Suppose they are not fundamental, suppose the ultimate layer of physics—maybe superstrings, maybe something else—generates the various outcomes in its own way, like a computer (digital or analog) forking processes...
and we subjectively experience outcomes according to the Born probabilities because this is the correct answer to the question about subjective experience probability.
That’s indeed what we should all be hoping for. But what possible set of “axioms” for subjective experience—never mind what possible underlying physics—could correspond to the Born probabilities, while solving the computer-processor trilemma as well?
Well… following this line of thought, we should expect that the underlying physics is not special, because any physics that satisfies certain generic properties will lead to subjective experience of the Born probabilities.
Suppose we can therefore without loss of generality take the underlying physics to be equivalent to a digital computer programmed in a straightforward way, so that the quantum and computer trilemmas are equivalent.
Is there any set of axioms that will lead (setting aside other intuitions for the moment) to subjective experience of the Born probabilities in the case where we are running on a computer and therefore do know the underlying physics? If there is, that would constitute evidence for the truth of those axioms even if they are otherwise counterintuitive; if we can somehow show that there is not, that would constitute evidence that this line of thought is barking up the wrong tree.
we should expect that the underlying physics is not special, because any physics that satisfies certain generic properties will lead to subjective experience of the Born probabilities.
Well basically, we start off with the claim (which I can’t confirm of my own knowledge, but have no reason to doubt) that the Born rule has certain special properties, as explained in the original post.
We observe that the Born rule seems to be empirically true in our universe.
We would like an explanation as to why our universe exhibits a rule with special properties.
Consider the form this explanation must take. It can’t be because the Born rule is encoded into the ultimate laws of physics, because that would only push the mystery back a few steps. It should be a logical conclusion that we would observe the Born rule given any underlying physics (within reason).
Of course there is far too much armchair handwaving here to constitute proof, but I think it at least constitutes an interesting conjecture.
Well, even if it turns out that there’re special properties of our physics that are required to produce the Born rule, I’d say that mystery would be a different, well, kind of mystery. Right now it’s a bit of “wtf? where is this bizzaro subjective nonlinearity etc coming from? and it seems like something ‘extra’ tacked onto the physics”
If we could reduce that to “these specific physical laws give rise to it”, then even though we’d still have “why these laws and not others”, it would, in my view, be an improvement over the situation in which we seem to have an additional law that seems almost impossible to even meaningfully phrase without invoking subjective experience.
I do agree though that given the special properties of the rule, any special properties in the underlying physics that are needed to give rise to the rule should be in some sense “non arbitrary”… that is, should look like, well, like a nonaribitrarily selected physical rule.
Sounds like a right question to me. Got an answer?
A related problem: If we allow unbounded computations, then, when we try to add up copies, we can end up with different limiting proportions of copies depending on how we approach t → infinity; and we can even have algorithms for creating copies such that their proportions fail to converge. (1 of A, 3 of B, 9 of A, 27 of B, etc.) So then either it is a metaphysical necessity that reality be finite, because otherwise our laws will fail to give correct answers; or the True Rules must be such as to give definitive answers in such a situation.
I’m afraid I’m not familiar enough with the Born probabilities to know how to approach an answer—oh, I’ve been able to quote the definition about squared amplitudes since I was a wee lad, but I’ve never had occasion to actually work with them, so I don’t have any intuitive feel about their implications.
As for the problem of infinity, you’re right of course, though there are other ways for that to arise too—for example, if the underlying physics is analog rather than digital. Which suggests it can’t be fiated away. I don’t know what the solution is, but it reminds me of the way cardinality says all shapes contain the same number of points, so it was necessary to invent measure to justify the ability to do geometry.
Deeply fundamentally analog physics, ie, infinite detail, would just be another form of infinity, wouldn’t it? So it’s a variation of the same problem of “what happens to all this when there’s an infinity involved?”
Sorry, I may have been unclear. I didn’t mean to make a claim that physics actually does have this property, but rather I was saying that if physics did have this property, it would just be another instance of an infinity, rather than an entirely novel source for the problem mentioned.
(Also, I’m unclear on the BB, if it takes into account possible future tech that may be able to manipulate the geometry of spacetime to some extent. ie, if we can do GR hacking, would that affect the bound or are the limits of that effectively already precomputed into that?)
That’s indeed what we should all be hoping for. But what possible set of “axioms” for subjective experience—never mind what possible underlying physics—could correspond to the Born probabilities, while solving the computer-processor trilemma as well?
Well… following this line of thought, we should expect that the underlying physics is not special, because any physics that satisfies certain generic properties will lead to subjective experience of the Born probabilities.
Suppose we can therefore without loss of generality take the underlying physics to be equivalent to a digital computer programmed in a straightforward way, so that the quantum and computer trilemmas are equivalent.
Is there any set of axioms that will lead (setting aside other intuitions for the moment) to subjective experience of the Born probabilities in the case where we are running on a computer and therefore do know the underlying physics? If there is, that would constitute evidence for the truth of those axioms even if they are otherwise counterintuitive; if we can somehow show that there is not, that would constitute evidence that this line of thought is barking up the wrong tree.
Elaborate on that bit please? Thanks.
Well basically, we start off with the claim (which I can’t confirm of my own knowledge, but have no reason to doubt) that the Born rule has certain special properties, as explained in the original post.
We observe that the Born rule seems to be empirically true in our universe.
We would like an explanation as to why our universe exhibits a rule with special properties.
Consider the form this explanation must take. It can’t be because the Born rule is encoded into the ultimate laws of physics, because that would only push the mystery back a few steps. It should be a logical conclusion that we would observe the Born rule given any underlying physics (within reason).
Of course there is far too much armchair handwaving here to constitute proof, but I think it at least constitutes an interesting conjecture.
Well, even if it turns out that there’re special properties of our physics that are required to produce the Born rule, I’d say that mystery would be a different, well, kind of mystery. Right now it’s a bit of “wtf? where is this bizzaro subjective nonlinearity etc coming from? and it seems like something ‘extra’ tacked onto the physics”
If we could reduce that to “these specific physical laws give rise to it”, then even though we’d still have “why these laws and not others”, it would, in my view, be an improvement over the situation in which we seem to have an additional law that seems almost impossible to even meaningfully phrase without invoking subjective experience.
I do agree though that given the special properties of the rule, any special properties in the underlying physics that are needed to give rise to the rule should be in some sense “non arbitrary”… that is, should look like, well, like a nonaribitrarily selected physical rule.
Sounds like a right question to me. Got an answer?
A related problem: If we allow unbounded computations, then, when we try to add up copies, we can end up with different limiting proportions of copies depending on how we approach t → infinity; and we can even have algorithms for creating copies such that their proportions fail to converge. (1 of A, 3 of B, 9 of A, 27 of B, etc.) So then either it is a metaphysical necessity that reality be finite, because otherwise our laws will fail to give correct answers; or the True Rules must be such as to give definitive answers in such a situation.
I’m afraid I’m not familiar enough with the Born probabilities to know how to approach an answer—oh, I’ve been able to quote the definition about squared amplitudes since I was a wee lad, but I’ve never had occasion to actually work with them, so I don’t have any intuitive feel about their implications.
As for the problem of infinity, you’re right of course, though there are other ways for that to arise too—for example, if the underlying physics is analog rather than digital. Which suggests it can’t be fiated away. I don’t know what the solution is, but it reminds me of the way cardinality says all shapes contain the same number of points, so it was necessary to invent measure to justify the ability to do geometry.
Deeply fundamentally analog physics, ie, infinite detail, would just be another form of infinity, wouldn’t it? So it’s a variation of the same problem of “what happens to all this when there’s an infinity involved?”
To the best of our understanding, there’s no such thing as “infinite detail” in physics. Physical information is limited by the Bekenstein bound.
Sorry, I may have been unclear. I didn’t mean to make a claim that physics actually does have this property, but rather I was saying that if physics did have this property, it would just be another instance of an infinity, rather than an entirely novel source for the problem mentioned.
(Also, I’m unclear on the BB, if it takes into account possible future tech that may be able to manipulate the geometry of spacetime to some extent. ie, if we can do GR hacking, would that affect the bound or are the limits of that effectively already precomputed into that?)
Yes, that is my position on it.