Yes, but at this stage of my philosophical journey, just some simple philosophical considerations, eg reality exists and is not observer dependent as in some interpretations of QM. Even just analysing QM, so it is in that form, has taken me decades - what I wrote in the QM post is the result of many years of struggle. I find the going tough when confronted with more complex philosophical issues. Due to my background being in math, I will often resort to mathematical arguments. They are logically sound. But, great physicists can see the ‘substance’ behind the equations. That represents a deep philosophical insight. They do it intuitively, These are people like Feynman, who, on the surface, was very anti-philosophy but was deeply philosophical. It’s just that this substance behind the equations came so naturally to him he saw no reason to take it any further formally. This can lead to confusion. For example, in arguments that QM is whacko, Feynman’s path integral approach is often bought up and, correctly attacked, as irrational - how can particles take all these different paths simultaneously? They forget that it is just a heuristic suggested by writing the equation in a certain way. Particles do not take all paths at the same time. Such people have not progressed to even looking at the superficial substance behind the equations.
Yes, but at this stage of my philosophical journey, just some simple philosophical considerations, eg reality exists and is not observer dependent as in some interpretations of QM. Even just analysing QM, so it is in that form, has taken me decades - what I wrote in the QM post is the result of many years of struggle. I find the going tough when confronted with more complex philosophical issues. Due to my background being in math, I will often resort to mathematical arguments. They are logically sound. But, great physicists can see the ‘substance’ behind the equations. That represents a deep philosophical insight. They do it intuitively, These are people like Feynman, who, on the surface, was very anti-philosophy but was deeply philosophical. It’s just that this substance behind the equations came so naturally to him he saw no reason to take it any further formally. This can lead to confusion. For example, in arguments that QM is whacko, Feynman’s path integral approach is often bought up and, correctly attacked, as irrational - how can particles take all these different paths simultaneously? They forget that it is just a heuristic suggested by writing the equation in a certain way. Particles do not take all paths at the same time. Such people have not progressed to even looking at the superficial substance behind the equations.
Thanks
Bill
How familiar are you with Objectivism as a philosophy? As a former academic of physics, I highly recommend it.
Interpretations of physics and in particular of QM are interesting but until we have a complete understanding of the mechanics of measurement (rather than a formalism and assumptions) I think they will remain rather fanciful and mystical… I have found THAT is where the mind goes when it encounters something it does not understand… not merely an acknowledgement of the unsolved but a kind of ecstasy in the “mysterious”.
I would suggest you hold onto as much of the solid foundations of thought as possible when you encounter the myriad flights of fancy of both your common and uncommon physicist. Be rigorous and disappointingly real about the distinctions between our abstractions and entities referenced by them.
I really should have started with the no interaction theorem. This states particles are unable have any interaction if the principle of relativity is satisfied. Take two charged particles […]
I was trying to put some order in our discussion, which is about a subject which is already complicated and doesn’t need a multiplication of issues.
I asked two questions. Please answer them. Here are they, with some of their context :
4 hours ago, AlexL said:
Quote
Electric fields, are necessary for well-understood laws to hold (eg Wigner proved if there were no electric fields, then conservation of momentum would not hold in violation of Noether’s Theorem.)
The implication seem to be that in an isolated system (isolated from external influences), where the constituents do NOT interact electrically (why only electrically, btw?), the total momentum is not conserved. (You added that this is specific to the 4-momentum, that is to special relativity only, because in the Newtonian mechanics the total 3-momentum is conserved.)
1. Do you agree that THIS would be the implication?
2. Do you insist that this is also _factually _true, that is that the total momentum of a system of non-interacting relativistic constituents is NOT conserved?
I believe there must be a misunderstanding somewhere, because the 4-momentum conservation of an isolated system is a well established observational fact – whatever the interaction between the constituents is, including when it is absent.
Depending on your answer, we will see
if there is indeed a contradiction between what we see and the results you’ve mentioned – the Wigner Theorem and the no-interaction theorem,
or that the results you’ve mentioned do not, in fact, imply non-conservation
PS: regarding the necessity to also account for the interaction fields - I already addressed this by specifying: “please note that I do not define “total momentum” as the sum of individual momenta.” This implies that the total momentum I was talking about also includes the contribution from the fields.
Do you insist that this is also _factually _true, that is that the total momentum of a system of non-interacting relativistic constituents is NOT conserved?
1. They are conserved - relativity demands it. In fact, the world lines of each particle must be straight. For charged particles that is not the case - hence the difficulty. For momentum to be conserved the field is needed and the field has momentum. The particles and field have momentum conserved.
1. They are conserved - relativity demands it. In fact, the world lines of each particle must be straight. For charged particles that is not the case - hence the difficulty. For momentum to be conserved the field is needed and the field has momentum. The particles and field have momentum conserved.
2. It is conserved as per point 1.
So: our common conclusion is now that for both free and interacting particles, the total momentum of a closed system is conserved in the Newtonian, as well as in relativistic mechanics.
For the Wigner Theorem and the No-interaction Theorem this means that, whatever they say [you didn’t really specify…], they do not , in fact, imply non-conservation.
PS: Your justifications/comments to point #1 seem extremely confusing to me. We can discuss this, if you wish.
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