How Does Velocity Addition in Special Relativity Ensure u' Remains Less Than c?

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Homework Help Overview

The discussion revolves around the concept of velocity addition in the context of special relativity, specifically focusing on how the velocity of an object in one reference frame (S') remains less than the speed of light (c) when analyzed from another reference frame (S). Participants are exploring the implications of the velocity addition equations in three dimensions.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to apply the velocity addition equations to demonstrate that u' remains less than c. Some are questioning the necessity of differentiation in the process, while others suggest focusing on the ratios derived from the Lorentz transformation equations.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some guidance has been offered regarding the use of Lorentz transformations and the ratios of differentials, but there is no explicit consensus on the best approach yet.

Contextual Notes

There appears to be some confusion regarding the application of differentiation versus direct substitution in the velocity addition equations, indicating varying levels of familiarity with the topic among participants.

byerly100
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Consider two reference frames, S and S', moving with speed v (<c) with respect to one another along the x direction.

If a certain object moves with velocity u (u<c) with respect to S, and velocity u' with respect to S', use the velocity addition equations (in three dimensions) to show that u'<c.
 
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What have you tried?
 
byerly100 said:
Consider two reference frames, S and S', moving with speed v (<c) with respect to one another along the x direction.

If a certain object moves with velocity u (u<c) with respect to S, and velocity u' with respect to S', use the velocity addition equations (in three dimensions) to show that u'<c.
Just write down the equations and substitute.
Then find u"^2.
 
Are you saying to take the derivative of u'?
 
Don't you know the vdlocity addition eqs in SR?
If not you have to find the ratio dx'/dt' and dy'/dt' in terms of the unprimed using the Lorentz transformation eqs. Just take the ratios. Differentiation is not needed. If the know the eqs., just substitute.
 

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