As it is the Many Worlds Interpretation, I think it is reasonable to expect there to be worlds in the resulting ontology.
Allow me to refresh your memory of what I said previously. “Not really. I suspect that what you’re referring to as “MWI” contains the idea that, in addition to a wavefunction evolving unitarily under the Schrödinger equation, there are also ontologically primitive “branches” (or “worlds”) which “split”.”
You ignored one of the words—do you see which one?
But if you wish to defend a worldless version of MWI which just contains “a wavefunction evolving unitarily under the Schrödinger equation”, feel free to explain how that is compatible with special relativity.
Again, this is elementary. I suggest you read that MWI FAQ. You’ll find more authoritative sources if you look around, but it’s a good place to start.
Congratulations, it looks like you’re pioneering a whole new stage in the appropriation of names for consciousness by people who claim it doesn’t exist … But apparently, not any more. What on earth it does mean, coming from you, I have no idea.
Are you unfamiliar with analytic functionalism? Of course you’re not. Then why are you pretending to be?
The idea that one can coherently conceive of “phenomenal consciousness” separately from structure and function (and vice versa) is precisely the intuition that leads people to think that zombies are conceivable. The denial that zombies are conceivable is one of the standard positions in the philosophy of mind. Spare me your disingenuous and patronising tone of ‘mind-boggled befuddlement’.
You espouse a physical ontology in which there are no “worlds”
I didn’t say that, I said there were no ontologically primitive worlds, which only leaves open a yawning chasm of logical room for “ontologically non-primitive worlds”. Do you think that “temperature” not being ontologically fundamental disqualifies all statements of the form “the temperature of this gas is …”?
or in which the existence of a world is somehow an approximate thing, a matter of opinion or perspective,
Is the temperature of a gas a matter of opinion or perspective? Is it approximate? Well ultimately yes it is “approximate”, though there isn’t much to be said for calling it a “matter of opinion” is there?
even though you’re in a world.
The notion of “you” is as “approximate” as the notion of “’world”.
Here’s something I find mind-boggling: Why does your side always conflate “fuzzy around the edges” with “non-existent”. For instance, Dennett in Time and the Observer makes a powerful case for denying that our consciousness consists of a linear sequence of “moments” such that for each moment there is unique, well-defined ‘fact of the matter’ as to what you’re conscious of at that moment. Perhaps I’m not speaking for all of you here, but why do many of you think that conceding this point entails denying that consciousness exists? Does observing that the “temperature of a single gas molecule” makes no sense entail that temperature doesn’t exist?
The distinctive unifying idea of special relativity is that the geometry of the universe is that of Minkowski space. The reality of things is a four-dimensional partially ordered set of point events which can be divided into hypersurfaces of equal coordinate time in a variety of ways. Two events may be simultaneous in one description of a physical process, but if they are spatially separated, then we can transform to another description in which they are no longer simultaneous. Simultaneity is a coordinate artefact and there is no universal time.
Wavefunctions are always defined with respect to a particular time-slicing, a particular foliation of space-time into hypersurfaces. All a Lorentz transform can do is change the tilt of those hypersurfaces with respect to the time axis of your coordinate system; you’re still stuck with a particular preferred foliation as the ontological base of your wavefunction’s time evolution. If you reify the wavefunction, you end up reifying your coordinate system as well.
That is the substance of MWI’s problem with relativity. A physicist might call it “ontological gauge-fixing”. In theories with a gauge symmetry, you’re allowed to work in a particular gauge for the purposes of calculation, but the end product, the quantitative predictions, must be gauge-invariant. If they show a dependence on your choice of gauge, you’ve done something wrong.
Here, we’re trying to construct an ontology for quantum theory. The ontological significance of special relativity for time is that universal time is a coordinate artefact, yet in MWI ontologies, we end up with an objective universal time. That’s evidence of a mistake, and the mistake is that you are treating a wavefunction as an objectively existing thing, when it is just a frame-dependent tabulation of probability amplitudes.
Versions of MWI which fix a universal time and a particular Hilbert-space basis (such as position) may not be believable, but at least they are clear and explicit about what it is that is supposed to exist. When I think of supposedly more sophisticated approaches to MWI, where That Which Exists is just the universal wavefunction, in its sublime purity, beyond all specific choices of coordinate and basis, and where the contingent particularities of individual worlds are supposed to be logically implicit in its structure somehow… my overall impression is of utterly contemptible vagueness and handwaving, often suffused with a mystic adoration of the Big Psi.
Let’s pretend for a moment that I don’t have an issue with the idea that the world only exists “approximately”, and that the ultimate objective reality is some sort of wavefunction. That’s your hypothesis, fine. Can you tell me the nature of this approximateness? Are we taking some sort of limit? If so, can you be more specific? Your original words were
“Branches” are just patterns that emerge when you zoom out to the macro-scale
I asked for more details and you linked to the MWI FAQ—which I have seen many times before, and which mostly consists of word-pictures. That is not enough, although a word-picture can be a fine way to fool yourself into thinking that your ideas make sense.
I am going to pose a challenge to you. The issue which is ultimately at stake: whether a “Many Approximate Worlds Interpretation” even makes sense as a theory. However, we won’t try to resolve that directly. The actual challenge is much simpler. I ask merely that you exhibit a mathematically exact definition of an “approximate world”. This is theoretical physics we’re discussing, it uses exact mathematics, and if the concept is genuinely relevant, it will have a mathematical formulation and not just a verbal one.
Since these approximate worlds are supposed to be contained implicitly within the universal wavefunction, that is the relationship which I am expecting to see formally elucidated. I don’t expect to see statements about a theory of everything; supposedly all of this can be explained at the level of nonrelativistic quantum mechanics. I just want to see an exact statement of what the relationship between world and wavefunction is supposed to be.
If you want to point to a particular proposition in a paper somewhere, fine. Just give me more to work with than shapeless verbal formulations!
There are many other things to discuss in your comment, we can return to those later. You should also feel free to delay responding to what I said about relativity if doing so would interfere with this challenge. What I want from you now, more than anything else, is an exact definition of what a “world” or an “approximate world” is, stated in the same mathematical language that we use to talk about everything else in quantum theory. If you can’t tell me what you mean, we have nothing to talk about.
I appreciate that you chose to “raise the bar” here.
That is the substance of MWI’s problem with relativity.
I agree that when we’re seeking to ‘interpret’ a theory like QFT, which is Lorentz-invariant, we ought to postulate an ontology which respects this symmetry. However, from a certain perspective, I think it’s obvious that it must be possible to paint a mathematical picture of a Lorentz-invariant “many worlds type” theory.
Let’s assume that somehow or other, it’s possible to develop QFT from axiomatic foundations, and in such a way that when we take the appropriate low-velocity, low-energy limit, we recover “wavefunctions” and the Schrödinger equation exactly as they appear in QM. As far as I know, QFT and (non-relativistic) QM are, broadly speaking, cut from the same cloth: Both of them make predictions through a process of adding up quantum amplitudes for various possibilities then interpreting the square-norms as probabilities. Neither of them stipulate that there is a fact of the matter about which slit the electron went through, unless you augment them with ‘hidden variables’. Neither of them can define what counts as a “measurement”. In both theories, the only strictly correct way to compute the probabilities of the results of a second measurement, in advance of a first, is to do a calculation that takes into account all of the possible ways the first measuring device might ‘interfere’ with the stuff being measured. In practice we don’t need to do this—in any remotely reasonable experiment, when some of the degrees of freedom become entangled with a macroscopic measuring device, we can treat them as having “collapsed” and assumed determinate values. But in theory, there’s nothing in QM or QFT to rule out macroscopic superpositions (e.g. you can do a “two-slit experiment” with people rather than electrons).
The reason I’m pointing all of these things out is to motivate the following claim: A ‘no collapse, no hidden variable’ interpretation of QFT is every bit as natural as a ‘no collapse, no hidden variable’ interpretation of QM. By ‘natural’ I mean that unless you deliberately ‘add something’ to the mathematics, you won’t get collapses or hidden variables. (The real problem for Everettians is that (prima facie) you won’t get Born probabilities either! But we can talk about that later.)
Next, I claim that a ‘no collapse, no hidden variable’ theory (taken together with the metaphysical assumption that ‘the entities and processes described are real, not merely instruments for computing probabilities’) is obviously a ‘many worlds’ theory. This is because it implies that the man over there, listening to a Geiger counter, is constantly splitting into superpositions. Although his superposed selves are overwhelmingly like to carry on their lives independently of each other, there’s no limit to how many of them we may need to take account of in order to get our predictions right.
Finally, since the predictions of QFT are Lorentz-invariant, if it can be given a mathematical foundation at all then there must be some way to give it a Lorentz-invariant mathematical foundation.
Putting all of this together, I have my claim.
I’m “cheating” you’ll say because I haven’t done any hard work—I haven’t told you how one can have a Lorentz-invariant ontology of things resembling “wavefunctions”. Regretfully I’m not able to do that—if I could I would—but for present purposes I don’t think it’s necessary.
When I think of supposedly more sophisticated approaches to MWI, where That Which Exists is just the universal wavefunction, in its sublime purity, beyond all specific choices of coordinate and basis, and where the contingent particularities of individual worlds are supposed to be logically implicit in its structure somehow… my overall impression is of utterly contemptible vagueness and handwaving, often suffused with a mystic adoration of the Big Psi.
Personally I’d just say that That Which Exists is whatever it is that, when supplemented with co-ordinates and a position basis, and passing to the nonrelativistic limit, looks like a wavefunction. I don’t know whether that has to take the form of a ‘universal wavefunction’. (By the way, I don’t think the position basis is an ‘arbitrary choice’ in the same way that a foliation of Minkowski space is arbitrary. This is because of the analogy with classical mechanics, where the elements of a basis correspond to points in a phase space, and changing basis is like changing co-ordinates in the phase space. But a phase space is a symplectic manifold, not an unstructured set. I’m guessing that in quantum theory too there must be some extra structure in the Hilbert space which implies that some bases (or more generally, some Hermitian operators) are “physical” and others not.)
Anyway, I don’t really have any idea what a maximally elegant mathematical presentation of the Underlying Reality would look like. I just think it’s misleading to use the words “MWI is inconsistent with special relativity” when what you actually mean is that “no-one has yet formulated an axiomatic presentation of QFT”. Because the very moment we have the latter, we will (immediately, effortlessly) have a version of MWI that is consistent with SR, simply by making the same interpetative ‘moves’ that Everett made. (This is a point which the MWI FAQ tries to drive home.) And if we cannot put QFT on firm mathematical foundations then all metaphysically realistic interpretations will suffer equally badly.
Finally, let’s switch briefly to the outside view. I’ve never before seen a critique of MWI made along the lines that it presupposes a notion of absolute simultaneity. Now that could be because I just haven’t been looking hard enough (but actually I have read a fair few attacks on MWI), or not understanding what I’ve been reading (but I think I have, at least in outline), and it could be because almost everyone who writes about this is distracted by whatever agendas and pet theories they have, and missing the more ‘obvious’ line of attack right under their noses; but I think it’s much more likely that you’ve misunderstood the relation between MWI and the QM-style wavefunction, which isn’t as close as you think.
Actually, the overall impression I had prior to this conversation with you is that compatibility with SR is one of MWI’s greatest strengths (especially when compared with Bohm’s theory.)
Let’s move on.
I am going to pose a challenge to you. The issue which is ultimately at stake: whether a “Many Approximate Worlds Interpretation” even makes sense as a theory. However, we won’t try to resolve that directly. The actual challenge is much simpler. I ask merely that you exhibit a mathematically exact definition of an “approximate world”. This is theoretical physics we’re discussing, it uses exact mathematics, and if the concept is genuinely relevant, it will have a mathematical formulation and not just a verbal one.
I’d have to do a lot of reading before I could answer this properly. From what I’ve seen so far, the critical concepts seem to be einselection and decoherence. The universe can be thought of as a collection of interacting ‘systems’ (such that the Hilbert space of the whole universe is the tensor product of the Hilbert spaces corresponding to each system). When a system interacts with its environment, its reduced density matrix changes exactly as if the environment was performing a ‘measurement’ on it. However, the environment is much more likely to perform certain ‘measurements’ than others. Those states which are sufficiently near to being eigenstates of a ‘typical measurement’ thus have a degree of stability not shared by an arbitrary superposition of such states. In this way, the environment selects a so called “measurement basis” (which consists of what we can call “classical states”).
A ‘world’ is just a component of the universe’s wavefunction, when decomposed with respect to this “measurement basis”. As I understand it, this notion of ‘world’ coincides with (or at least is closely related to) the thermodynamic concept of a ‘macrostate’. In particular, one can no more (and no less) give a mathematically rigorous definition of ‘world’ than one can of ‘macrostate’. This is just an assumption on my part, but I don’t think the “measurement basis” is strictly speaking a basis—it’s more like a decomposition of the Hilbert space as a direct sum of subspaces which are themselves fairly large. The indeterminacy (“approximateness”) in the notion of world arises from the indeterminacy of what counts as a ‘typical’ interaction between systems. There may be no “fact of the matter” about whether or not two subspaces ought to be ‘merged together’ (i.e. whether or not a particular property somewhere between the ‘micro’ and ‘macro’ scales deserves to be called ‘macroscopic enough’ to make the difference between two macrostates).
Possibly I understand your outlook better now. For you, worlds are like hills in a landscape. You’re on one of them, there’s a local maximum, but there’s no need to demarcate exactly where one hill ends and another begins. What is real is the landscape.
You don’t experience a whole world, just a small part of one, so you are not epistemically compelled to think of whole worlds as sharply bounded entities. However, if you consider your own place in this ontology, you’re not just near a local maximum or on a local maximum, you are a local maximum, and here you no longer have the option of indeterminacy. Your experience definitely exists—it is, after all, the only reason you know that anything exists; it is, by hypothesis, not all that exists; and so, within That Which Exists, there is a sharp and objective distinction between That Which You Experience and That Which You Do Not Experience.
It should also be apparent that you don’t just exist or experience featurelessly; you are something, a particular entity, and you are experiencing something particular. This is what you are denying when you say that there are situations where there is no fact about what your state of consciousness is or even whether you have one. To which all I will say is that that is the ultimate in irrationalism. I can only guess that you are thinking of consciousness in “third person” terms, as a hypothesized entity which may or may not be posited (according to one’s theoretical preference) and whose nature is a matter of definition (and therefore potentially vague or conventional), rather than as the substance of everything you know and cannot deny, unless you wish to deny reality itself.
We shall see if this latest lecture of mine on the necessity of the objectivity of your existence makes an impression. But proceeding from that premise, it follows that, if you wish to maintain that reality in its totality is something like a universal wavefunction, you must find at least one sharply delineated entity in it, because you are a sharply delineated entity that exists, and you are not identical with the whole.
P.S. On the topic of relativity and QFT: It’s difficult to rigorously define the interacting field theories which physicists actually use in a self-contained way, because they probably only exist as equivalence classes of approximations to deeper trans-QFT theories (like superstring vacua). This is the contemporary understanding of the meaning of renormalization that emerged in the 1970s. You have an unknown self-contained theory whose low-energy behavior can be approximated by a finite number of parameters, and renormalizable QFTs are the language in which this approximation is expressed. They can’t be axiomatized as functionals over a space of field configurations, which then get approximated by a power series of Feynman diagrams. The most you can do is develop a formal algebra of these power series themselves. For a rather technical example of this (but worth a look if you want to see the real thing), see the latest paper by Richard Borcherds.
But assuming that string theory or some other framework removes that technical obstacle, what’s the status of my argument that relativity contradicts MWI? The argument does suppose that we are talking about exactly specified whole-universe worlds that “split” instantly on some hypersurface of simultaneity. I don’t see how any such model can avoid the “ontological gauge-fixing” I mentioned in the previous comment. The only alternatives I can see are (1) Gell-Mann and Hartle’s decoherent histories, which are self-contained (no splitting) and coarse-grained (lacking some properties by classical ontological standards), and (2) a hypothetical “blistering” model of world-splitting, where instead of being instantaneous along a preferred hypersurface, it starts at a point and a sheaf of new worlds peels away from the parent world in a local and causal way, with the blister spreading at light-speed. In this second model, one has to imagine the descendant worlds in the separating sheaf themselves beginning to blister and split even while the split that created them continues to propagate and grow, and so one has sheaves of part-worlds growing upon sheaves of part-worlds. A picture like that might be made ontologically relativistic in some complicated way. Each of these options introduces further issues, but I’ll leave them alone for now unless someone takes them up.
Thanks. This exchange really awakened me, not so much to the fact that MWI is ‘wrong’ (I still don’t think it is), but to the enormity of the philosophical challenge one faces in justifying it.
To clarify, there are two senses in which MWI could be ‘right’ or ‘wrong’.
(a) Do we in fact live in a multiverse?
(b) Could we have found ourselves in a multiverse? That is, in a hypothetical universe where objective physical reality is exactly as MWI theorists describe it, and supposing it contained structures that behaved like conscious observers, could we successfully predict ‘what it would be like’ to be those observers, and would it be ‘essentially’ like our own experiences (whatever we deem the ‘essential’ aspects of our experience to be)? (From my perspective, this is the same as asking: If you did a simulation of an MWI universe on an ordinary computer, would the ‘simulated beings’ have experiences like ours (in the relevant respects)?)
Leaving aside (a) for the moment, I think the ‘disconnect’ between our respective worldviews works out like this:
I think that, since nonrelativistic QM is a self-contained theory, if we’re given a model of this theory—a ‘toy universe’ if you like—it must be possible to deduce a priori what conscious observers there are in this universe, if any, and what they are conscious of (albeit with my usual caveat that we shouldn’t expect perfectly “sharp” answers.) If you accept this premise, then you don’t need to poison the ontological simplicity of MWI by adding ‘Worlds’, ‘Histories’ or ‘Minds’. All you need to do is carefully ‘unpack’ what’s already in front of you. (The “Bare Theory” is enough, modulo a lot of analytic reasoning.)
(This presupposes the truth of analytic functionalism.)
On the other hand, I suspect you regard it as obvious—so obvious that it should go without saying—that the Bare Theory isn’t enough. That the work you need to do in order to generate empirical predictions must be ‘synthetic’ rather than ‘analytic’. That bringing ‘many worlds’ to life requires axioms rather than mere definitions.
Your experience definitely exists—it is, after all, the only reason you know that anything exists; it is, by hypothesis, not all that exists; and so, within That Which Exists, there is a sharp and objective distinction between That Which You Experience and That Which You Do Not Experience.
Sorry but I’m unpersuaded. I mean, when a hill gets smaller it gradually and continuously loses its identity as a ‘thing’, to the local topographical variations around it. Likewise, the ‘boundary’ of a hill is somewhat indeterminate (just as the boundary of the Sun’s gravity well is somewhat indeterminate).
It should also be apparent that you don’t just exist or experience featurelessly; you are something, a particular entity, and you are experiencing something particular. This is what you are denying when you say that there are situations where there is no fact about what your state of consciousness is or even whether you have one. To which all I will say is that that is the ultimate in irrationalism.
The ultimate in irrationalism? To me those conclusions look unavoidable. Don’t Dennett’s examples make any impression on you? Consider change blindness: you’re alternately shown two slides A and B which depict the same scene, but with a significant alteration which under normal circumstances would ‘leap out at you’. But because there’s a short delay between presentations of A and B, the slides can be switched many times before you notice the difference. Then Dennett wants to say that there’s no ‘right answer’ to the question of whether, prior to noticing the change, your visual phenomena included the bit of the scene that was changing.
And doesn’t pointing out the inevitable arbitariness of any attempt to single out ‘the first appearance of consciousness in the tree of life’ cut any ice? To me it’s the most obvious thing in the world that there isn’t always a determinate answer to the question “is that thing conscious?” I honestly find it baffling that so many thinkers resist this conclusion.
For a rather technical example of this (but worth a look if you want to see the real thing), see the latest paper by Richard Borcherds.
Thanks for the reference—I’m always meaning to teach myself about this stuff.
User DZS has directed me to a paper which provides a relativistically covariant ontology for QFT! Consistent histories already had this, but the histories there can be arbitrarily sparsely specified. This ontology, “space-time state realism”, goes to the opposite extreme and it does so very ingeniously. It uses the “Heisenberg picture” of QFT rather than the “Schrodinger picture”. The Schrodinger picture is the usual one in which the state vector evolves in time and the operators do not. The Heisenberg picture is usually described as using a state vector which doesn’t evolve in time and operators which do; but the important fact, for the purposes of interpretation, is that the operators are associated to space-time points and so form a manifold-like set that can be relativistically transformed.
Operators are not yet states, however. What these authors (Wallace and Timpson) do, is to define a Hilbert space for an arbitrary space-time region, and then a way to construct a state in that Hilbert space, using data about how the field operators in that region behave with respect to the unique “initial” state used in the Heisenberg picture. So in their ontology, absolutely every space-time region and subregion (every open set, maybe? haven’t gone over the details) has a quantum state attached, in a way that is consistent across regions. It’s very clever, and it’s just enough overkill to guarantee that the true ontology is almost certainly hiding somewhere in there.
Allow me to refresh your memory of what I said previously. “Not really. I suspect that what you’re referring to as “MWI” contains the idea that, in addition to a wavefunction evolving unitarily under the Schrödinger equation, there are also ontologically primitive “branches” (or “worlds”) which “split”.”
You ignored one of the words—do you see which one?
This is standard stuff.
Again, this is elementary. I suggest you read that MWI FAQ. You’ll find more authoritative sources if you look around, but it’s a good place to start.
Are you unfamiliar with analytic functionalism? Of course you’re not. Then why are you pretending to be?
The idea that one can coherently conceive of “phenomenal consciousness” separately from structure and function (and vice versa) is precisely the intuition that leads people to think that zombies are conceivable. The denial that zombies are conceivable is one of the standard positions in the philosophy of mind. Spare me your disingenuous and patronising tone of ‘mind-boggled befuddlement’.
I didn’t say that, I said there were no ontologically primitive worlds, which only leaves open a yawning chasm of logical room for “ontologically non-primitive worlds”. Do you think that “temperature” not being ontologically fundamental disqualifies all statements of the form “the temperature of this gas is …”?
Is the temperature of a gas a matter of opinion or perspective? Is it approximate? Well ultimately yes it is “approximate”, though there isn’t much to be said for calling it a “matter of opinion” is there?
The notion of “you” is as “approximate” as the notion of “’world”.
Here’s something I find mind-boggling: Why does your side always conflate “fuzzy around the edges” with “non-existent”. For instance, Dennett in Time and the Observer makes a powerful case for denying that our consciousness consists of a linear sequence of “moments” such that for each moment there is unique, well-defined ‘fact of the matter’ as to what you’re conscious of at that moment. Perhaps I’m not speaking for all of you here, but why do many of you think that conceding this point entails denying that consciousness exists? Does observing that the “temperature of a single gas molecule” makes no sense entail that temperature doesn’t exist?
The distinctive unifying idea of special relativity is that the geometry of the universe is that of Minkowski space. The reality of things is a four-dimensional partially ordered set of point events which can be divided into hypersurfaces of equal coordinate time in a variety of ways. Two events may be simultaneous in one description of a physical process, but if they are spatially separated, then we can transform to another description in which they are no longer simultaneous. Simultaneity is a coordinate artefact and there is no universal time.
Wavefunctions are always defined with respect to a particular time-slicing, a particular foliation of space-time into hypersurfaces. All a Lorentz transform can do is change the tilt of those hypersurfaces with respect to the time axis of your coordinate system; you’re still stuck with a particular preferred foliation as the ontological base of your wavefunction’s time evolution. If you reify the wavefunction, you end up reifying your coordinate system as well.
That is the substance of MWI’s problem with relativity. A physicist might call it “ontological gauge-fixing”. In theories with a gauge symmetry, you’re allowed to work in a particular gauge for the purposes of calculation, but the end product, the quantitative predictions, must be gauge-invariant. If they show a dependence on your choice of gauge, you’ve done something wrong.
Here, we’re trying to construct an ontology for quantum theory. The ontological significance of special relativity for time is that universal time is a coordinate artefact, yet in MWI ontologies, we end up with an objective universal time. That’s evidence of a mistake, and the mistake is that you are treating a wavefunction as an objectively existing thing, when it is just a frame-dependent tabulation of probability amplitudes.
Versions of MWI which fix a universal time and a particular Hilbert-space basis (such as position) may not be believable, but at least they are clear and explicit about what it is that is supposed to exist. When I think of supposedly more sophisticated approaches to MWI, where That Which Exists is just the universal wavefunction, in its sublime purity, beyond all specific choices of coordinate and basis, and where the contingent particularities of individual worlds are supposed to be logically implicit in its structure somehow… my overall impression is of utterly contemptible vagueness and handwaving, often suffused with a mystic adoration of the Big Psi.
Let’s pretend for a moment that I don’t have an issue with the idea that the world only exists “approximately”, and that the ultimate objective reality is some sort of wavefunction. That’s your hypothesis, fine. Can you tell me the nature of this approximateness? Are we taking some sort of limit? If so, can you be more specific? Your original words were
I asked for more details and you linked to the MWI FAQ—which I have seen many times before, and which mostly consists of word-pictures. That is not enough, although a word-picture can be a fine way to fool yourself into thinking that your ideas make sense.
I am going to pose a challenge to you. The issue which is ultimately at stake: whether a “Many Approximate Worlds Interpretation” even makes sense as a theory. However, we won’t try to resolve that directly. The actual challenge is much simpler. I ask merely that you exhibit a mathematically exact definition of an “approximate world”. This is theoretical physics we’re discussing, it uses exact mathematics, and if the concept is genuinely relevant, it will have a mathematical formulation and not just a verbal one.
Since these approximate worlds are supposed to be contained implicitly within the universal wavefunction, that is the relationship which I am expecting to see formally elucidated. I don’t expect to see statements about a theory of everything; supposedly all of this can be explained at the level of nonrelativistic quantum mechanics. I just want to see an exact statement of what the relationship between world and wavefunction is supposed to be.
If you want to point to a particular proposition in a paper somewhere, fine. Just give me more to work with than shapeless verbal formulations!
There are many other things to discuss in your comment, we can return to those later. You should also feel free to delay responding to what I said about relativity if doing so would interfere with this challenge. What I want from you now, more than anything else, is an exact definition of what a “world” or an “approximate world” is, stated in the same mathematical language that we use to talk about everything else in quantum theory. If you can’t tell me what you mean, we have nothing to talk about.
I appreciate that you chose to “raise the bar” here.
I agree that when we’re seeking to ‘interpret’ a theory like QFT, which is Lorentz-invariant, we ought to postulate an ontology which respects this symmetry. However, from a certain perspective, I think it’s obvious that it must be possible to paint a mathematical picture of a Lorentz-invariant “many worlds type” theory.
Let’s assume that somehow or other, it’s possible to develop QFT from axiomatic foundations, and in such a way that when we take the appropriate low-velocity, low-energy limit, we recover “wavefunctions” and the Schrödinger equation exactly as they appear in QM. As far as I know, QFT and (non-relativistic) QM are, broadly speaking, cut from the same cloth: Both of them make predictions through a process of adding up quantum amplitudes for various possibilities then interpreting the square-norms as probabilities. Neither of them stipulate that there is a fact of the matter about which slit the electron went through, unless you augment them with ‘hidden variables’. Neither of them can define what counts as a “measurement”. In both theories, the only strictly correct way to compute the probabilities of the results of a second measurement, in advance of a first, is to do a calculation that takes into account all of the possible ways the first measuring device might ‘interfere’ with the stuff being measured. In practice we don’t need to do this—in any remotely reasonable experiment, when some of the degrees of freedom become entangled with a macroscopic measuring device, we can treat them as having “collapsed” and assumed determinate values. But in theory, there’s nothing in QM or QFT to rule out macroscopic superpositions (e.g. you can do a “two-slit experiment” with people rather than electrons).
The reason I’m pointing all of these things out is to motivate the following claim: A ‘no collapse, no hidden variable’ interpretation of QFT is every bit as natural as a ‘no collapse, no hidden variable’ interpretation of QM. By ‘natural’ I mean that unless you deliberately ‘add something’ to the mathematics, you won’t get collapses or hidden variables. (The real problem for Everettians is that (prima facie) you won’t get Born probabilities either! But we can talk about that later.)
Next, I claim that a ‘no collapse, no hidden variable’ theory (taken together with the metaphysical assumption that ‘the entities and processes described are real, not merely instruments for computing probabilities’) is obviously a ‘many worlds’ theory. This is because it implies that the man over there, listening to a Geiger counter, is constantly splitting into superpositions. Although his superposed selves are overwhelmingly like to carry on their lives independently of each other, there’s no limit to how many of them we may need to take account of in order to get our predictions right.
Finally, since the predictions of QFT are Lorentz-invariant, if it can be given a mathematical foundation at all then there must be some way to give it a Lorentz-invariant mathematical foundation.
Putting all of this together, I have my claim.
I’m “cheating” you’ll say because I haven’t done any hard work—I haven’t told you how one can have a Lorentz-invariant ontology of things resembling “wavefunctions”. Regretfully I’m not able to do that—if I could I would—but for present purposes I don’t think it’s necessary.
Personally I’d just say that That Which Exists is whatever it is that, when supplemented with co-ordinates and a position basis, and passing to the nonrelativistic limit, looks like a wavefunction. I don’t know whether that has to take the form of a ‘universal wavefunction’. (By the way, I don’t think the position basis is an ‘arbitrary choice’ in the same way that a foliation of Minkowski space is arbitrary. This is because of the analogy with classical mechanics, where the elements of a basis correspond to points in a phase space, and changing basis is like changing co-ordinates in the phase space. But a phase space is a symplectic manifold, not an unstructured set. I’m guessing that in quantum theory too there must be some extra structure in the Hilbert space which implies that some bases (or more generally, some Hermitian operators) are “physical” and others not.)
Anyway, I don’t really have any idea what a maximally elegant mathematical presentation of the Underlying Reality would look like. I just think it’s misleading to use the words “MWI is inconsistent with special relativity” when what you actually mean is that “no-one has yet formulated an axiomatic presentation of QFT”. Because the very moment we have the latter, we will (immediately, effortlessly) have a version of MWI that is consistent with SR, simply by making the same interpetative ‘moves’ that Everett made. (This is a point which the MWI FAQ tries to drive home.) And if we cannot put QFT on firm mathematical foundations then all metaphysically realistic interpretations will suffer equally badly.
Finally, let’s switch briefly to the outside view. I’ve never before seen a critique of MWI made along the lines that it presupposes a notion of absolute simultaneity. Now that could be because I just haven’t been looking hard enough (but actually I have read a fair few attacks on MWI), or not understanding what I’ve been reading (but I think I have, at least in outline), and it could be because almost everyone who writes about this is distracted by whatever agendas and pet theories they have, and missing the more ‘obvious’ line of attack right under their noses; but I think it’s much more likely that you’ve misunderstood the relation between MWI and the QM-style wavefunction, which isn’t as close as you think.
Actually, the overall impression I had prior to this conversation with you is that compatibility with SR is one of MWI’s greatest strengths (especially when compared with Bohm’s theory.)
Let’s move on.
I’d have to do a lot of reading before I could answer this properly. From what I’ve seen so far, the critical concepts seem to be einselection and decoherence. The universe can be thought of as a collection of interacting ‘systems’ (such that the Hilbert space of the whole universe is the tensor product of the Hilbert spaces corresponding to each system). When a system interacts with its environment, its reduced density matrix changes exactly as if the environment was performing a ‘measurement’ on it. However, the environment is much more likely to perform certain ‘measurements’ than others. Those states which are sufficiently near to being eigenstates of a ‘typical measurement’ thus have a degree of stability not shared by an arbitrary superposition of such states. In this way, the environment selects a so called “measurement basis” (which consists of what we can call “classical states”).
A ‘world’ is just a component of the universe’s wavefunction, when decomposed with respect to this “measurement basis”. As I understand it, this notion of ‘world’ coincides with (or at least is closely related to) the thermodynamic concept of a ‘macrostate’. In particular, one can no more (and no less) give a mathematically rigorous definition of ‘world’ than one can of ‘macrostate’. This is just an assumption on my part, but I don’t think the “measurement basis” is strictly speaking a basis—it’s more like a decomposition of the Hilbert space as a direct sum of subspaces which are themselves fairly large. The indeterminacy (“approximateness”) in the notion of world arises from the indeterminacy of what counts as a ‘typical’ interaction between systems. There may be no “fact of the matter” about whether or not two subspaces ought to be ‘merged together’ (i.e. whether or not a particular property somewhere between the ‘micro’ and ‘macro’ scales deserves to be called ‘macroscopic enough’ to make the difference between two macrostates).
Possibly I understand your outlook better now. For you, worlds are like hills in a landscape. You’re on one of them, there’s a local maximum, but there’s no need to demarcate exactly where one hill ends and another begins. What is real is the landscape.
You don’t experience a whole world, just a small part of one, so you are not epistemically compelled to think of whole worlds as sharply bounded entities. However, if you consider your own place in this ontology, you’re not just near a local maximum or on a local maximum, you are a local maximum, and here you no longer have the option of indeterminacy. Your experience definitely exists—it is, after all, the only reason you know that anything exists; it is, by hypothesis, not all that exists; and so, within That Which Exists, there is a sharp and objective distinction between That Which You Experience and That Which You Do Not Experience.
It should also be apparent that you don’t just exist or experience featurelessly; you are something, a particular entity, and you are experiencing something particular. This is what you are denying when you say that there are situations where there is no fact about what your state of consciousness is or even whether you have one. To which all I will say is that that is the ultimate in irrationalism. I can only guess that you are thinking of consciousness in “third person” terms, as a hypothesized entity which may or may not be posited (according to one’s theoretical preference) and whose nature is a matter of definition (and therefore potentially vague or conventional), rather than as the substance of everything you know and cannot deny, unless you wish to deny reality itself.
We shall see if this latest lecture of mine on the necessity of the objectivity of your existence makes an impression. But proceeding from that premise, it follows that, if you wish to maintain that reality in its totality is something like a universal wavefunction, you must find at least one sharply delineated entity in it, because you are a sharply delineated entity that exists, and you are not identical with the whole.
P.S. On the topic of relativity and QFT: It’s difficult to rigorously define the interacting field theories which physicists actually use in a self-contained way, because they probably only exist as equivalence classes of approximations to deeper trans-QFT theories (like superstring vacua). This is the contemporary understanding of the meaning of renormalization that emerged in the 1970s. You have an unknown self-contained theory whose low-energy behavior can be approximated by a finite number of parameters, and renormalizable QFTs are the language in which this approximation is expressed. They can’t be axiomatized as functionals over a space of field configurations, which then get approximated by a power series of Feynman diagrams. The most you can do is develop a formal algebra of these power series themselves. For a rather technical example of this (but worth a look if you want to see the real thing), see the latest paper by Richard Borcherds.
But assuming that string theory or some other framework removes that technical obstacle, what’s the status of my argument that relativity contradicts MWI? The argument does suppose that we are talking about exactly specified whole-universe worlds that “split” instantly on some hypersurface of simultaneity. I don’t see how any such model can avoid the “ontological gauge-fixing” I mentioned in the previous comment. The only alternatives I can see are (1) Gell-Mann and Hartle’s decoherent histories, which are self-contained (no splitting) and coarse-grained (lacking some properties by classical ontological standards), and (2) a hypothetical “blistering” model of world-splitting, where instead of being instantaneous along a preferred hypersurface, it starts at a point and a sheaf of new worlds peels away from the parent world in a local and causal way, with the blister spreading at light-speed. In this second model, one has to imagine the descendant worlds in the separating sheaf themselves beginning to blister and split even while the split that created them continues to propagate and grow, and so one has sheaves of part-worlds growing upon sheaves of part-worlds. A picture like that might be made ontologically relativistic in some complicated way. Each of these options introduces further issues, but I’ll leave them alone for now unless someone takes them up.
Thanks. This exchange really awakened me, not so much to the fact that MWI is ‘wrong’ (I still don’t think it is), but to the enormity of the philosophical challenge one faces in justifying it.
To clarify, there are two senses in which MWI could be ‘right’ or ‘wrong’.
(a) Do we in fact live in a multiverse?
(b) Could we have found ourselves in a multiverse? That is, in a hypothetical universe where objective physical reality is exactly as MWI theorists describe it, and supposing it contained structures that behaved like conscious observers, could we successfully predict ‘what it would be like’ to be those observers, and would it be ‘essentially’ like our own experiences (whatever we deem the ‘essential’ aspects of our experience to be)? (From my perspective, this is the same as asking: If you did a simulation of an MWI universe on an ordinary computer, would the ‘simulated beings’ have experiences like ours (in the relevant respects)?)
Leaving aside (a) for the moment, I think the ‘disconnect’ between our respective worldviews works out like this:
I think that, since nonrelativistic QM is a self-contained theory, if we’re given a model of this theory—a ‘toy universe’ if you like—it must be possible to deduce a priori what conscious observers there are in this universe, if any, and what they are conscious of (albeit with my usual caveat that we shouldn’t expect perfectly “sharp” answers.) If you accept this premise, then you don’t need to poison the ontological simplicity of MWI by adding ‘Worlds’, ‘Histories’ or ‘Minds’. All you need to do is carefully ‘unpack’ what’s already in front of you. (The “Bare Theory” is enough, modulo a lot of analytic reasoning.)
(This presupposes the truth of analytic functionalism.)
On the other hand, I suspect you regard it as obvious—so obvious that it should go without saying—that the Bare Theory isn’t enough. That the work you need to do in order to generate empirical predictions must be ‘synthetic’ rather than ‘analytic’. That bringing ‘many worlds’ to life requires axioms rather than mere definitions.
Sorry but I’m unpersuaded. I mean, when a hill gets smaller it gradually and continuously loses its identity as a ‘thing’, to the local topographical variations around it. Likewise, the ‘boundary’ of a hill is somewhat indeterminate (just as the boundary of the Sun’s gravity well is somewhat indeterminate).
The ultimate in irrationalism? To me those conclusions look unavoidable. Don’t Dennett’s examples make any impression on you? Consider change blindness: you’re alternately shown two slides A and B which depict the same scene, but with a significant alteration which under normal circumstances would ‘leap out at you’. But because there’s a short delay between presentations of A and B, the slides can be switched many times before you notice the difference. Then Dennett wants to say that there’s no ‘right answer’ to the question of whether, prior to noticing the change, your visual phenomena included the bit of the scene that was changing.
And doesn’t pointing out the inevitable arbitariness of any attempt to single out ‘the first appearance of consciousness in the tree of life’ cut any ice? To me it’s the most obvious thing in the world that there isn’t always a determinate answer to the question “is that thing conscious?” I honestly find it baffling that so many thinkers resist this conclusion.
Thanks for the reference—I’m always meaning to teach myself about this stuff.
User DZS has directed me to a paper which provides a relativistically covariant ontology for QFT! Consistent histories already had this, but the histories there can be arbitrarily sparsely specified. This ontology, “space-time state realism”, goes to the opposite extreme and it does so very ingeniously. It uses the “Heisenberg picture” of QFT rather than the “Schrodinger picture”. The Schrodinger picture is the usual one in which the state vector evolves in time and the operators do not. The Heisenberg picture is usually described as using a state vector which doesn’t evolve in time and operators which do; but the important fact, for the purposes of interpretation, is that the operators are associated to space-time points and so form a manifold-like set that can be relativistically transformed.
Operators are not yet states, however. What these authors (Wallace and Timpson) do, is to define a Hilbert space for an arbitrary space-time region, and then a way to construct a state in that Hilbert space, using data about how the field operators in that region behave with respect to the unique “initial” state used in the Heisenberg picture. So in their ontology, absolutely every space-time region and subregion (every open set, maybe? haven’t gone over the details) has a quantum state attached, in a way that is consistent across regions. It’s very clever, and it’s just enough overkill to guarantee that the true ontology is almost certainly hiding somewhere in there.