That's so Random

Can randomness come from deterministic machines?

Your not-so-random coin flip...

Throughout life we use coin flips... pseudo Random Preditable because:

• Initial forces
• starting position
• Anular momentum
• air resistance

It's just a complex mathematical equation. We call this epistemic randomness (think of epistemology in philosphy) -> randomness due to lack of knowledge.

In quatum randomness, or true randomness, the perceived randomness isn't due to nature itself, the outcome is inherently probalistic. We call this ontic randomness (think of ontology in philosophy), pertaining to being.

The collapse of the wavefunction, assuming a coprenhagen interpretation, (even if you knew the wavefunction beforehand) into a single state is the onticly random process. There are other ideas of how this randomness manifests like if actually all possible outcomes are occurring simultaneously and we can only observe one. But regardless, the randomness is still present.

You may now be asking the same question I did when first condsidering different types of randomness: how can we prove that quantum events are truely 'onticly' random and there aren't jus some hidden variables we're missing? We'll know you're with an esteemed crowed; Einstein also asked and hoped for an affirmative answer to this question in the early 1900s; "God does not play dice with the universe".

Fortunately John Bell found a remarkable way to test this. Let's start with a concrete example. Imagine we have a source creating pairs of entangled particles. We send one particle to Alice and one to Bob, who are far apart. Each can measure their particle's spin along any axis they choose. Quantum mechanics says these measurements will be correlated in specific ways. Now, here's the key insight: If there were hidden variables determining the outcomes, these variables would have to be "local" - meaning they can't communicate faster than light. Bell realized this locality requirement would put mathematical constraints on how correlated Alice's and Bob's measurements could be. Here's how the math works: Let's say Alice and Bob each can measure their particle's spin along three different angles (call them 1, 2, and 3). For each particle pair, hidden variables would have to pre-determine what result Alice and Bob would get for any measurement angle they might choose. This is like having a list of instructions carried along with each particle. Bell showed that if such hidden variables exist, then this inequality must be true: |C(1,2) - C(1,3)| ≤ 1 + C(2,3) Where C(a,b) is the correlation between measurements at angles a and b. This is one form of Bell's inequality. But - and this is the revolutionary part - quantum mechanics predicts correlations that violate this inequality! For certain measurement angles, quantum mechanics says the correlations will be stronger than any local hidden variable theory could possibly produce. Think about what this means: Bell found a way to mathematically prove that no theory based on local hidden variables could ever reproduce the predictions of quantum mechanics. It's not just that we haven't found the right hidden variables - Bell proved they cannot exist. The experimental tests of Bell's inequalities involve measuring many pairs of entangled particles at different angles and calculating these correlations. Modern experiments have confirmed quantum mechanics' predictions with extraordinary precision, ruling out local hidden variables conclusively. This leads to a profound conclusion: either we must give up locality (allowing faster-than-light influences), or we must accept that the quantum world is inherently indeterministic. Most physicists accept the second option, as it preserves special relativity.

How do random number generators work?

True and pseduo randomness

Quatum randomness

Where is the qunatum randomness (wavefor collapse - copenhagen, multi-worlds etc)

Explain "what about if we don't have all the information"?

Explain it back into Bells experiment (1964)

Link it back into quantum random number generators