What convervation law is required by the Lorentz Transformations

In summary, the conversation discusses the various invariances present in physics and how they imply conservation laws. Time invariance implies conservation of energy, while space invariance implies conservation of momentum. The Lorentz invariance implies conservation of angular momentum, as seen through Noether's theorem for classical fields. The Lorentz transformations preserve the four-interval and are related to both spatial rotation and boost symmetries. There is also a discussion on how gauge symmetry and conservation of charge may relate to conservation of the spacetime interval.
  • #1
metrictensor
117
1
Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?
 
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  • #2
Angular momentum. Immediate by Noether's theorem for classical fields.

Daniel.
 
  • #3
The Lorentz transformations by definition preserve the four-interval [tex]c^2t^2 - x^2 - y^2 - z^2[/tex].
 
  • #4
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.
 
  • #5
selfAdjoint said:
The Lorentz transformations by definition preserve the four-interval [tex]c^2t^2 - x^2 - y^2 - z^2[/tex].
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.
 
  • #6
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
 
  • #7
Thinking by analogy, shouldn't it imply conservation of the stress-energy tensor?
 
  • #8
Nope, stress- energy tensor is linked to space-time translations.

Daniel.
 
  • #9
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.
 

Question 1: What is the conservation law required by the Lorentz Transformations?

The conservation law required by the Lorentz Transformations is the conservation of energy and momentum. This means that the total energy and momentum of a system remains constant in all inertial reference frames.

Question 2: Why is the conservation of energy and momentum important in the Lorentz Transformations?

The conservation of energy and momentum is important in the Lorentz Transformations because it is a fundamental principle of physics that helps us understand the behavior of particles and systems in different reference frames. It also helps us make accurate predictions and calculations in relativistic situations.

Question 3: How does the conservation of energy and momentum apply to the Lorentz Transformations?

The conservation of energy and momentum applies to the Lorentz Transformations through the equations for energy and momentum in special relativity. These equations take into account the effects of time dilation and length contraction, ensuring that energy and momentum are conserved in all inertial reference frames.

Question 4: What happens if the conservation of energy and momentum is not satisfied in the Lorentz Transformations?

If the conservation of energy and momentum is not satisfied in the Lorentz Transformations, it would mean that there is a violation of the fundamental laws of conservation in physics. This would indicate a flaw in the calculations or assumptions made, and further analysis would be needed to correct the error.

Question 5: Are there any exceptions to the conservation of energy and momentum in the Lorentz Transformations?

There are no exceptions to the conservation of energy and momentum in the Lorentz Transformations. This principle holds true in all inertial reference frames, regardless of the relative velocities of the observer and the observed. However, in non-inertial reference frames, such as accelerating frames, the conservation laws may not hold true and additional factors need to be considered.

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