How does maximum symmetry compare to its corresponding minimum symmetry?

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Discussion Overview

The discussion explores the relationship between maximum and minimum symmetries within mathematical systems, particularly in the context of temperature and magnetic fields. Participants consider how these concepts might relate to Noether's theorem and the implications of absolute zero and negative temperatures.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the definition of "maximum" and "minimum" symmetry and how symmetries are ordered.
  • Another participant suggests a comparison of "maximum" and "minimum" temperatures in relation to magnetic fields, questioning their symmetry.
  • A further contribution refines this idea by specifying "temperature approaching infinity" and "temperature approaching negative infinity" as the extremes being considered.
  • One participant raises the concept of absolute zero and its relevance to the discussion of temperature in mathematical systems.
  • Another participant recalls a theoretical discussion from Scientific American regarding negative temperatures and their symmetry in relation to absolute zero.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of maximum and minimum symmetries, particularly in relation to temperature. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are limitations regarding the definitions of symmetry and temperature in mathematical contexts, as well as the implications of absolute zero and negative temperatures that are not fully explored.

Loren Booda
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In a mathematical system, what similarities are there between the most and least absolute symmetries?

Might Noether's theorem explain this?
 
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Before anyone can answer this, you will need to specify what you mean by "maximum" and "minimum" symmetry. How are you ordering symmetries?
 
I was thinking in part of "maximum" temperatures and "minimum" temperatures, as considered with a magnetic field -- are they of equal symmetry?
 
Loren Booda said:
I was thinking in part of "maximum" temperatures and "minimum" temperatures, as considered with a magnetic field -- are they of equal symmetry?

Make that temperature "approaching infinity" and temperature "approaching negative infinity."
 
You do understand "absolute zero" do you not?

But, in what sense does a mathematical system have a "temperature"?
 
I believe I once saw in Scientific American the concept of negative temperature relative to "absolute" zero. The system discussed was of a theoretical magnetic field that represented a temperature approaching infinity, but in a similar symmetric configuration could (ironically) represent temperature approaching negative infinity.
 

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