Linked Questions

94
votes
14answers
22k views

QM without complex numbers

I am trying to understand how complex numbers made their way into QM. Can we have a theory of the same physics without complex numbers? If so, is the theory using complex numbers easier?
16
votes
7answers
2k views

How does quantization arise in quantum mechanics?

BACKGROUND I'm trying to build an intuition for what quantization really means and came up with the following two possible "visualizations": The quantization of the energy levels of a harmonic ...
1
vote
3answers
673 views

Can we derive Schrödinger equation from classical wave equation?

In classical mechanics wave equation is $$y=A\sin(kx-\omega t)$$ $y$=instantaneous displacement, $A$=maximum displacement, $\omega$=angular velocity, $x$=position of particle, $k$=wave number Now in ...
14
votes
1answer
261 views

On the finiteness of quantum gravity$.$

Consider naïve quantum gravity, defined by $$ Z=\int e^{-\frac{1}{\hbar}\int R}\mathrm dg $$ where $R$ denotes the Ricci scalar, and $\mathrm dg$ a path integral over all metrics. I have set $G_N=1$ ...
1
vote
2answers
132 views

How does a vanishing $[x, p]$ work with the group theoretical definition of $p \propto \frac{\partial}{\partial x}$?

Thought about this while I was looking at some stuff on quantum-classical correspondence and where precisely the difference between quantum and classical comes from. Usually it's said that the key/...
1
vote
3answers
169 views

Where is the line between Quantum and Relativity?

Its often said QM is for the very small and GR for the very large. This brings to mind that there should be some limit at which one starts to apply and the other stops. Now I know there are more ...
3
votes
1answer
79 views

What's quantum about quantum discord?

Quantum discord is a quantity that relates two subsystems of a quantum state. It reduces to the entanglement entropy for pure states, but it differs for mixed states; separable states have zero ...
0
votes
2answers
94 views

Does the electro-dynamical lagrangian contain a (Dirac) wave-function?

Consider a lagrangian for quantum electro-dynamics. It contains the two fields: the vector $A$-potential inside $F_{\mu\nu}$ and the matter field $\psi$ (Dirac's spinor). A series of questions arise ...
0
votes
0answers
81 views

Differentiating quantum mechanics and string theory

It was surprising to learn how difficult it is classify a theory as classical or quantum based on criteria (PDE, complex numbers, axioms, probabilities, Planck constant, and realism). Rreference, “...
1
vote
1answer
53 views

Classical analog of state vector

I can’t believe I don’t know the answer to this question. What is the classical analog of the state vector of quantum mechanics?