Monday, July 08, 2019

The Trouble with Many Worlds

Ten years ago I wrote an essay entitled "The Trouble with Shadow Photons" describing a problem with the dramatic narrative of what is commonly called the "many-worlds" interpretation of quantum mechanics (but which was originally and IMHO more appropriately called the "relative state" interpretation) as presented by David Deutsch in his (otherwise excellent) book, "The Fabric of Reality."  At the end of that essay I noted in an update:
Deutsch just referred me to this paper which is the more formal formulation of his multiple-worlds theory. I must confess that on a cursory read it seems to be a compelling argument. So I may have to rethink this whole thing.
That paper is entitled "The Structure of the Multiverse" and its abstract is delightfully succinct.  I quote it here in its entirety:
The structure of the multiverse is determined by information flow.
Those of you who have been following my quantum adventures know that I am a big fan of information theory, so I was well primed to resonate with Deutsch's theory.  And I did resonate with it (and still do).  Deutsch's argument was compelling (and still is).  Nonetheless, I never wrote a followup for two reasons.  First, something was still bothering me about the argument, though I couldn't really put my finger on it.  Yes, Deutsch's argument was compelling, but on the other hand, so was my argument (at least to me).  The difference seemed to me (as many things in QM interpretations do) a matter of taste, so it seemed pointless to elaborate.  And second, I didn't think anyone reading this blog would really care.  So I tabled it.

But last May the comment thread in the original post was awakened from its slumber by a fellow named Elliot Temple.  The subsequent exchange led me to this paper, of which I was previously unaware.  Here's the abstract, again, in its entirety:
The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom.  But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic, axioms of quantum theory, together with the non-probabilistic part of classical decision theory.
The "special probabilistic axiom" to which Deutsch refers is called the Born rule (named after Max Born).  The "remaining, non-probabilistic axioms of quantum theory" comprises mainly the Schrödinger equation.  (To condense things a bit I'll occsaionally refer to these as the BR and the SE.)

The process of applying quantum mechanics to real-world situations consists of two steps: first you solve the SE.  The result is something called a "wave function".  Then you apply the BR to the wave function and what pops out is a set of probabilities for various possible results of the experiment you're doing.  Following this procedure yields astonishingly accurate results: no experiment has ever been done whose outcome is at odds with its predictions.  The details don't matter.  What matters is: there's this procedure.  It yields incredibly accurate predictions.  It consists of two parts.  One part is deterministic, the other part isn't.

This naturally raises the question of why this procedure works as well as it does.  In particular, why does the procedure have two parts?  And why does it only yield probabilities?  Answering these questions is the business of "interpretations" of quantum mechanics.  Wikipedia lists almost twenty of these.  The fact that after nearly 100 years no consensus has emerged as to which one is correct gives you some idea of the thorniness of this problem.

So the paper that Elliot referred me to was potentially a Big Deal.  It is hard to overstate the magnitude of the breakthrough this would be.  It would show that there are not in fact two disparate parts to the theory, there is only one: the SE.  Such a unification would be of the same order of magnitude as the discovery of relativity.  It would be headline news.  David Deutsch would be a Nobel Laureate, on a par with Newton and Einstein.  But the fact that there is still an active debate over the issue shows that Deutsch's claim has not been universally accepted.  So there would seem to be only two possibilities: either Deutsch is wrong, or he's right and the rest of the physics community has failed to recognize it.

Normally when a claim of a major result like this fails to be recognized by the community it's because the claim is wrong.  In fact, more than 99% of the time it's because the claimant is a crackpot.  But Deutsch is no crackpot.  He's a foundational figure in quantum computing.  He discovered the first quantum algorithm.  Even if he got something wrong he very likely got it wrong in a very interesting way.

So I decided to do a deep dive into this.  It led me down quite the little rabbit hole.  There are a number of published critiques of Deutsch's work, and counter-critiques critiquing the critiques, and counter-counter-critiques.  They're all quite technical.  It took me a couple of months of steady effort to sort it all out, and that only with the kind of help of a couple of people who understand all this stuff much better than I do.  (Many thanks to Tim Maudlin, David Wallace, and especially the patient, knowledgeable, and splendidly-pseudonymed /u/ididnoteatyourcat on Reddit.)

In the rest of this post I'm going to try to describe the result of going down that rabbit hole in a way that is accessible to what I think is the majority of the audience of this blog.  The TL;DR is that Deutsch's argument depends on at least one assumption that is open to legitimate doubt.  Figuring out what that assumption is isn't easy, and whether or not the assumption is actually untrue is arguable.  That's the reason that Deutsch hasn't won his Nobel yet.

I have to start with a review of the rhetoric of the many-worlds interpretation of quantum mechanics (MWI).  The rhetoric says that when you do a quantum measurement it is simply not the case that it has a single outcome.  Instead, what happens is that the universe "splits" into multiple parts when a measurement is performed, and so all of the possible outcomes of an experiment actually happen as a matter of physical fact.  The reason you only perceive a single outcome is that you yourself split into multiple copies.  Each copy of you perceives a single outcome, but the sum total of all the "you's" that have been created collectively perceive all the possible outcomes.

I used the word "rhetoric" above because, as we shall see, there is a disconnect between what I have just written and the math.  To be fair to Deutsch, his rhetoric is different from what I have written above, and it more closely matches the math.  Instead of "splitting", on Deutsch's view the universe "peels apart" (that's my terminology) in "waves of differentiation" (that is Deutsch's terminology) rather than "splitting" (that is everyone else's terminology) but this is a detail.  The point is that at the end of a process that involves you doing a quantum measurement with N possible outcomes, there are, again in point of actual physical fact, N "copies" of you (Deutsch uses the word "doppelgänger").

Again, to be fair to Deutsch, he acknowledges that this is not quite correct:
Universes, histories, particles and their instances are not referred to by quantum theory at all – any more than are planets, and human beings and their lives and loves. Those are all approximate, emergent phenomena in the multiverse.  [The Beginning of Infinity, p292, emphasis added.]
All of the difficulty, it will turn out, hinges on the fidelity of the approximation.  But let us ignore this for now and look at Deutsch's argument.

Deutsch attempts to capture the idea of probability in a deterministic theory using game theory, that is, by looking at how a rational agent should act, applying a few reasonable-looking assumptions about the utility function, and showing that a rational agent operating under the MWI would act exactly as if they were using the Born rule.  The argument is long and technical, but it can be summarized very simply.

[Note to nit-pickers: this simplified argument is in fact a straw man because it is based on the assumption that branch counting is a legitimate rational strategy, which is actually false on the Deutsch-Wallace view.  But since the conclusion I am going to reach is the same as Deutsch's I consider this legitimate rhetorical and literary license because the target audience here is mainly non-technical.]

For simplicity, let's consider only the case of doing an experiment with two possible outcomes (let's call them A and B).  The game-theoretical setup is this: you are going to place a bet on either A or B and then do the experiment.  If the outcome matches your choice, you win $1, otherwise you lose $1.

If the experiment is set up in such a way that the quantum-mechanical odds of each outcome are the same (i.e. 50-50) then there is no conflict between the orthodox Born-rule-based approach and the MWI: in both cases, the agent has no reason to prefer betting on one outcome over the other.  The only difference is the rationale that each agent would offer: one would say, "The Born rule says the odds are even so I don't care which I choose" and the other would say, "I am going to split into two and one of me is going to experience one outcome (and win $1) and the other of me is going to experience the other outcome (and lose $1), and that will be situation no matter whether I choose A or B, so I don't care which I choose."

[Aside: Deutsch goes through a great deal more complicated argument to prove this result because it is based on an assumption that Deutsch rejects.  In fact, he goes on from there to put in a great deal more effort to extend this result to an experiment with N possible outcomes, all of which have equal probabilities under the Born rule.  He has to do this because my argument is based on a tacit assumption that Deutsch rejects.  We'll get to that.  My goal at this point is not to reproduce Deutsch's reasoning, only to convince you that this intermediate result is plausibly true.]

Now consider a case where the odds are not even.  Let's arrange for the probabilities to be 2:1 in favor of A (i.e. A happens 2/3 of the time, B happens 1/3 of the time, according to the Born rule).  Now we have a disconnect between the two world-views.  The Bornian would obviously choose A.  But what possible reason could the many-worlder have for doing the same?  After all, the situation is unchanged from before: again the many-worlder is going to split into two (because there are still only two possible outcomes).  What possible basis could they have for preferring one outcome over the other that doesn't assume the Born rule and hence beg the question?

Deutsch's argument is based on an assumption called branching indifference.  Deutsch himself did not make this explicit in his original paper, it was clarified by David Wallace in a follow-up paper.  Branching indifference says that a rational agent doesn't care about branching per se.  In other words, if an agent does a quantum experiment that doesn't have a wager associated with it, then the agent has no reason to care whether or not the experiment is performed or not.

The reasoning then proceeds as follows: suppose that the many-worlder who ends up on the A branch does a follow-up experiment with two outcomes and even odds, but without placing a bet.  Now there are three copies of him, two of which have won $1 and one of which has lost $1.  But (and this is the crucial point) all of these copies are now on branches that have equal probabilities.  Because of branch indifference, this situation is effectively equivalent to one where there was a single experiment with three outcomes, each with equal probability, but two of which result in winning $1, and where the agent had the opportunity to place the bet on both winning branches.

So that sounds like a reasonable argument.  In fact, it is a correct argument, i.e. the conclusions really do follow from the premises.

But are the premises reasonable?  Well, many many-worlders think so.  But I don't.  In particular, I cast a very jaundiced eye on branching indifference.  There are two reasons for this.  But first, let's look at Wallace's argument for why branching indifference is reasonable:
Solution continuity and branching indifference — and indeed problem continuity — can be understood in the same way, in terms of the limitations of any physically realisable agent. Any discontinuous preference order would require an agent to make arbitrarily precise distinctions between different acts, something which is not physically possible. Any preference order which could not be extended to allow for arbitrarily small changes in the acts being considered would have the same requirement. And a preference order which is not indifferent to branching per se would in practice be impossible to act on: branching is uncontrollable and ever-present in an Everettian universe.
If that didn't make sense to you, don't worry, I'll explain it.  But first I want to take a brief diversion.  Trust me, I'll come back to this.

Remember how I said earlier that my simplified argument for Deutsch's conclusion was based on a premise that Deutsch would reject?  That premise is called branch counting.  It is the idea that the number of copies of me that exist matters.  This seems like an odd premise to dispute.  How could it possibly not matter if there is one of me winning $1 or a million of me each winning $1?  The latter situation might not have a utility that is a million times higher than the former, but if I'm supposed to care about "copies of me" at all, how can it not matter how many there are?

Here is Wallace's answer:
Why it is irrational: The first thing to note about branch counting is that it can’t actually be motivated or even defined given the structure of quantum mechanics. There is no such thing as “branch count”: as I noted earlier, the branching structure emergent from unitary quantum mechanics does not provide us with a well-defined notion of how many branches there are.
Wait, what???  There is no "well defined notion of how many branches there are?"

No, there isn't.  Wallace reiterates this over and over:
...the precise fineness of the grain of the decomposition is underspecified 
There is no “real” branching structure beyond a certain fineness of grain... 
...agents branch all the time (trillions of times per second at least, though really any count is arbitrary) 
...in the actual physics there is no such thing as a well-defined branch number
Remember how earlier I told you that there was a disconnect between the rhetoric and the math?  That the idea of "splitting" or "peeling apart" or whatever you want to call it was an approximation?  Well, this is where the rubber meets the road on that approximation.  Branching indifference is necessary because branching is not a well-defined concept.

So what about the rhetoric of MWI, that when you do an experiment with N possible outcomes that you split/peel-apart/whatever-you-want-to-call-it into N copies of yourself?  That is an approximation to the truth, but like classical reality itself, it is not the truth.  The actual truth is much more complex and subtle, and it hinges on what the word "you" means.

If by "you" you mean your body, which is to say, all the atoms that make up your arms and legs and eyes and brain etc. then it's true that there is no such thing as a well-defined branch count.  This is because every atom — indeed, every electron and every other sub-atomic particle — in your body is constantly "splitting" by virtue of its interactions with other nearby particles, including photons that are emitted by the sun and your smart phone and all the other objects that surround you.  These "splits" propagate out at the speed of light and create what Deutsch calls "waves of differentiation", what I call the "peeling apart" of different "worlds".  (If you are a regular reader you will have heard me refer to this phenomenon as creating "large systems of mutually entangled particles".  Same thing.)  This process is a continuous one.  There is never a well-defined "point in time" where the entire universe splits into two, and no point in time where you (meaning your body) splits into two.  There is a constant and continuous process of "peeling apart".  Actually many, many (many!) peelings-apart, all of which are happening continuously.  To call it mind-boggling would be quite the understatement.

On the other hand, if by "you" you mean "the entity that has subjective experiences and makes decisions based on those experiences" then things are much less clear.  I don't know about you, but my subjective experience is that there is exactly one of me at all times.  I consider this aspect of my subjective experience to be an essential component of what it means to be me.  I might even go so far as to say that my subjective experience of being a single unified whole defines what it is to be "me".  So the only way that there could be a "copy of me" is if there is another entity that has a subjective experience that is bound to the same past as my own, but whose present subjective experience is somehow different from my own e.g. my experiment came out A and theirs came out B.  An entity whose subjective experience is indistinguishable from my own isn't a copy of me, it's me.

The mathematical account of universes "peeling apart" has nothing to say about when the peeling process has progressed far enough to be considered a fully-fledged universe in its own right and so it has nothing to say about when I have "peeled apart" sufficiently to be considered a copy.  That is why branch count is not a coherent concept.

And yet, if I am going to apply the notion of branching to myself (which is to say, to the entity having the subjective experience of being a coherent and unified whole) then branch count must be a coherent concept.  It might not be possible to know the branch count, but at any point in time whatever underlying physical processes are really going on,  it has to either qualify as me branching or not.  There is no middle ground.

So we are faced with this stark choice: we can either believe the math, or we can believe our subjective experiences, but we can't do both, at least not at the same time.  We can take a "God's eye view" and look at the universal wave function, or we can take a "mortal's-eye view" and see our unified subjective experience as real.  But we can't do both simultaneously.  It's like a Necker cube.  You can see it one way or the other, but not both at the same time.

Interestingly, this is all predicted by the math!  In fact, the math tells us why there is this dichotomy.  Subjective experience is necessarily classical because it requires copying information.  In order to be conscious, you have to be conscious of something.  In order to make decisions, you have to obtain information about your environment and take actions that affect your environment.  All of these things require copying information into and out of your brain.  But quantum information cannot be copied.  Only classical information can be copied.  And the only way to create copyable classical information out of a quantum system is to ignore part of the quantum system.  Classical behavior emerges from quantum systems (mathematically) when you trace over parts of the system.  Specifically, it emerges when you consider a subset of an entangled system in isolation from the rest of the system.  When you do that, the mathematical description of the system switches from being a pure state to being a mixed state.  Nothing physical has changed.  It's purely a question of the point of view you choose to take.  You can either look at the whole system (in which case you see quantum behavior) or you can look at part of the system (in which case you see classical behavior) but you can't do both at the same time.

As a practical matter, in our day-to-day lives we have no choice but to "look" only at "part" of the system, because "the system" is the entire universe.  (In fact, it's an interesting puzzle how we can observe quantum behavior at all.  Every photon has to be emitted by, and hence be entangled with, something.  So why does the two-slit experiment work?)  We can take a "God's-eye view" only in the abstract.  We can never actually know the true state of the universe.  And, in fact, neither can God.

Classical reality is what you get when you slice-and-dice the wave function in a particular way.  It turns out that there is more than one way to do the slicing-and-dicing, and so if you take a God's-eye view you get more than one classical universe.  An arbitrary number, in fact, because the slicing-and-dicing is somewhat arbitrary.  (It is only "somewhat" arbitrary because there are only certain ways to do the slicing-and-dicing that yield coherent classical universes.  But even with that constraint there are an infinite number of possibilities, hence "no well-defined branch count".)  But the only way you can be you, the only way to become aware of your own existence, indeed the only way to become aware of anything, is to descend from Olympus, ignore parts of the wave function, and become classical.  That leaves open the question of which parts to ignore.  To me, the answer is obvious: I ignore all of it except the parts that measurably effect the "branch" that "I" am on.  To me, that is the only possible rational choice.

57 comments:

Elliot Temple said...

> Now consider a case where the odds are not even. Let's arrange for the probabilities to be 2:1 in favor of A (i.e. A happens 2/3 of the time, B happens 1/3 of the time, according to the Born rule). Now we have a disconnect between the two world-views. The Bornian would obviously choose A. But what possible reason could the many-worlder have for doing the same? After all, the situation is unchanged from before: again the many-worlder is going to split into two (because there are still only two possible outcomes).

The reason is simple. Not all universes exist in equal quantities. There could be e.g. twice as many of universe A as of universe B. So he’d prefer to make the bet where he wins in 2/3 of (the relevant branch of) the multiverse over the one that wins in 1/3 of the multiverse. More copies of him will win.

The idea of there being exactly one copy of a person for each type of universe (e.g. win bet type or lose bet type) is incorrect.

There are many identical universes. When they “split” (aka “branch” or “differentiate”), the split does not have to happen with equal proportions.

You don’t split from one into two. You split from many into many (the same number as before – no universes are created nor destroyed). “Splitting” means some universes become different that were, previously, identical. You can split into e.g. 2/3 of one outcome and 1/3 another outcome.

(Warning: speaking about universes is an approximation. They have no fundamental role in physics. One of the reasons is along the lines Ron states in the quote below that begins “This process is a continuous one.” Plus universes are big but quantum physics is local – change spreads at the speed of light or less.)

Wallace writes:

https://arxiv.org/pdf/0906.2718.pdf

> **Branching Indifference:** An agent doesn’t care about branching per se: if a certain measurement leaves his future selves in N different macrostates but doesn’t change any of their rewards, he is indifferent as to whether or not the measurement is performed.

Ron writes:

> Branching indifference says that a rational agent doesn't care about branching per se. In other words, if an agent does a quantum experiment that doesn't have a wager associated with it, then the agent has no reason to care whether or not the experiment is performed or not.

This is unclear or is different than Wallace because it speaks of a *wager* rather than a *reward*. A wager means betting money, whereas a reward is anything that is good or bad according to an agent’s preferences.

Wallace is basically saying that an agent is indifferent to branching into copies *if*, after branching, no copy of the agent is worse (or better) off in any way.

That sounds totally unobjectionable to me. If a particular branching has no downsides or upsides (in any universe), according to an agent’s preferences, then an agent is indifferent to it. In other words, agents care about positive and negative rewards rather than branching itself (branching sometimes, but not always, has consequences for rewards).

Being pedantic, one could say the same thing about any other physical events (eating breakfast, getting fired, hitting a homerun, winning the lotto, etc.) – it’s not the event itself, per se, which matters, but whether or not there is any change in reward according to the agent’s preferences. E.g. “sleep indifference” states that agents are indifferent to how much sleep they get, per se, as long as there is no positive or negative change to their rewards.

In other words, if an agent has no preference about something, then that agent is indifferent to it. And agents don’t necessarily have preferences about all possible multiversal branching.

> if I'm supposed to care about "copies of me" at all, how can it not matter how many there are?

You can care about a *measure* of copies that isn’t simple quantity/count (a quantity/count of marbles is an example of simple quantity/count).


(continued in the next comment due to 4096 char length length)

Elliot Temple said...


> So what about the rhetoric of MWI, that when you do an experiment with N possible outcomes that you split/peel-apart/whatever-you-want-to-call-it into N copies of yourself?

That is *not* the MWI position. You split into N *different versions* of yourself, but not into N copies of yourself (that’s different because it could be e.g. 3 copies of the first version, 8 copies of the second version, etc. But they’re harder to measure than simple counting.)

> This process is a continuous one. There is never a well-defined "point in time" where the entire universe splits into two, and no point in time where you (meaning your body) splits into two.

Agreed.

> subjective

I think it’s better to start by considering how physics works without worrying about conscious or “subjective” experiences. Let’s discuss all the other stuff first and only tackle issues related to consciousness after agreeing on the rest (like what happens with dice, photons, mirrors and cups of water). That’s what I’ve done above.

> You can either look at the whole system (in which case you see quantum behavior) or you can look at part of the system (in which case you see classical behavior) but you can't do both at the same time.

But if you look in certain parts you do *not* see classical behavior. Classical physics being *false* and *refuted by some experiments* is why we have quantum theory. Classical physics is a good approximation in many cases people encounter in their daily lives, but not in all cases. Agreed?

Ron said...

@Elliot:

First, thanks for the constructive feedback.

I'm going to respond out of order, saving the most important point for last.

> You split into N *different versions* of yourself, but not into N copies of yourself

I don't normally like quibbling over terminology, but in this case I agree that "versions" is a better, more descriptive term than "copies" here.

> You don’t split from one into two. You split from many into many

Yes, I understand that that's what the math says. The problem is that I don't feel like many. I feel like one. If I am many, why don't I feel like it?

Also, if I'm many, how many am I?

(Feel free to consider those rhetorical questions. We don't actually disagree on the physics, we disagree on the philosophy. See below.)

> Not all universes exist in equal quantities.

Yes, but what do those quantities have to do with *decisions*? You can't just *assume* that "higher-quantity" universes should have a greater weight in decision-making. That is begging the question.

> This is unclear or is different than Wallace because it speaks of a *wager* rather than a *reward*.

A wager is a specific kind of decision. Deutsch frames his argument in terms of decision theory. So speaking of wagers should not be too surprising.

But I'm happy to just substitute "no reward" for "no wager" here. It amounts to the same thing in this case.

> it’s not the event itself, per se, which matters, but whether or not there is any change in reward according to the agent’s preferences

Yes, I agree with that. The problem is that in a branching universe the phrase "the agent" no longer has a well-defined referent.

> Classical physics is a good approximation in many cases people encounter in their daily lives, but not in all cases. Agreed?

Yes, of course.

> I think it’s better to start by considering how physics works without worrying about conscious or “subjective” experiences.

This is our biggest disconnect. My subjective experience is the only data I have direct access to. It's the only reason I have to even suspect that there is such a thing as "the laws of physics" out there to be discovered. So you can start by considering how physics works if you like, but if you want to tell a complete story of how the world works then sooner or later you're going to have to circle back and consider how *considering* works.

Alan said...

>> I think it’s better to start by considering how physics works without worrying about conscious or “subjective” experiences.
>
> This is our biggest disconnect. My subjective experience is the only data I have direct access to. It's the only reason I have to even suspect that there is such a thing as "the laws of physics" out there to be discovered. So you can start by considering how physics works if you like, but if you want to tell a complete story of how the world works then sooner or later you're going to have to circle back and consider how *considering* works.

Considering is a form of information processing. A universe is a structure within the multiverse where information can flow from one system to another. For example, there are versions of me sitting 1 inch to the right of my current position. I can't exchange information with those other version of me. I can't see whether one of those versions of me is sitting with his legs crossed. That is why those versions of me count as separate versions in separate universes.

Now, I have a record in my memory of writing the first version of this paragraph. There is also information in the environment about what I typed, e.g. - information in sound waves from my typing in light reflecting off the keys and so on. This information can be used to decide whether I am the same person as the person who wrote the first paragraph of this reply. Other versions of me wrote a different second paragraph but also have records of the same first paragraph. The fact that there is more than one version of me with such a record doesn't change the fact that the identification can be made.

A similar story about identifying objects using records can be told about other objects like the keyboard I'm typing on, the pen sitting on the desk behind the keyboard and so on. Any decision you're going to make has to use the same kinds of records that would be used to identify the pen or the keyboard or whatever. From the point of view of physics, there is no particular reason to make a special case for people as opposed to pens or computers or whatever. So we might as well consider a computer programmed to maximise its rewards rather than a person. We know how to program a computer to just follow a particular rule. Programming a person to just follow a particular rule is difficult and raises irrelevant moral problems, so discussing a computer program makes more sense.

Ron said...

@Alan:

I agree with everything you said. But...

> I can't exchange information with those other version of me.

So is there any reason I should *care* about the existence other versions of me (except perhaps as an intellectual curiosity)?

Alan said...

> So is there any reason I should *care* about the existence other versions of me (except perhaps as an intellectual curiosity)?

The only direct reason to be interested in the existence of other versions of you is wanting to have a consistent worldview that actually explains how the world works. If you don't care about this you will make many more uncorrected mistakes since you remove constraints on your ideas that might improve them. This will include mistakes in actions you take directly and mistakes in picking politicians, advisors etc. To understand this issue read the title essay from Ayn Rand's book "Philosophy: Who Needs It".

Elliot Temple said...

I've posted a reply twice and it hasn't appeared. So let's try just a link to the text instead of the actual text and maybe that will work:

https://curi.us/2209-physics-discussion#c12987

Elliot Temple said...

> So is there any reason I should *care* about the existence other versions of me (except perhaps as an intellectual curiosity)?

The "you" that places the wager consists of multiple identical copies. For simplicity, we'll call it 100. So there are 100 clones of you which, as a group, place a wager. Why would "you" care about "other versions" of you? Because "you" (as of the start of the scenario where you make a choice about a wager) are 100 people, you should bet in a way that gives the best outcome for those 100 people.

You should try to maximize outcomes for the versions of you that placed the wager, precisely because they are part of the entity that placed the wager. Each of them is a real person who is making a wager and wants to win. If you bet so that 2/3 of them win, that that's better for the group, and also then each of them individually has a 2/3 chance to win rather than e.g. a 1/3 chance.

PS Because your captcha system seems to block some of my comments and also keeps presenting me with many captchas in a row (e.g. 5 in a row, I've done ~two dozen in total), I don't want to continue discussing here. If you want to discuss further, please post at https://curi.us/2209-physics-discussion where you can post without any captcha or moderation, and with better formatting too. If you don't care enough to do that then I think I'll, sadly, give up because the software here is too broken and/or user hostile.

Ron said...

Alan: The only direct reason to be interested in the existence of other versions of you is wanting to have a consistent worldview that actually explains how the world works. [Emphasis added.]

elliot: Why would "you" care about "other versions" of you? Because "you" (as of the start of the scenario where you make a choice about a wager) are 100 people, you should bet in a way that gives the best outcome for those 100 people.

So which is it?

> wanting to have a consistent worldview

There is nothing inconsistent in Bohmian mechanics or GHZ collapse, not even, for that matter, in the Copenhagen interpretation. So this can't be the reason.

> The "you" that places the wager consists of multiple identical copies. For simplicity, we'll call it 100.

Call it whatever you like, this cannot be a correct explanation. If I am N identical copies, then after O(log(N)) splits I will be 1. What happens then?

Note also that, according to Wallace, splits happen "trillions of times per second at least". (That's an actual quote, not a scare quote.) I am approximately 10^9 seconds old, so I have already undergone at least 10^20 splits, so when I started out, I must have consisted of at least 2^10^20 copies. And in fact it is even worse than that because most splits are not the result of doing well-controlled spin measurements using a Stern-Gehrlach apparatus, it's the result of natural decoherence, which cause N-way splits for very large values of N. So "call it 100" is a laughably inaccurate oversimplification. And the implication that the number of copies that you consist of at any one time is a finite integer is simply false because, again as Wallace points out, branch count is not well-defined.

From the article you linked to:

> The short, approximate version is that it's better to win $1 in 66 universes and lose $1 in 34 than vice versa.

This is branch-counting, and Wallace himself debunks this in his paper. If it were valid, then branching-indifference would not hold and Deutsch's proof would not carry through. So this is not a "short, approximate version", it is simply wrong.

> your captcha system seems to block some of my comments and also keeps presenting me with many captchas in a row

It's not my captcha system, it's Google's. But it has a bug that allows it to be easily defeated if you're posting from a blogger account (which you are): when a captcha appears, just ignore it. Click anywhere outside the captcha. It will disappear. The checkbox next to "I'm not a robot" will not be checked, but the publish button should work at this point nonetheless. At least that works for me.

Ron said...

> It's not my captcha system, it's Google's.

FWIW, I just checked my settings and I actually have the captcha disabled, so the fact that it appears at all is a bug in Blogger (which might account for why it is so easily defeated). I'm sorry about that, but this is something over which I obviously have no control. Blogger's comment system has always been annoying in one way or another, and I've considered switching to another platform on a number of occasions, but I've been on blogger for over fifteen years now (since long before Google bought them) so the inertia is high.

Ron said...

Just one more note on the captcha: I posted my last comment without clicking on the "I'm not a robot" button *at all* and it worked. So try that.

Elliot Temple said...

test

Elliot Temple said...

lol it posted without click "I'm not a robot".

OK in that case I'll keep trying here.

Please note that the link I gave above:

https://curi.us/2209-physics-discussion#c12987

Was *not* for the text of the comment after it. It's a separate comment which I did not post here successfully.

Elliot Temple said...

(this is the linked comment in 2 parts. i tried again with no captcha and discovered it was slightly longer than the length limit. i think that is why it wouldn't post before, except that i did not get the error message when i was using the captcha.)

> Yes, I understand that that's what the math says. The problem is that I don't feel like many. I feel like one. If I am many, why don't I feel like it?

MWI is an *objective* theory based on *scientific observations and math*, **not** based on a philosophical theory of consciousness. While *I* could comment on the matter, and DD also has opinions on the matter, they are a separate issue than MWI.

If you told me that due to misunderstandings of consciousness (which you could name and explain), some of experimental data needed to be reconsidered or rejected, that would be relevant. Same if you rejected some math, logic or prior-to-QM physics claims. But if you accept all the experimental data and all the math, logic and physics premises, then doesn't MWI (or a few other options which mostly differ from MWI by their claims about objective reality, not by their theories of consciousness) follow?

> Yes, but what do those quantities have to do with *decisions*? You can't just *assume* that "higher-quantity" universes should have a greater weight in decision-making. That is begging the question.

The point of DD's paper is to prove that, in terms of betting by the "rational agents" of decision theory, you should do betting-decision-making according to "higher-quantity" universes (in order to maximize multiverse-wide betting returns). He does not assume this point nor beg this particular question. Your objections related to consciousness do not constitute a criticism of DD's proof of this matter from his premises.

The short, approximate version is that it's better to win $1 in 66 universes and lose $1 in 34 than vice versa. What they have to do with decisions is that you (a group of many fungible, identical, indistinguishable instances of a person) would prefer that more of you (more of those instances that already exist and are part of the group of instances that make the decision) would prefer that more of your instances win over fewer winning.

Elliot Temple said...

(part 2)

> The problem is that in a branching universe the phrase "the agent" no longer has a well-defined referent.

Do you mean because an agent has microscopic changes which haven't propagated to his entire body at once (before some changes finish propogating, others begin, so there are always some changes which have not propgated to his entire body)? (And the same point works with just his brain.) Is that the issue?

I think that issue of defining a particular agent and its preferences in a world that is in constant flux is not really a QM or MWI issue. Heraclitus could have made a similar complaint. And I don't think other QM interpretations, which do not contradict the math and observations, will change this problem much. DD's point in the paper is that *if* you accept certain claims of decision theory (which are pretty widely accepted), including that you can take as a starting point an agent with a well-defined set of preferences, *then* various things follow. The details of how to deal with a world (including agents) in constant flux is a separate matter not covered in that paper.

I think this separate matter of dealing with flux is widely believed to be soluble, and that DD and I have that belief. And I think it can be approached without getting into the problems of consciousness or subejctivism that I avoided above. Like you could have a software agent, which isn't even (general) intelligent, and it bets trying to maximize some function, and it too would have the constantly-undergoing-change issue. The solution, in short, is that despite the ongoing flux/chaos/change *in some respects*, there are some things which change very very little over some short time periods, so they can be taken as approximately constant at that time when they are approximately unchanging.

Something being approximately constant, rather than exactly constant, means that error correction is needed, which is getting pretty far afield (though covered a bit in BoI which explains the advantage of digital over analog for error correction). Very briefly it's like how computer circuits deal with electrical signals that are approximate, not exact, in terms of strength and timing. Minor fluctuations can be and are dealt with.

Ron said...

@Elliot:

> 4096 char length limit

Yeah, that's annoying, but unfortunately I have no control over that.

Feel free to put content somewhere else and just post links here if that works better for you.

> I'll keep trying here.

Happy to hear that.

> if you accept all the experimental data and all the math, logic and physics premises,

I do, but note that I include my own subjective experience in the "experimental data". In fact, as I've pointed out before, my subjective experience is in fact the *only* experimental data I have direct access to. That includes the subjective experience of interacting with other people, reading physics papers. And yes, I know about DD's argument that indirect evidence is *better* than direct evidence, and I agree with that argument. Nonetheless, my subjective experience is still something that a complete theory of reality needs to account for as far as I'm concerned.

> then doesn't MWI (or a few other options which mostly differ from MWI by their claims about objective reality, not by their theories of consciousness) follow?

There are at least four interpretations of QM that are widely considered viable in the sense that the cannot be ruled out on the evidence alone: MWI, Bohm, GRW collapse, and Copenhagen. I personally subscribe to a fifth interpretation which is similar enough to MWI that I'm pretty confident that it is logically viable even though it is not as popular as the other four, but that's neither here nor there. If the case for MWI were the kind of slam-dunk that you seem to feel that it is, there would not be any controversy. It would be widely considered to be settled science, as uncontroversial as relativity. But it isn't.

One cannot definitively rule out the possibility that MWI is in fact the only logically tenable interpretation and that the majority of the physics community is just too stupid to understand this. My Bayesian prior on this is pretty low.

> The point of DD's paper is to prove that, in terms of betting by the "rational agents" of decision theory, you should do betting-decision-making according to "higher-quantity" universes (in order to maximize multiverse-wide betting returns). He does not assume this point nor beg this particular question.

No, that's not true. What DD's paper shows is that *if* a rational agent accepts the quality metric of maximizing multiverse-wide betting returns biased according to branch *weights* (and not branch *counts*) *then* a rational agent should behave *as if* the Born rule were true.

> Your objections related to consciousness do not constitute a criticism of DD's proof of this matter from his premises.

You're right, because my criticism is not a criticism of the claim that Deutsch actually makes (as I have re-stated it above).

Here, verbatim, is the claim Deutsch actually makes:

"[A]ll the practical consequences of [probabilistic quantum] predictions follow from the remaining, non-probabilistic, axioms of quantum theory, together with the non-probabilistic part of classical decision theory"

And I accept that, but with one important and necessary proviso: an agent has to adopt the correct utility function. It is in the definition of the utility function that Deutsch begs the question. Yes, if you adopt a utility function that is logically equivalent to the Born rule then it is no surprise that the resulting rational decisions will be the same as if the agent had simply adopted the Born rule. But Deutsch never justifies his utility function. Wallace tries to, but he fails. He has to assume branching indifference, and that, it turns out, is where the Born rule is hiding.

(This is no small thing, BTW. Reducing the Born rule to branching indifference is significant progress, and I think actually leads to some deep insights. But it doesn't actually solve the problem.)

[Cont'd...]

Ron said...

@Elliot: (2 of 2)

> The short, approximate version is that it's better to win $1 in 66 universes and lose $1 in 34 than vice versa.

Yes, that's obviously true. The problem is that if these 100 universes already existed before the experiment was done, then that completely undermines the argument that led us to believe in quantum theory in the first place. Here's a quote from TFoR:

"Could it be that the photon splits into fragments which, after passing through the slits, change course and recombine? We can rule that possibility out too. If, again, we fire one photon through the apparatus, but use four detectors, one at each slit, then at most one of them ever registers anything. Since in such an experiment we never observe two of the detectors going off at once, we can tell that the entities that they detect are not splitting up."

The only reason there was a problem in the first place is because a photon was taken (on good evidence) to be an indivisible unit that could not "split up". So which is it? Can a photon split up or not?

The answer (as I explained in the OP) is that it depends on your point of view. From a God's-eye point of view, it can. From a mortals-eye point of view, it can't.

> > The problem is that in a branching universe the phrase "the agent" no longer has a well-defined referent.

> Do you mean because an agent has microscopic changes which haven't propagated to his entire body at once

No, I mean that "the agent" can refer to either the pre-split agent, or any one of the N post-split agents. If you're going to talk about *the* agent (singular) then you have to specify which of the N+1 agents you mean.

> Heraclitus could have made a similar complaint.

Indeed, but he wasn't trying to do physics. If you're going to do that, you should expect to be held to a higher standard.

> I think this separate matter of dealing with flux is widely believed to be soluble

And I'm pretty sure that you're wrong. In fact, I'm pretty sure that I can *prove* that you're wrong (or at least advance a pretty compelling argument)! It might even be a publishable result. But here's a preview:

> Minor fluctuations can be and are dealt with.

Dealing with "minor fluctuations" often requires a radical departure from the conventional wisdom. Explaining the precession of the orbit of Mercury requires a lot more than a minor tweak to Newtonian mechanics. And going from the discrete to the continuous can be highly problematic, particularly if you think about it in terms of information theory.

Elliot Temple said...

> Call it whatever you like, this cannot be a correct explanation. If I am N identical copies, then after O(log(N)) splits I will be 1. What happens then?

OK, you want less approximate. Some BoI quotes (not in order):

> Thus the information in the fictional multiverse flows along a branching tree, whose branches – histories – have different thicknesses (measures) and never rejoin once they have separated.

> *Instances* In parts of the multiverse that contain universes, each multiversal object consists approximately of ‘instances’, some identical, some not, one in each of the universes.

> In quantum physics, information flow in the multiverse is not as tame as in that branching tree of histories I have described. That is because of one further quantum phenomenon: under certain circumstances, the laws of motion allow histories to rejoin (becoming fungible again).

> In principle, a phenomenon could appear unpredictable to observers for one or more of three reasons. [...] The third – which had never been imagined before quantum theory – is that two or more initially fungible instances of the observer become different.

> Then they know that, when they run the transporter, an infinite number of fungible instances of themselves, all sharing the same history, are doing so at the same time.

> Our fictional theory has not provided enough structure in its multiverse to give a meaning to ‘half the universes’, but the real quantum theory does. As I explained in Chapter 8, the method that a theory provides for giving a meaning to proportions and averages for infinite sets is called a *measure*. A familiar example is that classical physics assigns *lengths* to infinite sets of points arranged in a line. Let us suppose that our theory provides a measure for universes.

You don't actually count universes, you measure them, just like you don't count points, you measure them.

You don't run out of points when you divide up an inch repeatedly. Same with instances in the multiverse.

Elliot Temple said...

> Nonetheless, my subjective experience is still something that a complete theory of reality needs to account for as far as I'm concerned.

Yes, but there is nothing about MWI which contradicts any of your subjective experiences. It never said "You will never subjectively experience X" for any X that you have experienced.

> No, that's not true. What DD's paper shows is that *if* a rational agent accepts the quality metric of maximizing multiverse-wide betting returns biased according to branch *weights* (and not branch *counts*) *then* a rational agent should behave *as if* the Born rule were true.

If a multiversal agent in N states tries to maximize the outcomes for its states, it should... (Except you have to measure, not count, those "N" states. It's the same sort of problem as saying a line containing "N points", which is sorta misleading but I don't know a better wording.)

> [Wallace] has to assume branching indifference, and that, it turns out, is where the Born rule is hiding.

No, as I explained previously branching indifference is trivial.

> The only reason there was a problem in the first place is because a photon was taken (on good evidence) to be an indivisible unit that could not "split up". So which is it? Can a photon split up or not?

Single-universe photons do not split. Multiversal photons do not split but are already pre-"split" in a way very similar to how a 2-inch line segment is already pre-"split" into points instead of being an indivisible whole.

> No, I mean that "the agent" can refer to either the pre-split agent, or any one of the N post-split agents. If you're going to talk about *the* agent (singular) then you have to specify which of the N+1 agents you mean.

The agent at the start of the scenario is a collection of N fungible (identical) agents.

There is no splitting, ever New agents are never created. There is only differentiating: agents that already existed, and were formly identical, become different.

> Dealing with "minor fluctuations" often requires a radical departure from the conventional wisdom.

A tiny fraction of minor fluctuations turn out not to be minor. Most really are minor, e.g. if you measure a length, weight or temperature of a glass of water there will be tiny fluctuations (of the glass, the water, and the measuring instrument) that affect your measurement but they are usually too minor for you to even notice.

Elliot Temple said...

(Quoting myself.)

> If a multiversal agent in N states tries to maximize the outcomes for its states, it should... (Except you have to measure, not count, those "N" states. It's the same sort of problem as saying a line containing "N points", which is sorta misleading but I don't know a better wording.)

What about from the perspective of an individual agent instance? That's a bit of an approximation because what really exists are multiversal objects, not single universe objects. But it works pretty OK. From that perspective, basically what happens is probability: if 2/3 of the instances in the multiversal object get outcome X then from the perspective of a single instance it has a 2/3 chance to get outcome X.

Peter Donis said...

@Elliot Temple:
There is no splitting, ever New agents are never created. There is only differentiating: agents that already existed, and were formly identical, become different.

What does this correspond to in the math? I don't see anything in the math that looks to me like multiple agents that start out identical and then become different.

Elliot Temple said...

Peter, have you read *The Beginning of Infinity* by David Deutsch, particularly chapter 11, The Multiverse? Start there for an explanation.

Ron said...

@Elliot:

You should know that Peter is a physicist. You don't need to talk down to him.

(It is nonetheless salient to note that TBoI has numerous references to "splitting".)

@Peter:

The actual answer to your question (such as it is) can be found here.

Elliot Temple said...

I did not talk down to Peter.

It concerns me that you believe that. It shows that you read totally inoffensive text as offensive. I think that has caused problems between us in the past and will in the future.

Ron said...

@Elliot:

> You don't actually count universes, you measure them, just like you don't count points, you measure them.

Ah. How is that done exactly? If I wanted to "measure" the universe I inhabit, how would I do it? If I measured my universe before and after a quantum event, would I get a smaller result the second time?

> there is nothing about MWI which contradicts any of your subjective experiences

Of course there is. MWI says that there are many of me (that's what the M in MWI stands for!) But my subjective experience is that there is only one of me.

> you have to measure, not count, those "N" states

And what exactly compels me to measure and not count? Why am I compelled to use the measure of a universe to make decisions rather than coalescing all of the fungible versions of me into one equivalence class and treating that as a single entity?

> branching indifference is trivial

Being trivial and being the root of the begging of the question are not mutually exclusive.

> Single-universe photons do not split.

Wait, what? What is a "single-universe photon"? Just now you were telling me that "you don't actually count universes, you measure them" and that this is the reason that universes can split/differentiate/whatever-you-want-to-call-it forever. So what on earth can a "single-universe photon" possibly mean?

Are you familiar with single-photon sources?

https://en.wikipedia.org/wiki/Single-photon_source

Do those emit "single-universe photons" that "do not split"? If so, what exactly happens if I run one of those through a beam splitter?

> The agent at the start of the scenario is a collection of N fungible (identical) agents.

Is N an integer?

> > Dealing with "minor fluctuations" often requires a radical departure from the conventional wisdom.

> A tiny fraction of minor fluctuations turn out not to be minor. Most really are minor, e.g. if you measure a length, weight or temperature of a glass of water there will be tiny fluctuations (of the glass, the water, and the measuring instrument) that affect your measurement but they are usually too minor for you to even notice.

For day-to-day life that is certainly true. But we're talking about quantum physics here. In that realm, tiny fluctuations matter *a lot*.

Ron said...

@Elliot:

> I did not talk down to Peter.

I didn't say you did. I just said that you don't need to.

Peter asked you a question about the mathematics of MWI and you answered by referring him to a text that contains no math. I can think of only two possible explanations:

1. You thought Peter was a layman and referred him to a popular text because you thought that would be appropriate.

2. You knew Peter was not a layman, but referred him to a popular text nonetheless for reasons that I cannot even begin to guess. (Surely it wasn't because you were unaware of the Deutsch paper. You know the MWI literature better than I do.)

So I guessed #1 to be the case and decided to give you the heads-up. That's all.

Elliot Temple said...

I would refer anyone to BoI. I think it's the best thing to read first to understand this, even if one can and will read DD's papers too.

Elliot Temple said...

> > branching indifference is trivial

> Being trivial and being the root of the begging of the question are not mutually exclusive.

If you have some argument about why branching indifference is false, or has some other problem in this context, please explain it. As far as I could tell, your objections to it came from not understanding it (or, in the alternative, understanding it differently than I do). So I explained what I thought it meant. IIRC you seemed to agree with me. But now you bring it up again as problematic.

> Ah. How is that done exactly? If I wanted to "measure" the universe I inhabit, how would I do it? If I measured my universe before and after a quantum event, would I get a smaller result the second time?

Measures can be abstract or hypothetical. They aren't only things you can actually measure. The concept of a measure does not require a physical process does performs that measure. Here is some explanation of measures, and relates issues, based on conversations with Deutsch (he taught it to me):

https://curi.us/1955-explaining-infinite-sets-measures-and-mappings-for-quantum-physics

That is not a full explanation of everything. It's just a starting point. If you agree with what I've said so far, in my comment and a the link, I'll continue from there. If there's a disagreement with this part, then we can talk about that first.

> > there is nothing about MWI which contradicts any of your subjective experiences

> Of course there is. MWI says that there are many of me (that's what the M in MWI stands for!) But my subjective experience is that there is only one of me.

You have never in your life observed the absence of other instances of you in the multiverse. You have looked only at a limited portion of the multiverse and didn't see more of you. That is fully compatible with MWI.

Your experience, taken more literally, is e.g. that you looked down and saw your foot. Observations like that are valid data but do not contradict MWI. You seem to be mixing up your personal (= made by you instead of someone else) observations with vague feelings which are not really obsrvation data but are intellectual intuitions.

> And what exactly compels me to measure and not count? Why am I compelled to use the measure of a universe to make decisions rather than coalescing all of the fungible versions of me into one equivalence class and treating that as a single entity?

It's like the difference between 1 inch and 2 inches. If you just say "a linear set of points" and treat all such sets as equivalent, you will deal with distance poorly.

Peter Donis said...

I would refer anyone to BoI.

I have read too many pop science books by physicists that misrepresent the actual physics, so I don't trust pop science books to properly present the physics. Since I'm perfectly capable of reading the actual papers and understanding the actual math, that's what I do.

(It's possible that the pop science book you refer to is an exception and actually does properly present the physics. But the only way I can know that is to look at the actual physics, i.e., the papers and the math. So it's still a waste of time for me to read the pop science book.)

I'll do some looking at the literature and come back if I have further questions.

Ron said...

> I would refer anyone to BoI. I think it's the best thing to read first to understand this

BoI is a pretty good intro for a layman (though I think TFoR was better). But it's inappropriate for anyone seeking technical detail. It doesn't connect the intuitions to the math at all, and it puts way too much emphasis on the transporter metaphor IMHO.

> why branching indifference is false

Branching indifference is not false. What is false is the proposition that an agent must accept branching indifference in order to be considered rational. That turns out to be the Born rule in disguise.

To illustrate how a plausibly rational agent could reject branching indifference (this example is due to Tim Maudlin, though I've reframed it here): suppose I am offered a choice between chocolate or vanilla ice cream. I like them both, and would prefer to have both, but I can't. I have to choose (maybe I only have enough money for one scoop). Instead of choosing according to my free will, I instead perform a quantum experiment in order to split myself into two. One of me chooses chocolate, the other chooses vanilla. A rational agent could plausibly prefer this state of affairs (assuming they care about the multiverse *at all*) to one where only one flavor is actually chosen.

A more fundamental problem is that you cannot a priori rule out branch counting as a plausibly rational strategy. Wallace argues against it by retreating from the proposition that "branch" is a meaningful concept (thereby undermining all of the popular rhetoric of the MWI, but let's leave that aside) but this argument fails because I can just *define* some way of coalescing slices of the universe into equivalence classes which I call "branches", and then I can count them. Wallace concedes this: "...within the stylised context of my decision theory, the branch count is defined." And then, remarkably, he actually goes on to (tacitly) concede that he has begged the question! "... so of course (given the representation theorem) the branch counting rule must violate some of my axioms. In fact, it violates ... branching indifference ..."

> Measures can be abstract or hypothetical. They aren't only things you can actually measure.

Yes, I understand that. (You are either severely underestimating my grasp of the basics of the MWI, or I am overestimating yours.) My question is: is the "measure" of the universe I inhabit something I can actually measure? (Answer: no, it isn't. You knew that right?)

(cont'd...)

Ron said...

(2 of 2)

> https://curi.us/1955-explaining-infinite-sets-measures-and-mappings-for-quantum-physics

Yes, I understand measure theory.

> You seem to be mixing up your personal (= made by you instead of someone else) observations with vague feelings which are not really observation data but are intellectual intuitions.

No. I accept, for example, that black holes exist despite the fact that I have never personally experienced one. The difference is that *in principle* (and nowadays in actual practice) there are experiments one can do to demonstrate the existence of black holes. But the MWI says that the existence of other versions of me is not experimentally demonstrable (to me) *even in principle*, not even with arbitrarily advanced technology. That's what makes the MWI untenable.

> The concept of a measure does not require a physical process does performs that measure.

It does if you want me to take it seriously as something that makes contact with reality. If I can't measure it, not even in principle (and I can't) then It's an IPU -- an Invisible Pink Unicorn -- no different than particle positions in the Bohm interpretation. (In fact, if you work out the math, branch weights play *exactly* the same role in the MWI as particle positions play in Bohmian mechanics: they are the IPU, the unmeasurable-even-in-principle quantity, where the Bornian randomness is carefully hidden.)

> It's like the difference between 1 inch and 2 inches.

The difference being: I can demonstrate a physical process that allows me to measure and compare distances in a meaningful and logically coherent way. (This is quite a remarkable fact about the universe, BTW.) You cannot do the same for the measure of a universe, not even in principle.

Alan said...

> Branching indifference is not false. What is false is the proposition that an agent must accept branching indifference in order to be considered rational. That turns out to be the Born rule in disguise.
>
> To illustrate how a plausibly rational agent could reject branching indifference (this example is due to Tim Maudlin, though I've reframed it here): suppose I am offered a choice between chocolate or vanilla ice cream. I like them both, and would prefer to have both, but I can't. I have to choose (maybe I only have enough money for one scoop). Instead of choosing according to my free will, I instead perform a quantum experiment in order to split myself into two. One of me chooses chocolate, the other chooses vanilla. A rational agent could plausibly prefer this state of affairs (assuming they care about the multiverse *at all*) to one where only one flavor is actually chosen.

What is the sense in which this is supposed to be rational? How would one enact this rule in a way that's consistent with quantum mechanics, having consistent preferences over time and so on?

Wallace and Deutsch have given answers to those questions. You haven't AFAIK.

>> It's like the difference between 1 inch and 2 inches.
>
> The difference being: I can demonstrate a physical process that allows me to measure and compare distances in a meaningful and logically coherent way. (This is quite a remarkable fact about the universe, BTW.) You cannot do the same for the measure of a universe, not even in principle.

You can measure the measure of a universe:

https://arxiv.org/abs/1108.5329

More generally, any experiment you conduct to test quantum mechanics has to take into account the amplitude of different possible outcomes. This includes experiments in which macroscopic objects exist in multiple versions. You have offered no alternative explanation.

Elliot Temple said...

> > Branching indifference is not false. What is false is the proposition that an agent must accept branching indifference in order to be considered rational. That turns out to be the Born rule in disguise.
> >
> > To illustrate how a plausibly rational agent could reject branching indifference (this example is due to Tim Maudlin, though I've reframed it here): suppose I am offered a choice between chocolate or vanilla ice cream. I like them both, and would prefer to have both, but I can't. I have to choose (maybe I only have enough money for one scoop). Instead of choosing according to my free will, I instead perform a quantum experiment in order to split myself into two. One of me chooses chocolate, the other chooses vanilla. A rational agent could plausibly prefer this state of affairs (assuming they care about the multiverse *at all*) to one where only one flavor is actually chosen.
>
> What is the sense in which this is supposed to be rational? How would one enact this rule in a way that's consistent with quantum mechanics, having consistent preferences over time and so on?

Ron, branching indifference is not directly related to the Born rule, let alone equivalent. I think you must be combining it with some other ideas to reach something like a Born rule equivalent. You think that, along with some other premises, and via some reasoning, it *implies* the born rule. Right? If you disagree, please define branching indifference, define the born rule, and then point out the equivalence. If I'm right, please actually provide the reasoning involved.

Regarding the ice cream, I have a guess at what Ron might have in mind. Suppose I flip a coin so that I get each flavor in ~half of the universes. Then I can eat chocolate in a particular universe and think to myself "I would have liked to have both flavors; but I don't have them; but I know that, right now, versions of me are eating vanilla and that thought brings me a portion fo the satisfaction i would have gotten from personally having a half-portion of vanilla."

I think what's going on is the agent prefers to eat chocolate *and to have this thought* than to eat chocolate alone. In other words, the agent gets a higher reward, and more satisfaction from the ice cream, due to certain thoughts and the coin flipping action (his satisfaction from these thoughts depends on his belief this is really happening, and the coin flip enables that so that he isn't worried that he chose chocolate in ~all universes).

In this scenario, we're comparing alternatives with unequal rewards. So that is why one is preferred. This does not contradict branch indifference which is just saying that agents don't care about branching *indpendent of* any change in rewards.

If you drop the thought process about the multiverse from the scenario, then what is happening in those other universes cannot be relevant to the satisfaction/reward for an agent in a particular universe. That is, consider 2 hypothetical agents in separate multiverses. These are different scenarios. One eats chocolate and so do all his clones. The other eats chocolate but half his clones eat vanilla. Neither agent has any thoughts about what his multiversal clones are doing. Everything else being equal, the rewards are equal – rewards cannot depend on stuff you don't know about which never affects you in the future.

Ron said...

@Alan:

> What is the sense in which this is supposed to be rational?

In the sense that Deutsch defines in his original paper: "‘Rationality’ ... means conformity to a set of constraints on a decision maker’s preferences."

> How would one enact this rule in a way that's consistent with quantum mechanics, having consistent preferences over time and so on?

Quantum mechanics does not require a rational agent to have consistent preferences over time, what Wallace calls diachronic consistency. That is another assumption that Wallace and Deutch have to make in order to achieve their result. I could just as well have challenged that as branching indifference, but decided not to for the sake of brevity. Nonetheless, diachronic consistency is clearly not necessary to be rational. Rational agents can change their preferences, e.g. on the basis of new information. If diachronic consistency were required for rationality, no human being could ever be rational.

But I'd really prefer not to get into those weeds.

> Wallace and Deutsch have given answers to those questions. You haven't AFAIK.

I just did.

> You can measure the measure of a universe:

That paper does not support your claim. The word "universe" doesn't even appear in it, nor does it appear on the Wikipedia page for "quantum tomography."

You're going to have a very hard time explaining to me how you can measure the measure of a universe in light of the fact that "universe" is not actually a well-defined term under the MWI. But that's kind of beside the point because the question I actually asked was not "can I measure the measure of *a* universe" but rather "Can *I* measure the measure of *the* universe that *I* inhabit?" And the answer to that question is: no (because that would allow me to violate the no-cloning theorem).

Ron said...

@Elliot:

> You think that, along with some other premises, and via some reasoning, it *implies* the born rule. Right?

Well, yeah, of course. You have just described David Wallace's paper.

I *accept* the argument that Wallace presents, i.e. I accept that the conclusion follows from the premises. But I reject (some of) the premises. Specifically, I reject branching indifference as a precondition on rationality. (I also reject diachronic consistency as a precondition on rationality, but let's focus on one thing at a time.)

Branching indifference is equivalent to the Born rule in the same sense that Euclid's parallel postulate is equivalent to (for example) the proposition that the sum of the internal angles of a triangle equals the sum of two right angles.

Elliot Temple said...

> Specifically, I reject branching indifference as a precondition on rationality.

Oh, you *reject branching indifference as a precondition on rationality*. Either you didn't say it quite like that before (with the "as" part) or I missed it. That makes more sense to me.

So, do you accept that that branching indifference fits with a standard game theory view of a "rational agent"? Or do you deny that too? I think that's the relevant issue because the goal is not talking about rationality in general, just to see what conclusions one can reach based on non-probabilistic parts of QM and some game theory premises.

And a good next step would be to give a counter example (a rational agent violating branching indifference), although if you have a different way of arguing your point that'd be OK too. I think the ice cream scenario was intended to be a counter example, but I think I've answered that one.

Ron said...

@Elliot:

> Oh, you *reject branching indifference as a precondition on rationality*. Either you didn't say it quite like that before (with the "as" part) or I missed it. That makes more sense to me.

I didn't say it because I thought it was obvious. The only reason we're talking about "branching indifference" *at all* is that David Wallace introduces it as an assumption in the paper I cited. In that paper, "branching indifference" is an assumption introduced in a section entitled "The dictates of rationality" and specifically introduced by a paragraph beginning with the phrase, "The remaining rationality axioms..." I assumed you knew all that.

> So, do you accept that that branching indifference fits with a standard game theory view of a "rational agent"?

That depends on what you mean by "fits". A rational agent certainly *can* adopt branching indifference. I dispute that a rational agent should be *required* to adopt it in order to be considered rational. (That's actually a pretty easy case to make: I believe that an agent could plausibly be rational in a purely classical world, i.e. without accepting quantum mechanics *at all*. So requiring the acceptance of branching indifference aaPoR is a lot to ask.)

> I think the ice cream scenario was intended to be a counter example, but I think I've answered that one.

Yes, and your restatement of my position was exactly right (except for the minor quibble that a regular coin flip does not suffice. You have to do a *quantum* coin flip.)

The problem with your counter-argument is this:

> If you drop the thought process about the multiverse from the scenario

That is a very peculiar counterfactual for a proponent of MWI to raise. If you "drop the thought process about the multiverse from the scenario", then the entire argument completely falls apart. You can't have it both ways: either the evidence logically compels the belief that MWI is true, or it does not. If the evidence compels the belief that MWI is true, then a rational agent who is aware of the evidence cannot simply decide to ignore this and act as if it weren't true. *That* really is a compulsory part of what it means to be rational.

Elliot Temple said...

> (That's actually a pretty easy case to make: I believe that an agent could plausibly be rational in a purely classical world, i.e. without accepting quantum mechanics *at all*. So requiring the acceptance of branching indifference aaPoR is a lot to ask.)

I don't think it's a branching indifference violation to live in a classical world. It makes sense to be indifferent to impossibilities rather than to have preferences about them.

> That is a very peculiar counterfactual for a proponent of MWI to raise. If you "drop the thought process about the multiverse from the scenario", then the entire argument completely falls apart. You can't have it both ways: either the evidence logically compels the belief that MWI is true, or it does not. If the evidence compels the belief that MWI is true, then a rational agent who is aware of the evidence cannot simply decide to ignore this and act as if it weren't true. *That* really is a compulsory part of what it means to be rational.

If an agent is unaware of the multiverse, or not currently thinking about it, then *for many isolated scenarios*, a classical analysis is OK.

If the agent is thinking about the multiverse, then the state of the multiverse (as known to that agent's thoughts) is relevant to the agent's preferences and rewards, so there is no conflict with branching indifference. Of course, the agent may still be indifferent to the particular branching in question even if he considers it. And, of course, the state of the multiverse will also be relevant, whether the agent thinks about it or not, if it actually interacts with the agent ever again.

Ron said...

@Elliot:

> I don't think it's a branching indifference violation to live in a classical world.

> If an agent is unaware of the multiverse

You appear to have lost the plot here.

This entire discussion is about the claim that the Born rule can be derived from the unitary dynamics of QM plus decision theory. Specifically, the claim is (quoting Wallace):

"... the only rational strategy for an agent in an Everettian universe is to follow the Born rule."

This is true (or at least it has been proven) only if it is necessary for an agent who knows they are living in a multiverse to subscribe to branching indifference (and diachronic consistency) in order to be considered rational. It it were possible to prove this to be the case, Wallace would have proved it instead of adopting this as axioms. (I suppose it's possible that these can be proved but neither Wallace nor Deutsch are clever enough to figure out how to do it. I hope we can agree to discount this possibility.)

So they are axioms, and from these axioms the conclusions do indeed follow. The problem is that neither of these axioms is self-evidently true, at least not to me. In fact, the necessity of branching indifference for rationality for an agent that knows it is living in an Everettian universe seems self-evidently false to me, as illustrated by the ice-cream example. Unless you can explain to me why my preference for ice cream flavor variety in the multiverse is necessarily irrational, the argument fails.

Here's another way to look at it. Recall this from the explanation of why branch counting is irrational:

"...within the stylised context of my decision theory, the branch count is defined, so of course (given the representation theorem) the branch count- ing rule must violate some of my axioms. In fact, it violates the combination of branching indifference and diachronic consistency."

But I do not accept the necessity of branching indifference and diachronic consistency for rationality, so I do not accept the irrationality of branch counting. Branch counting, within the "stylised context of [Wallace's] decision theory" seems eminently rational to me. Why is it not rational to desire to maximize the reward for the greatest number of distinct agents? That's a perfectly admissibly objective function for a rational agent in a single universe, so why not for the multiverse? If I, say, win the lottery, why should I not rationally prefer to split myself as much as possible in order to create as many copies/versions of myself as possible, all of which can enjoy copies (and in this case they really are copies, not versions) of my lottery winnings?

And remember that you have to answer this question without reference to weights because that too is sneaking the Born rule in through the back door.

Elliot Temple said...

> You appear to have lost the plot here.

But before that you said:

> Yes, and your restatement of my position was exactly right

Then when I restated part of my own restatement, talking about the same thing again, instead of it being "exactly right" you decided I'd lost the plot. I don't think you understood either of my messages.

Now, after claiming my refutation of your ice cream example was "exactly right", you claim you've already won the argument via the ice cream example. You are lost.

> And remember that you have to answer this question without reference to weights because that too is sneaking the Born rule in through the back door.

"Weights" are a fundamental, non-probabilistic part of QM which can be legitimately referenced. I think the biggest is that you are not on board with DD's premises about QM. So let's try this. Tell me which of the following quotes you think are false:

https://arxiv.org/pdf/quant-ph/0104033.pdf

> In other words, when such sub-networks are in identical states, they are *fungible*. The term is borrowed from law, where it refers to objects, such as banknotes, that are deemed identical for the purpose of meeting legal obligations. In physics we may define entities as fungible if they are not merely deemed identical but *are* identical, in the sense that although they can be present in a physical system in varying numbers or amounts, permuting them does not change the physical state of that system. Fungibility is not new to physics. Many physical entities, such as amounts of energy, are fungible even in classical physics: one can add a Joule of energy to a physical system, but one cannot later extract the same Joule.

> A multiset is like a set except that some of its elements are fungible. Each element is associated with an integer, its *multiplicity*, which specifies how many instances of it appear in the multiset.

> An ensemble is a limiting case of a multiset where the total number of elements M goes to infinity but all the proportions [...] tend to definite limits.

> I shall refer to a non-empty sub-ensemble in which all the computers are in the same state as a branch of the ensemble

> These properties give each branch a well-defined identity over time, even though the values of its bits change.

> There are such things as fungible processes as well as fungible objects.

> The effect of an *n*-qubit quantum gate during one computational step is to transform the *3n* matrices representing the *n* participating qubits into functions of each other in such a way that the relations (14) are preserved.

> in order to model information flow we are using local interactions (gates) of the network to model local interactions in general quantum systems

> Given the universality of the Toffoli gate, all these properties must hold whenever a quantum network, or any part of it, performs a classical computation. In other words, whenever any quantum network (including a sub-network of another network) is performing a classical computation f, the matrices [...] for that network evolve independently of all its other descriptors.

Elliot Temple said...

> Thus in any sub-network *R* of a quantum computational network where a reversible classical computation is under way, half the parameters describing *R* are precisely the descriptors of an ensemble of classical networks. It is half the parameters because, from (14), any two of the three components [...] determine the third. This does not imply that such a subsystem constitutes half the region of the multiverse in which *R* exists. Proportions in the latter sense – which formally play the role of probabilities under some circumstances, as shown in Deutsch (1999) – are determined by the Heisenberg state as well as the observables, and do not concern us here because the present discussion is not quantitative.
>
> The other half of the parameters, [...] contain information that is physically present in *R *(it can affect subsequent measurements performed on *R *alone) but cannot reach the ensemble (the descriptors of the ensemble being independent of that information). But the reverse is not true: as (19) shows, information can reach the quantum degrees of freedom from the ensemble.

> The proposition that parts of the multiverse have the same description as an ensemble with given properties is not quite the same as the proposition that such an ensemble is actually present in those parts of the multiverse, for the description might refer to entities that are not present in addition to those that are. In particular, an ensemble has an alternative interpretation as a *notional *collection, only one member of which is physically real, with the multiplicity of a given branch representing the probability that the properties of that branch were the ones prepared in the real system at the outset, by some stochastic process. However, no such interpretation is possible if the branches affect each other, as they do in general quantum phenomena, and in quantum computations in particular (see Benjamin 2001).

> When a quantum computational network is performing a general computation, it need not be the case that the descriptors of any part of the network over two or more computational steps constitute a representation of an evolving e-algebra. [...] so the conditions discussed in Section 3 for branches to have an identity over time need not hold.

> In a typical quantum algorithm, [...] the qubits first undergo a non-classical unitary transformation [...], then a reversible classical computation, and finally another unitary transformation which is often the inverse [...] of the first one. Despite the fact that the branches lose their separate identities during the periods of the quantum transformations [...] we can still track the flow of information reasonably well in terms of ensembles:

Elliot Temple said...


> Therefore, if some sub-network of a quantum network performs a classical computation for a period if the network is isolated, and then it is run with some or all of the observables [...] being repeatedly measured between computational steps, it will still perform the same classical computation and will contain an ensemble identical to that which it would contain if it were isolated (though its other descriptors will be very different).

> Since a generic quantum computational network does not perform anything like a classical computation on a substantial proportion of its qubits for many computational steps, it may seem that when we extend the above conclusions to the multiverse at large, we should expect parallelism (ensemble-like systems) to be confined to spatially and temporally small, scattered pockets. The reason why these systems in fact extend over the whole of spacetime with the *exception *of some small regions (such as the interiors of atoms and quantum computers), and why they approximately obey classical laws of physics, is studied in the theory of decoherence (see Zurek 1981, Hartle 1991). For present purposes, note only that although most of the descriptors of physical systems throughout spacetime do not obey anything like classical physics, the ones that do, form a system that, to a good approximation, is not only causally autonomous but can store information for extended periods and carry it over great distances. It is therefore that system which is most easily accessible to our senses – indeed, it includes all the information processing performed by our sense organs and brains. It has the approximate structure of a classical ensemble comprising ‘the universe’ that we subjectively perceive and participate in, and other ‘parallel’ universes.

Alan said...

>> What is the sense in which this is supposed to be rational?
>
> In the sense that Deutsch defines in his original paper: "‘Rationality’ ... means conformity to a set of constraints on a decision maker’s preferences."

DD didn't pick constraints arbitrarily.

>> How would one enact this rule in a way that's consistent with quantum mechanics, having consistent preferences over time and so on?
>
> Quantum mechanics does not require a rational agent to have consistent preferences over time, what Wallace calls diachronic consistency. That is another assumption that Wallace and Deutch have to make in order to achieve their result. I could just as well have challenged that as branching indifference, but decided not to for the sake of brevity. Nonetheless, diachronic consistency is clearly not necessary to be rational. Rational agents can change their preferences, e.g. on the basis of new information. If diachronic consistency were required for rationality, no human being could ever be rational.

If you change your priorities then the way you value outcomes will change. But without diachronic consistency it's impossible for you to enact preferences consistently regardless of whether you change your mind.

> But I'd really prefer not to get into those weeds.

I'm puzzled. Do you want to discuss substantive issues or not? Are you just wasting your time and mine?

>> Wallace and Deutsch have given answers to those questions. You haven't AFAIK.
>
> I just did.

Above you denied that consistent decisions are possible because you might change your mind about something. Now you're saying you provided a consistent rule for rational decision making. Also, you haven't provided a detailed discussion of how one would go about enacting your rule, so you haven't provided answers.

>> You can measure the measure of a universe:
>
> That paper does not support your claim. The word "universe" doesn't even appear in it, nor does it appear on the Wikipedia page for "quantum tomography."
>
> You're going to have a very hard time explaining to me how you can measure the measure of a universe in light of the fact that "universe" is not actually a well-defined term under the MWI.

Universes are an approximation. If I pick some particular approximation and stick to it then there's no reason I can't discuss the measure of a universe.

> But that's kind of beside the point because the question I actually asked was not "can I measure the measure of *a* universe" but rather "Can *I* measure the measure of *the* universe that *I* inhabit?" And the answer to that question is: no (because that would allow me to violate the no-cloning theorem).

You can do experiments to test the evolution of the amplitudes of different possible outcomes a system over time. This doesn't require measuring the measure of the system you're currently in over the entire multiverse.

Ron said...

@Elliot:

> after claiming my refutation of your ice cream example was "exactly right"

No, that's not what I said. I said that your re-statement of my example was (almost) exactly right, i.e. this part:

> Suppose I flip a coin so that I get each flavor in ~half of the universes. Then I can eat chocolate in a particular universe and think to myself "I would have liked to have both flavors; but I don't have them; but I know that, right now, versions of me are eating vanilla and that thought brings me a portion fo the satisfaction i would have gotten from personally having a half-portion of vanilla."

I don't accept your subsequent refutation because...

> Then when I restated part of my own restatement, talking about the same thing again, instead of it being "exactly right" you decided I'd lost the plot.

Yes, that's right, because you started talking about agents who do not accept MWI. It's not that what you said about these agents was *wrong*, it's that talking about agents who do not accept MWI is *irrelevant* here (except as it informs the choice of criteria for what should be considered rational in general) for the reasons that I explained in my previous comment.

> "Weights" are a fundamental, non-probabilistic part of QM which can be legitimately referenced.

Yes, of course. But you have to remember that the only way we can ever actually know the weight of a quantum system is if it has been *prepared*. We cannot know the weight of an unprepared system because of the no-cloning theorem. So yes, weights can be legitimately referenced. It does not follow that "the weight of a universe" can be legitimately referenced because universes cannot be prepared.

> Tell me which of the following quotes you think are false:

None of them are false. But I don't see why you think any of them are relevant to a discussion of whether or not branching indifference should be assumed to be a precondition for rationality.

Ron said...


@Alan:

> DD didn't pick constraints arbitrarily.

Of course he didn't. He chose constraints that lead to the result he wanted to demonstrate. (BTW, Deutsch never mentions branching indifference at all. In his paper, it's a tacit assumption, and one that is by no means easy to discern. Only in the Wallace paper is it explicitly discussed.)

> > But I'd really prefer not to get into those weeds.

> I'm puzzled. Do you want to discuss substantive issues or not? Are you just wasting your time and mine?

I would prefer to deal with one issue at a time. When we have resolved the question of whether branching indifference should be assumed to be a precondition for rationality then we can go on, if you wish, to examine the question of whether diachronic consistency should likewise be assumed.

> Universes are an approximation. If I pick some particular approximation and stick to it then there's no reason I can't discuss the measure of a universe.

Of course you can *discuss* it. The question is whether "the measure of a universe" corresponds to something physically real, or whether it's an artificial mathematical construct, like Bohmian positions, inside of which Bornian probabilities have been cleverly hidden. I claim it's the latter. And my support for this is that the measure of a universe, like Bohmian positions, cannot ever be known to the inhabitants of that universe even in principle.

> You can do experiments to test the evolution of the amplitudes of different possible outcomes a system over time.

No, you can't. Once you do an experiment on a quantum system you *change* it in such a way that you cannot go back and do another experiment on the same system. Specifically, to perform an experiment on a system you have to entangle that system with a measurement apparatus in a thermodynamically irreversible way.

The best you can do is perform the same experiment on a *plurality* of systems that have been prepared in (presumably) identical states and then go back and retroactively try to tell a story to explain the behavior that you observe. It turns out that when you do this, two interesting things happen:

1. The outcomes of your experiments will not always yield the same results despite your best efforts to prepare the systems in identical states.

2. The only way to describe the prepared state of a quantum system in general that is consistent with the evidence is with a function whose domain is phase space and whose range is complex numbers.

That's really it. All the rest, including "particles" and "universes", is dramatic narrative.

wrf3 said...

Ron, FWIW your good friend Lubos just posed yet another take-down of MWI here.

Ron said...

@wrf3:

> Lubos

Ah, good old Lubos. Talk about burying the lede:

"... the wave function is not an objectively real object. Instead, it is a collection of numbers describing the observer's knowledge about the world."

He doesn't get around to this until the very last paragraph.

Well, Lubos, if this "collection of numbers" describes someone's "knowledge about the world", what exactly is the nature of this thing of which the possessor of this collection of numbers has knowledge? Particularly in light of the fact that these are *complex* numbers we're talking about here. (This is usually the point at which Copenhagenists say, "Shut up and calculate.")

(Just for the record, Lubos's statement is actually wrong, or, at best, an oversimplification. The wave function is not a "collection of numbers", it's a *function*, and in particular, it's a function on *phase space*, not physical space. If this function represents "knowledge", what exactly is the nature of the thing that it is knowledge *of*? Because it ain't classical reality.)

One of the frustrating things about this whole QM interpretation debacle is that *everyone* is wrong about *something* (except me, of course. I understand it all perfectly, but I seem to be the only one ;-)

wrf3 said...

He doesn't get around to this until the very last paragraph.
Not quite. In the middle of his post he says:

"The observer-dependence may be seen e.g. in the Wigner's friend setup. Wigner observes a friend who observes an elementary particle. They will unavoidably have a different description because the friend collapses the wave function after his measurement, while Wigner hasn't made any measurement by that time, and describes the whole lab as an entangled state of the friend and the particle. So Wigner and his friend clearly use a different wave function."

Is the "wave function" objectively real, or not? Lubos says it isn't, MWI says that it is.

what exactly is the nature of this thing of which the possessor of this collection of numbers has knowledge
We don't know. All we know is how it behaves, not what it really is. At least, according to Feynman. Do you know what it is?

*everyone* is wrong about *something*
Other than Lubos' oversimplification, what is he wrong about in his post?

Ron said...

> Other than Lubos' oversimplification, what is he wrong about in his post?

The fundamental problem that *everyone* makes is insisting that existence is a binary quality. A thing either exists, or it does not. This seems like a plausible assumption, but it is in fact false, and so if you base your reasoning on it you will go seriously astray. And it's not just physicists. Theologians get this wrong too. (This may be one reason why arguing with hard-core many-worlders like Elliot and Alan often feels very similar to me to arguing with YECs.)

It is simply not the case that the wave function either exists or does not exist. The wave function is simply in an ontological category of its own, a category that is distinct from the ontological category of rocks (classical objects), which is in turn distinct from the ontological category of Darth Vader (fictional characters), which are all distinct from the ontological category of Invisible Pink Unicorns (unfalsifiable things) and four-sided triangles (logically impossible things). And even that is nowhere close to an exhaustive list of all the ontological categories that exist (!).

Peter Donis said...

@Ron:
The wave function is not a "collection of numbers", it's a *function*, and in particular, it's a function on *phase space*, not physical space.

I don't think the "function on phase space" part is correct. The wave function is a function on the configuration space of the system, but that's not the same as phase space.

For example, consider two spinless particles each moving along one dimension, which is the simplest case for which the wave function cannot be viewed as a simple function on physical space. The wave function is a function of either two positions (in the position representation) or two momenta (in the momentum representation). Those are functions on (representations of) configuration space, which is a two-dimensional space because there are two particles each with one degree of freedom (adding spin or more spatial dimensions would add more degrees of freedom per particle). But the *phase* space of the system is a *four* dimensional space, since it has a dimension for the position and momentum of each particle.

Ron said...

@Peter:

You're right, I meant configuration space. My mistake.

Elliot Temple said...

Ron, do you think that the multiverse is an ensemble? If so, of what and with what multiplicities?

Ron said...

@Elliot:

> do you think that the multiverse is an ensemble?

Presuming that by "ensemble" you mean this:

https://en.wikipedia.org/wiki/Statistical_ensemble_(mathematical_physics)#Quantum_mechanical

then no, obviously not. An ensemble is, by definition, a system in a mixed state. The multiverse, by *definition*, is always in a pure state.

Why do you ask?

Elliot Temple said...

I just asked about your agreement with statements including:

> An ensemble is a limiting case of a multiset where the total number of elements M goes to infinity but all the proportions [...] tend to definite limits.

But now you don't know what I'm talking about when I talk about an ensemble.

I don't think you understand or think about DD's paper.

Ron said...

> I just asked

Well, no, you didn't "just ask." You asked that two days ago.

It may come as a surprise to you, but corresponding on this blog is not the only thing I do day to day. I have a life. And when someone asks me a question that includes a word with a well-established technical meaning, I can sometimes forget that that word has been locally redefined earlier in the conversation, especially after some time has passed.

So now that I know what you're talking about, sure, the multiverse is a Deutschian-ensemble (let's abbreviate that D-ensemble to distinguish it from the more usual meaning of statistical ensemble). So? I *still* don't see why you think this is relevant to a discussion of whether or not branching indifference should be assumed to be a precondition for rationality.

Elliot Temple said...

It is your responsibility to take into account the context of a discussion such as my immediately prior message and, more broadly, the literature under discussion which you claim to have deep dived on and to have understood in detail. You failed at your responsibility of taking into account discussion context and are now belligerent about your error. That is unreasonable and is representative of the general carelessness with which you approach intellectual matters.

You have still neglected to actually answer my question. The multiverse is an ensemble *of what* with *what multiplicities*?

The reason I'm talking about the multiverse in general is because we disagree about it (or understand it differently, or something) and that disagreement is a major underlying factor in the probability discussion. It comes up in e.g. your claims about branch counting.

Ron said...

@Elliot:

> It is your responsibility...

Funny, I don't remember entering into any kind of contractual relationship with you that obligates either of us in any way.

> You failed...

Yes, I did. I'm a fallible human being. If you want to interact with someone who never fails you will need to go elsewhere.

> and are now belligerent

Yes, I'm a crotchety old man, and I sometimes get belligerent when I'm dealing with self-righteous twits. It's another failing of mine.

> The multiverse is an ensemble *of what* with *what multiplicities*?

I have no idea, and I don't see how this can possibly shed any light on the matter at hand. If you want to explain why you think that branching indifference should be assumed as a pre-requisite for rationality, or otherwise defend your position, by all means go for it. But I'm not playing your stupid Socratic game.