What convervation law is required by the Lorentz Transformations

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Discussion Overview

The discussion revolves around the conservation laws implied by Lorentz transformations in the context of special relativity. Participants explore the relationship between symmetries, such as time and space invariance, and the corresponding conservation laws, including energy, momentum, and angular momentum.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that time invariance implies conservation of energy, while space invariance implies conservation of momentum.
  • Daniel proposes that angular momentum conservation is linked to spatial rotation invariance, which is part of the Lorentz group.
  • There is a mention of the four-interval, c²t² - x² - y² - z², being preserved by Lorentz transformations.
  • One participant questions whether Lorentz invariance implies conservation of the stress-energy tensor, drawing an analogy to other conservation laws.
  • Another participant asserts that the stress-energy tensor is connected to space-time translations, not Lorentz invariance.
  • A participant notes that while there are many four-vector invariants in special relativity, classical conservation laws typically refer to specific quantities rather than a variety of invariants.
  • There is a discussion about gauge symmetry and its relation to conservation laws, particularly in the context of Maxwell's equations and the spacetime interval.
  • One participant humorously suggests that the position of the center of mass could be a conserved quantity in the absence of external forces.

Areas of Agreement / Disagreement

Participants express differing views on what conservation law is implied by Lorentz invariance, with no consensus reached on a definitive answer. The discussion includes multiple competing perspectives regarding the implications of Lorentz transformations.

Contextual Notes

Some participants reference previous discussions on the topic but do not recall the conclusions reached. There is also mention of various symmetries and their associated conservation laws, indicating a complex interplay of concepts without clear resolution.

metrictensor
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Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?
 
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Angular momentum. Immediate by Noether's theorem for classical fields.

Daniel.
 
The Lorentz transformations by definition preserve the four-interval c^2t^2 - x^2 - y^2 - z^2.
 
dextercioby said:
Angular momentum. Immediate by Noether's theorem for classical fields.

Daniel.

Conservation of angular momentum is generated by spatatial rotation invariance. Space rotation invariance is indeed part of the Lorentz group. But I suspect the original poster was interested in the symmetries related to the Lorentz boost, not by the spatial rotation part of the Lorentz group.

I seem to recall that this question was discussed before, but I don't recall the conclusion that we came to.
 
selfAdjoint said:
The Lorentz transformations by definition preserve the four-interval c^2t^2 - x^2 - y^2 - z^2.
I was thinking the same thing but there are many 4-vector invariants in SR. Energy-momentum, space-time. The classical conservation laws have one specific quantity conservered not a variety.
 
metrictensor said:
Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?

Read the stuff here.

Regards,
George
 
Thinking by analogy, shouldn't it imply conservation of the stress-energy tensor?
 
Nope, stress- energy tensor is linked to space-time translations.

Daniel.
 
This should be a straightforward question with an obvious answer - but authors seem to skirt the issue
spatial displacement symmetry - conservation of momentum
temporal displacement symmetry - conservation of energy
isotropic symmetry - conservation of angular momentum

When gauge symmetry is applied to Maxwells's em equations, one consequence is conservation of charge - isn't conservation (invariance) of the spacetime interval also consequent to gauge symmetry?
 
Last edited:
  • #10
George Jones said:
Read the stuff here.

Regards,
George

It is a funny answer... the position of the center of mass? Ok, in absence of external forces, the center of mass is a preserved quantity, so it makes sense, or sort of.
 

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