How does maximum symmetry compare to its corresponding minimum symmetry?

In summary, the conversation discusses the similarities between the most and least absolute symmetries in a mathematical system. The question is whether Noether's theorem can explain this, but it is first necessary to specify what is meant by "maximum" and "minimum" symmetry. The conversation then delves into the comparison between "maximum" and "minimum" temperatures in a magnetic field and whether they have equal symmetry. The concept of "absolute zero" and the idea of a mathematical system having a "temperature" are also discussed, including the concept of negative temperature relative to "absolute" zero.
  • #1
Loren Booda
3,125
4
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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  • #2
Before anyone can answer this, you will need to specify what you mean by "maximum" and "minimum" symmetry. How are you ordering symmetries?
 
  • #3
I was thinking in part of "maximum" temperatures and "minimum" temperatures, as considered with a magnetic field -- are they of equal symmetry?
 
  • #4
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."
 
  • #5
You do understand "absolute zero" do you not?

But, in what sense does a mathematical system have a "temperature"?
 
  • #6
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.
 

1. What is maximum and minimum symmetry?

Maximum symmetry refers to a situation where all elements of a system are arranged in such a way that they are indistinguishable from one another. This results in a high level of balance and order. On the other hand, minimum symmetry refers to a situation where the elements of a system are arranged in a way that highlights their differences and lack of balance.

2. How do you measure symmetry?

Symmetry can be measured by looking at the arrangement of elements in a system and determining how closely they match each other. This can be done visually or mathematically by using symmetry operations such as reflections, rotations, and translations.

3. What causes a change in symmetry?

A change in symmetry can be caused by external factors such as physical forces or internal factors such as changes in temperature or pressure. It can also be influenced by the inherent properties of the system, such as the shape and arrangement of its elements.

4. How does maximum symmetry compare to minimum symmetry in terms of stability?

Maximum symmetry is often associated with a higher degree of stability as it represents a state of balance and order. On the other hand, minimum symmetry can be less stable as it highlights the differences and imbalances within a system.

5. Can maximum symmetry ever become minimum symmetry?

Yes, it is possible for maximum symmetry to become minimum symmetry. This can occur through external factors or internal changes within the system that disrupt the balance and order of its elements. However, it is also possible for a system to maintain a high level of symmetry even in the face of external challenges.

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