I know that according to the many worlds interpretation, there is no randomness and rather there is a universal wave function that simulates an observer with a continuously branching timeline. My question is if we assume that the theory simulates only one timeline, can we deduce that the the distribution of points in space-time where a photon is absorbed really is algorithmically random?

My question is not whether apparent randomness can be explained by the chaotic nature of hidden variables. If the universe follows such a hidden variable theory and the state at the beginning of time is algorithmically random, the fully deterministic chaotic nature will still produce an algorithmically random sequence of observations. My question is whether the distribution of points in space time where photons get absorbed is random, not whether the future can't be predicted from the present and if the universe follows such a theory of hidden variables with an algorithmically random state at the beginning of time, the answer will still be yes.

Have researchers submitted a photon interference pattern into a computer and run an algorithm to compute whether it has all sorts of properties of randomness? If they did and it computed it not to have all those random properties, then quantum interference is not random. If not, that doesn't necessarily mean it's random. In fact, if it is random, we can never prove it's random. It's easy to prove that for any computable function no matter how rapidly growing, there exists an algorithm that computes within the time of a more rapidly growing function, a number that is algorithmically random within the time of that function.


closed as unclear what you're asking by Aaron Stevens, John Rennie, user191954, Jon Custer, glS Oct 1 '18 at 16:04

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    $\begingroup$ It would help if your question was not just one big block of text :) $\endgroup$ – Aaron Stevens Oct 1 '18 at 3:55

[After discussion with OP, this does not answer the question as intended]

Quantum Theory, as originally formulated, is a stochastic theory. That is the basic mathematical terms in the theory provide predictions in the form of a probability distribution. No attempt is made to explain the algorithmic origin of these distributions.

As you point out, the many worlds interpretation of quantum theory is presented as deterministic theory. However the special way it turns quantum theory into a deterministic theory result in the theory having no more predictive power than the original quantum theory. (It achieves this by essentially giving an anthropic principle type explanation for the apparent quantum randomness).

As a result your question "Have researchers submitted a photon interference pattern into a computer and run an algorithm to compute whether it has all sorts of properties of randomness?" is as ill founded for many worlds theory as it is for the original stochastically formulated quantum theory.

The photon interference pattern only ever provides probabilistic information in either theory.

  • $\begingroup$ Why is my question ill founded? Although we can't know where a photon will land in the future, we can know where photons have landed in the past. I'm just wondering if somebody has run photons through a single slit or double slit at a very low intensity and gotten a record of where all the photons emitted from the source during the experiment that got detected by the screen are and then run a computer program with that specific scattering of dots as an input to see whether it has the expected random properties. $\endgroup$ – Timothy Oct 2 '18 at 18:17
  • $\begingroup$ Yes could do that sorry - I misunderstood you meant using empirical data. I was thinking as a theorist. That makes all my answer invalid to your question. $\endgroup$ – Bruce Greetham Oct 2 '18 at 19:53
  • $\begingroup$ Now your question makes better sense. As far I a know the answer is there is no pattern to the data beyond what QM predicts. LHC has produced enough data to analyse - I assume they would have found something if it was there. $\endgroup$ – Bruce Greetham Oct 2 '18 at 20:02
  • $\begingroup$ Maybe the universe follows De-Broglie Bohm theory with a definable state at the beginning of time so although it's chaotic, interference is not algorithmically random but requires exponential time to compute and since our observations were so long after the beginning of time, we've had nowhere near enough time to detect a pattern in them. $\endgroup$ – Timothy Oct 3 '18 at 2:40
  • $\begingroup$ Don't know - maybe. $\endgroup$ – Bruce Greetham Oct 3 '18 at 7:06

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