What is the physical meaning of renormalization in field theories?

>Please read Weinberg before embarrassing yourself.
Good post

Well that one kinda makes sense to me.

You have infinite energy outside the plates, but the infinite energy inside the plates is slightly less, so you get internal pressure.

Or that's how I interpret what's going on.

This is a good answer.

Why does everyone mention scaling? You can integrate out degrees of freedom in ways that have nothing to do with scaling. You can have a channel coupled to a device and integrate out the channel degrees of freedom.

You get a self-energy term in the Green's function, etc.

Scaling is the most initiative type of renormilization

Sure, but "scaling" shouldn't be used as a definition of renormalization. It obfuscates the general point.

You have to renormalize the definition.

This is how renormalization is taught by people who just want their students to compute things quickly.
This is the Wilsonian picture of renormalization. It's not really unique.
>A prof I know believes that all theories in nature are effective field theories of some kind
My adviser would agree.

I like that analogy.

you both have good points
Talking about physical scales is a good way to illustrate that some of the degrees of freedom of a model are not as relevant as others. To any feasible degree of accuracy, the physics of b quarks is unimportant to calculating the lamb-shift of Hydrogen. A simple way of arguing to someone why that's true is just to compare the distance scales at which these effects become important.

>"scaling" shouldn't be used as a definition of renormalization
It isn't. It's the physical intuition behind renormalization. The definition is the shifting of poles of the S-matrix elements. On the generating functional level this manifests as integrating out momentum shells of the theory (which can't always be done).