Shut Up and Calculate: Exploring Feynman's Ideas on Physics

[yossell]

In the advanced courses, you don't even USE numbers for most of the work. It's all variables. The variables represent real, physical, measureable things.

But there are mathematical variables used in physics that don't represent real, physical, measurable things, the most famous being classical quantum mechanics' values of the complex wave function that are solutions of S's equation. Although \Phi is mathematically manipulated in the theory, it's |\Phi| which receives a physical, probabilistic interpretation. Indeed, it was probably the amount of brain power wasted arguing over what the wave represented that gave the shut up and calculate brigade a big boost.

It's not for nothing that the root of minus one is called imaginary!

Line elements, Riemannian metric fields, infinite dimensional Hilbert spaces, dirac delta functions...these mathematical objects appear in our physical theories, but it's not at all clear to me that they represent real, physical, measurable things - though of course, we can and do use them in mathematical operations to get results about things that are measurable - as we do with \Phi.

 

[Pythagorean]

But there are mathematical variables used in physics that don't represent real, physical, measurable things, the most famous being classical quantum mechanics' values of the complex wave function that are solutions of S's equation. Although \Phi is mathematically manipulated in the theory, it's |\Phi| which receives a physical, probabilistic interpretation. Indeed, it was probably the amount of brain power wasted arguing over what the wave represented that gave the shut up and calculate brigade a big boost.

It's not for nothing that the root of minus one is called imaginary!

Line elements, Riemannian metric fields, infinite dimensional Hilbert spaces, dirac delta functions...these mathematical objects appear in our physical theories, but it's not at all clear to me that they represent real, physical, measurable things - though of course, we can and do use them in mathematical operations to get results about things that are measurable - as we do with \Phi.

Agreed. (Though, imaginary truly is a terrible term for imaginary numbers).

I don't think this conflicts with my point though. We start with observables in physical modeling... and end with them.

 

[SixNein]

Agreed. (Though, imaginary truly is a terrible term for imaginary numbers).

I don't think this conflicts with my point though. We start with observables in physical modeling... and end with them.

I prefer complex instead of imaginary. Imaginary should have never been adopted as the name.

Like string theory? Anyway, I'll retract.