SaudiBombsYemen

I agree, nice discussion!

but if we do?

Cant you construct global symmetries by infinitesimal changes?

infinitesimal symmetries imply global symmetries though

Not for trivial cases but for more elaborate ones you do

But in general you do need some sort of symmetry

I also think it wouldn't be that easy to prove momentum wouldnt be conserved in the case you stated since momentum lost between the 2 particles could be compensated with the varying force (momentum change)

Ok, now I see what you mean, I still disagree with this vision of forces being generated from nowhere, you are considering just part of the system, where of course momentum, energy and pretty much nothing is conserved.

Why wouldn't momentum be conserved in the collision?

I said to imply some degree of translational symmetry is needed for third law

The case where potential or force depends on some sort of absolute position (which implies no symmetry), case in which third law doesnt hold

What do you think about the case I stated with no symmetry?

In which case momentum will always conserve

Yes but newtonian dynamics speaks about particles exerting forces on each other, you require 2 particles to have an action and a reaction

I don't agree where you say the field responds with another force, it is like directly taking third law as an axiom

And also I would like to say that a certain amount of symmetry is required, for instance, if potential depended on position rather than relative distance particles at different positions would exert different forces on each other, resulting in action not equaling reaction

But newton's third law speaks about forces between particles, here you are just considering more abstract constructions like fields

I dont see how 3rd law holds in a particle in a well, where reaction being applied?

@John there is conservation of momentum if you took into account the particles creating the potential. I'm curious to know where do you see a single system particle in simple harmonic motion obeys third law. What particle is suffering the reaction? And who is even causing the action? If you assume momentum is not conserved then $$\frac{dp_t}{dt}=F_t = F_{action}+F_{reaction}\neq 0 \implies F_{action}\neq F_{reaction}$$ No third law.

@John I haven't suggested Newton's third law implies Noether's theorem, but the reciprocal. And as I said 100 times symmetry is also required for third law to work.

This "answer" doesnt explain why Newtons third law is true. You just ate 150 years of physics history.

As I see it, the reason why newtons third law works is not because coulombs formula tells us, since that is an empirical formula that of course matches our observations: forces between 2 charges are equal and opposite. The reason why it is how it is, is because Noethers theorem, because of symmetry.

No kidding, some users here are cytotoxic

I hope so

ACM won?? I think I'll leave this site till next elections

Man I hope you did

Who won

@CuriousOne I'll do it, thanks for the advice.

@CuriousOne I would if I understood blackbody radiation...

I mean the whole discussion doesn't relate much to the question

It's funny how some people always post meaningless comments, but never answer the question. Perhaps to look inteligent?

@JAmeslarge Yes, I know, but I think is more of an exaggeration to gain people's attention, as it is very unlikely, but as I said it, is NOT imposible.

I think is just an exageration to show how chaotic some systems like the atmosphere are. If you had such a cumule of casualities it could happen but I guess it doesnt.

It's ironic how someone who uses Ad Hominem falacies ("he is against the government blah blah") sends me that link. Ahh western world, I love your hypocrisy

Noo, the US doesnt finance terrorists... Well, its happening right now in Syria, moderate rebels are not that moderate...

@AndrewGrimm Seriously, these things are not random, events in history have a cause 99% of the time. Why would Hillary even make that up? It's not going to give her more votes. Think what you want, seriously.

@AndrewGrimm ok, just believe what you want. I really like history and if something I know is that coincidences dont exist. The US financed "call them whatever" (I'll call them terrorists). The newspaper is REAL, it's not a montage dood, do you think Fox News or CBS would show that? No. Who shows it? Someone who is tired of your manipulated media. Is is Bin Laden. It is imposible, even knowing he was a millionaire that he organized such a bit terrorist cell.

@AndrewGrimm I DID provide links! Bad links to you? Then do your own research and share us the truth.

@AndrewGrimm in wikipedia you have links, do your own research

@AndrewGrimm its a newspaper article (?) what do you want more than that? Do you think someone pro-government would say "Yes, we financed these groups, and now they are sorrounded by terrorists, but who cares, it's not my country"

@sklivvz thanks, I'm sorry, I didnt think it was going to generate so much controversy

If you guys want to see the original answer check the edit... it was far more interesting

@user568458 I'll try to find more references.It's very find to find them though. I know some historians but they speak spanish.