Conservation laws and relativistic dynamics

[bernhard.rothenstein]

do you consider that conservation laws of momentum and energy are compulsory in the derivation of the fundamental equations of relativistic dynamics

 

[robphy]

In my opinion,... no, they are not compulsory.

Conservation laws arise from symmetries in the situation and may suggest interesting dynamical quantities. However, the lack of such symmetries shouldn't preclude the definition of relativistic dynamical quantities and the formulation of equations involving them.

 

[Meir Achuz]

do you consider that conservation laws of momentum and energy are compulsory in the derivation of the fundamental equations of relativistic dynamics

Yes. If not, you are talking about a new theory.

 

[Garth]

But note in GR the conservation law is that of the conservation of energy-momentum, not in general energy, as energy is a frame dependent quantity and energy-momentum is frame independent.

Garth

 

[bernhard.rothenstein]

But note in GR the conservation law is that of the conservation of energy-momentum, not in general energy, as energy is a frame dependent quantity and energy-momentum is frame independent.

Garth

i have in mind only the special relativity case

 

[samalkhaiat]

do you consider that conservation laws of momentum and energy are compulsory in the derivation of the fundamental equations of relativistic dynamics

The fundamental equations of dynamics(equations of motion) contain (within them) the laws of conservation. We derive those equations of motion from ACTION PRINCIPLE.


regards

sam

 

[samalkhaiat]

OK Bernhard, I had a look at your paper (arxiv physics/0505025).
I am afraid, I saw no dynamical equation in it. The transformation equations of some dynamical quantities are not the "fundamental" equations of dynamics. It is the "equation of motion" like Newton's, Dirac's, Maxwell's, Schrodinger's and other's equation that represents the fundamental equations of dynamics.

In your paper, you seem to have derived (though I did not check the accuracy) the relativistic transformation of energy and momentum from strange combination of a result from SR (adding velocities) with some sort of "thought" experiment. But why bother yourself with this when the two postulates of SR can do all your work plus more without any thought (or otherwise) experiment?

regards

sam

 

[bernhard.rothenstein]

OK Bernhard, I had a look at your paper (arxiv physics/0505025).
I am afraid, I saw no dynamical equation in it. The transformation equations of some dynamical quantities are not the "fundamental" equations of dynamics. It is the "equation of motion" like Newton's, Dirac's, Maxwell's, Schrodinger's and other's equation that represents the fundamental equations of dynamics.

In your paper, you seem to have derived (though I did not check the accuracy) the relativistic transformation of energy and momentum from strange combination of a result from SR (adding velocities) with some sort of "thought" experiment. But why bother yourself with this when the two postulates of SR can do all your work plus more without any thought (or otherwise) experiment?

regards

sam

thank you. all the textbooks i know, derive the transformation equations for mass, momentm and energy (i have considered that they are the fundamental equations of relativistic dynamics) from collisions, less or more complicated, not very easy to teach without mnemonic aids using conservation of momentum, mass, energy or of the center of mass. do you know a derivation of them without conservation laws?
sine ira et studio

 

[Meir Achuz]

thank you. all the textbooks i know, derive the transformation equations for mass, momentm and energy (i have considered that they are the fundamental equations of relativistic dynamics) from collisions, less or more complicated, not very easy to teach without mnemonic aids using conservation of momentum, mass, energy or of the center of mass. do you know a derivation of them without conservation laws?
sine ira et studio

All you have to do is to define the 4-velocity as U^\mu=dx^\mu/d\tau, and the 4-momentum as p=mU, where m is a scalar. Then the transformation laws of mass, momentum, and energy follow immediately.

Jackson just confuses this by an irrelevant 8 page discussion of collisions.
PMB wants to confuse it by giving mass an awkward velocity dependence.

 

[dicerandom]

All you have to do is to define the 4-velocity as U^\mu=dx^\mu/d\tau, and the 4-momentum as p=mU, where m is a scalar. Then the transformation laws of mass, momentum, and energy follow immediately.

Jackson just confuses this by an irrelevant 8 page discussion of collisions.
PMB wants to confuse it by giving mass an awkward velocity dependence.

IMO, the problem with doing the development in this way is that the student generally has no idea as to what the 4-velocity really is, why it is that the derivative must be taken with respect to proper time, or how the 4-momentum differs from regular momentum, aside from the fact that it now has an extra component. In order to get a real conceptual understanding of the framework of SR I believe it is important to get a solid grasp of the geometry of Minkowski space and the implied consequences this has on previously well defined quantities such as spatial and temporal intervals and simultenaity before the mathematics are introduced.

The main problem with the method I've proposed is that it typically takes much longer than the more traditional method, however the advantage is that the students get a much better understanding of the underlying theory and are more able to apply it to situations which are new to them.

 

[Meir Achuz]

IMO, the problem with doing the development in this way is that the student generally has no idea as to what the 4-velocity really is, why it is that the derivative must be taken with respect to proper time, or how the 4-momentum differs from regular momentum, aside from the fact that it now has an extra component..

"the student generally has no idea" only if the teacher and textbook don't explain this.

 

[Meir Achuz]

In order to get a real conceptual understanding of the framework of SR I believe it is important to get a solid grasp of the geometry of Minkowski space and the implied consequences this has on previously well defined quantities such as spatial and temporal intervals and simultenaity before the mathematics are introduced.

The math of Minkowski space is so simple and straightforward (with a good teacher and textbook) that I find students get a better understanding using math rather than handwaving grasps. I agree with Sam on this.

 

[Meir Achuz]

IMO,
The main problem with the method I've proposed is that it typically takes much longer than the more traditional method, however the advantage is that the students get a much better understanding of the underlying theory and are more able to apply it to situations which are new to them.

Where do you propose your method?
Also, what is IMO?