Are all physical quantities an equivalence relation?

Click For Summary
SUMMARY

The discussion centers on whether all physical quantities can be classified as equivalence relations. It posits that if object A has the same mass as objects B and C, then B must have the same mass as C, highlighting the transitive nature of equivalence relations. However, the conversation questions the existence of physical quantities that may not adhere to this principle, specifically in cases where properties do not maintain transitivity or right Euclidean characteristics. The conclusion emphasizes that while quantities are properties, equivalence relations are defined between these properties, suggesting a nuanced distinction in physical measurements.

PREREQUISITES
  • Understanding of equivalence relations in mathematics
  • Basic knowledge of physical quantities and their properties
  • Familiarity with thermodynamic laws, particularly the zeroth law
  • Concepts of transitivity and right Euclidean properties in relations
NEXT STEPS
  • Research the properties of equivalence relations in mathematical contexts
  • Explore the zeroth law of thermodynamics and its implications
  • Study examples of non-transitive relations in physics
  • Investigate the implications of mass conservation in fusion and fission processes
USEFUL FOR

Students of physics, mathematicians, and anyone interested in the foundational principles of physical measurements and their mathematical representations.

Happiness
Messages
686
Reaction score
30
Consider this self-evident proposition: "If object A has the same mass as object B and object C separately, then object B has the same mass as object C." Why isn't this stated as a law, but the zeroth law of thermodynamics is?

Is there a physical quantity u such that the u of A is equal to the u of B and separately to the u of C, but the u of B is not equal to the u of C? (It is not right Euclidean.)

Is there a physical quantity u such that the u of A is more than the u of B, and the u of B is more than the u of C, but the u of A is not more than the u of C? (It is not transitive.)

Edit: More precisely, the topic question should be "is the relation brought about by every physical quantity an equivalence relation?", which is rather mouthful.
 
Last edited:
Physics news on Phys.org
A quantity is a property or an attribute, whereas a equivalence relation is a relation between two properties. So its per se not the same thing. As soon as you measure quantities or describe qualities you normally use equations which are per definition a equivalence relation.
E.g. if you look at fusion or fission processes you see that you cannot simply add up masses.
 

Similar threads

Undergrad Variant and Invariant Physical Quantities....
  • · Replies 10 ·
Replies
10
Views
5K
Undergrad Physical reality of nontrivial loops in SO(3)
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Is energy a fundamental physical quantity or a derived one?
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Is "nondimensionalization" a misnomer?
  • · Replies 19 ·
Replies
19
Views
2K
High School Showing that formulae are invariant for all values in the domain
  • · Replies 2 ·
Replies
2
Views
2K
Graduate The Exceptional Jordan Algebra in physics
  • · Replies 4 ·
Replies
4
Views
4K
Equality sign and equivalence relations
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Evidence of Strong Equivalence Principle Violations?
  • · Replies 3 ·
Replies
3
Views
3K
Proving that mass is an additive quantity
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Quantum properties and Van Hove singularty
  • · Replies 5 ·
Replies
5
Views
508