# Primacy of conservation laws

by russell2pi
Tags: conservation, laws, primacy
P: 10
 Quote by harrylin No "momentum flow" in classical mechanics: it is a conserved quantity, not a fluid. ... F=dp/dt "The alteration of motion is ever proportional to the motive force impressed".
Alteration of motion is momentum flow. If you object to the word "flow", that's why the third law is there. Whatever momentum is lost by one object is necessarily gained by another - it flows from one to the other any time a force is acting. I doubt Newton would dispute that. The issue is simply whether the force causes the flow, or the force is just a name for the flow.
P: 5,462
 You are trying to artificially limit discussion to a static case.

 Many fluid mechanics texts use the phrases "destruction of horizontal momentum" and "appearance of vertical momentum" to descibe what happens when a flowing fluid is directed at a wall.
@ russell2pi

I clearly have a different definition of the principle of conservation of linear momentum than whatever you are thinking of.
 Sci Advisor P: 2,406 harrylin, you solve a lot of many-body problems analytically? Every single real world application of principles of physics is numerical. So yes, ability to take your problem and put in the form you can feed to a solver of some kind is what determines whether the method is useful or not. Studiot, do you have a point? You are jumping all over the place and making counter points that have no common thesis. OP asked about forces. Fact is, nearly all of the physics has moved away from the force as a primary concept. Even in Classical Mechanics, once you move past Newtonian Physics, individual forces is not something you frequently consider. Newton's Laws have their applications. They do make many problems simpler. But they are neither the dominant explanation nor a dominant method even in mechanics. Hamilton's Principle and Conservation Laws are used instead. I have provided arguments and explanation for this position. You just pick at individual phrases rather than have any sort of kind of point. That's not how you construct a counter-argument.
P: 5,403
 Quote by russell2pi Is this a physics forum or an engineering forum? As stated in the OP, this is about the philosophy of mechanics.
I'm not going to apologize for being an engineer, and I'm quite happy to solve problems using Lagrangian mechanics, or by hitting something with a 20lb hammer - whichever is the more effective tool to solve for the problem in question.

Limiting yoursefl to only one philosophical toolkit doesn't have any advantage than I can see. The more ways you can use to intuitively "see" what's going on the better, IMO.
P: 3,180
 Quote by K^2 [..] ability to take your problem and put in the form you can feed to a solver of some kind is what determines whether the method is useful or not.
I think that usefulness is not what Studiot meant with "simple"; he can tell us. And of course, russell2pi can tell us if that is what he/she is after.
P: 3,180
 Quote by russell2pi Alteration of motion is momentum flow. If you object to the word "flow", that's why the third law is there. Whatever momentum is lost by one object is necessarily gained by another - it flows from one to the other any time a force is acting. I doubt Newton would dispute that. The issue is simply whether the force causes the flow, or the force is just a name for the flow.
Thus you agree with me that Newton's second law describes force like you do? (note that I wrote mistakenly "defined" while it is a law which was found to be inaccurate for high speeds with the classical definition of mass).
However, as others already mentioned, no momentum is lost or gained by an object in static cases that force is applied. Force is in classical mechanics a more general concept than change of momentum.

Do the links help or do you need more?

PS You forgot to elaborate how the Coulomb interaction affects contact force and Hooke's law.
P: 2,406
 Quote by harrylin I think that usefulness is not what Studiot meant with "simple"; he can tell us. And of course, russell2pi can tell us if that is what he/she is after.
It doesn't matter. Any criterion you put on it, in general, Lagrangian approach wins out. That's why it was invented and why it was used to solve more advanced problems. Newtonian mechanics is only simpler with very simple choices of DoF, coordinate systems, and constraints. Poor generalization is a good indication that the set of laws is not fundamental. That's the criterion on which we chose one model over another. If you just look at the Sun, it's easier to say that Sun goes around the Earth. But if you throw in the planets, Geocentric system becomes impractically cluttered. It's the same kind of principle.

Lagrangian mechanics generalizes trivially. Newtonian mechanics does not.
 P: 925 Any possible continuous symmetry can be described by the invariance of lagrangian under certain transformation.It is really helpful when one does not get ideas from newtonian eqn.lagrangian can be written down without having much detail of forces which is certainly not the case with newtonian mechanics.
 P: 5,462 Since those who believe momentum to be one of the fundamental quantites have avoided my previous question about fluid dynamics I suppose that they will avoid this simple one as well. Consider an isolated universe, empty except for a single particle. What is the momentum of that particle?
 Sci Advisor P: 2,406 You did not actually ask a question about fluid mechanics. Nor do you have a thesis still. What exactly are you arguing? What are your points and what are your arguments for these points? Because I don't know your thesis, I am forced to guess your point about a lone particle. I'm guessing, you are trying to say "Force is absolute. Momentum is not." Well, you are wrong. If you take Relativity into account, force is frame-dependent just like momentum is. If you don't, then in Classical Mechanics I'm free to chose an absolute coordinate system and measure absolute momentum. Yes, even for one particle in the universe. So either both are relative or both are absolute depending on the kind of physics we are talking about.
Mentor
P: 15,569
 Quote by Studiot Consider an isolated universe, empty except for a single particle. What is the momentum of that particle?
That depends on the reference frame. Momentum is not an intrinsic property of a particle.
P: 5,462
The quote below will be the third time (in this thread) I have posted this and the quote above will be the second time (in this thread) you have incorrectly reported my posts in an abusive manner.

 Many fluid mechanics texts use the phrases "destruction of horizontal momentum" and "appearance of vertical momentum" to descibe what happens when a flowing fluid is directed at a wall. I ask for a mathematical description, equivalent to the classical analysis, using the modern theory to compare and see if it is actually simpler and easier, as claimed.
 Sci Advisor P: 2,406 Fluid dynamics is derived from classical field theory. I still have no idea what it is that you are asking. The entire topic is an example of how you work with momenta directly without ever considering forces.
P: 5,462
 Fluid dynamics is derived from classical field theory. I still have no idea what it is that you are asking. The entire topic is an example of how you work with momenta directly without ever considering forces.
I mentioned the word "force" precisely once in this thread, and that was before I asked a fluid mechanics related question.

On my last question.

In my opinion momentum in my uniparticular universe is indeterminate since the particle's velocity is indeterminate.
Mentor
P: 15,569
 Quote by Studiot In my opinion momentum in my uniparticular universe is indeterminate since the particle's velocity is indeterminate.
It is frame variant, but not indeterminate. In any given frame it has a definite velocity and therefore a definite momentum.
 P: 5,462 A definite velocity relative to what?
 Mentor P: 15,569 Relative to the reference frame. That is how velocities are always defined.
 P: 5,462 So where in this empty infinite universe is the origin of this reference frame?

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