Here's a weird thing about randomness that has always bothered me:
In quantum mechanics, if you measure two incompatible observables (like position and momentum) of a system, and then repeat that experiment many times, you will get two lists of real numbers. QM says you can predict the distribution of these numbers, but you cannot predict the individual numbers themselves. The popular way of thinking nowadays is that "the universe is just inherently random".
So I posed the question on the Physics Stack Exchange: how do we know these numbers are truly random, and not the result of some as-yet-undiscovered pseudorandom number generator that is nonetheless deterministic? Luboš Motl (Czech string theorist) replied (a bit abrasively I might add) that yes, the numbers are truly random and plenty of experiments have ruled out the loopholes. Now, there's no way to determine if a set of numbers are truly random, so how he made this bold matter-of-fact statement is beyond me.
Einstein initially believed in "hidden variable" theories, undiscovered properties of quantum systems. Most of these have been ruled out by experiment (this is what Lubos mentioned), but really, this doesn't apply at all to my question of whether those numbers are random or not. Superdeterminism seems to still allow non-randomness, but for some reason, most physicists (notably excepting Gerard t'Hooft) have discounted superdeterminism as nonsense.
Maybe the issue is the Einstein-Podolsky-Rosen problem: if the numbers are being generated deterministically, they're somehow being communicated superluminally between entangled particles, which implies that in some relativistic frames of reference they're being communicated into the past? I guess I should learn enough about QM to really understand this stuff instead of guessing.
Yes, that is the thing: Bell's inequality has been verified experimentally and that leads to a non-hidden variables reality (for the usual meaning of 'reality'):
I'm just an engineer, so I'm not actually trying to challenge accepted thinking.
However, it is well known that any QM system can be simulated using a classical computer, with the penalty of exponential slowdown. Let's say that I have a hypothetical, ultra-powerful classical computer and I want to simulate a gigantic system of particles including aggregates of particles (e.g. people) performing measurements of other particles. When it comes time to determine the particular values for these measurements, I must generate a random number from a Gaussian distribution. So I use something like the Mersenne Twister. From the perspective of the simulated people, their observations would entirely match our own observations in studying a quantum system.
tl,dr: state isn't necessarily a one particle concept or a local concept. Individual particles have their own properties (spin, charge, etc.) and then maybe a collection of a million particles also has unique properties.
But my proposal is basically superdeterminism, which -- while being a loophole that has yet to be ruled out -- is unpopular. Since I'm not sure why, I guess I would need to get a degree in theoretical physics to find out.
Comments
Here's a weird thing about randomness that has always bothered me:
In quantum mechanics, if you measure two incompatible observables (like position and momentum) of a system, and then repeat that experiment many times, you will get two lists of real numbers. QM says you can predict the distribution of these numbers, but you cannot predict the individual numbers themselves. The popular way of thinking nowadays is that "the universe is just inherently random".
So I posed the question on the Physics Stack Exchange: how do we know these numbers are truly random, and not the result of some as-yet-undiscovered pseudorandom number generator that is nonetheless deterministic? Luboš Motl (Czech string theorist) replied (a bit abrasively I might add) that yes, the numbers are truly random and plenty of experiments have ruled out the loopholes. Now, there's no way to determine if a set of numbers are truly random, so how he made this bold matter-of-fact statement is beyond me.
Einstein initially believed in "hidden variable" theories, undiscovered properties of quantum systems. Most of these have been ruled out by experiment (this is what Lubos mentioned), but really, this doesn't apply at all to my question of whether those numbers are random or not. Superdeterminism seems to still allow non-randomness, but for some reason, most physicists (notably excepting Gerard t'Hooft) have discounted superdeterminism as nonsense.
Motl, abrasive? Surprised?
Maybe the issue is the Einstein-Podolsky-Rosen problem: if the numbers are being generated deterministically, they're somehow being communicated superluminally between entangled particles, which implies that in some relativistic frames of reference they're being communicated into the past? I guess I should learn enough about QM to really understand this stuff instead of guessing.
Yes, that is the thing: Bell's inequality has been verified experimentally and that leads to a non-hidden variables reality (for the usual meaning of 'reality'):
http://en.wikipedia.org/wiki/Bell%27s_theorem
Even weirder http://arstechnica.com/science/2012/04/decision-to-entangle-...
how do you expect to implement the "as-yet-undiscovered pseudorandom number generator" without any state ("hidden variables")?
I'm just an engineer, so I'm not actually trying to challenge accepted thinking.
However, it is well known that any QM system can be simulated using a classical computer, with the penalty of exponential slowdown. Let's say that I have a hypothetical, ultra-powerful classical computer and I want to simulate a gigantic system of particles including aggregates of particles (e.g. people) performing measurements of other particles. When it comes time to determine the particular values for these measurements, I must generate a random number from a Gaussian distribution. So I use something like the Mersenne Twister. From the perspective of the simulated people, their observations would entirely match our own observations in studying a quantum system.
tl,dr: state isn't necessarily a one particle concept or a local concept. Individual particles have their own properties (spin, charge, etc.) and then maybe a collection of a million particles also has unique properties.
But my proposal is basically superdeterminism, which -- while being a loophole that has yet to be ruled out -- is unpopular. Since I'm not sure why, I guess I would need to get a degree in theoretical physics to find out.