Energy, Time, Position, Momentum which is more fundamental?

[compton]

Is energy more fundamental than time or vice versa?
Is Momentum more fundamental than position or vice versa?
Is the quantization of energy, more fundamental than the quantization of charge, or vice versa?

 

[muppet]

As far as QM is concerned, position and momentum are both observable quantities, so neither is in any way more fundamental than the other -you're just changing the basis of your mathematical space. Conceptually, time is more awkward to interpret in QM- at least in a non-relativistic context- but I'm not really sure the question makes much sense. In a relativistic context it might be the case that time can be treated as an observable, as we're trying to treat it on a similar footing to space, but I've never seen a "time" operator, or eigenstates thereof, so I'm hesitant to say so for certain- I'm only beginning to learn QFT.
There is, however, a sense in which "quantisation" of charge is more fundamental than that of energy, but really they're quite different concepts. Really, we talk about charge as being a discrete quantity, rather than quantised. "Quantised" in QM really means "a dynamical variable being promoted to an operator on hilbert space". So the quantisation of energy is really that we declare it to be an observable quantity with which we associate an operator. The fact that in an atom (say) the spectrum of this operator- the possible results of measuring the energy- is discrete is really a consequence of the boundary conditions, and certain sources actually provide continuous spectra of radiation.

 

[naima]

Hi Compton

Can't we say that environment, though decoherence, prefers position better than momentum?

 

[muppet]

I don't know much about decoherence- can you elaborate?

 

[naima]

Decoherence explains how one vector basis is choosen(momentum or position) when a particle interacts with its environment which may (or not) contain a measure apparatus. It is a branch or QM so it does not determine the result of the measure.
As we see things in term of a position space and not in a momentum space, i said this position basis must be more often choosen.