2-body problem - conservation of angular momentum

[jbriggs444]

That's not how physics works. Assumptions must be justified.

It is enough that their consequences are, in principle, falsifiable. That is how physics works.

 

[DrStupid]

It is enough that their consequences are, in principle, falsifiable.

That also applies to the opposite assumptions. What makes you assumption better than assuming that there is no restriction for the possible direction of forces?

 

[jbriggs444]

That also applies to the opposite assumptions. What makes you assumption better than assuming that there is no restriction for the possible direction of forces?

The one is predictive and falsifiable. The other is neither.

It is usually better to have physical laws that predict something rather than physical laws that do not.

In Feynmans words: "First, we guess it (audience laughter), no, don’t laugh, that’s the truth. Then we compute the consequences of the guess, to see what, if this is right, if this law we guess is right, to see what it would imply and then we compare the computation results to nature or we say compare to experiment or experience, compare it directly with observations to see if it works."

If you can't falsify it, you can't do science with it.

 

[DrStupid]

The one is predictive and falsifiable. The other is neither.

The other is at least as falsifiable as conservation of angular momentum. And of what avail is a predictable assumption if you have no idea if the prediction is correct or not? (And you have no idea if the assumption lacks proper justification.)

I still do not agree with your claim, that the 3rd law conserves angular momentum if you just assume the additional restriction of the direction of forces. It is your assumption that, together with the 3rd law, conserves angular momentum. Such a restriction must be justified (e.g. by experimental observations). If you just assume it than the resulting conservation of momentum is an assumption as well.

 

[etotheipi]

The strong form of Newton III is needed to prove conservation of angular momentum via a torque argument, whilst you cannot prove it directly in this manner if only the weak form is used.

But conservation of angular momentum of an isolated system is a more fundamental concept, arising from rotational symmetry. It applies no matter whether the internal forces are central or not. I believe this is what @kuruman was referring to with the example about the dipoles.

I assume that any construction using arbitrary non-central forces in which the angular momentum of an isolated system is not conserved is unphysical. Please correct if this part is wrong!

 

[jbriggs444]

The other is at least as falsifiable as conservation of angular momentum. And of what avail is a predictable assumption if you have no idea if the prediction is correct or not? (And you have no idea if the assumption lacks proper justification.)

I still do not agree with your claim, that the 3rd law conserves angular momentum if you just assume the additional restriction of the direction of forces. It is your assumption that, together with the 3rd law, conserves angular momentum. Such a restriction must be justified (e.g. by experimental observations). If you just assume it than the resulting conservation of momentum is an assumption as well.

I am back to being baffled with what you are arguing about.

 

[dyn]

Angular momentum actually is conserved due to the central nature of the force. Forces have a build in conservation of linear momentum (thanks to Newton's 3rd law) but it is not obvious that they also conserve angular momentum. There must be an additional restriction that is not included into the definition of force. Why shouldn't it be mentioned in a book?

Angular momentum is conserved due a system being isolated from external torques. The central nature of any internal forces is irrelevant and angular momentum would be conserved if the internal forces were not central as long as the system was isolated from external torques

 

[DrStupid]

I am back to being baffled with what you are arguing about.

As I wrote above: I do not agrere that the 3rd law conserves angular momentum just beause you make an arbitrary assumption.

 

[DrStupid]

Angular momentum is conserved due a system being isolated from external torques.

That's obvious. We do not need to discuss about that. The question is if forces comply with conservation of angular momentum. They don't do that by definition (in contrast to conservation of linear momentum). There must be additional restrictions. That's where the central nature of internal forces comes into play.

 

[etotheipi]

That's obvious. We do not need to discuss about that. The question is if forces comply with conservation of angular momentum. They don't do that by definition (in contrast to conservation of linear momentum). There must be additional restrictions. That's where the central nature of internal forces comes into play.

I'm shooting in the dark here, but sometimes in the cases where the forces in question are not central, don't you also need to worry about a bunch of other things like the momenta of fields? Self forces seemingly "violate" Newton III but apparently everything turns out okay if you factor in the momentum of the field. Is that relevant here?

 

[DrStupid]

I'm shooting in the dark here, but sometimes in the cases where the forces in question are not central, don't you also need to worry about a bunch of other things like the momenta of fields?

Yes, if the forces are not central, momentum must be conserved otherwise and the moment of the field is one posibility. Lorentz force is an example where momentum is primary exchanged with a field and where the force doesn't act in the direction from the source of the field (for the case it has a clear location) to the affected particle. Something like that exceeds the original definition of forces which is limited to interactions between bodies.