Relativistic velocity transformations

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Homework Help Overview

The problem involves relativistic velocity transformations, specifically examining the speed of a gamma ray emitted from a krypton-80 nucleus moving at a significant fraction of the speed of light. The original poster seeks to determine the speed of the gamma ray relative to the sun under two scenarios: when emitted in the direction of the nucleus's motion and when emitted in the opposite direction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the relativistic velocity transformation formula for both scenarios but questions the validity of their results, particularly regarding the speed of light. They express uncertainty about how to approach the second part of the problem.

Discussion Status

Some participants clarify that the speed of light is constant for all observers, which is a key principle of relativity. They encourage the original poster to think critically about the implications of this principle before proceeding with calculations for the second scenario. There is an acknowledgment of the need to verify results through the transformation formula.

Contextual Notes

The discussion includes assumptions about the nature of light and the constraints of relativistic physics, particularly regarding the speed of light and its implications for different observers. The original poster's uncertainty about the second scenario indicates a potential gap in understanding the application of the transformation formula.

trevorr93
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Homework Statement



An excited nucleus of krypton-80 emits a gamma ray that travels at the speed of light relative to the nucleus. The nucleus itself has a speed of 0.60c relative to the sun. Use a relativistic velocity transformation to determine the speed of the gamma ray relative to the sun if the gamma ray is emitted: a) in the direction of motion of the nucleus and b) opposite to the direction of motion of the nucleus


The Attempt at a Solution



a)

u = u' + v / 1 + vu'/c^2
u = 1 + 0.6 / 1 +(0.6)(1)/c^2
u = 1 c

Does this make sense? Can a particle not move faster then the speed of light?

b) Not sure how to approach this! would a number be negative?
 
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Looks like you fell for it :-)

A gamma ray is actually just light. That's why it can, and in fact must, travel at the speed of light. What you have shown in a) is one of the postulates of relativity (from which the transformation rule for velocities is derived), namely that light travels at the speed of light for all observers, irrespective of their relative velocity.

Now before you do b), try to think what the answer should be ... then plug in the numbers and see if you are right. If you did get a negative number, how would you explain that?
 
oh okay. so b would be equal to 1 as well because of the postulate. thank you for your help!
 
Yep*, but you should also be able to get this explicitly from the formula!

*) Actually, almost yep! - I suggest to give it a try anyway.[/size]
 

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