Can Velocity Reversal Alter Temporal Order in Special Relativity?

In summary, the problem involves two events, A and B, with given spacetime coordinates in an inertial frame. The nature of the interval between them is determined to be "Spacelike". The task is to transform to another inertial system, O', moving at velocity vi relative to O, while maintaining the reversed temporal order of the events (t'(B) ≤ t'(A)). The condition imposed on the velocity, v, for this requirement is unknown and requires further analysis.
  • #1
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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  • #2
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 seperated.)
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?
 

What is special relativity?

Special relativity is a theory developed by Albert Einstein that describes the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, and that the speed of light is constant for all observers regardless of their relative motion.

How is special relativity different from Newtonian mechanics?

Special relativity differs from Newtonian mechanics in that it takes into account the fact that the laws of physics are the same for all observers, regardless of their relative motion. It also introduces the concept of time dilation and length contraction, which are not accounted for in Newtonian mechanics.

What is time dilation in special relativity?

Time dilation is the phenomenon where time appears to pass slower for objects that are moving at high speeds. This is due to the fact that the speed of light is constant, so as an object's speed increases, the time it experiences slows down in order to maintain the constant speed of light.

What is length contraction in special relativity?

Length contraction is the phenomenon where objects appear to become shorter in the direction of their motion when they are moving at high speeds. This is also due to the constant speed of light and the fact that the laws of physics are the same for all observers, regardless of their relative motion.

What are some practical applications of special relativity?

Special relativity has many practical applications, including the development of the GPS system, particle accelerators, and nuclear power plants. It also plays a crucial role in our understanding of the universe and the behavior of objects at high speeds.

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