One can think of Everettian multiverse quantum mechanics as beginning by proposing two theses:
The global wavefunction evolves according to the Schroedinger equation.
Superpositions in the global wavefunction can be correctly interpreted as equally real branches in a multiverse.
But prima facie, these two theses don’t fit with observation. If one prepares a quantum system in a (3/5)|↑⟩+(4/5)|↓⟩ spin state, and then observes the spin, one will will observe spin up in |3/5|^2=9/25 cases and spin down in |4/5|^2=16/25 cases. But (roughly speaking) there will be two equally real branches corresponding to this result, and so prima facie one would expect equally likely observations, which doesn't fit observation. But the Everettian adds a third thesis:
- One ought to make predictions as to which branch one will observe proportionately to the square of the modulus of the coefficients that the branch has in the global wavefunction.
Since Aristotelian science has been abandoned, there has been a fruitful division of labor between natural science and philosophy, where investigation of normative phenomena has been relegated to philosophy while science concerned itself with the non-normative. From that point of view, while (1) and (less clearly but arguably) (2) belong to the domain of science, (3) does not. Instead, (3) belongs to epistemology, which is study of the norms of thought.
This point is not a criticism. Just as a doctor who has spent much time dealing sensitively with complex cases will have unique insights into bioethics, a scientist who has spent much time dealing sensitively with evidence will have unique insights into scientific epistemology. But it is useful, because the division of intellectual labor is useful, to remember that (3) is not a scientific claim in the modern sense. And there is nothing wrong with that as such, since many non-scientific claims, such as that one shouldn’t lie and that one should update by conditionalization, are true and important to the practice of the scientific enterprise.
But (3) is a non-scientific claim that is absurd. Imagine that a biologist came up with a theory that predicted, on the basis of their genetics and environment, that:
- There are equal numbers of male and female infant spider monkeys.
You might have thought that this theory is empirically disproved by observations of a lot more female than male infant spider monkeys. But our biologist is clever, and comes up with this epistemological theory:
- One ought to make predictions as to the sex of an infant spider monkey one will observe in inverse proportion to the ninth power of the average weight of that sex of spider monkeys.
And now, because male spider monkeys are slightly larger than females, we will make predictions that roughly fit our observations.
Here’s what went wrong in our silly biological example. The biologist’s epistemological claim (5) was not fitted to the actual ontology of the biologist’s theory. Instead, basically, the biologist said: when making predictions of future observations, make them in the way that you should if you thought the sex ratios were inversely proportional to the ninth power of the average weights, even though they aren’t.
This is silly. But exactly the same thing is going on in the Everett case. We are being told to make predictions in the way you should if the modulus squares of the weights in the superposition were chances of collapse. But they are not.
It is notorious that any scientific theory can be saved from empirical disconfirmation by adding enough auxiliary scientific hypotheses. But one can also save any scientific theory from empirical disconfirmation by adding an auxiliary philosophical hypothesis as to how confirmation or disconfirmation ought to proceed. And doing that may be worse than obstinately adding auxiliary scientific hypotheses. For auxiliary scientific hypotheses can often be tested and disproved. But an auxiliary epistemological hypothesis may simply close the door to refutation.
To put it positively, we want a certain degree of independence between epistemological principles and the ontology of a theory so that the ontology of the theory can be judged by the principles.
Comment delete due to sarcasm. Sad, because there was actually a point in that was important.
ReplyDeleteAlex
ReplyDeleteWhy don't you simply address the important point?
Fair enough. As I remember it, the idea was basically to consider a case where we have a region R divided into two subregions, A and B, of unequal non-zero areas, and a point is randomly chosen in R, and the universe branches depending. Then it's a mistake to think there are only two branches coming out. There are infinitely many, one for each point in R. It then makes sense to identify the probabilities of A and B with the areas of the two regions.
ReplyDeleteIn response, I'd first say that there are some difficulties here. Technically, both regions have the same infinite number of points (the cardinality of the continuum) so there are equally many A-type and B-type branches. So the proposal to go with the area needs further work to justify.
But more importantly, the way the quantum spin probabilities work, it's not like there are more ways of getting spin down than spin in my case. Spin up and spin down are the only two possible outcomes (assuming we idealize; in a non-ideal situation, there are other options such as the observational apparatus catching on fire, etc.; moreover, there is branching going on due to all sorts of other quantum stuff going on all the time in the universe). The differences in spin up/down probabilities are NOT due to differences in numbers or measures of more fine-grained results. There is just up and down. So there are only two branches (again, idealizing).
I wasn't sarcastic here, Alexander.
ReplyDeleteI still don't know, how exactly your previously stated and claimed "theorem" follows from an "ad reductio absurdum". Nothing in that roughly put - really roughly put "proof" of yours makes any sense at all.
Besides that, from "equally real" branches doesn't follow those branches to be "equally likely", since the number of realizations of those "equally real" branches might differ from each other of those branches.
Apropos number of realizations of those "equally real" branches. Of course there are two subregions A and B in the phase space of spins with different sizes in your example. You specifically set ratio of the sizes of those two regions (spin up:spin down) to be 9:16. You are just ignorant here about the proper mathematical description of quantum mechanics with its very specific mathematical space and its very specific METRIC and its very specific MEASURMENT.
You are basing your scepticism of quantum mechanics or Everettian's quantum mechanics on misconceptions and straw mans really.
On reflection, I shouldn't have focused on equal probability. There just is no probability there, because there are no facts to assign probability to.
DeleteWhile I'm not convinced either, the most developed Everettian answer to this by David Wallace argues that branch number isn't well defined in the first place, so branch density is the only relevant consideration. I think that deserves response, since it's really the leading theory out there.
ReplyDeleteDoesn't the density issue just mean there are equal infinite numbers of branches?
DeleteHere is a nice introduction to quantum mechanics: "Chapter 1: Elements of quantum theory - physik.fu-berlin.de"
ReplyDeleteI think, that regarding this post the last remark of section 1.1 expresses quite nicely into a single point, what I think about this scepticism and reasoning here:
"What matters for all outcomes in all experiments is the density operator, not the mixed ensemble we have started with.
Sometimes, people use notions of the kind, “the system is in some pure state vector |ψj>, j = 1, . . . , n, we simply do not know which one”. Such reasoning is not quite precise and can be plain wrong, in which case it is referred to as preferred ensemble fallacy."
Well the "fact" is, that quantum information is never lost or to say, that it is always conserved:
ReplyDelete∑p_k=1 ⇒ |ψ>=∑√p_k·exp(i·θ_k)·|φ_k>∈HilbertSpace
with |φ_k>∈HilbertSpace being an orthonormal basis of the considered HilbertSpace.
Wallace has a pretty extended argument that branch number is undefined rather than infinite, because it's dependent on a choice of grain.
ReplyDeleteThe latter point seems much more salient to me. Worlds, according to Wallace, are basically Lewisian (Alastair Wilson makes this explicit): they're maximal coherent sets of macro facts. But what's supposed to ground those macro-facts are non-world-bounded superpositions. So first, worlds aren't fully definite--and thus can't have probabilities for quantum facts. And second, worlds are dependent on pragmatic choices, so the facts become pragmatic. Now, for Wallace, probabilities are pragmatic--they're just decision theory. But it seems to me that classical decision theory, which he embraces, relies on there being determine outcomes on which to base the pragmatics.
Thanks for the clarification. Undefined makes it even worse, I think. This is just not a metaphysics with probabilities. The probabilities are inserted as a non-scientific epistemological posit, and an implausible one.
ReplyDeleteYears back, I argued against open future views on the grounds that the probability of p should be equal to the probability of p being true. The same applies here.
Zsolt:
ReplyDeleteThe information conservation theorems assume unitarity of the evolution, which is denied by collapse theories.
Ah cool. So then where is the experiment confirming the collapse theory?
DeleteEither way, here is the experiment confirming the No-Hiding theorem and the conservation of quantum information:
"Experimental Test of Quantum No-Hiding Theorem" by Jharana Rani Samal, Arun Kumar Pati, Anil Kumar
GRW collapse theories are in principle distinguishable from non-collapse theories, but I believe not with the present level of technology (at least for certain values of the collapse parameter). Thus, at the present level of technology, experiments confirming conservation of quantum information are insufficient to determine whether the kind of failure of conservation involved in GRW collapse has occurred. The question between collapse and no-collapse theories is still empirically unsettled, even though it is actually a bona fide empirical question.
ReplyDeleteAhh. So that's the current state of affairs.
ReplyDeleteBy the way, is it really the case that collapse theories are denying the unitary time evolution of a physical system?
If so, then why is there the Hamilton operator in the GWR master equation for the time evolution of the density operator?!?
The Hamilton operator is the generator of unitary dynamics. That's weird.
"This is silly. But exactly the same thing is going on in the Everett case. We are being told to make predictions in the way you should if the modulus squares of the weights in the superposition were chances of collapse. But they are not.
ReplyDeleteYes. We are "being told" to make predictions in way you should if the modulus squares of the weights in the superposition were chances of course collapse - we are being told by empirical evidence to do so, since those predictions explain quite well our observations and measurements.
"Can particles really be in two places at once? Featuring @Arvin Ash" by Sabine Hossenfelder
What is so difficult about opening your eyes to any empirical evidence?!?
The only doctrine of science is, that any theory or hypothesis is valid, if and only if that is somewhat capable of predicting and explaining our made empirical observations and measurements.
If you are criticizing a theory or hypothesis, which is capable and trying to predict and explain our made empirical observations and measurements without addressing those made empirical observations and measurements or how that to be criticized theory or hypothesis is actually not capable of accounting for those made observations and measurements, then you are not properly criticizing that theory or hypothesis.
And you are not doing that properly here with that disanalogous example of yours, Alexander, or with that ignorance about our current understanding of quantum mechanics.