I would think “probabliistic” should be reserved for things that are actually governed by probabilities. As you know, amplitudes don’t really work like probabilities; if they did, the MWI hypothesis would be unneeded.
You would expect so, but amplitudes just don’t work like probabilities. (Of course, if you are considering the whole wavefunction as the state, then it is deterministic.)
By the way, you might like to read the Scott Aaronson lecture I linked to in my post. Here’s a quote:
I’m going to show you why, if you want a universe with certain very generic properties, you seem forced to one of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics.
Yeah but you can make a “probabilistic” system look “deterministic” as long as you define the “state” in such a way as it includes the entire distribution.
Of course, a person could never observe that ‘final state’, but neither can a person observe the entire wavefunction.
For instance, you’re only allowed to extract one bit of information about the spin of a given electron, even though the wavefunction (of the spin of a single electron) looks like a point on the surface of a sphere. This is analogous to how, given a {0,1}-valued random quantity, when you observe it you only extract one bit of information about it, even though its expectation value could have been anywhere in the interval [0,1].
My motto here is that if a theory is assigning weights to possible worlds then it’s as far away from being deterministic as it’s possible to be.
Suppose you have access to a ‘true random number generator’, and you read off a string of N random bits. You also take N electrons, and you prepare the spins of the electrons such that the i-th electron has spin “up” if the i-th bit is 1, or else “down” if the i-th bit is 0.
Now here’s an interesting fact: There is no experiment anyone could do to determine whether you had chosen “up”/”down” or “left”/”right” as spin directions for your electrons.
In other words, quantum uncertainty and probabilistic uncertainty can combine ‘seamlessly’ in such a way that it’s impossible to say where one ends and the other begins.
You’re ruling out the possibility that the laws of physics are objectively probabilistic. (If they can be ‘objectively quantum’ why not ‘objectively probabilistic’?)
Even if you dogmatically insist that this is impossible in principle, we could still imagine a variation of my ‘Theory 2’ where the coin events are determined by the values of an algorithmically random sequence. The algorithmic randomness would be a property of the sequence itself, not anyone’s knowledge of it.
Quantum superposition has nothing to do with how much you know.
Quantum superposition has “quite a lot” to do with the Born probabilities, and (according to you) the Born probabilities, being mere probabilities, have everything to do with how much you know.
I’m not saying a quantum universe is a probabilistic one. But that’s really the whole point—it’s neither probabilistic nor deterministic (except in the same vacuous sense that you can make it look deterministic if you carry the entire distribution around with you).
We could still imagine a variation of my ‘Theory 2’ where the coin events are determined by the values of an algorithmically random sequence. The algorithmic randomness would be a property of the sequence itself, not anyone’s knowledge of it.
How do you get your hands on an algorithmically random sequence? If our physics isn’t objectively probabilistic, then we can’t even simulate Theory 2.
Is it possible to predict the final state given only the initial state? If so, it’s deterministic. If not, it’s probabilistic.
I would think “probabliistic” should be reserved for things that are actually governed by probabilities. As you know, amplitudes don’t really work like probabilities; if they did, the MWI hypothesis would be unneeded.
You would expect so, but amplitudes just don’t work like probabilities. (Of course, if you are considering the whole wavefunction as the state, then it is deterministic.)
By the way, you might like to read the Scott Aaronson lecture I linked to in my post. Here’s a quote:
Yeah but you can make a “probabilistic” system look “deterministic” as long as you define the “state” in such a way as it includes the entire distribution.
Of course, a person could never observe that ‘final state’, but neither can a person observe the entire wavefunction.
For instance, you’re only allowed to extract one bit of information about the spin of a given electron, even though the wavefunction (of the spin of a single electron) looks like a point on the surface of a sphere. This is analogous to how, given a {0,1}-valued random quantity, when you observe it you only extract one bit of information about it, even though its expectation value could have been anywhere in the interval [0,1].
My motto here is that if a theory is assigning weights to possible worlds then it’s as far away from being deterministic as it’s possible to be.
So, it’s probabilistic?
Read and then get back to me if you still don’t understand where I’m coming from.
I’m not sure how much of a parallel can be drawn between probability and their extension of it.
Probability is a state of your knowledge. Quantum superposition has nothing to do with how much you know.
One last thing—make of it what you will.
Suppose you have access to a ‘true random number generator’, and you read off a string of N random bits. You also take N electrons, and you prepare the spins of the electrons such that the i-th electron has spin “up” if the i-th bit is 1, or else “down” if the i-th bit is 0.
Now here’s an interesting fact: There is no experiment anyone could do to determine whether you had chosen “up”/”down” or “left”/”right” as spin directions for your electrons.
In other words, quantum uncertainty and probabilistic uncertainty can combine ‘seamlessly’ in such a way that it’s impossible to say where one ends and the other begins.
Two things to say:
You’re ruling out the possibility that the laws of physics are objectively probabilistic. (If they can be ‘objectively quantum’ why not ‘objectively probabilistic’?)
Even if you dogmatically insist that this is impossible in principle, we could still imagine a variation of my ‘Theory 2’ where the coin events are determined by the values of an algorithmically random sequence. The algorithmic randomness would be a property of the sequence itself, not anyone’s knowledge of it.
Quantum superposition has “quite a lot” to do with the Born probabilities, and (according to you) the Born probabilities, being mere probabilities, have everything to do with how much you know.
I’m not saying a quantum universe is a probabilistic one. But that’s really the whole point—it’s neither probabilistic nor deterministic (except in the same vacuous sense that you can make it look deterministic if you carry the entire distribution around with you).
How do you get your hands on an algorithmically random sequence? If our physics isn’t objectively probabilistic, then we can’t even simulate Theory 2.