How are degrees of freedom understood in QM?

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Discussion Overview

The discussion revolves around the concept of 'degrees of freedom' in Quantum Mechanics, exploring its definition, implications for physical systems, and the relationship between observers and observed systems. Participants seek to clarify how degrees of freedom are quantified and whether observations influence these degrees.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on what constitutes a 'degree of freedom' in Quantum Mechanics, questioning if it relates to the number of observations of a physical system.
  • Another participant states that for a system of N particles, the degrees of freedom are typically 3N, while a quantum field has an infinite number of degrees of freedom, noting that other coordinates like spin may also be considered but are less common.
  • There is a discussion about the observer's role, with one participant asserting that the observer is conventionally outside the observed system and not included in its state space.
  • A later reply challenges this by suggesting that the act of observation may interact with the system, potentially affecting the degrees of freedom in a new observer-state space.
  • Another participant counters that observation does not change the degrees of freedom but rather alters the specific state within the state space of the system.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between observation and degrees of freedom, with no consensus reached on whether observation affects the degrees of freedom or merely the state of the system.

Contextual Notes

Participants have not fully resolved the implications of observation on degrees of freedom, and the discussion includes varying interpretations of how observers relate to the state space of a system.

Posy McPostface
I'm having a hard time understanding 'degrees of freedom'. Could someone please provide an example in terms of Quantum Mechanics about what a 'degree of freedom' could be represented as? Is it simply a number of observations of a physical system to determine the arrangement of particles within that system? Does the accuracy increase with a number of observations made or is one observation enough?

On a deeper level, is there a demarcation that can be said about the observer and the state space of a system or does that line blur away once an observation is made?
 
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For a system of N particles, the number of degrees of freedom is 3N, one for each position coordinate of each particle. On the other hand, a quantum field has an infinite number of degreeess of freedom.

This is the most typical usage. In a generalized sense, one may consider other (e.g., spin) coordinates as degrees of freedom but this is far less common (and must be inferred from the context).

In any case, this has nothing to do with observation.

The observer is conventionally always assumed to be completely outside the observed system, and hence not represented in the latter's state space.
 
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A. Neumaier said:
The observer is conventionally always assumed to be completely outside the observed system, and hence not represented in the latter's state space.
Thank you for the explanation. I understand now.

Doesn't the observer interact with the system by observing it and thus affecting the degrees of freedom in the new observer-state space?
 
Posy McPostface said:
Thank you for the explanation. I understand now.

Doesn't the observer interact with the system by observing it and thus affecting the degrees of freedom in the new observer-state space?
Observation doesn't change the degrees of freedom but only the particular state in the state space of the system.
 
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