G

#### glen herrmannsfeldt

(snip)

Thinking about it again, the coupling between the two, classically,

is the probability of the particle emitted from one hitting the other.

That makes the argement for it being squared more obvious.

You can predict something based upon that overlap, but what you can

predict is only a shift in the probability distribution. The actual

decay time is still a perfectly random selection from that distribution.

You cannot predict the actual time until the next decay. No matter how

much information you have, the time until the next decay could be either

arbitrarily long or arbitrarily short, without violating any of the laws

of quantum physics as they are currently understood. That is the

fundamental distinction between quantum randomness and

pseudo-randomness. If you knew the full internal state of a

pseudo-random number generator, and the algorithm it uses, you could

determine the next random number precisely.

Yes. About the only point I was trying to make is that in quantum

mechanics things are rarely infinite and rarely zero, but instead

really huge and really tiny.

(snip)

It's not just a matter of some of the universe's state information being

hidden from us. Einstein, Podalsky and Rosen (EPR) tried to interpret

quantum uncertainty as being due to "hidden variables" - state

information about the universe that we were unaware of (and which we

might inherently be incapable of being aware of). They deliberately left

the details of what that state information was and how it influences the

measurements completely unspecified. Despite leaving it unspecified,

they were able to describe a quantum-mechanical experiment, and a

statistic that could be calculated from measurements that could be taken

while running that experiment. They rigorously derived a requirement

that this statistic must be greater than or equal to 1, regardless of

how the hidden variables actually worked. Quantum mechanics, on the

other hand, predicted that the value of that statistic should be 0.5.

From this, EPR concluded that quantum mechanics was unrealistic, and

could therefore be, at best, only an approximation to reality.

OK, but it is a slightly different problem. To make EPR tests work,

you have to be careful that you don't disturb the quantum state.

For quantum randomness, you want the systems to be uncoupled, but

will find that there is (a very small amount) of coupling.

At the time their paper was published, it was not possible to conduct

the experiment with sufficient precision to clearly distinguish a value

of 1 from a value of 0.5. Many years later, when scientist were finally

able to perform it, reality decided not to cooperate with EPR's concept

of "realism". The measured value unambiguously confirmed the quantum

mechanical prediction, violating the constraint that EPR had derived

from assuming that hidden variables were involved.

Scientists still believe that quantum mechanics can only be an

approximation to reality - but it's no longer because of the

fundamental role that true randomness plays in the theory.

More specifically, and the experiment that took longer to do than

some other ones, two particles can be created coupled, separated

in distance, and then have their state measured. Even when the

time between the two measurements is less than the distance

bewteen them divided by c, (so that no signal could propagate)

they are still found to keep their state.

I don't want to start an extended discussion of EPR - even experts get

into long pointless arguments talking about it. I just want to say that,

when I talk about "really random", I'm talking about the kind of thing

that EPR were implicitly assuming was inherently impossible when they

derived their limit equation.

Yes. The point that I was trying to make, with a very simplified

example, is that quantum systems, like PRNGs, have a finite number

of states. It might be a really huge number, though.

And then you have to extract some of that state information and

generate bits from it.

-- glen