Feynman's proof that Newton's laws are invariant under spatial translation

[gmax137]

There's an important distinction here.

Yes, and unfortunately this thread bounces back and forth between the two ideas.

 

[Ibix]

Yes, and unfortunately this thread bounces back and forth between the two ideas.

Actually, I think the original quote does too: "Since the equations are the same, the phenomena appear the same." (Or I'm missing something...)

 

[hutchphd]

So Feynman is proving that his model of the laws of physics are translation invariant and hence his equipment is predicted to be translation invariant. He does not prove (and you cannot prove) that this is a correct model of reality, but it's been an accurate model every time so far.

But this caveat is, unless specifically stated otherwise , fundamentally part of the physics canon.
Perhaps Feynman should have said "Since the equations are the same, canonically the phenomena must appear the same." but this seems a bit pedantic. The book is after all a physics text.

 

[Ibix]

But this caveat is, unless specifically stated otherwise , fundamentally part of the physics canon.

Indeed. But I certainly managed to get a long way through my physics education without coming across a clear statement of the distinction between the mathematical models (about which you can formally prove things) and reality (where you can only test). I don't think Feynman's being particularly clear on that distinction here, and perhaps you are right that it would be pedantic of him to do so, but I wonder if it's confused the OP.

 

[mark2142]

The idea is that if you do an experiment in your bathtub, you don't have to look up the laws of physics that apply specifically in your bathtub. You can use the same laws of fluid mechanics that everyone else uses.

Otherwise, we'd have a different set of laws of physics for every bathtub - and every swimming pool etc.

That I understand. I meant how it’s right everywhere from the logic I gave?

This does not happen. We can write the correct laws using the new coordinates. There is no absolute space and origin from which the laws are right.

 

[hutchphd]

I, for one, do not understand the distinction you are trying to create. Perhaps you could succinctly restate your question.

 

[mark2142]

I, for one, do not understand the distinction you are trying to create. Perhaps you could succinctly restate your question.

Ok! I am simply asking how is “right everywhere” is same as “right from everywhere”?

This does not happen. We can write the correct laws using the new coordinates. There is no absolute space and origin from which the laws are right. So it’s right everywhere or from everywhere ?

You can see in the logic I had put a question mark. The math says only “right from everywhere” not “right everywhere”.

 

[Ibix]

Ok! I am simply asking how is “right everywhere” is same as “right from everywhere”?

Take a piece of equipment and study it. Move it somewhere and study it again from a distance. Is it working the same? Repeat and repeat until you are convinced that the laws you have that describe the instrument are "right everywhere".

Bring the equipment back to you. Now you move somewhere and study it again from a distance. The laws governing your function don't change (we just established that) and the equipment hasn't moved. Thus the results will be the same and the laws are "right from everywhere".

 

[mark2142]

Take a piece of equipment and study it. Move it somewhere and study it again from a distance. Is it working the same? Repeat and repeat until you are convinced that the laws you have that describe the instrument are "right everywhere".

Bring the equipment back to you. Now you move somewhere and study it again from a distance. The laws governing your function don't change (we just established that) and the equipment hasn't moved. Thus the results will be the same and the laws are "right from everywhere".

It’s already been explained before in many posts and I already know the laws don’t change upon displacement. I want to understand the proof that Feynman gave. I am unable to follow from math that laws don’t change upon displacement. The math is proving the law is same for different observers.

 

[vanhees71]

I'm not aware that Feynman anywhere proved Noether's theorem in his textbooks. Do you have the source. I'm sure, it's a masterpiece. Otherwise you'll find this proof in any modern textbook on classical analytical mechanics, e.g.,

F. Scheck, Mechanics (5th ed.), Springer (2007)

 

[hutchphd]

Is the OP aware of the Messenger Lecture on symmetry? He does some fun hand waving on Noether.

 

[gmax137]

It’s already been explained before in many posts and I already know the laws don’t change upon displacement. I want to understand the proof that Feynman gave. I am unable to follow from math that laws don’t change upon displacement. The math is proving the law is same for different observers.

I think @Ibix has answered this question, essentially, "Feynman has not proved that the 'real' laws don’t change upon displacement"

... So Feynman is proving that his model of the laws of physics are translation invariant and hence his equipment is predicted to be translation invariant. He does not prove (and you cannot prove) that this is a correct model of reality, but it's been an accurate model every time so far.

"his model" in this case is Newton's $\vec F = m \vec a$

 

[Ibix]

The math is proving the law is same for different observers.

I think the only difference is how you interpret the offset, $a$. Is it the distance between two coordinate system origins, or is it the negative of the x displacement between two pieces of identical equipment measured in the same coordinate system? (I may have incorrectly assigned the negative sign there, so beware.) Depending which way you interpret it you are proving either.

 

[mark2142]

Depending which way you interpret it you are proving either.

(Now this means that there exists a way to measure x, y, and z on three perpendicular axes, and the forces along those directions, such that these laws are true.)
Do we measure x by scale and F by some machine?
Can you tell how do we measure and write newtons law?

 

[PeroK]

Can you tell how do we measure and write newtons law?

By doing physics theory in the classroom and experiments in the lab.

 

[mark2142]

So if we assume right most vertical line as origin and the body move to middle vertical line y’ then we can write a law which we call newtons law for the displacement. Then body moves to left most line y and again we can write the same law with different coordinates. So if we see we can realise that the law doesn’t change from middle line y’ to left most line y. Law is translational invariant. That’s what I think of. Yes?