Is Quantum randomness true randomness? [closed]

Question

I would like you guys to read it, and see whether it makes sense, and correct me if anything is wrong.

I'm not an expert on these topics, so I understand if very wrong. It would be wonderful if you could provide advice, and any changes that would correct any mistakes I made.

(Don't judge!)

Thanks.

True randomness

What is randomness? Randomness to humans can be considered, ‘unknown, unidentified, or suspiciously out of place’. For example, let’s say you flip a coin. Whether it lands heads or tails, you would say that this experiment has a random outcome. However, this definition of random could be considered subjective; if you gave all the initial conditions of the coin flip, from the force applied on the coin, to the temperature and pressure of the atmosphere, to a computer. Provided given enough time, the computer would be able to exactly predict the final outcome, showing that a coin flip is actually only pseudorandom; statistically random, but not truly random. Its outcome is causal, and so deterministic.

So in the end, what humans consider random, is only in fact a limitation in the computational power of our minds, where there are too many factors to take into consideration. Or to an extent, where the tiniest change to one of an infinite number of factors can completely change the outcome of anything that has a probabilistic result. This is a great demonstration of chaos theory, and how so many things in this universe seem to lack order or pattern. How even the smallest differences in the variables of an equation, can cause an exponential change in its result; the butterfly effect.

Does true randomness exist? Theodore Motzkin said ‘while disorder is more probable in general, complete disorder is impossible’; ‘true randomness is impossible to achieve’. If true randomness existed, that would assume that the universe can be completely random, ignoring all laws and principles of mathematics that define ‘order’. That would prove that mathematics is contingent, and so all mathematical propositions would be empirical propositions. However, this statement could be rebutted, through the appearance of seemingly ‘truly’ random events in the quantum world.

Quantum indeterminacy When involving the quantum world, true randomness becomes evident. Quantum theory itself, is not a deterministic theory. In a quantum experiment, its outcomes are truly probabilistic. Could still be pseudorandom, we only assume it to be true randomness.

Schrödinger’s cat is a great example that demonstrates the indeterminacy of quantum systems. If you were to seal a cat in a box with a vial of poison, you would not be able to tell if the cat was still alive or had accidentally knocked the vial poisoning itself. Until you open the box, the cat could be considered as both simultaneously dead and alive; in a state of superposition. Quantum systems can also exist in superposition; their position or states are unknown until measured. Wave functions can be used as a mathematical way to describe the wave state of a particle. Were you to fire a single photon at a double slit, the photon would have a set probability of passing through either slit. So without measuring it, the photon is in a state of superposition, travelling through both simultaneously, where its wave function denotes the probabilities of which slit it will travel through. If we were to detect which slit the photon passed through, then its wave function would essentially ‘collapse’. This is because we have forced the photon into a position eigenstate, where it has to travel through only one of the slits. There is no way to predict which slit the photon's forced position will be in, so the result is truly random.

Proof of quantum randomness (Arguments for true randomness) Einstein himself rejected quantum indeterminism, as he famously said, ‘God does not play dice with the universe’, believing that quantum mechanics was merely incomplete. Albert Einstein, Brian Podolsky and Nathan Rosen wrote an article that questioned the completeness of quantum mechanics. This paper then became the basis of a thought experiment known as the EPR paradox. EPR theory states that the theories in quantum mechanics must be local, meaning their objects that cannot travel faster than the speed of light. If the EPR theory is correct, then quantum mechanics is incomplete, as it has to be explained by local theories, which makes quantum theory deterministic. This theory specifically points out how quantum entanglement is counter-intuitive, as ‘communication’ between particles cannot be faster than the speed of light.

However, this has been proven wrong because of Bell’s theory. In 2022, Physicians won a Nobel prize for proving Bell’s theory, which states that there are no hidden local variable theories in quantum theory. ‘All theories with hidden variables should show a correlation between the results that must be lower or at most equal to a specific value; bells inequality‘

They proved this using entangled photons, which violated Bell’s inequality, showing that quantum entangled particles are connected, and so the EPR theory is false as there are no local hidden variable theories that can explain otherwise. As quantum entanglement is dependent on the superposition of both particles, then the theories of superposition must be non-local, as no local hidden variable theories can accurately predict quantum mechanics. Making it truly indeterministic.

In the end, Bell's theory shows that quantum theories have to be non-local because local (and classical) theories cannot be used to explain the indeterminacy of the quantum world, and so there is clear evidence to prove that quantum theory is complete and that there are no hidden factors that we are missing.

This would imply that the quantum world is definitively probabilistic and so truly random.

Answer 1

I think both Nathan and Flatterman have the right idea in the comments. Perhaps they are not saying it right. Here is my attempt.

There are technical definitions of randomness, but I think an intuitive feel for it might be more helpful here. Perhaps the key idea might be predictability.

Before quantum mechanics, the universe was thought to be deterministic - ruled by cause and effect. If you knew the state of the universe perfectly and the laws of physics, you could predict all future states.

If you did not know it perfectly, you can make a prediction, but it won't be perfectly accurate. You can repeatedly set up an experiment and make a measurement. You can predict the outcome based on your best estimate of the state. You cannot predict errors, the deviations from that outcome. The errors are random. This is one meaning of the word random. Unpredictable because you don't have enough knowledge. Somebody with more accurate knowledge might make better predictions.

Quantum randomness is something else. The state of a system is a wave function. It allows you to predict probabilities of various outcomes of measurements. Beyond the probabilities, the outcomes are unpredictable. Nothing in the universe correlates to the actual outcomes. No better knowledge exists that could improve predictions. Again this is randomness.

So there are two closely related concepts. Calling one "true" randomness is vocabulary.