Well, this is precisely the issue that Einstein, Dirac, Bohr, Heisenburg and others were discussing around the 1920s. It was very much the 'hot topic' of the day.
Why does there appear to be a
necessary incompleteness, a randomness, in every physical system?
Could it be that there is some deeper, more powerful theory at work? Some theory that involves hidden variables that work a classical, deterministic way and yet still agrees with the probabilistic results of quantum mechanics?
The answer is
no, and the reason is by something called
Bell's theorem. I can try and explain it in fairly simple terms, but bear in mind there's a lot I'm leaving out..
Anovis and Bobbert are doing an experiment on some particle which is either
or
depending on the angle at which you look at it.
Some source emits entagled pairs of these particles, so if you look at them from the same angle they will
both look the same. The two are sent in opposite directions.
Anovis has a detector at one end of the room, Bobbert has a detector at the other end of the room. The detectors tell whether the particle is
or :gbk:, and the detectors are independent of eachother.
Anovis and Bobbert randomly rotate their detectors at one of three angles, after every time the source emits a particle. Because the particles are entagled, Anovis and Bobbert will report the same thing every time they happen to be at the same angle. Also, Anovis and Bobbert will measure the same thing for half of all runs when their detectors are set arbitrarily and independently to one of the three angles.
Suppose there is a particle that looks
from angles 1 and 2, and
from angle 3.
Anovis and Bobbert will both observe the same thing when:
- Anovis is at angle 1, and Bobbert is at angle 1.
- Anovis is at angle 2, and Bobbert is at angle 2.
- Anovis is at angle 1, and Bobbert is at angle 2.
- Anovis is at angle 2, and Bobbert is at angle 1.
- Anovis is at angle 3, and Bobbert is at angle 3.
There are
five different configurations for Anovis and Bobbert to observe the same thing.
Anovis will observe
and Bobbert will observe
when:
- Anovis is at angle 3, and Bobbert is at angle 1.
- Anovis is at angle 3, and Bobbert is at angle 2.
- Anovis is at angle 1, and Bobbert is at angle 3.
- Anovis is at angle 2, and Bobbert is at angle 3.
There are
four different configurations for Anovis and Bobbert to observe different things.
So, with Anovis and Bobbert randomly rotating their detectors to one of three angles, the probability of them observing the same thing is
5/9.
Now, remember that Anovis and Bobbert can only measure one angle at a time, and what they learn from one angle cannot tell them what they will observe from another. So there are only two pieces of information learnt (one from each particle), out of a possible three (three angles). The one unobserved value is the hidden variable.
So, with this (classical, deterministic) hidden variable, the proportion of times the detectors measure the same shape must be greater than 5/9.
However, Quantum Mechanics predicts that the same shape occurs only 1/2 of the time.
So Quantum Mechanics and 'local hidden variable' theory are incompatable. This was, for a long time, seen as a weakness in Quantum Mechanics - but after copious experimental work, it is found that Quantum Mechanics is correct. In fact, Quantum Mechanics is the most experimentally verified theory ever. There are no 'hidden variables'.
The random, probabilistic nature that Quantum Mechanics predicts and experimentalists have confirmed must be due to something else..
