Terence Tao

But because they're both coming from the Hamiltonian, the Hamiltonian controls everything.

Every time the Hamiltonian has a symmetry, the equations will have a conservation law.

So once you have the right language, it actually makes things a lot cleaner.

One of the problems why we can't unify quantum mechanics and general relativity yet

We haven't figured out what the fundamental objects are.

For example, we have to give up the notion of space and time being these almost Euclidean-type spaces.

And we kind of know that at very tiny scales, there's going to be corner fluctuations, there's space-time foam.

And trying to use Cartesian coordinates X, Y, Z, it's a non-starter.

But we don't know what to replace it with.

We don't actually have the mathematical concepts.

The analog of Hamiltonian that sort of organized everything.

I believe so.

I mean, the history of physics has been that of unification.

much like mathematics over the years.

Electricity and magnetism were separate theories, and then Maxwell unified them.

Newton unified the motions of the heavens for the motions of objects on the Earth and so forth.

So it should happen.

It's just that the... Again, to go back to this model of observations and theory...

Part of our problem is that physics is a victim of its own success.

Our two big theories of physics, general relativity and quantum mechanics, are so good now that together they cover 99.9% of all the observations we can make.