What does p = mv (momentum) really mean?

[voko]

What application would momentum have if it wasn't conserved?

My question can only be answered with "yes" and "no", not with some other answer, and certainly not with a question. Can you just answer my question? Thank you.

 

[A.T.]

Do I understand you correctly that a statement like "the magnitude of the vehicle's velocity is X" is infinitely more significant than "the magnitude of the vehicle's momentum is Y", because the latter statement does not deal with conservation of momentum?

No, you did not understand me correctly.

 

[voko]

Then one of the following must be true:

(1) A statement like "the magnitude of the vehicle's velocity is X" is infinitely more significant than "the magnitude of the vehicle's momentum is Y" because Z is true for some Z, where Z is not related to conservation of momentum.

(2) A statement like "the magnitude of the vehicle's velocity is X" is infinitely more significant than "the magnitude of the vehicle's momentum is Y" because Z is false for any Z.

Which one of the above is true?

 

[A.T.]

If you want to claim that there is more significance to momentum than its conservation, then it's up to you to point out what it is. Not for others to answer your convoluted questions.

 

[voko]

If you want to claim that there is more significance to momentum than its conservation, then it's up you to point out what it is. Not for others to answer your convoluted questions.

Michalos, Alex (1969). Principles of Logic. Englewood Cliffs: Prentice-Hall. p. 370. "usually one who makes an assertion must assume the responsibility of defending it. If this responsibility or burden of proof is shifted to a critic, the fallacy of appealing to ignorance is committed."

(quoted from http://en.wikipedia.org/wiki/Philosophic_burden_of_proof)

Shall I remind that it was a certain A.T. who asserted the following:

It's only significance is its conservation under certain conditions. That's the only reason why it is defined this way.

The afore-mentioned A.T. is now on the verge of committing the fallacy of appealing to ignorance.

 

[A.T.]

Shall I remind that it was a certain A.T. who asserted the following:

It's only significance is its conservation under certain conditions. That's the only reason why it is defined this way.

Yep, and that claim can only be proven wrong, by pointing out another significance of momentum. Let me know when you have found one.

 

[voko]

Yep, and that claim can only be proven wrong, by pointing out another significance of momentum. Let me know when you have found one.

I hope you realize that I could do so trivially by defining the term "significance" any way I see fit, exploiting yet another fallacy in your reasoning?

 

[A.T.]

...defining the term "significance" any way I see fit...

Yes, you can play some semantic games with yourself, if that pleases you. Have fun.

 

[Dale]

Voko, as a third party, I also think that your question is very convoluted. I wouldn't answer it either.

I don't think that I would go so far as to say that momentum is only significant due to its conservation, but I cannot think of a counter example. For example, in a pendulum problem the momentum of the pendulum is not conserved, and momentum is not used to solve pendulum problems.

 

[Dale]

I cannot think of a counter example.

I just thought of a counter-example. Momentum is used to find wavelength per deBroglie. That is a significance of momentum which could be important regardless of conservation.

 

[vjacheslav]

Would you to give any conditions of conserving momentum, please?

 

[voko]

Yes, you can play some semantic games with yourself, if that pleases you. Have fun.

The semantic player here is you. You made a categorical statement involving an undefined notion. Your statement is not falsifiable as such. When confronted with critique, your required your critics to prove your statement wrong via a counter-example, which is impossible because it is not falsifiable. Your statement is fallacious, and your attitude, now that your fallacies have been demonstrated, is questionable.

Voko, as a third party, I also think that your question is very convoluted.

I think I made them - at the very least I was genuinely trying - to make them simple yes/no questions. The reason is that the original statement felt wrong to me, but at that point I had not really formulated to myself why it felt wrong, so I tried to use those questions to understand what was really meant and why that felt wrong to me. But we have moved on since then. The true reason is, the statement is meaningless. "Significance" is subjective. It means something to some person, and something different to another. It is entirely possible that A.T.'s perception of his statement is fully tautological: momentum's significance is in its conservation, period; that requires no proof and cannot be proven wrong; but that is quite possibly not true to anyone else.

 

[A.T.]

I just thought of a counter-example. Momentum is used to find wavelength per deBroglie. That is a significance of momentum which could be important regardless of conservation.

Yes, that would be a counter-example, unless the derivation of the deBroglie equations depends on momentun conservation itself. I wasn't thinking about quantum mechanics in the context of this sub-forum.

 

[olivermsun]

It is entirely possible that A.T.'s perception of his statement is fully tautological: momentum's significance is in its conservation, period; that requires no proof and cannot be proven wrong; but that is quite possibly not true to anyone else.

Well, in the Newtonian viewpoint, momentum is the quantity which is conserved in inertial frames; you could call this somewhat tautological, since inertial frames are the ones in which momentum is conserved.

Nevertheless, it's a pretty profound concept that, having been given a name, "the thing which is conserved" follows the Second Law.

 

[DrStupid]

Nevertheless, it's a pretty profound concept that, having been given a name, "the thing which is conserved" follows the Second Law.

In non-inertial frames of references momentum is not conserved but still follows the Second Law. Fictitious forces just violate the Third Law.

 

[olivermsun]

So what you're saying is, if you posit additional, fictitious forces you can even make a non-inertial frame conserve momentum?

 

[DrStupid]

So what you're saying is, if you posit additional, fictitious forces you can even make a non-inertial frame conserve momentum?

No. If the frame of reference conserves momentum it would be no longer non-inertial.

 

[olivermsun]

You say the second law is still obeyed in a non-inertial (e.g., rotating) frame, but this is only because the (apparently spontaneous) change in momentum is explained by introducing a fictitious force.

Without the fictitious force, which doesn't obey the third law (and therefore does not obey conservation of momentum), motion in the rotating frame actually does not obey the 1st and 2nd laws.

Also, it's called fictitious because it doesn't conserve "facts."

So now I'm getting confused: what is actually being conserved, and what is not here?

 

[DrStupid]

You say the second law is still obeyed in a non-inertial (e.g., rotating) frame, but this is only because the (apparently spontaneous) change in momentum is explained by introducing a fictitious force.

Fictitious forces result from the second law in non-inertial frames - not vice versa. Nothing needs to be explained or introduced here.

So now I'm getting confused: what is actually being conserved, and what is not here?

As fictitious forces violate the third law (that's why they are called fictitious) they do not conserve momentum.

 

[olivermsun]

Fictitious forces result from the second law in non-inertial frames - not vice versa. Nothing needs to be explained or introduced here.

Now you're turning circular. Forces (fictitious or otherwise) don't "result" from the second law in any frame AFAIK. What would be "vice versa"—the second law resulting from fictitious forces in non-inertial frames?

As fictitious forces violate the third law (that's why they are called fictitious) they do not conserve momentum.

I always thought they are called fictitious (or pseudo-) because they don't arise from any interaction of bodies, but only from the "interaction" of reference frames.

But anyway this is getting silly. You must have missed all the smileys I put in my previous posts.

Let's let them carry on with the original inane discussion.

 

[Dale]

Also, it's called fictitious because it doesn't conserve "facts."

Facts (i.e. the outcome of specific experimental measurements) are not conserved to begin with. However, they are invariant, including in non-inertial frames.

There is a big difference between "conserved" (does not change over time) and "invariant" (is agreed on by different reference frames). Mass is invariant and conserved. Energy is conserved but not invariant. Proper acceleration is invariant but not conserved. Position is neither conserved nor invariant.

 

[olivermsun]

Facts (i.e. the outcome of specific experimental measurements) are not conserved to begin with. However, they are invariant, including in non-inertial frames.

Just to clarify something: I meant "facts" as in "the fact that a force exists." In the example we're talking about, no force exists—only a pseudo force that allows Newton's second law to be apparently obeyed in the non-inertial frame.

There is a big difference between "conserved" (does not change over time) and "invariant" (is agreed on by different reference frames).

The body which is at rest or in motion in the non-inertial frame experiences a change in momentum (changes over time) which is apparently not caused by any force. (Of course we know that it's actually the frame of reference, not the body, that is in nonuniform motion.)

 

[DrStupid]

Forces (fictitious or otherwise) don't "result" from the second law in any frame AFAIK.

The second law says F=dp/dt - without any restrictions.

What would be "vice versa"—the second law resulting from fictitious forces in non-inertial frames?

Vice versa means the second law is valid in non-inertial frames because there are fictitious forces. Actually there are fictitious forces in non-inertial frames because the second law is valid.

I always thought they are called fictitious (or pseudo-) because they don't arise from any interaction of bodies, but only from the "interaction" of reference frames.

Thats the violation of the third law. The first and second law say there is a force. The third law says that's not a force.

 

[olivermsun]

The second law says F=dp/dt - without any restrictions.

The usual interpretation is that the 2nd law is asserted to hold in an inertial frame (i.e., under the conditions in which the 1st law holds).

Vice versa means the second law is valid in non-inertial frames because there are fictitious forces. Actually there are fictitious forces in non-inertial frames because the second law is valid.

We introduce fictitious forces because we want to proceed as if the second law were valid even in the non-inertial frame.

On the other hand, it's pretty clear if you consider, e.g., the motions of equation in a rotating frame of reference, that the pseudo-forces look nothing like what we think of as forces in an inertial frame.

Thats the violation of the third law. The first and second law say there is a force. The third law says that's not a force.

You could try and read it that way I suppose…

 

[DrStupid]

The usual interpretation is that the 2nd law is asserted to hold in an inertial frame (i.e., under the conditions in which the 1st law holds).

The usual interpretation is that all three laws are asserted to hold in an inertial frame. If at least one of them is violated the system is not inertial. As the third law is designed to conserve momentum it would stand to reason that that this law is violated in non-inertial frame. Assuming the second law to be invalid is not useful.

We introduce fictitious forces because we want to proceed as if the second law were valid even in the non-inertial frame.

We get the fictitious forces if we assume the second law to be valid. Nothing has to be introduced here.

 

[olivermsun]

The usual interpretation is that all three laws are asserted to hold in an inertial frame.

I can agree with that. The 2nd law is indeed one of the three laws.

We get the fictitious forces if we assume the second law to be valid. Nothing has to be introduced here.

This is true. If you start with an incorrect but convenient assumption, then nothing else has to be introduced.

 

[DrStupid]

If you start with an incorrect but convenient assumption, then nothing else has to be introduced.

Try to proof that the assumption is not correct.

 

[olivermsun]

I think I'll pass. We already have equations of motion in rotating frames which have been "proofed" to be consistent with Newton's 2nd law, provided the 2nd law is assumed to hold in inertial frames.

 

[porcupine137]

Questions such as "What really is momentum?" or "What really is mass?" etc. are utterly useless as far as the science is concerned. Answering them adds nothing to the predictive or explanatory power of the theories they derive from. All you have to know is that momentum is well-defined both mathematically and operationally. Anything else that might be said about them is simply philosophical sophistry.

I'll have to disagree. I bet neither S.R. nor G.R. would have been discovered with that sort of mindset, just for starters.

 

[porcupine137]

Talk to someone with no idea of the Maths involved in Physics and you usually hear a pretty poor model of the World. Maths is so crucial to understanding at any but the very superficial level. Imagine trying to have a conversation about Finances without a common knowledge of the Arithmetic of Interest and Profit. The consequence of not using appropriate Maths is constantly being demonstrated by how people are regularly conned into bad deals. The numbers (and the Algebra) always count.
I think many of the preceding comments have been made by people who do, in fact, have an appreciation of the Maths but it is so familiar to them that they are hardly aware of it.

Yes, but don't forget also that getting buried in pure math or looking at nothing but the math seems to be what those who have never made any of the great discoveries in physics do.