Do you use set theory in Physics?

[marmoset]

I started reading a book on writing proofs (it is all about set theory), and I really enjoy it. If I do physics at uni, will I get to use things like set theory and to write proofs? And if so what specific applications does set theory have in physics?

 

[Phlogistonian]

Physics classes emphasize problem-solving over proof-writing. Set theory is not used directly except in advanced mathematical physics, which you're not likely to see in undergraduate classes. While rigor is preferable to non-rigor, physicists often use non-rigorous "proofs" if they give the right answer (to the perpetual consternation of mathematicians :). If you want to see set theory and proof-writing, take math classes.

 

[sir-pinski]

Yes, set theory is definitely used in physics. In fact, it is a fundamental tool in many areas of physics, including statistical mechanics, quantum mechanics, and relativity.

In statistical mechanics, set theory is used to describe the state space of a system and the interactions between different particles. This is important in understanding the behavior of systems with large numbers of particles, such as gases and liquids.

In quantum mechanics, set theory is used to describe the states of particles and their interactions. For example, the set of all possible states of a particle can be represented by a vector space, and the operators that represent physical observables act as functions on this space.

In relativity, set theory is used to describe the geometry of spacetime and the relationships between different points in space and time. This is essential in understanding the behavior of objects moving at high speeds or in strong gravitational fields.

Overall, set theory is a powerful tool for understanding the fundamental principles and relationships in physics. So if you decide to pursue physics at university, you will definitely encounter it and have the opportunity to use it in your studies.