I was making two arguments in the thread, one of which had little to do with Gleason but argued a lesser point, namely:
In your description of the burden, you can't define what 'probability' means in a model-independent way. You can't point at anything verifiable to be explained
call me bluesky-brained but I can't tell whether this is a joke abt being your own worst enemy or you actually have a nemesis
Don't Be A Wokescold About The Enslaved Races is my favorite HP plotline
if you do imaginary time, it must be an ensemble average over vacua.. If not you need boundary conditions which should determine it
(for spont. symmetry breaking one takes the size limit before the limit Ξβ0 of the external field for I think this reason)
There are also branches on which it has always been the left light activating, whenever a gadget is held in a certain orientation and used.
There is nothing special abt these branches, which is exactly why the equal likelihood distribution over branches has itself a special place.
Now I have this big tree. Are there branches which are more 'unlikely' than others? Meaningless question; there simply Are all of these branches. But if I pick one at random I'll see a world in which inhabitants have come to expect a stochastic equal likelihood sampling.
for comparison, imagine a world which as a matter of base reality has a *discrete* branching binary tree structure. Branch points are induced only by 'branch gadgets', which are devices that inhabitants can use to perform a binary measurement. One of 2 lights turns on, and the gadget is used up.
be *actual probabilities* corresponding to my future experience') is incoherent, born from trying to apply single-branch concepts of identity&probability beyond their domain of applicability.
I do think you can't actually give me a Corn rule (Gleason) and this is part of the answer in the 1st sense
what do you mean by 'why I should follow it', though? There is a weak sense of the statement for which the usual theorems, self-locating uncertainty etc, are adequate.
The strong metaphysical interpretation ('why should I expect these numbers that I can uniquely assign to measurement outcomes
I've been consistent abt this I think: 'proving the Born' rule in this very strong sense that you (or also Emily Adlam) want is too strong an ask. Yet this does not count against MWI imo!
(also consistent with observations I should say. Ofc I don't believe other interpretations are consistent with all predictions of textbook QM but that's a separate matter)
The kinds of Born rule violations Rochelle is talking about aren't subtle hard-to-detect things, but separate from that in realistic treatment of MWI certainly the Born rule is only a good approximation
yes, what I'm describing is completely unphysical. But it's only supposed to argue against a specific idea which is itself kind of metaphysical..
of course other interpretations are also consistent; which means we have to weigh the evidence. But the point is that 'it doesn't produce our experience' is not counter-evidence bc not true. And trying to claim it as counter-evidence implicitly makes the exact fallacy you are accusing Everettians of
It's compatible with our observations that we are such, and to say that it doesn't force us to assign future probabilities according to Born rule makes reference to a different notion of probability which you can't define
this is referring to the parenthetical here? In the end I'm probably not saying anything different than Gleason's theorem with that. But it's also not really relevant for the greater point, right? You give me this unitary system; I show you Born-rule agents inside.
that you can sample from it without crossing layers of emergence. If you sampled under the restriction "I always choose spin down for this particular Stern-Gerlach apparatus", that would be cheating
(another thing is that branches presumably don't get arbitrarily thinβat some point of dilution I expect there is just a lot of interference and noise and no emergent branching structure discernible. This kind of thing can actually be clarified in simulations)
If you now say: But it seems a priori unlikely that a Born-rule-experiencer up to time t will continue to follow Born rule, you've made the same move you say is disallowed; assigned some kind of platonic probability to branches.
So I've found Born-rule-following thinking emergent consciousnesses inside of the WF. Whatever else exists, they do. Did the pointer, without influencing the system, create them?(It's also not clear imo whether I could even in principle give an algorithm for finding non-Born-rule-following agents).
Then I choose to externally implement a pointer which picks out a Born-rule-sampled state at all times (or with some tick rate or whatever you need to make it work). If I play back the states pointed at like a movie, I can see a causal world with maybe thinking ppl in it.
imo the fact that a useful emergent description in terms of probabilities exists at all is what emergence means. It's the whole ballgame. But here's a Gedankenexperiment:
Say I have all of this setup of a branching WF but am not convinced that probabilities can emerge for people inside.
we'll just start with the most fundamental physical thing and then go upwards
when C is a stable bound state of A&B, from an S-matrix POV it's in principle just as correct to say that B is a bound state of C&anti-A. The math might be simpler in one presentation, but that's a human thing
inventing "ced" to annoy you
It's been almost two years and still I hear of people calling my IPCO lecture a scandal π
and for uh fans of nonassociative normed division algebras
yes. Sphere or cube is not so important. But if we imagine that fields can take entirely independent values in each individual patch, the entropy would have to scale with the volume as we enlarge our regionβentropy is additive for unions of systems. But it seems to only scale quadratically
with some wishful thinking this shifts the question to 'what makes two patches of space in a D-1 dim. spacetime without gravity distinct?'
