Relationship Of Physics And Theorems

[BOAS]

Hello,

this question is born out of my first semester of lab coursework where for the first time, I was properly introduced to understanding error propagation.

I'll get right to the question and expand upon it afterwards.

What is the role of theorems in physics?

I've heard people go on and on about how proof is for mathematics and alcohol, but clearly they do have a place in physics, and not just in the maths classes. To take a simple example, the work-energy theorem states that W = K.E_f - K.E_i. I'm aware of how one arrives at this by bringing together a number of ideas, but not the actual proof, though that's not really what I'm trying to get at.

So, when doing an experiment I measure my quantities involved and estimate the uncertainties in their values and propagate the errors accordingly. But, this does assume that the equations used to relate ideas together are 'true'.

I really don't want to have a discussion about "what if all of it is wrong", because I understand that theories get shown to be inadequate, we make better ones and move on. But what I do wish to know, is how do we come up with theorems that describe the natural world when there is uncertainty in all the quantities.

One solution to my question that would make some sense is that certain quantities are defined. Momentum is mass * velocity and so on.

Thanks for reading, I hope my points are clear.

BOAS

 

[mathman]

The general idea is to try to put together coherent theories to describe physical phenomena. The theory starts with certain assumptions about reality and theorems deduced from these assumptions lead to testable results.

Simple example - special relativity: Assume the speed of light is constant in all inertial reference frames - from this the Lorentz transformation and the mass-energy equivalence can be deduced.

 

[Claude Bile]

Equations contain quantities are either defined (like work, momentum, etc.) or themselves possesses an uncertainty.

Even fundamental constants have uncertainties based on how well we can measure them.

Claude.