relative to the first with velocity v, the object is seen to have velocity -v. Is that what you meant?
It isn't really relevant to this problem however.
You have been given the spacetime coordinates of two events in some inertial frame. (And you found that the events are spacelikely separated.)
The spacecoordinates of the events will be different in an inertial frame moving relative to the first. What is the relation between the coordinates in the two frames as a function of v?
 

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