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

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Discussion Overview

The discussion explores the fundamental nature of various physical concepts, specifically energy, time, position, and momentum. Participants examine whether one of these concepts is more fundamental than the others, considering implications from quantum mechanics (QM) and the role of decoherence.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant questions whether energy is more fundamental than time, or if momentum is more fundamental than position, and whether the quantization of energy is more fundamental than that of charge.
  • Another participant argues that in quantum mechanics, position and momentum are both observable quantities, suggesting that neither is more fundamental than the other, and raises concerns about the interpretation of time in QM.
  • A later reply introduces the concept of decoherence, proposing that the environment may favor position over momentum when a particle interacts with it.
  • Another participant requests clarification on decoherence, indicating a lack of familiarity with the concept.
  • One participant explains decoherence as a process that determines which basis (momentum or position) is chosen during interactions with the environment, suggesting that position is more frequently selected in observations.

Areas of Agreement / Disagreement

Participants express differing views on the fundamental nature of energy, time, position, and momentum, with no consensus reached on which concept is more fundamental. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants note the complexity of the concepts involved, particularly in relation to quantum mechanics and the implications of decoherence, without resolving the underlying assumptions or definitions.

compton
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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?
 
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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.
 
Hi Compton

Can't we say that environment, though decoherence, prefers position better than momentum?
 
I don't know much about decoherence- can you elaborate?
 
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.
 

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