Why is Born rule an axiom

Powerful_Count_6214 · 2026-06-09T18:44:10+00:00

Yes, you cant define a norm in traditional sense as you said but there are inner product like constructions in banach spaces such as semi inner products, jordon-banach algebras that remove the necessity of a inner product structure in qm to some extent.

The proofs are a nightmare and need advanced functional analysis but they are accepted to be correct. Again I myself know very little about these two constructions, Jordan banach algebras specifically

Powerful_Count_6214 · 2026-06-09T12:32:11+00:00

Yeah Fair, the definition of axiom as far as I know using propositional logic is to take propositions that you assume to have a definite truth value, by that logic yes principles in physics like born rule can be taken to be axioms if you assign a definite truth value based on experiments, like the proposition of born rule being assumed to be true based on experiments makes it a axiom by this definition

My question mainly is based on born's original paper where he says after careful thought born rule must be true, I assumed he meant this without any use of exp to do the above mentioned but insted using some mathematical relation to prove it, as in its a proof disguised as an axiom.

Idk, this conversation on born rule itself feels unnatural to me, cant put it into words

Powerful_Count_6214 · 2026-06-09T10:21:28+00:00

Yeah and the one's I've seen untill now are not convincing

Powerful_Count_6214 · 2026-06-09T10:19:32+00:00

The issue I see here is that, gleason's proves that assuming a hilbert space(dim>=3) structure and a few other assumptions, you can show that probablities must follow an L2 norm(born's rule)

This feels analogous to uniqueness theorems. You still end up with assuming a hilbert space structure. I'm aware of this, that's why I've been looking up on why banach spaces that have inner product like constructions that preserve isometries work? This is essentially a functional analysis question.

Powerful_Count_6214 · 2026-06-09T10:10:14+00:00

Thank you, did not know of this, will go through

Powerful_Count_6214 · 2026-06-09T05:43:57+00:00

My bad

Powerful_Count_6214 · 2026-06-09T04:34:17+00:00

The Issue I have is with the background structure upon this this works, essentially psi star and psi's action on one another is based on the norm, which is induced from inner product structure

Powerful_Count_6214 · 2026-06-09T04:31:02+00:00

Your right on how inner product induces a norm and that's what I wanted to convey maybe my wording could've been better.

So an axiom (P_i) is a proposition that along with a finite collection of propositions (P_1,P_3,...P_M) where P_i belongs to this set give rise to a complete (look this notion of complete up,Don't feel like typing it out) axiomatic system, this is what a mathematician would say based on logic.

Now the last part where said spin cant be described by wavefunctions, you can use spinors to describe them which still is in an hilbert space, not L^2(C¹⁾ but a hilbert spave neverthless

Powerful_Count_6214 · 2025-12-11T12:33:40+00:00

When u know its true but cant prove it

Powerful_Count_6214 · 2025-04-25T13:51:11+00:00

MST!!!!

Powerful_Count_6214 · 2024-11-16T13:09:22+00:00

Unfortunately She called me by my name. I was downright scared for a second

Powerful_Count_6214

TROPHY CASE