Teach me about classical mechanics please

[Krunchyman]

I have no prior experience in physics, but I am a math undergrad so I know calculus, differential equations, linear algebra and stuff like that. So I'm ready to move from the conceptual "bedtime story physics" to stuff with real mathematical rigor.

So, what is classical mechanics all about? What are the big theorems and results?

 

[Drakkith]

This wikipedia article should give you a good overview of what classical mechanics is all about. Note that this article links to almost everything else about classical mechanics, so you should follow all the links, especially the ones in the expandable/collapsible table in the upper right of the page.

 

[ISamson]

This might not 100% relate to the OP, but it caught my eye...

 

[vanhees71]

With real mathematical rigor (but still recognizing the physics):

https://www.amazon.com/dp/0387968903/?tag=pfamazon01-20

 

[Krunchyman]

View attachment 214443

This might not 100% relate to the OP, but it caught my eye...

Does quantum field theory try to unify relativity and quantum mechanics? If not, what it is supposed to do?

 

[Ibix]

Quantum Field Theory is special-relativistic quantum theory. No one has worked out a quantum theory that plays nicely with general relativity, although a lot of effort has gone into looking.

 

[Krunchyman]

Quantum Field Theory is special-relativistic quantum theory. No one has worked out a quantum theory that plays nicely with general relativity, although a lot of effort has gone into looking.

Can mathematicians contribute to this problem?

 

[A.T.]

Can mathematicians contribute to this problem?

Definitely. But ideally they would contribute to the solution.

 

[Krunchyman]

Definitely. But ideally they would contribute to the solution.

To what extend can they contribute to the solution? What are the research areas?

 

[Ibix]

To what extend can they contribute to the solution? What are the research areas?

I'm not qualified to comment directly. My reading of what little I know is that we have no shortage of skilled mathematicians and no shortage of candidates for theories. But none is totally satisfactory, basically because theorists are shooting more or less blind. We haven't yet probed the regime (we may find we need something bigger than CERN) where existing theories differ significantly from experiment.

A.T. is being funny, but I think that's the long form of what he's saying.

You may wish to look at the current (or recently) featured thread on a "krisis" in physics.

 

[George Jones]

View attachment 214443

This might not 100% relate to the OP, but it caught my eye...

I prefer the cube:

 

[robphy]

The Bronstein cube https://en.wikipedia.org/wiki/Matvei_Petrovich_Bronstein
apparently the author of the first dissertation on Quantum Gravity.
http://people.bu.edu/gorelik/cGh_FirstSteps92_MPB_36/MPB-all_94_e_TOC.htm
http://people.bu.edu/gorelik/cGh_Bronstein_UFN-200510_Engl.htm
http://people.bu.edu/gorelik/MPBronstein_100/MPBronstein_100.htm

In my dissertation, I have a hypercube, with an additional "discreteness of spacetime" parameter ranging from discrete to continuous.

 

[Hendrik Boom]

Yes. One of the issues is that it is difficult to do the calculations on the various quantum gravity theories to determine just what they predict. The math is *hard*. So mathematicians have their work cut out for them -- to find enough structure in the theories so that the calculations become feasible. Just about everything from analysis, Lie group theory, topology, category theory, and the lot seems to get involved. All of which tells me we need more theoretical insights into the theories we already have and better calculating techniques.