Monday, April 20, 2009

The trouble with shadow photons

Chapter 7 of David Deutsch's "The Fabric of Reality" should be considered required reading for anyone who wants to understand the scientific process. Unfortunately, it is embedded in a book that is full of some crazy ideas, at least one of which is wrong even by Deutsch's own standards. This one mistake, which Deutsch makes very early on, infects the rest of his reasoning like a virus. This is very unfortunate because I think this is at least in part to blame for the fact that the book as a whole has not gotten the attention it deserves.

It makes a very interesting intellectual exercise to try to uncover Deutsch's mistake on your own. You don't need to be a physicist to find it. Here are two hints to get you started: the mistake is in chapter 2, and everything you need to know in order to figure it out is in this paper, which is written to be accessibly to a lay audience.

So at the risk of sounding like a broken record, get ye over to Amazon and buy a copy of Deutsch's book. Read chapter 7. Then read chapter 2 and try to solve this puzzle for yourself before you read any further. I promise you it will be time well spent. This post is not just about pointing a finger at David Deutsch and saying "ha! ha!" I want to make a much deeper point about how challenging it can be to figure out what is "true". It will help if you have the visceral experience of reading Deutsch's argument and trying to figure out for yourself what is wrong with it even if (perhaps especially if) you don't succeed.

Last warning. Spoiler alert.

Deutsch's mistake is in this paragraph, which in my copy is on page 43:

"Could it be that the photon splits into fragments which, after passing through the slits, change course and recombine? We can rule out that possibility 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."

In my "Quantum Mysteries Disentangled" paper I use the metaphor of a magic trick to describe how popular accounts of QM spread confusion. Most people think that magic is all about gimmicks and skillful sleight-of-hand, but the heart of a good magic trick is a narrative that seems plausible but in fact does not reflect the underlying reality. The elements of this narrative can be quite subtle. I take the Queen of Spades and I turn it face down and I put it, uh, over here. But in fact the card that I'm putting over here is not the queen of spades at all; I've already switched it out for a different card. Much later when the true identity of the card is revealed, you will swear on a stack of Bibles that that card was the queen of spades. You saw it with your own eyes. And you were watching it like a hawk the whole time. Except that by the time you started watching like a hawk the trick was already done. It happened during that little moment of confusion, when I lost my focus and couldn't quite remember what I was supposed to do next. In fact, I didn't lose my focus. Every move was scripted in minute detail. I say "uh" to make it look like I've lost my train of thought. That makes you take your guard down because if I've lost my train of thought then I'm not doing the trick. I look around trying to decide what I'm supposed to do with the card, and your gaze follows mine because deep down in your brain there are instincts that say when a member of your tribe is focusing their attention somewhere you should check it out too because they might be looking at a saber-tooth tiger. In that instant, I absent-mindedly put the card briefly back on the top of the deck before I put it over here. And in that instant I make the switch. Except that I don't even have to make a switch because in fact that card that I put on top of the deck was not the queen of spades either, it was two cards, with the queen of spades on the bottom.

Deutsch's mistake is a sin of omission: he fails to mention the crucial fact that when you do this experiment with the four detectors the interference goes away. This is a devastating fact for Deutsch's theory of shadow photons, but before I explain why there is another important thing to take note of, namely, that at this point in the argument Deutsch has not yet introduced the theory of shadow photons. This is what makes it so easy to miss that Deutsch has omitted an important fact.

The fact that adding detectors destroys interference is fatal for the theory of shadow photons. To understand why, we need to recap exactly what it is that the theory of shadow photons says: something influences the behavior of "real" (what Deutsch calls "tangible") photons to produce interference. Whatever that "something" is behaves just like "real" photons, except that it is "detectable only indirectly through ... interference effects ...". So we might as well call them (shadow) photons. Since shadow photons exist (because they have observable effects), it must be the case that entire shadow universes exist spanning an incomprehensible gamut of possible configurations, including some (actually incomprehensibly many) where David Deutsch does not exist, and therefore -- and this is crucial -- some in which the detectors on the slits do not exist.

This is the odd thing about shadow photons: they behave just like photons that exist in parallel universes except that their movements correspond exactly to the movements of photons in this universe. There are only two possibilities. One is that our universe is somehow privileged, and what we do here produces miraculous effects in the myriad shadow universes. If we decide to cover our slits then the photons in all the shadow universes are blocked, even those in shadow universes where the slits are still open. Imagine how puzzled those poor scientists must be trying to figure out why light behaves as it does. There is no correspondence between how light behaves in their universe and the physical configuration of their universe. Sometimes light passes through blocked slits, and sometimes it fails to pass through open slits. From this behavior they could likewise infer the presence of what is to them a shadow universe (which to us is the real universe) that governs the behavior of photons in their universe, but that just begs the question of why we happen to inhabit the one privileged universe whose macroscopic configuration governs the behavior of light in all of the shadow universes.

The other possibility is to postulate a new rule for shadow photons: only those shadow photons that come from shadow universes whose macroscopic configuration is the same as the "real" universe are allowed to influence "real" photons. But if we postulate that then it immediately follows that shadow universes with different macroscopic configurations have no influence on our universe whatsoever and therefore, by Deutsch's own criteria, do not exist.

One way or another, there is no escaping the fact that our universe is somehow special.

Now, the interesting this about this to me is not so much that Deutsch was wrong per se, but the process by which he came to be wrong. Unlike a magician, I'm pretty sure Deutsch did not set out intentionally to deceive. I'm also pretty sure that Deutsch didn't get it wrong because he was simply being stupid. To the contrary, I think Deutsch is probably brilliant, a lot smarter than me. For one thing, he's actually a physicist, which I'm pretty sure even now still makes an effective filter for idiocy. So what went wrong?

I have no way of knowing for sure, of course, but here's my best guess: I think Deutsch actually managed to fool himself. Deutch's book is, notwithstanding that much of it is actually wrong, a model of clear thinking. To find the flaw in his reasoning is not easy, in no small measure because of subtle details of how he presents his argument. This is why I urged you to actually do the exercise yourself.

The real point of this essay is not to harsh on David Deutsch, but to show that even very smart people, even scientists (sometimes especially scientists) can and do get things wrong, and sorting out the resulting mess is not always easy. This is one of many reasons why both scientists and Scientists ought always to maintain a healthy measure of humility.

UPDATE:

Here's what David Deutsch had to say about this (via email -- I'm pretty sure he hasn't actually read this post):


RG: I know you probably hear this a lot, but I believe I have found a serious flaw in the theory of shadow photons. In a nutshell, the rules of motion for shadow photons are governed by the macroscopic configuration of *our* universe. If a slit is open in *our* universe, both tangible and shadow photons pass through. If a slit is blocked in *our* universe, both tangible and shadow photons are blocked. It seems to me there are only two possibilities: either the macroscopic configuration of *our* universe governs the movement of shadow photons (in which case shadow-scientists must be mightily puzzled why their tangible photons sometimes pass through solid objects, and sometimes fail to pass through open slits), or we have to postulate that only shadow photons from universes whose macroscopic configuration matches our own can interact with our tangible photons.

DD: The latter is, to a good approximation, the case.

RG: But if we postulate this, then shadow photons from universes whose macroscopic configurations do not match ours cannot interact with our universe in any way, and therefore by your own criteria do not exist. Or have I missed something?

DD: You're claiming there's an inadequacy in the criterion for existing that I presented, not a flaw in the 'theory of shadow photons' (which is aka quantum theory). However, that criterion was not intended as a criterion of what *doesn't* exist. If it were used in that way, then we would have to classify all the photons that have left the sun, and passed the Earth, and are never going to strike anything in the future, as being nonexistent.


My response:

1. I find it disingenuous to claim that the theory of shadow photons is "a.k.a. quantum theory." The theory of shadow photons is in fact a.k.a. Hugh Everett's relative state formulation of quantum mechanics, which was later renamed the many-worlds interpretation by Bryce DeWitt. To be sure it is taken seriously by a great many people, but to say without qualification that it is quantum theory is just flat-out wrong. I appreciate Deutsch's intellectual honesty in essentially admitting that my criticism is valid, but I'm puzzled by how he can rail against arbitrary complexity in scientific explanations on the one hand, and then accept as essentially inarguable the proposition that parallel universes are causally connected on a microscopic level by virtue of their macroscopic configurations. It seems plain to me that such an "explanation" of QM gets you exactly nowhere. But I suppose we'll just have to agree to disagree about that.

2. John Cramer's transactional interpretation of quantum mechanics actually does consider photons that never interact with anything to be non-existent, so this is not as outlandish a notion as Deutsch implies.

UPDATE 2:

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.

Just for the record, my (current) disagreement with Deutsch is not huge. It's clear from the structure of QM that the proposition that there is only one (classical) universe is untenable. But that still leaves you with the choice of an infinite number of universes (Deutsch's position) or zero (mine). It has always seemed to me that zero was the more parsimonious choice, but I'm now beginning to have some doubts.

38 comments:

Don Geddis said...

Ah, darn it. I was just coming back (to the previous post) to suggest that very paragraph myself. But now, since you posted first, I can't really prove it, you'll just have to take my word for it.

My critique was going to be a little different. Namely, Deutsch's paragraph says that "at most one of them ever registers anything", but (following your lead that measurement = entanglement) the point is actually that EACH of the detectors DOES measure "a" photon -- as a single event -- but you (the scientist) then also get entangled with each such measurement, so "you" only appear to see one detector go off.

In other words, his mistake is assuming that the human experimenter is not made of quantum stuff too, and thus can't superimpose. So when he says that "we never observe two of the detectors going off at once", he means to imply that they can't actually do so.

But he misses the real resolution, that there are different versions of "you", each of which notices a different detector go off.

This isn't the exact same critique you gave. On the other hand, I did focus on the same paragraph :-).

Anonymous said...

Thanks for the enlightening discussion. I’m just now beginning to read Fabric of Reality and having a hard time getting into it. His harangue on reductionism is bothersome (and obsolete) and then he dives into reductionist techniques to prove his concepts. He is also messing with microcosmic interactions and using macrocosmic examples and explanations; oh, that way madness lies, along with action at a distance, the EPR puzzle, and all that fuzzy noise. When I got to the page 44 and read the description of shadow photons I had to stop. It was an astounding leap, so I Googled “shadow photons” and found your critique. I guess I’ll continue with the book since I enjoy theoretical speculation, but your example of the card trick is right, this is more persuasion than forthright deliberation.

Rumi045 said...

Reading books on the iPad Kindle app is almost like a new way of reading. I too got to this site by Googling "shadow photons" while reading Fabric of Reality. I attempted to find the error, but failed ; although I saw and learned interesting new ideas (for me) along the way. Now back down the rabbit hole.

Elliot Temple said...

> 1. I find it disingenuous to claim that the theory of shadow photons is "a.k.a. quantum theory." The theory of shadow photons is in fact a.k.a. Hugh Everett's relative state formulation of quantum mechanics, which was later renamed the many-worlds interpretation by Bryce DeWitt.

DD has argued publicly that MWI *is* quantum theory. He has reasons for that terminology, and the details of what he means are available to interested parties (and already known to you, anyway), so I don't see the problem. He does use other terminology sometimes to avoid confusion.

> and then accept as essentially inarguable the proposition that parallel universes are causally connected on a microscopic level by virtue of their macroscopic configurations

They aren't, they are connected or disconnected on a microscopic level by virtue of their microscopic configuration. But when objects macroscopically differ, we know they are part of "separate universes" without needing to look at microscopic details. The macroscopic states are due to the microscopic states, and give us a shortcut to knowing some things about the microscopic states.

If you have further questions about DD's books, or want to share your understanding of the epistemology or physics for criticism, or want to read other's thoughts, I invite you to join the successor forums to the FoR, BoI, and TCS[1] forums. DD wrote thousands of posts in the past and you can talk with the people who best know his work. http://fallibleideas.com/discussion

[1] TCS is DD's theory of parenting and education based on applying Critical Rationalism. See e.g. http://fallibleideas.com/taking-children-seriously and https://curi.us/tcs/

Elliot Temple said...

> But he misses the real resolution, that there are different versions of "you", each of which notices a different detector go off.

DD knows that. (Source: thousands of conversations with him.)

Ron said...

@Eliot:

Hi, and welcome to RR! If you don't mind my asking, how did you find this post?

> DD has argued publicly that MWI *is* quantum theory.

Yes, I know, that's exactly what I'm criticizing: his claim that MWI is the *only* tenable interpretation of QM. It isn't.

Furthermore, MWI is often presented in a caricatured way that is actually false. The popular view of MWI is one of discrete universes that "split" when "measurements" are made, i.e. at any point in time there exists some definite finite integral number of universes. That's not how it works. DD obviously knows this, but you'd be hard pressed to find this idea debunked in any of his non-technical writings.

(Just for the record, this post was written ten years ago, and my thinking has changed somewhat since then, though I do still stand behind the substance of my criticism here.)

Elliot Temple said...

Found because https://news.ycombinator.com/item?id=19888093

> Furthermore, MWI is often presented in a caricatured way that is actually false. The popular view of MWI is one of discrete universes that "split" when "measurements" are made, i.e. at any point in time there exists some definite finite integral number of universes. That's not how it works. DD obviously knows this, but you'd be hard pressed to find this idea debunked in any of his non-technical writings.

If you mean that DD should blog more, I agree. But below is an example of DD rejecting the splitting idea in non-technical writing. I still don't see what is "disingenuous" about his position that MWI is what you get when you take QM math seriously, and I don't know why you didn't respond to the physics issue I also addressed, which I thought was more important.


Begin forwarded message:

From: David Deutsch
Subject: Re: Conservation Laws and MWI
Date: June 29, 2010 at 3:38:01 AM PDT
To: Fabric-of-Reality@yahoogroups.com
Reply-To: Fabric-of-Reality@yahoogroups.com

On 28 Jun 2010, at 11:30pm, Elliot Temple wrote:

> Conservation laws are actually very important to physics. See, for example, the Feynman Lectures on Physics (volume 1).

For what it's worth, the conservation laws, in the senses in which they are fundamental to physics, wouldn't be violated in the 'splitting universes' version of the Everett interpretation.

There are several ways of expressing the law of the conservation of energy. One of them is: it is impossible to build a perpetual motion machine of the first kind (a device that delivers net work to its environment and returns to its original state). Evidently splitting universes would not provide any means of building such a machine. Another is that the rate of flow of energy out through any closed surface in space is equal to minus the rate of change of the total energy in the volume enclosed by that space. Again, this would still be true if universes split.

The version of the conservation laws that *is* violated by splitting universes is something like: 'the sum of the energies of all physical systems in existence is constant'. But this only applies to systems whose energies are additive. Who told us that energies are additive across universes when they split? In fact, the other two versions of the conservation law tell us that they are not. (Or rather, would not be, if universes did split in the manner envisaged in that version of the Everett interpretation.)

The fundamental problem in the 'splitting universes' version is simply that there is no feature of the quantum-mechanical description of physical systems that corresponds to the moment, or the process, of splitting.

-- David Deutsch




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Ron said...

@Eliot:

> I don't know why you didn't respond to the physics issue I also addressed, which I thought was more important.

Not sure what you're referring to by "the physics issue." Can you please me more explicit?

Elliot Temple said...

My comment addressed two issues. It had two quotes and a reply to each quote. You did not respond to the second issue, which was about physics. Here it is:

>> and then accept as essentially inarguable the proposition that parallel universes are causally connected on a microscopic level by virtue of their macroscopic configurations

> They aren't, they are connected or disconnected on a microscopic level by virtue of their microscopic configuration. But when objects macroscopically differ, we know they are part of "separate universes" without needing to look at microscopic details. The macroscopic states are due to the microscopic states, and give us a shortcut to knowing some things about the microscopic states.

Elliot Temple said...

FYI Alan Forrester, a physicist and expert on Popper and Deutsch, has written a reply to this blog post at: http://curi.us/2192-alan-discussion#c12353

Ron said...

@Eliot:

> [Multiple universes] are connected or disconnected on a microscopic level by virtue of their microscopic configuration

No. Please re-read the post paying particular attention to paragraph that begins, "The fact that adding detectors destroys interference is fatal for the theory of shadow photons," as well as the subsequent two paragraphs.

Please note that I am not disputing the MWI. My quarrel is with the "shadow photon" dramatic narrative, which is doomed to fail because it tries to side-step the issue of entanglement. That's like trying to describe relativity without mentioning that the speed of light in a vacuum is constant in all inertial frames.

If you doubt this, then explain to me in terms of shadow photons why adding detectors to the slits destroys the interference (a fact that Deutsch, as also noted in the OP, neglects to mention.)

> If, according to the simplest explanation, an entity is complex and autonomous, then that entity is real.

That is actually not enough. The entity also has to have observable effects (it has to "kick back" to quote Deutsch quoting Johnson), otherwise the invisible pink unicorn would count as real. And that's the problem: QM itself insures that shadow photons in universes with macroscopic configurations different from our own CANNOT POSSIBLY UNDER ANY CIRCUMSTANCES have any observable effects on our universe (to be technical about it. That should at least make us slightly suspicious that they qualify as "real".

Alan said...

>> If, according to the simplest explanation, an entity is complex and autonomous, then that entity is real.
>
> That is actually not enough. The entity also has to have observable effects (it has to "kick back" to quote Deutsch quoting Johnson), otherwise the invisible pink unicorn would count as real. And that's the problem: QM itself insures that shadow photons in universes with macroscopic configurations different from our own CANNOT POSSIBLY UNDER ANY CIRCUMSTANCES have any observable effects on our universe (to be technical about it. That should at least make us slightly suspicious that they qualify as "real".

The actual existence of invisible pink unicorns isn't the simplest explanation of anything, so they are not real by that standard. Do you think that objects cease to exist when they pass the event horizon of a black hole? Such objects can't have any effect on objects outside the event horizon, so they do they exist?

Ron said...

@Alan:

> The actual existence of invisible pink unicorns isn't the simplest explanation of anything, so they are not real by that standard.

Fair enough, but that does rather beg the question because it's hard to define simplicity. There are a lot of people who report feeling the presence of the Holt Spirit. One way to explain this is that the Holy Spirit is real and these people do in fact feel its presence. Another way to explain it is that all of these people are suffering from the same delusion. Which explanation is simpler?

> Do you think that objects cease to exist when they pass the event horizon of a black hole?

That depends on what you mean by "exist". Existence is not a binary property. See:

http://blog.rongarret.info/2015/02/31-flavors-of-ontology.html

I would say that an object that passes the event horizon of a black hole transitions to a different ontological category (probably -- the jury is still out on exactly what happens around event horizons).

Elliot Temple said...

> > [Multiple universes] are connected or disconnected on a microscopic level by virtue of their microscopic configuration

> No. Please re-read the post paying particular attention to paragraph that begins, "The fact that adding detectors destroys interference is fatal for the theory of shadow photons," as well as the subsequent two paragraphs.

All influence is local (happens at a microscopic location). Macroscopic objects (like labs, detectors or universes) have no direct role in QM, just like they don't in classical physics which deals with e.g. atoms (or arguably actually just sub-atomic particles which imply how atoms work) but not, directly, chairs (chairs are due to the implications of the properties of tiny things and the local rules of physics governing those tiny things).

When you say "no" to me above, are you denying locality? Do you think what I said contradicts QM math? And do you remember the stuff about waves of differentiation from BoI?

Ron said...

> All influence is local

That depends on what you mean by "influence". QM has some inherently non-local aspects, c.f. Bell's theorem.

> Macroscopic objects (like labs, detectors or universes) have no direct role in QM

Again, this depends on what you mean. The macroscopic configuration of the/a universe is what determines the Hamiltonian of a system. I don't know if you consider the Hamiltonian to have a "direct role" in QM. Its role seems pretty "direct" to me but I don't want to quibble over terminology.

But all this is beside the point because we're not talking about QM, we're talking about a *story*, specifically, the story that says that the reason that we see interference with single photons is that there are shadow photons going through the other slit, and that this happens if and only if the other slit is open. Slits are macroscopic things (by the standards of QM).

> do you remember the stuff about waves of differentiation from BoI?

I have no idea what you're referring to here.

Elliot Temple said...

>> do you remember the stuff about waves of differentiation from BoI?

> I have no idea what you're referring to here.

The phrase “wave(s) of differentiation" is used in BoI 13 times. It's important to DD's explanation of the multiverse and to the issues we’re talking about. Please reread ch 11 before trying to continue this discussion.

> QM has some inherently non-local aspects, c.f. Bell's theorem.

No, QM is fully local. See:

https://arxiv.org/abs/quant-ph/0003146

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

Ron said...

> The phrase “wave(s) of differentiation" is used in BoI 13 times

Ah. Sorry, I misunderstood. I read the final capital I as a lower-case L and thought you had written "Bol" and that this was someone's name. I didn't realize it was an acronym for The Beginning of Infinity. I also thought that "differentiation" in this context was referring to calculus.

So yes, now that I know what you're referring to, I do understand "waves of differentiation". What was the point you were trying to make with those?

> QM is fully local. See:

Responding to that is going to be *way* beyond the scope of a comment. I'll have to write up a whole blog post on that. I'll just say here that was deliberately vague when I chose to use the phrase "some inherently non-local aspects", and what you mean by "fully local" is not what that phrase is generally taken to mean in discussions of this topic. In particular, I would not consider the goings-on in universes that I (which is to say, the entity with which you are conducting this discussion) do not inhabit to be "local".

But here's a quick question for you to make sure we're on the same page with respect to MWI: if you and I conduct an EPR experiment with both of our measurements conducted along the same axis, how many universes do we end up with at the end of that process? What about if our measurements are conducted along axes that are misaligned by a small angle?

Elliot Temple said...

> Responding to that is going to be *way* beyond the scope of a comment. I'll have to write up a whole blog post on that.

OK, though I would think that if these papers contained known errors (known to you but not me) that you would refer me to an existing paper instead of writing a post. Do you have something novel to say?

> what you mean by "fully local" is not what that phrase is generally taken to mean in discussions of this topic. In particular, I would not consider the goings-on in universes that I (which is to say, the entity with which you are conducting this discussion) do not inhabit to be "local".

In this kind of discussion, "local” is generally taken to mean, basically, "no faster than light motion or faster than light information flow”. (Source: multiple physicists.) That is what I mean.

Being unable to interact with something due to decoherence (what you're calling being in a different universe) is not a locality issue (it’s not an issue of of being unable to interact due to spacelike or timelike separation). And decoherence spreads between systems by local processes (information about system 1 has to reach system 2). That spread of information, which causes decoherence, is what the wave of differentiation is.

re EPR: 2 for same axis, 4 for different axis. Note that the process by which those universes arise involves *three* measurements: the two initial measurements and the later measurement comparing them (which happens after the information from the first two measurements has been brought together to the same place and time).

Ron said...

> I would think that if these papers contained known errors (known to you but not me) that you would refer me to an existing paper instead of writing a post.

If that were the case then yes, that is exactly what I would do. But you've neglected to consider a third possibility: that the papers contain errors that are known neither to you nor to me, but are known to someone. And you've also neglected a fourth possibility: that the papers contain errors that are not yet known to anyone, but will be found by someone in the future.

But the reason I need to write a post is that our difference here is (I'm pretty sure) not one of substance, it's one of language, and differences in language are extraordinarily difficult to resolve and must be done with great care. Otherwise things can spin wildly out of control, as they are currently doing in our discussion on FI. I don't want that to happen here, and avoiding it is going to require quite a bit of effort on my part because you can be quite the stickler for detail.

> Do you have something novel to say?

Novel with respect to what state of knowledge? The whole of humanity? Probably not. You? Maybe, I don't know. Why don't you wait and see what I have to say and then you can decide for yourself.

> "local” is generally taken to mean, basically, "no faster than light motion or faster than light information flow”

OK. On that definition I agree with you that QM is "fully local."

> Being unable to interact with something due to decoherence (what you're calling being in a different universe) is not a locality issue

As you've defined locality, you're right, it's not. But it is a problem with the ontology of MWI. (A fatal one IMHO, but I'm not ready to defend that claim to you.)

> decoherence spreads between systems by local processes

Agreed.

> 2 for same axis, 4 for different axis.

OK. So suppose we do the experiment with entangled photons in the Bell state |00> + |11> and axes rotated relative to each other by (say) one degree. I will offer you a bet at 2:1 odds that the outcomes of our measurements will be the same, i.e. if they are the same you pay me $1, and if they are different I pay you $2. I presume you will not take that bet (if I'm wrong about that, by all means let us do this experiment!) but how do you justify not taking it?

Alan said...

>>>But here's a quick question for you to make sure we're on the same page with respect to MWI: if you and I conduct an EPR experiment with both of our measurements conducted along the same axis, how many universes do we end up with at the end of that process? What about if our measurements are conducted along axes that are misaligned by a small angle?
>
>> 2 for same axis, 4 for different axis.
>
> OK. So suppose we do the experiment with entangled photons in the Bell state |00> + |11> and axes rotated relative to each other by (say) one degree. I will offer you a bet at 2:1 odds that the outcomes of our measurements will be the same, i.e. if they are the same you pay me $1, and if they are different I pay you $2. I presume you will not take that bet (if I'm wrong about that, by all means let us do this experiment!) but how do you justify not taking it?

For an angle of 1 degree, the probability of them being different is sin^2(1 degree), which is about 3*10(-4). So the expected payoff of taking the bet is $(2*3*10(-4)-(1-3*10(-4))) which is approximately -$1. So that particular bet would not pay off. I don't bet as a matter of general policy, but even if I did that bet would suck.

Alan said...

Actually the probability is sin^2(1/2 degree), which is about 8*10^(-5), but the payoff is still approximately -$1 so I wouldn't take the bet.

Ron said...

@Alan:

Thanks very much for that analysis, but I asked that question in service of preparing a response to Elliot, so I really need to know whether or not *he* would take the bet and why. In the MWI there are no probabilities. There are only (in this scenario) four universes. In two of them he wins $2 and in two of them he loses $1. All of this is deterministic, there are no probabilities involved. So why refuse the bet?

Elliot Temple said...

I agree with Alan, and FYI I would be more interested in answering the question if I knew what the point of it was (where are you going with it).

I now guess the reason you asked the question is you are unfamiliar with the literature, e.g. https://arxiv.org/abs/quant-ph/9906015

Ron said...

@Elliot:

> I now guess the reason you asked the question is you are unfamiliar with the literature

I knew about the paper you cited, but I'd never studied it in detail. But that's not the reason I asked. The reason I asked is that I wanted to see what you would cite as your justification.

Note that your justification is different from Alan's. Alan invoked probability directly. There's nothing wrong with that, of course, that's what most people would do. But a many-worlder can't invoke probability directly because everything in MWI is deterministic. That's why I wanted to know how you would justify your answer. For some reason I feel the need to be exquisitely careful not to assume anything about your world view for which I do not have direct evidence.

Having given the paper a cursory reading, the general argument seems to go like this: start with a system of N eigenstates with N>>1 and all of equal amplitudes. By symmetry, a rational agent would be indifferent to betting on any of those outcomes. Now "coalesce" these eigenstates into groups that correspond to the actual amplitudes of some actual state. Larger groups are preferred over smaller groups, and by doing the "coalescing" in the right way, the result can be made to exactly mirror the usual math. Real numbers are approached in the limit as N->infinity. Or something like that.

Is that anywhere close to being correct?

Elliot Temple said...

Since the paper doesn't use the word "coalesce", I regard your unwillingness to use quotes in true ways to be a major problem. I also find it strange that you're trying to differentiate my view from Alan's when I said I agree with Alan (and FYI DD, the paper author, also agrees with Alan about this).

Ron said...

> I regard your unwillingness to use quotes in true ways to be a major problem.

Those are scare quotes:

https://en.wikipedia.org/wiki/Scare_quotes

I'm sorry, Elliot, but I just can't deal with your level of nit-pickery. Good bye.

Alan said...

>> I now guess the reason you asked the question is you are unfamiliar with the literature
>
> I knew about the paper you cited, but I'd never studied it in detail. But that's not the reason I asked. The reason I asked is that I wanted to see what you would cite as your justification.
>
> Note that your justification is different from Alan's. Alan invoked probability directly. There's nothing wrong with that, of course, that's what most people would do. But a many-worlder can't invoke probability directly because everything in MWI is deterministic. That's why I wanted to know how you would justify your answer. For some reason I feel the need to be exquisitely careful not to assume anything about your world view for which I do not have direct evidence.

I invoked probability because it is unproblematic in the MWI. It is problematic in all the other interpretations.

> Having given the paper a cursory reading, the general argument seems to go like this: start with a system of N eigenstates with N>>1 and all of equal amplitudes. By symmetry, a rational agent would be indifferent to betting on any of those outcomes. Now "coalesce" these eigenstates into groups that correspond to the actual amplitudes of some actual state. Larger groups are preferred over smaller groups, and by doing the "coalescing" in the right way, the result can be made to exactly mirror the usual math. Real numbers are approached in the limit as N->infinity. Or something like that.
>
> Is that anywhere close to being correct?

No. Even setting aside your careless misquoting you're not close to being correct. For a start you don't state what counts as being a rational agent or why that matters

Ron said...

> I invoked probability because it is unproblematic in the MWI. It is problematic in all the other interpretations.

OK, I get that you believe that to be true. But you do understand that there is not a consensus on this, yes?

> > Is that anywhere close to being correct?

> No.

OK, thanks for letting me know. I'll go back and give it a more careful read.

If you want to give me or point me to an ELI5 version that would be appreciated.

Ron said...

> If you want to give me or point me to an ELI5 version that would be appreciated.

Never mind, I found it on my own:

http://blogs.discovermagazine.com/cosmicvariance/2012/04/16/quantum-mechanics-and-decision-theory/

My initial understanding turns out to be completely correct. Your criticism:

"you don't state what counts as being a rational agent or why that matters"

is invalid. *Deutsch* defines "rational decision maker" in his paper. I was simply using "rational agent" as a shorthand synonym.

(You really seem to have a problem with the concept of synonyms. Why is that?)

Alan said...

> My initial understanding turns out to be completely correct. Your criticism:
>
>> you don't state what counts as being a rational agent or why that matters"
>
> is invalid. *Deutsch* defines "rational decision maker" in his paper.

I know that Deutsch defines what counts as rationality in decision theory in his paper. In order to refute his argument you would have to be able to state it. That's why it matters whether you have described what counts as a rational decision maker.

Ron said...

@Alan:

> In order to refute his argument

Wow, we have an enormous disconnect here. I wasn't trying to refute his argument. I was just trying to do a sanity check on whether or not I was anywhere close to *understanding* it. Why did it even enter your mind that I was trying to *refute* something in the comment to which you were responding?

At this point I feel the need to ask: what is your goal in this exchange? Are you trying to teach me something? Learn something from me? Persuade me of something (and, if so, what?) Jerk my chain?

Also, are you the same Alan with whom I was corresponding on the FI mailing list?

Ron said...

Just for the historical record: I have now done a very deep dive into this issue, which ended up here. Wallace explicitly lays out the assumptions required for Deutsch's proof to carry through, and I dispute one of them: branch indifference. It is not at all clear, on the rhetoric of multiple worlds, that branch indifference holds. If I am going to care about "copies of me" *at all* then it is far from clear that I should be indifferent between having one of me receiving a reward and having N>1 of me receiving that same reward. In fact, I believe that Deutsch and Wallace have surreptitiously snuck the Born rule into their analysis through this assumption. The Everettian decision-theoretic outcome is only in conflict with the Born rule in the case of unequal weights. If the weights of all the branches are equal then the Born rule is equivalent to branch counting (insofar as branch counting can be considered a coherent concept at all). Branching indifference is *essential* to extending the argument to the case of unequal weights, which is the only case that is at all interesting because it is the only case where Everettian and orthodox intuitions can possibly diverge. So the entire argument hangs on branching indifference.

It might be possible to justify branching indifference (though I don't see how). But Deutsch and Wallace take it as an unjustified axiom, and hence their entire argument is simply begging the question.

Elliot Temple said...

> If I am going to care about "copies of me" *at all* then it is far from clear that I should be indifferent between having one of me receiving a reward and having N>1 of me receiving that same reward.

Deutsch does *not* claim that one should be indifferent to what proportion of (a branch of) the multiverse something good or bad happens to versions of you in.

Ron said...

@Elliot:

> Deutsch does *not* claim that one should be indifferent to what proportion of (a branch of) the multiverse something good or bad happens to versions of you in.

I never said he did. That's not what "branching indifference" [1] means. Have you read the Wallace paper that I linked to above?

[1] Since you are a stickler for detail, I should note that I wrote "branch indifference" rather than "branching indifference" above. Wallace uses both spellings. AFAICT he intended these to be synonyms.

Alan said...

I quote from page 12 of the Wallace paper you chose to cite:

"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."

I have other arguments on top of this, but you haven't even criticised the arguments in the paper.

Ron said...

@Alan:

> you haven't even criticised the arguments in the paper

That's true. It's because after you failed to respond to this question:, which I asked back in May...

> At this point I feel the need to ask: what is your goal in this exchange? Are you trying to teach me something? Learn something from me? Persuade me of something (and, if so, what?) Jerk my chain?

> Also, are you the same Alan with whom I was corresponding on the FI mailing list?

... I assumed that you and Elliot had both tuned out of this thread and so there didn't seem to be any point in putting a lot of effort into my comment. It really was, as I said, just for the historical record.

Now that I know that you two are still paying attention I might take the time to write up a more extensive response. I'd be more inclined to do that if you would answer my questions above, particularly the first one.

Ron said...

Once more for the record, I just posted an extended followup:

http://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html

Alan said...

> At this point I feel the need to ask: what is your goal in this exchange? Are you trying to teach me something? Learn something from me? Persuade me of something (and, if so, what?) Jerk my chain?

I'm just interested in the topic.

> Also, are you the same Alan with whom I was corresponding on the FI mailing list?

Yes.

I didn't reply cuz the questions weren't interesting to me.