2 ms·
Q: So what is the dimension of my Hilbert Space? A: Just enough to describe all your independent physical states, which is proportional to the number of your p
by mikhailfranco 3y ago
Q: So what is the dimension of my Hilbert Space?
A: Just enough to describe all your independent physical states, which is proportional to the number of your particles.
Q: So if some interaction creates more particles I have to increase the dimension of my Hilbert Space?
A: Yes, I'm afraid so.
Q: But I am used to physics providing some constant background to goings-on here and now. It was absolute Newtonian space and time, then it was warped Einsteinian spacetime, now you say it depends on how many particles I create?
A: Yes.
Q: But that's insane?
A: Yes.
A: OK, I'll allow you to create or destroy as many particles as you like, especially if you have an really big Large Hardon Collider.
Q: Are you sure I can keep my Hilbert Space the same?
A: Yes, aha, I have thought of a special number that does not change when you add or remove finite integers...
Q: There is no such number ... oh wait, you mean infinite dimensional?
A: Yes, infinite dimensional, and complex, of course.
Q: Of course.
Q: Does not sound in the least bit plausible. How do you add particles?
A: It's called the second quantization of Quantum Field Theory using Fock Spaces.
Q: Makes perfect Focking sense.