3 ms·
Well I define random to mean whenever P(X|Y) is neither always 1 nor 0, or to put that in causal modal terms: given an exhaustive description of all possible c
by mjburgess 4y ago
Well I define random to mean whenever P(X|Y) is neither always 1 nor 0, or to put that in causal modal terms:
given an exhaustive description of all possible causes of Y, say X, then if X causes Y, *NECESSARILY* Y given X
causation is a form of necessity, necessarily Y occurs or it doesnt
In this case P(Future|Past) and P(Past|Future) are somewhere between 0 and 1. This isnt consistent with causation.
ie., All possible information about all possible causes of Y (the future), say X (the past) are insufficient to gaurentee any given Y (any particular future).
The "interpretation" element of QM is to say that we are really in this case, ie., that we have X = all possible information.
There are several ways of denying that P(Y|X) in the case of QM should be read this way. You can say X is incomplete, either by saying there is non-local information we don't have, or global information we don't have. Of the "global" kind, which of many worlds we are in is a kind of global ignorance.
So that if we had, P(Y|X, which-world) then we'd observe P(Y|X, whichworld) = either 1 or 0 --- as with classical mechanics
P(CatDead|PoisonBox, worldA) = 1
P(CatDead|PoisonBox, worldB) = 0
etc.
and, eg., P(F|G,M,m,r) = 1 if F=GMm/r^2
- blueprint 4y agowhat do you mean by the term information? My question is, rather, whether a system needs to be able to know it knows that information for it not to still be causal. Because it doesnt observe its whole wavefunction
- mjburgess 4y agoI dont understand your use of "knows", knowing isnt part of the problem. Imagine, for simplicty sake, a world is a series of four switches which we can describe by 0 (off),1 (on). Eg., world A at time 0 is 0000, at time 1, 0001, ... Now a change from 0000 to 0001 is causal if in every physically possible world 0001 follows 0000, ie., P(0001|0000) = 1 Now suppose that we enumerate every possible world, ie., all the worlds containing only this kind of switch, and only four of them. Now if 40% of the worlds had 0000->0001 and 60% had 0000->1000, then P(0001|0000) = 0.4 The question is how can it be that the fourth switch behaves randomly? Ie., without any necessary flip from 0 to 1. Nothing at all can cause that switch to flip, by definition, the world contains nothing else in it. What property does the switch have such that it turns on 40% of the time? NONE. Consider two resolutions to this problem: bite the bullet and say the switch is "miraculous in some sense" in that it "just turns on" sometimes; OR, say that this thought experiment is physically impossible and we're missing information. Eg., that there's a hidden switch: 10000->10001 always, and 00000->11000 always, we just can't see the first switch, so it looks random.
- blueprint 4y ago"Imagine, for simplicty sake, a world is a series of four switches which we can describe by 0 (off),1 (on)." If that's what the world is then there's no "we"