Does the Lorentz equation preserve causality?

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Homework Help Overview

The discussion revolves around the Lorentz equation and its implications for causality in the context of two observers moving relative to each other. The original poster presents a scenario involving two events measured by observers S and S', questioning the preservation of event order and causal relationships between them.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to analyze the relationship between the coordinates of events in different reference frames, specifically questioning the conditions under which the order of events might switch. Some participants question the assumptions made about the timing and location of the events, while others suggest examining the implications of the Lorentz transformations more thoroughly.

Discussion Status

Participants are exploring various interpretations of the Lorentz equation and its consequences for causality. There is an acknowledgment of the need to consider both Lorentz equations, and some guidance has been offered regarding the correct formulation to use. However, explicit consensus on the implications of the findings has not been reached.

Contextual Notes

Participants are navigating the complexities of the Lorentz transformation, particularly in relation to the timing of events and the conditions under which causality might be perceived differently by different observers. There is an emphasis on the need for clarity regarding the assumptions about the events' locations and timings.

silenzer
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Homework Statement



Observer S' moves at a speed u compared to observer S in x-direction. Two events happen on the x-axis of S, with the coordinates x1 and x2 at times t1 and t2 measured in S. Let L = x2-x1 and T = t2-t1.

a) If the events happen at the same time in S, does the same apply to S'? b) What relationship must there be between L and T for the order of the events become switched? c) Let there be a causal relationship between the events. Can the order seem different in S'?

Homework Equations



The Lorentz equation t = (gamma) * ( t' + x' * u / c^2 )

The Attempt at a Solution



a) The answer to this is no, because they happen at varying units of x. If they had happened at the same location, the answer would be yes.

b) Not really sure, other than to have the product on the right in the parentheses be larger than t', resulting in a negative time for t. Only thing is, I don't know what that means in terms of the Lorentz equation...

c) Obviously no.
 
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Let's assume that T > 0. Then, in (b), T' < 0. Find what T' is, and see what it takes for it to be negative, assuming T is positive.
 
You need to use both Lorentz equations, not just one of them. And you need to use the version where x' and t' are expressed in terms of x and t (rather than the other way around).

Chet
 
silenzer said:
c) Obviously no.
I think you're meant to show that the Lorentz transformation preserves causality.
 

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