Recovering Newton's energy conservation law for an Earth's lab

[vanhees71]

Why would you consider those to be valid paths? No physical object can take them. What sort of degradation of the word “valid” makes a physically impossible path “valid” in classical mechanics? Do you have some authoritative reference that asserts that this is the official meaning of a “valid” path in classical mechanics?

To be clear. Once again we are having a pointless semantic discussion. We have no disagreement on the physics but just what constitutes a “valid” path.

This is an important point in the derivation of Noether's theorem, and I thought you were discussing energy conservation in the context of Noether's theorem and thus the least-action principle. It's not by chance that Noether's great paper about the different theorems about the connection between symmetries and conservation laws was written in addressing precisely the puzzling question of "energy conservation" in GR, because it's the (in my opinion up to today) final answer: Global energy conservation holds if there is a corresponding translation invariance of the (variation of) the action. For the motion of a test particle in GR (no matter whether there are additional interactions than gravity or not) it's a sufficient condition that you can define coordinates, where the time-like coordinate doesn't occur in the Lagrangian.

 

[Dale]

Because he's talking about using the principle of least action, where you derive the equation of motion by extremizing the action integral. In the action integral, all paths are valid, not just those that satisfy the equation of motion.

I am not the only one that uses this terminology: “it is obvious why a solution that gives a minimum would be a valid path“. http://hep.physics.wayne.edu/~harr/courses/5210/w08/lecture08.htm

So again, this is a semantic question and my use of “valid” is valid. And furthermore my post that started this inane discussion was not even specifically about the action principle. You would have to go out of your way to read it like that and out of your way to deliberately misinterpret it as something that I am in need of correction about.

To me it doesn’t make sense to call the other paths valid. Only the one that extremizes the action is valid. The integral goes over other paths but why should we consider a path “valid” merely because the integral examines it and discards it?

In the context of QM there are people that call non-stationary paths “valid”, but I haven’t seen it in classical mechanics. And even if someone has, it still doesn’t make it more than a semantic choice.

I don’t need the lectures from either you or @vanhees71 when I make different semantic choices than you. If I mess up the actual physics then please correct me, but we have now hijacked this thread with an unnecessary slew of semantics.

 

[vanhees71]

You mess up the physics when using standard terms in a different meaning! This was an important mathematical point to clarify and not hijacking the thread, because it's the essence to answer the question asked about energy conservation in general relativity!

 

[Dale]

You mess up the physics when using standard terms in a different meaning!

This is not a “standard term” with only the @vanhees71-approved meaning. You immediately go into lecture mode to correct anyone who uses some word the slightest different from you. If someone doesn’t say it exactly the “@vanhees71-approved” way then they “mess up the physics”.

I neither need nor welcome another pointless semantic debate. Just because you use a word a specific way does not mean I need to.

It is insulting for you to continually place yourself in the role of my physics teacher, I don’t need your physics instruction. You should just assume that if there is something that you feel like lecturing me about then it is probably merely a semantic difference.

This was an important mathematical point to clarify and not hijacking the thread

Then make the important mathematical point directly to the OP and leave me out of it. I am not wrong simply because I use a word differently and I am not in need of correction or instruction from you.

Or at the least spend a few minutes to identify the semantic issue and point out that I am using a word differently than you.

 

[PeterDonis]

You mess up the physics when using standard terms in a different meaning!

Just so you know it isn't just @Dale who has issues with this viewpoint: this claim of yours is way, way, way too strong.

First, ordinary language is vague and ordinary language terms can have multiple meanings in physics discussions. If you really want to not mess up the physics, the proper way to ensure that is to use math. It is not a good strategy to use vague ordinary language terms with your preferred meaning and then pretend that's the only possible meaning of those vague ordinary language terms.

Note that the issue is not that your interpretation of "valid" in this context is unreasonable; it is reasonable. But so is @Dale's interpretation of "valid" in this context, as he explains it in post #32 (and note that he gives a reference to support it as well). So we have (at least) two reasonable interpretations of an ordinary language term in a physics context which are not consistent with each other. So talking as though someone who uses a different reasonable interpretation from your reasonable interpretation is "messing up the physics" is not, well, reasonable.

Second, when you find other SAs or Mentors disagreeing with you, it is (a) very impolite, and (b) a very unreasonable Bayesian prior, to assume that they reason they are disagreeing with you is that they do not understand the physics and need to have you explain it again. It is much, much more likely that the issue is just terminology. It would be very helpful if you would try to approach future disagreements with other SAs or Mentors with that mindset.

 

[PeterDonis]

Thread closed for moderation.