Relativistic Density - Check My Work & Learn Methods

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SUMMARY

The discussion centers on calculating relativistic density for a cube moving at 0.95c, starting with a rest density of 2.0 kg/m³. Participants clarify the correct application of length contraction and mass increase, emphasizing that only the dimension parallel to the motion contracts, while the density increases due to relativistic effects. The final calculated relativistic density is determined to be approximately 20.5 kg/m³, correcting earlier misconceptions about unchanged density.

PREREQUISITES
  • Understanding of relativistic physics concepts, particularly length contraction and relativistic mass.
  • Familiarity with the equations for length contraction: Lm = Ls / √(1 - v²/c²) and mass transformation: mm = ms / √(1 - v²/c²).
  • Basic knowledge of density calculations: Density = mass/volume.
  • Ability to manipulate and interpret mathematical equations involving square roots and significant figures.
NEXT STEPS
  • Study the implications of relativistic mass and its relevance in modern physics.
  • Learn about the concept of gamma (γ) in relativistic physics and its calculation.
  • Explore the effects of relativistic motion on different geometric shapes beyond cubes.
  • Review significant figures and their importance in scientific calculations to ensure accuracy.
USEFUL FOR

Students and educators in physics, particularly those focusing on relativity, as well as anyone interested in understanding the implications of relativistic effects on mass and density.

  • #31
I think @PeroK and myself are on the same page here. If you perceive a conflict, either of us can probably clarify it away.
 
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  • #32
Okay thank you!
 
  • #33
jbriggs444 said:
I think @PeroK and myself are on the same page here. If you perceive a conflict, either of us can probably clarify it away.

Yes, I agree.

I was distracted trying to find a way to show that it's true in general, even when motion is not in the same direction as one side of the cube. Which I've just spotted!
 
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  • #34
PeroK said:
I was distracted trying to find a clever way to show that it's true in general, even when motion is not in the same direction as one side of the cube. Which I've just spotted!
I was taking it as an obvious geometric property -- scale down one dimension by a factor of ##\gamma## and the volume clearly goes down proportionately.

I gave a moment's though to Terrell rotation, but it does not apply.
 
  • #35
jbriggs444 said:
I was taking it as an obvious geometric property -- scale down one dimension by a factor of ##\gamma## and the volume clearly goes down proportionately.

Yes, I was only thinking about cubes, parallelopipeds and the triple scalar product! Then, I realized ...

o:)
 

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