Backward Causation in Quantum Physics

Factual Questions
21

Thank you for the background and insight, but I’m actually more interested in mechanics at the moment.

I had a different image of how the manifold universes were created, being of the believe that they would already have to exist, even if infinite in number.

I see now that you mean instead that a new universe is spontaneously created for each and every quantum event and/or possibility and it comes into existence for the sole purpose of accommodating that event/possibility.

IOW, “our” universe is constantly branching off into an infinite number of other universes at an incomprehensible rate.

So a) is that close to being accurate and b) if so, can you please clarify my amalgam “event and/or possibility” by indicating if one, the other or both items are included?

22

Consider the case where your quantum theory has no interactions. You have, say, a single particle’s wave function. Suppose it is some continuous function, like a Gaussian, in the position basis. In the MWI, you could say that there is a universe corresponding to each of the uncountably infinite points along the x-axis where the wave function is non-zero. As you time-evolve the wave-function (Schrodinger’s equation), it’s shape changes, spreads out. Your distribution of universes is changing, but are they “multiplying”? No. Your wave function is normalized to unity. The “number” (if it is remotely sensible to use that word) of universes is constant. Please note, BTW, that when I say “universe” in the above, it is true in just a strictly mathematical sense. There is no need to start worrying that our description is becoming bloated or silly; the point of the MWI is to just observe that a wave function is in some sense mathematically equivalent to a statement about a distribution of particles described by non-interacting delta-functions (the Schrodinger equation is linear), and therefore the use of term “separate universe” to describe each of these delta functions is perhaps an appropriate semantical leap. One way of describing the MWI, is continuous wave function = infinite linear superposition of delta functions.

Now, let’s consider the case where our quantum theory has interactions. Each of these infinite separate parts (delta-functions) of each particles’ wave function now can interact with each of the infinite separate parts of every other particles’ wave functions. After each part interacts with another part, certain possibilities start contradicting other possibilities, due to conservation laws. For example, suppose one (of the infinitely many) parts of a particle’s wave function interacts with one (of the infinitely many) parts of another particle’s wave function, causing those parts of the wave function to scatter. One part goes one way with momentum p1, then other goes another way with momentum p2. Momentum is conserved. Now any further interactions with those parts of the wave function have to be consistent with that previous interaction. Correlations start developing between different parts of the wave function, and after some interactions, certain parts of the wave function become so uncorrelated with other parts, that they can effectively be called “separate universes”. This is the sense in which universes “multiply,” and the principle is called quantum decoherence, a principle that by now is completely canonical and agreed-upon among physicists.

So you see it may not be as simple or clear-cut as you described, but hopefully I’ve clarified questions a) and b). A new universe is not “spontaneously created for each and every quantum event and/or possibility”, at least not by magic, it happens as the universe’s wave function naturally evolves and interacts with various parts of itself, creating correlations and anti-correlations among different parts of its wave function, effectively isolating them from each other. Each of these parts continue to evolve, and the process continues ad infinitum. If you isolate parts of the universe and don’t let them interact at all with other parts, then they “stop multiplying”. For example, if you keep Schrodinger’s cat in the box, completely isolated from the rest of the universe, then there will never be a split into two universes (one in which the cat is dead, one in which the cat is alive) because you will never open the box so that each part of the cat’s wave function can become correlated with parts of your wave function. The various parts of the cat’s wave function (dead parts and alive parts) will just continue to evolve in the box. But if you open the box, the dead part can become correlated with a part of you, and the alive part can become correlated with a part of you, and those two parts of you will be anti-correlated with each other so that they cannot interfere with each other and will effectively represent two different universes.

23

Well, depends on what you mean by ‘around and kicking’, I suppose. There’s for instance the de Broglie-Bohm theory, which is a HV theory that is known to reproduce all predictions of quantum mechanics (at least in the non-relativistic case; the relativistic regime gets a bit more muddled). In principle, you can always adjoin some ‘hidden’ dynamics and make it fit, if you feel like it; the question is just whether or not it makes much sense to do so. Generally, Bell’s and similar theorems put such stringent conditions on the allowed hidden variable theories that you don’t really gain much insight or understanding from them – they necessarily contain so many counterintuitive features that you might just as well accept quantum mechanics as-is (or at least, so a lot of people feel).

You don’t need to appeal to things like the MWI, or specific interpretations in general, to understand this. Basically, entanglement can be considered as ‘correlation + superposition’, in a sense. Here, ‘correlation’ just means the following: you have two balls, one red, and one green, and two boxes to put them in. I give you one box, and keep the other; if you open yours, you will instantly know what color the ball in mine will be, no matter where in all of space and time I happen to be. So far, there’s no non-locality involved – the information just stems from the correlation put into the system due to its preparation.

Now, quantum systems can not only be in states like ‘red’ and ‘green’, which we can consider ‘real states’, or ‘elements of reality’, or ‘value definite’, but also in combinations of the two, typically written as |red> + |green>, where the weird brackets just mean ‘this is a quantum object; tread carefully’, for our purposes. It is important to realize that there is no ‘underlying reality’ to these states in the sense that the state is really |red> (or |green>), and we just describe it in this weird way due to our ignorance of the real fundamental level, but in this description, there actually is no real value to the balls’ color property.

So, let’s consider the possibilities. In the classical case, the state of the two balls is either |red, green> or |green, red>, where the first entry denotes the color of your ball, and the second the color of mine. Thus, if you open your box, find the ball to be green, you instantly know that the system’s state is |green, red> and that thus, my ball must be red, without any nonlocal influence.

Now, in the quantum case, the system can also be in the state |red, green> + |green, red>. This means that neither my ball nor your ball has any definite color, independently of what you find once you check – there is no element of reality attached to the balls’ color. However, once you check, you will find a definite color – say red – and again, instantly know the color of my ball, since then, only the state |red, green> is still compatible with the outcome of your checking. But there has again be no nonlocal influence at work, for the same reason there hasn’t been any in the classical case; what we have added was the element of superposition, the unique property of quantum systems to not have a definite, real value to all their properties at all times. (Note that I’m not talking about the ‘collapse of the wave function/state vector’, which could indeed be considered to be something of a distinctly nonlocal flavor. Instead, think of it more in the sense of conditional probabilities: once your knowledge becomes conditioned on your finding a particular color of ball in your box, the other possibility is no longer consistent with your (local) knowledge. Whether you want to consider this in terms of state-vector collapse, wave function branching, or whatever else tickles your fancy does not enter into things at this point.)

This may be putting a too fine point on things, but I think this is overly simplified. Everett’s original relative-state interpretation – which also does not add any excess ontological baggage to the Schrödinger equation – can well be considered agnostic on the front of whether or not there actually are ‘many worlds’, and so can a number of other modern interpretations; just considering the Schrödinger equation ‘as is’ does not automatically lead to the idea of branching universes (in fact, it was only Bryce DeWitt’s later popularization of Everett’s ideas that introduced the many-worlds concept in the sense of worlds that actually are there in some sense). Personally, I tend to agree with Everett (and with you re Copenhagen, which I’ve always considered the interpretation for people who haven’t really thought about the interpretation of quantum mechanics), but I’m less certain about DeWitt/Deutsch et al.'s many worlds.

24

The Stanford web site has a good overview of MWI but I’m not really inclined to wade through it today. Honestly, the idea of having a universe pop up just for the purpose of avoiding the issue of non-locality seems unduly contorted. Of course perhaps the math sings of its existence like a choir of angels. It wouldn’t be the first time they’ve testified to the bizarre. It’s just not the sort of thing that would ever be my first choice.

25

Really? I don’t see that necessarily follows. Locality, as I understand relativity, demands that events separated by a spacelike interval cannot causally effect each other. If locality is violated, then causality definitely will be, because the temporal order of events with spacelike intervals is reference frame-dependent.

I think that, for the general description of this theory, we don’t need to have these sorts of events affect each other. Rather, it’s that with two events separated by a timelike interval, the subsequent event can conceivably affect the prior event. (Temporal order of events separated by timelike intervals is not frame-dependent, even though the time difference is.) That violates causality, but not locality.

Or am I misunderstanding something?

26

(note: true, but examples can help)

I’m a bit confused what point you are making. Unless you misspoke you seem to be arguing that there is no such thing as a “non-locality” problem. Perhaps you can elaborate.

I disagree; but I think this is largely an issue of semantics. What I am calling “separate universes” are what are largely agreed upon by the physics community to come about in the process known as decoherence. Whether you call these decorrelated parts of the wave function “universes” is semantics, but I think it is silly to avoid the term, since they satisfy the usual definitions one might have for “universe.”

27

As I’ve tried to drive home, that’s not how it works. There is no postulate that “a universe pops up.” Everything is just a consequence of assuming that the universe is a wave function evolving according the the Schrodinger equation. A consequence, not an assumption.

28

I’ll let you step into the cage with Stanford.

from my link

29

Everything in that paragraph is correct except the first sentence. The first sentence is just plain wrong. Completely wrong. Read the paper yourself if you are so inclined (it is fantastic):

30

I think part of the problem is that science fiction conjures up a lot of ideas about “parallel universes” that aren’t true of the “worlds” of MWI.

In a “universe” something is either in the universe with you or it isn’t. If Evil Kirk is in the same universe as Evil Spock, and Evil Spock is in the same universe as Evil McCoy, then Evil McCoy must be in the same universe as Evil Kirk.

But in the Schrodinger’s cat experiment, both Live Cat and Dead Cat are both in the same world as us, even though Live Cat and Dead Cat would consider each other to be in different worlds. If MWI’s “worlds” were just like SciFi’s “universes” this could not happen.

Similarly, if you’re in a SciFi parallel universe, you’re in that universe forever, eternally completely separated from any other universe that currently exists (barring transporter accidents). MWI’s worlds don’t entirely work like that – if all histories in two worlds lead to the same state, the worlds could be said to have recombined entirely.

MWI’s worlds are a lot more porous than SciFi’s parallel universes.

31

One thing I failed to mention is this.

We all know that the universe is time(/charge/parity)-symmetric except for the neutral kaon. But Price claims that while at the macro-scale, there is an assymetry of entropy, giving us a basis upon which to feel a flow of time, nevertheless at the micro-scale, there is not generally such an assymetry. What he argues that this implies is that, while on the macro-scale correlated events generally trace to an event that lies in the past, on the micro-scale correlated events might trace to an event that lies either in the past or the future.

And in the book, Price points out that if people had arrived at this understanding of time-symmetry on the micro-scale before quantum physics, they would have predicted exactly the kinds of strange phenomena quantum mechanics predicts, precisely because of the backward influence that exists in a time-symmetric world. QM would have been seen as confirming things already known, rather than as seeming to introduce new and spooky metaphysics. (If you think the backward influence itself is spooky metaphysics, remember all this is supposed to be in the context of seeing things, fundamentally, “block universe” style, with no objective flow of time. Not popularly intuitive, but far from spooky as it’s an idea with a fairly old provenance.)

In this way, QM interpreted as involving backward influence can be seen to cohere with the rest of physics in a particularly parsimonious way.

32

Well, I’ve tried to give an explanation that doesn’t appeal to many worlds above…

And if you have backwards causation, they can: A and B are spacelike separated, and A influences B via exerting retrocausal influence on C, an event in A’s and B’s mutual causal past, which in turn influences B; picture two photons of an EPR pair, the measurement of one influences the preparation of the state at the source, which in turn influences the total state (and consequently, the other photon).

Not sure what’s confusing, although I don’t know what exactly you mean by nonlocality ‘problem’… It’s unambiguous that there is no local realistic model that reproduces the predictions of quantum theory, so you have to reject one or the other: either get a model that has definite values to all properties, which has to include nonlocal influences in order to reproduce Bell correlations, or abandon those definite values (or ‘counterfactual definiteness’).

All I mean is just that there are Everett-like interpretation in which there are multiple copies of ‘me’ experiencing different outcomes of branching events (which I would call genuinely ‘many worlds’), and some in which that isn’t the case.

33

Except that, in a typical topology, even if A and B are spatially separated, you can just find some event C that’s in the common past (or equivalently, common future) of both A and B, and therefore timelike separated from both. Then just go backwards from A to C, and forwards from C to B, and you’ve got A and B influencing each other.

Half Man Half Wit, you’re correct that, in the experiments you described, there’s no need to invoke non-locality (or anything else equivalently weird). That only comes in when you do slightly more complicated experiments. Let’s transition to a real quantum mechanical example: You’ve got two photons entangled so as to be in opposite polarization states. If you have vertical polarizers in front of both of your detectors, you’ll pass the photon through and detect it in one of them, and so if you detect your photon, the other guy won’t detect his, and vice-versa. Likewise, if one detector has a vertical polarizer and the other has a horizontal polarizer, then either both photons will be detected, or neither will, so again, as soon as you make your measurement, you know the results of the other one. So far, we still don’t need anything weird. Where the weirdness comes in is if you have the two polarizers at some intermediate angle, say, one vertical and the other diagonal. Now, based on the results of your experiment, you can’t predict for sure whether the other guy will detect the other photon, but you can calculate the probability that he’ll detect it. But what Bell proved is that the probabilities you’d calculate from quantum mechanics couldn’t possibly be the result of any local hidden variables in the particles. And the experiment has actually been done, and agrees with the predictions of quantum mechanics.

Finally, I wouldn’t say that the MWI is the dominant interpretation among physicists. The plurality interpretation among physicists, and possibly the majority, is the “shut up and calculate” interpretation, which is to say not bothering with any particular interpretation at all.

34

Ahem assuming the influence involved in these hidden variables goes only forward in time :wink:

35

I may have misunderstood you, but you seemed to be repeatedly emphasizing, in your own words “there has again be no nonlocal influence at work”. It sounded like you were arguing that the model you were describing was not nonlocal. I found this odd, and didn’t really get what point you were making. Chronos also seems to have noticed this in his most recent post responding to yours.

OK, I guess I’m not familiar with those. Or I have a different interpretation of those interpretations than you.

36

I would have gone with the quantum eraser experiment myself.

37

In my experience the preference of theorists and astrophysicists for MWI is near a majority (‘dominant’ would be too strong a word), while experimentalists are universally in the “shut up and calculate” camp. Overall, I would agree it is not dominant.

Here is an interesting quote from Tegmark:

Note: I would include “Consistent Histories” in with “Many Worlds”, as I think they are equivalent, but that is debatable.

38

Yes, I’m not questioning that. But there is no non-local influence at work in Bell correlations if you do not assume counterfactual definiteness, or whatever else you want to call it. There’s no ‘action at a distance’. (There’s not even any interaction Hamiltonian!) What you have is non-factorizability: you can’t describe those experiments using product distributions. This may be considered some kind of ‘holism’ or ‘non-separability’, but that’s not the same as nonlocality in, for instance, Bohmian mechanics, where the quantum potential actually and causally changes its value in a non-local fashion. Typically, the meaning of non-locality in these discussions is that you measure at point A, and as a result of this measurement, the distribution at point B instantaneously changes.

Well, there is no nonlocal influence: i.e. what happens at A does not ‘change’ anything at B. In a sense, the description is nonlocal, in so far as there is no description that takes into account only the subsystems on their own that reproduces quantum mechanics, but I think this is a very different kind of nonlocality from the kind we mean when we talk about ‘nonlocal influences’.

39

Your response emphasizing that there is no nonlocal influence (without ever mentioning the lack of counterfactual definitieness) was in response to the question:

So I think it would be worth emphasizing in the example you gave the reason you have to abandon counterfactual definiteness if your are explaining the behavior of particles via a local description.

40

I think we must be talking past each other… I have repeatedly emphasized that there is no measurement-independent reality, i.e. no ‘real value’, to be assigned to a state in superposition, so I’m not sure where the problem lies.