Problems with Many Worlds Interpretation

[BruceW]

Dear Ken G,

You make very valid points and thank you for providing a more wholesome view Bohemian mechanics. You draw out your arguments in a clear and concise way, but I fail to see how pilot waves are not local hidden variables.

Even according to the wiki, the Pilot wave description is listed as

"Principles
The Pilot Wave theory is a hidden variable theory...
The position and momentum of every particle are considered hidden variables; they are defined at all times, but not known by the observer; the initial conditions of the particles are not known accurately, so that from the point of view of the observer, there are uncertainties in the particles' states which conform to Heisenberg's Uncertainty Principle." http://en.wikipedia.org/wiki/Pilot_wave

In other words, if it is not a hidden variable theory it will break Heisenberg's Uncertainty Principle.

If you keep reading on that wikipedia page, it says that the Pilot wave description has nonlocality. Therefore, it is not a 'local hidden variable theory' because it is not a local theory.

The pilot wave description is deterministic and nonlocal. This may seem to defy relativity, but information never travels faster than the speed of light, so it is all fine.

 

[Samshorn]

Collapse occurs only in measurements and in order to perform a measurement, you have to interact with your system. Thus it is not isolated anymore.

What you're saying is unrelated to what I described.

 

[Hurkyl]

You draw out your arguments in a clear and concise way, but I fail to see how pilot waves are not local hidden variables.

...

The Pilot Wave theory is a hidden variable theory...

...

In other words, if it is not a hidden variable theory

Yes, BM is a hidden variable theory. But it's not a local hidden variable theory.

 

[dreamland37]

Here is a quote from wiki on the subject

"The de Broglie–Bohm theory is an example of a hidden variables theory. Bohm originally hoped that hidden variables could provide a local, causal, objective description that would resolve or eliminate many of the paradoxes of quantum mechanics, such as Schrödinger's cat, the measurement problem and the collapse of the wavefunction. However, Bell's theorem complicates this hope, as it demonstrates that there can be no local hidden variable theory that is compatible with the predictions of quantum mechanics. The Bohmian interpretation is causal but not local."

what does it mean that the Bohmain interpretation is causal but not local? Also as in the case of the two slit experiment I fail to see how the interference pattern of the wave function vanishes when a measuring device is put next to one of the two slits.

Otherwise it seems a very valid interpretation and also inline with the new E8 theory of everything posed by Garrett Lisi

 

[Ken G]

Ken G - Can I ask about the word holistic? I see it being used a lot but I'm not totally sure what it means..

Holism means something like 'the whole is more than just the parts together' right?

Right. So it is an alternative to local realism. In local realism, each piece "carries with it" all its own reality, so assembling the pieces is assembling the reality. But QM has many holistic elements, including the related issues of joint wave functions that are not separable, entanglement, and identical particles.

So a 'holistic theory' is a theory that can be applied to many different questions? And as an example, Einstein's general theory of relativity is holistic because it tells us that the laws of physics are the same for any observer. So this one theory tells us something about all other theories that obey relativity. Is all this roughly correct?

That isn't necessarily what I would call holistic, more like a meta-theory (a theory about theories). But there is a holistic element of relativity-- it's the idea that motion is a relationship between objects, rather than something any of the objects are doing by themselves. But by holistic I generally mean something more physical-- the system is not just the particles and the fields they generate, there is a kind of connection between the particles that you don't get if you just look at the parts independently.

 

[kith]

What you're saying is unrelated to what I described.

How can it be unrelated? You talked about what you think to be the basic hypothesis of the MWI and I expressed the view that this hypothesis also holds in the CI. If this is true, one can't "disprove" the MWI without disproving the CI as well.

 

[Ken G]

I think we've isolated the basic difference in our views. I differ with your above statement on two counts. First, essentially as a matter of definition, I think that in order for a conceptual model to qualify as an interpretation of a physical theory, it must establish an explicit and unambiguous mapping from the elements/features of the model to the empirical content of the theory. Your definition of "interpretation" is based just on the ontological elements, which I'll discuss below, but I really don't think that's a valid definition of a physical interpretation, because models could have the same ontology but different empirical behavior, and we surely wouldn't say they were interpretations of the same theory.

There are certainly some subtle points here. If you look at a MWI-favoring physicist doing a quantum mechanics calculation, you are not going to be able to tell they hold to MWI. The mechanics are all the same, leading to predictions of experiments that are all the same, so if predictions are what is meant by "empirical content," then it is the same with MWI. This is because MWI proponents don't shun the Born rule, they use it just like everyone else.

However, what will expose these people as MWI proponents is only what is going on in their heads when they apply the Born rule. They do not think that this rule is a fundamental statement about the ontology of the wavefunction, they think it is some kind of measure of the relative weights of the mutually incoherent "worlds" that a decohering unitary wavefunction evolution induces. They don't have a particularly insightful description of where that rule is coming from, or at least I've never seen one, but that isn't a good criticism of MWI because no other interpretation has one either (you can't count deBB because it's just a kind of shell game that replaces one ad hoc assumption with another). It would be a criticism of claims by MWI proponents that they don't need the Born rule, but I don't know if any of them claim that, because if you ask them to make a prediction, there will be the Born rule. So what differs is not the prediction, it is what they think the prediction means ontologically (which cannot be empirically tested so is not part of the "empirical content" of the theory).

Let V(t) denote the state vector of the overall universe, existing within the Hilbert space S, and let v(t) denote the state of the sub-world that we experience. The MWI tells us that at any given time t, our sub-world vector v is some kind of projection of V into a certain sub-space s, and it also tells us that the system described by v is perfectly isolated (going forward in time), so it's future evolution is, by hypothesis, also governed by the Schrodinger equation, as is the future evolution of V. The problem is that s cannot be constant if v is going to consistently represent the world of our experience over time, and if both V and v are evolving unitarily according to Schrodinger's equation.

The "worlds" of MWI are not evolving unitarily. If they did, we wouldn't need MWI at all! The worlds are subspaces, and it is in them that the nonunitariness of our experiences occurs. They are projections, yes, but they only evolve unitarily so long as they are not splitting into new worlds, which as I understand it is basically when there are no apparent collapses. When there are apparent collapses, unitarity is broken in the fragments-- it is only recovered by restitching the fragments back into their whole, but that whole isn't the space s.

And the rule for the evolution of s is essentially none other than the CI or something similar. So the axioms of a viable MWI, augmented to the point of actually being a genuine interpretation, are not a SUBset of the axioms of CI, they are a SUPERset.

I would say the rules for the evolution of s are just the same in CI or MWI, what is different is whether or not s is considered to be the whole reality. In CI, it is, but it is nonunitary. In MWI, it isn't, the reality stitches together the various s to restore unitarity. Yes MWI must use a CI-like rule for evolving s, but it claims that is a rule about our limited ability to perceive the full reality. It is like a rule for how a telescope blurs an image, which it distinguishes from the rules that govern what is being imaged. There is no difference in what is seen in the telescope of empirical verification, the difference is in the idea of what is being empirically verified. An empiricist knows that a blurry telescope image is a technological limitation that should not be confused with the "true" image, but the collapse is a fundamental limitation so we don't know what to make of that distinction any more. CI and MWI make something different of that distinction-- to CI, any image that is inescapably and fundamentally blurred is the reality of the image, but to MWI, it is still viewed as a blurred version of the reality.

That's why I say I'm not aware of any viable MWI - aside from the trivial one that postulates CI and then advises us to embedd all possible outcomes into a superstructure whose overall shape (unitary) we find more pleasing.

That's the key point right there. You are saying that you don't know of any MWI versions that are actually different theories from quantum mechanics, because everything that you can find in a quantum mechanics textbook you are calling CI. I agree, MWI is not mechanically different from CI, even if some practitioners hoped to find a way to make it so. It's just a different ontology, a very rationalistic one-- so although you may regard that difference as trivial scientifically, it isn't if one takes the ontology of a theory seriously. Shall we view things like "electrons" as real members of our universe, taking our ontologies seriously, or should we regard "electrons" as just pictures that physicists conjure while they do some calculation? That is the same issue as the differences between CI and MWI.

 

[dreamland37]

The trajectories the particles follow is altered by the presence of the experiment that determines the which-way information-- it has an effect on the pilot wave, and the pilot wave shepherds all the possible particle trajectories into doing what the Schroedinger equation says it should do, subject also to the informational constraints...

The two ways to hold that, MWI and consciousness-based collapsed, both seem rather mystical to a lot of physicists.

So the more I am learning the deeper characteristics of the debb the more I am fascinated by it. It seems so very mystical to me that I want to hold that both theories are correct. Because the environment registering the detection effectively alters the course of particles which can otherwise be viewed as the collapse of the WF. All the theory seems to do is transfer the role of the observer (collapsing the wave ect.) to the environment (a quantum conscious environment aware of all non local variables).

Therefore in the case of the double slit experiment, the environment is aware that there is a measuring apparatus placed by one of the slits. This has also been confirmed in experiments where the measuring device was placed after the photon was released to see if the photon would notice so to speak.

Basically Debb leads to the sublime notion that Nature is aware of itself which conforms to the semi-conscious behavior of particles which act as if they also are aware of their surroundings.

I also think that upon further reflection this theory can be unified with MWI and the collapse of the wave function. I have already been able to unify the last two into a single theory and with a few more thought experiments I might be able to incorporate the Pilot wave theory.

The basic assumption is to fully understand the role of the observer to unify these theories. Because we are apart of nature and therefore complementary to it.

 

[Ken G]

So the more I am learning the deeper characteristics of the debb the more I am fascinated by it. It seems so very mystical to me that I want to hold that both theories are correct. Because the environment registering the detection effectively alters the course of particles which can otherwise be viewed as the collapse of the WF. All the theory seems to do is transfer the role of the observer (collapsing the wave ect.) to the environment (a quantum conscious environment aware of all non local variables).

Someone who is more of a deBB proponent might wish to correct me, but I don't think that's the way the Bohmians think about it. I believe they treat every quantum state as if it was already collapsed, we just didn't have enough information to know which state it was. But the collapsed state in some sense takes into account the entire physical environment-- that's why the hidden variables are nonlocal. So the "informational constraints" I was referring to simply winnow down the possible trajectories, they don't "change" the trajectory from one to another. Which-way information means you have a different pilot wave, and a different bunch of potential trajectories any of which could be the "real one". Think of them as "virtual" trajectories, meaning only that they are possibilities we have to entertain, until we find otherwise, but the Bohmians think individual particles always follow definite predetermined trajectories.

Therefore in the case of the double slit experiment, the environment is aware that there is a measuring apparatus placed by one of the slits. This has also been confirmed in experiments where the measuring device was placed after the photon was released to see if the photon would notice so to speak.

Right, the pilot wave takes into account the full situation.

Basically Debb leads to the sublime notion that Nature is aware of itself which conforms to the semi-conscious behavior of particles which act as if they also are aware of their surroundings.

But in deBB, there is no more role for mind in quantum mechanics than there is in classical mechanics-- both QM and CM describe a fully predetermined future, from the deBB perspective (personally I don't think the effectiveness of either QM or CM imply that). But I suppose within the context of complete determinism, there is still the possibility for associating the pilot wave with some sort of mindlike function, for those who tend toward idealism.

The basic assumption is to fully understand the role of the observer to unify these theories. Because we are apart of nature and therefore complementary to it.

I believe that will be a key element, but I still haven't seen anything that I regarded as a different theory that guides new observations to test it-- I just see a lot of philosophical priorities in conflict. I think our philosophical priorities are important to us, but I also think history is quite clear that philosophical priorities show no tendency to converge.

 

[BruceW]

what does it mean that the Bohmain interpretation is causal but not local? Also as in the case of the two slit experiment I fail to see how the interference pattern of the wave function vanishes when a measuring device is put next to one of the two slits.

Otherwise it seems a very valid interpretation and also inline with the new E8 theory of everything posed by Garrett Lisi

In the Bohmian interpretation, there is the wave function and the particles. Both are real. The wave function is a function of all the particle's instantaneous positions, and the guiding equation uses the wave function to give the velocity of a given particle. Since the wave function depends on all the particle's instantaneous positions, the velocity of one particle depends on all the instantaneous positions of the other particles. The other particles may be very far away, which is why the Bohmian interpretation is nonlocal.

I'm not certain of what the mathematical meaning of 'causal' is, but Bohmian interpretation is said to be causal. I think this is because the path of each particle is directly influenced by the positions of the other particles via the wave function (and this link is the causation).

In the two-slit experiment, in the Bohmian interpretation, the particle definitely goes through one slit. But the wave function is affected by the presence of a measuring device in front of the other slit. And the wave function guides the motion of the particle. Therefore, the motion of the particle is affected by objects that are not near it. (Another example of the nonlocality of this interpretation).

 

[dreamland37]

I still haven't seen anything that I regarded as a different theory that guides new observations to test it-- I just see a lot of philosophical priorities in conflict. I think our philosophical priorities are important to us, but I also think history is quite clear that philosophical priorities show no tendency to converge.

I would tend to believe that just as Einstein said that science without religion is lame and religion without science is blind, I feel that in the same regard, unless any philosophical theory can model a mathematical framework it is almost meaningless to talk about it as far as ontology or metaphysics is concerned. But the same is true for any mathematical models which do not fit the empirical description of our world. Einstein wrote a few papers which were complete unified field theories. He even found a solution which didn't even need Planck's constant. But his colleagues told him that his papers didn't have any connection to physical reality as his theory of relativity had. Within a year he had abandoned it and again continued his quest.

Although I believe that MWI doesn't interfere with our empirical description of the world but in a sense acts as the mathematical framework for out mental construct. In other words, it can been seen as the mathematical course of our thoughts in terms of a probability wave inherent within the system, which means that our thoughts are deterministic to a level.

A short and detailed description is:

1.In reality there are objects and there are thoughts. Both are merely two sides of the same mental phenomena, which is the mind. In a sense, the observer is nothing more than the perceiver of his or her own mind. It's almost like the world is a really awesome dream with a mathematical base to it.

2.Thoughts and Objects occupy the same space.

3.Thoughts are nothing more than the probabilities of objects which can been seen as the pilot wave determining the course of every action in the universe. That pilot wave is proportional to the observer. In other words, it means that the observer is the center of the universe and there is no big bang singularity.

This is in agreement with Arto Annila who just won the nobel prize for his equations that showed the true nature of the expanding universe and that dark matter is no longer necessary. He says "General relativity in terms of Einstein's field equations is a mathematical model of the universe, whereas we need the physical account of the evolving universe provided by Maupertuis' principle of least action," .....

"On-going expansion of the universe is not a remnant of some furious bang at a distant past, but the universe is expanding because energy that is bound in matter is being combusted to freely propagating photons, most notably in stars and other powerful celestial mechanisms of energy transformation,"


4. Every thought has a number. That number is equal to a probability.

5. No object is ever stand still, but is following the most probabilistic course of any given system.

6. Objects follow the course of the greatest probability that we can govern with our thoughts.

Conclusion: Thoughts are the probabilistic value of any given system. MWI is right in the sense that every probability is a reality just as every thought is a reality. But just as the world we live in is a superposition or combined effect of everyone's projected mental reality, a single collective picture of reality emerges. That single picture is the determined outcome of every single probability in an instant, or as close to an instant as we can get.

It is not to say that the other realities don't co-exist, it is just that since the effects are so small we don't see them, their probabilities being smaller.

The consequences of this theory is that our thoughts actually capture the essence of whatever it is we are thinking about.When our imagination runs loose, we are creating other realities that exist as waves of possibilities.

One so-called example is listed in a movie, What the Bleep Do We Know?, where a Buddhist monk blesses a number of different bottles of water with different blessings. Before
the experiment, each bottle of water had a random molecular structure but after the blessings, each one changed differently into a beautiful snowflake-like shape. There have been a few more experiments that I read about such as in the book the Holographic Universe. My point, however, is that if thoughts influence the physical world, then the reverse must be true.

Now, I am no Einstein. He found the mathematical equivalency between matter and energy and my visceral assumption is that a similar equation exists for MWI which is the proportional relationship between the many other worlds of our probabilistic imaginations and the one that shows itself to our direct experience.

Are there any mathematical models are predictions you can think of? Or are there any arguments you know of that might work against such a theory. For even Einstein's theory of relativity wasn't complete until he added his mathematical framework to it. Until than it was just a philosophy which many scientists disagreed with.

 

[Samshorn]

There are certainly some subtle points here. If you look at a MWI-favoring physicist doing a quantum mechanics calculation, you are not going to be able to tell they hold to MWI... because MWI proponents don't shun the Born rule, they use it just like everyone else.

But by dealing with apparently classical outcomes and using the Born rule to compute the probabilities of those outcomes they are not holding to MWI, because according to MWI they should really be making decoherence calculations on the wavefunction of an entire isolated system including both the experimental subject and the observer, with the suitable Hamiltonian for this whole isolated system (which, for the reasons explained before, can hardly be smaller than the entire universe), and at best this will lead only to approximately classical outcomes, so the application of the Born rule to the results of this hypothetical calculation, even if it could be carried out, would be inherently ambiguous... But of course no one has ever made such a calculation, and of course no one ever will, and they have never offered more than hand-wavy plausibility arguments that they ever could do such a calculation, even in principle.

The point is that just because someone who espouses (some version of) MWI avails himself of the calculational recipes of ordinary quantum mechanics, it doesn't follow that his calculations really are consistent with his philosophical beliefs. This consistency needs to be established. Much ink has been spent by people trying to establish this, and making adjustments to their conceptions of MWI in order to help establish this, but there are deep and subtle issues involving the concept of a wave function and Hamiltonian of the entire universe (for example), the arrow of time, etc., not to mention the fact that we know Schrodinger's equation is wrong, because it isn't relativistic, so we're led to consider quantum field theory, which has its own issues. You may choose to carry on your philosophical considerations based on the assumption that some version of MWI actually is consistent with quantum mechanics, but this is far from having been established.

The "worlds" of MWI are not evolving unitarily. If they did, we wouldn't need MWI at all!

I hoped it wouldn't be necessary to fill in so many details, but to clarify, what I mean is that at some instant t there is a self-consistent subworld described by v that branches off into isolation from all the rest of the universe. Now, v immediately can be regarded as splitting into sub-sub-worlds v1, v2, v3..., and each of those splits into sub-sub-sub-worlds such as v2a, v2b, v2c,..., and each of those splits into worlds such as v2b1, v2b2, v2b3,... But the point is that these are all constituents of the isolated system v, which does not interact with anything else. The isolated system v(t), by your hypothesis, can be modeled by unitary evolution according to the Schrodinger equation in some suitable Hilbert space with some suitable Hamiltonian and initial conditions. All the sub-sub-worlds that it spawns within itself are, according to MWI, implicit within the unitarily evolving wavefunction v(t).

Now, according to MWI, the state v(t1) at some time t1 is some projection from the universal wave function V(t1) in the universal Hilbert space S down into some subspace s, and of course by making this projection we gloss things and would arrive at a mixed state for the subsystem, but thereafter that subsystem is isolated, so according to your hypothesis it undergoes unitary evolution thereafter, within some suitable Hilbert space s with suitable... etc.

But of course the world we experience at a sequence of times t1, t2, t3, t4... is not v(t1), v(t2), v(t3), v(t4)..., it is something like v(t1), v2(t2), v2b(t3), v2b1(t4),... and so on. Obviously this sequence of worlds is not evolving in a unitary way (viewed by itself), but the point is that the projections from the universal wave function V(t) (which IS evolving in a unitary way) down to each of these instantaneous worlds cannot be going to the same subspace s, they must be projections to a sequence of sub-spaces s, s2, s2b, s2b1,... so in order to place the terms of the MWI model into explicit correspondence with the measures of our experience in accord with quantum mechanics, we need more than just the Schrodinger rule for evolving isolated systems, we also need the rule for evolving the projection subspaces... and this is MUCH more than just the Born rule for assigning probailities, we need the rule to define the (approximate) subspaces to which the Born rule is applied. Explicitly defining this sequence of subspaces is what the projection postulate in ordinary quantum mechanics does, on a piece-meal basis.

I agree, MWI is not mechanically different from CI, even if some practitioners hoped to find a way to make it so.

I don't agree. MWI actually is mechanically different from CI, for the reasons explained above (e.g., CI has classical entities, whereas MWI has only approximately classical entities, even according to the hand-wavy defenses of it). Now, I personally don't think CI is free of conceptual difficulties either. But I would say that CI comes closer to being a legitimate interpretation of quantum mechanics than does MWI, probably because CI is really not too far removed from just shutting up and calculating.

 

[kith]

I hoped it wouldn't be necessary to fill in so many details, but to clarify, what I mean is that at some instant t there is a self-consistent subworld described by v that branches off into isolation from all the rest of the universe. Now, v immediately can be regarded as splitting into sub-sub-worlds v1, v2, v3..., and each of those splits into sub-sub-sub-worlds such as v2a, v2b, v2c,..., and each of those splits into worlds such as v2b1, v2b2, v2b3,... But the point is that these are all constituents of the isolated system v, which does not interact with anything else.

I don't think that's right. How does v split? By decoherence. What is the cause of decoherence? Interactions with the environment. Thus in isolation, there is no splitting. If v splits it is not isolated.

Also note that Schrödinger's equation does hold in QFT. See for example this wikipedia entry, where the free-field Hamiltonian is given.

 

[Ken G]

One so-called example is listed in a movie, What the Bleep Do We Know?, where a Buddhist monk blesses a number of different bottles of water with different blessings. Before the experiment, each bottle of water had a random molecular structure but after the blessings, each one changed differently into a beautiful snowflake-like shape.

Well, I wouldn't base your argument on that. What you're describing sounds like water being frozen in random ways that give rise to the well-known symmetry-breaking properties of frozen snowflakes, which are not molecules but are structures of molecules (that is not what is normally meant by "molecular structure"), and freeze in different but random ways. If I "bless" five different random number generators with five different blessings, and get five different numbers out, I'm not going to conclude that the numbers were different because of differences in my blessing until I can show with a double-blind test that the blessings repeatably correlated with the outcomes of multiple trials. It really doesn't sound like anything like that was done in the movie, it sounds more like the way parlor magic tricks can fool non-magicians.

Are there any mathematical models are predictions you can think of? Or are there any arguments you know of that might work against such a theory. For even Einstein's theory of relativity wasn't complete until he added his mathematical framework to it. Until than it was just a philosophy which many scientists disagreed with.

That's the rub-- philosophical ideas can give us a sense of mental satisfaction, but they are not science until they motivate a mathematical description that makes testable predictions that are different from the ones we already have.

 

[BruceW]

I think that the most important thing I have learned from this thread is that everyone has a different definition for each interpretation of QM.
And the definition of interpretation is vague, since it sometimes means a particular way of looking at standard QM theory and sometimes it means a totally different theory to standard QM, even though it is still called an interpretation.
I think I will be careful in the future to ask what people mean by the terms they use when it comes to the discussion of QM interpretations.

 

[Ken G]

But by dealing with apparently classical outcomes and using the Born rule to compute the probabilities of those outcomes they are not holding to MWI, because according to MWI they should really be making decoherence calculations on the wavefunction of an entire isolated system including both the experimental subject and the observer, with the suitable Hamiltonian for this whole isolated system (which, for the reasons explained before, can hardly be smaller than the entire universe), and at best this will lead only to approximately classical outcomes, so the application of the Born rule to the results of this hypothetical calculation, even if it could be carried out, would be inherently ambiguous... But of course no one has ever made such a calculation, and of course no one ever will, and they have never offered more than hand-wavy plausibility arguments that they ever could do such a calculation, even in principle.

So it is as I said above-- you simply equate the mathematical machinery that can be found in any quantum mechanics textbook with CI, and say that MWI has to use some other currently nonexistent mathematical machinery or it isn't MWI. That just doesn't seem like a realistic requirement to call something MWI to me, and I don't think the proponents of MWI need to disallow themselves to use quantum mechanics textbooks when they do calculations.

The point is that just because someone who espouses (some version of) MWI avails himself of the calculational recipes of ordinary quantum mechanics, it doesn't follow that his calculations really are consistent with his philosophical beliefs. This consistency needs to be established.

I would be careful about that requirement-- you are saying that anyone who claims to have an interpretation must make a demonstrable link from their interpretation to the equations they are using the interpretation to understand. I actually don't think any interpretation in the history of physics can satisfy that demand, for the simple reason that mathematics is just one thing-- mathematics. No one can ever prove that an interpretation really does "establish the consistency" of the interpretation with the mathematics. If I interpret forces as real but action as a mathematical trick, according to your stated criteria, I could never use a Lagrangian approach to calculate a constraint force-- I'm being inconsistent with my interpretation that says forces are real and Lagrangians are just mathematical tricks. I'd be turning my back on my philosophical beliefs as soon as I wrote down the Lagrangian, because it isn't something accepted in the ontology of my interpretation.

Since I don't think any interpretation can ever prove itself to be consistent with the theory it interprets (the latter being a mathematical idealization, the former being a philosophical stance-- apples and oranges), I feel the actual standard we should hold interpretations to needs to be much looser-- they need to give us a sense that we understand the meaning of the operations we are carrying out. That's true even if the meaning is sometimes "this doesn't correspond to anything real but it's useful anyway". Thus someone who doesn't believe particles are real in their interpretation of physics can still talk about electrons all the same, without feeling like a turncoat to their interpretation. Similarly, MWI proponents can employ the Born rule.

Much ink has been spent by people trying to establish this, and making adjustments to their conceptions of MWI in order to help establish this, but there are deep and subtle issues involving the concept of a wave function and Hamiltonian of the entire universe (for example), the arrow of time, etc., not to mention the fact that we know Schrodinger's equation is wrong, because it isn't relativistic, so we're led to consider quantum field theory, which has its own issues.

But it certainly isn't fair to drop any of those things on the doorstep of MWI, because they all fall on the doorstep of any interpretation of nonrelativistic quantum mechanics. No one ever said physics had to be exact or perfectly internally consistent, and so no interpretation has to be those things either. We cannot hold interpretations of physical theories to higher standards then we would ever hold the theory itself to! But I do agree that this is the very reason that we should take neither our theories, nor their interpretations, as seriously as some seem to. I don't believe in building "world views" based on interpretations of physical theories, because of the limitations in both the interpretations, and in the theories themselves. Indeed, exactly how I look at interpretations is as a way to see a theory from a different philosophical angle, and nothing more or less than that.

I hoped it wouldn't be necessary to fill in so many details, but to clarify, what I mean is that at some instant t there is a self-consistent subworld described by v that branches off into isolation from all the rest of the universe. Now, v immediately can be regarded as splitting into sub-sub-worlds v1, v2, v3..., and each of those splits into sub-sub-sub-worlds such as v2a, v2b, v2c,..., and each of those splits into worlds such as v2b1, v2b2, v2b3,... But the point is that these are all constituents of the isolated system v, which does not interact with anything else.

Actually, I don't think there is a requirement for the subsystem v to not interact with anything else, the sole requirement is that it not interact with anything else in a way that leaves a signature or trace. That is essentially the definition of an "other world" (when it is not true, we use the term superposition instead). This means that if "other worlds" affect v, they do so in ways that look completely unpredictable and nondeterministic.

In other words, such influences would go into all the things that we have already chosen not to track about v-- it is only if we could somehow track those things that we would ever see those interactions. Since the interactions are impossible to track in practice, the net effect of having those other worlds, and not having them, is exactly the same-- it is untraceable, but that is not the same as requiring they be nonexistent. The fundamental connection between the worlds is the maintenance of unitarity of the whole, and that might require all kinds of "interactions" between the systems, much like entanglements in the EPR paradox. But note that if you are never allowed to communicate with anyone doing experiments on an entangled partner, you never see anything in your own entangled partner that gives the least clue of the presence of that entanglement. So it would be with the many worlds.

But of course the world we experience at a sequence of times t1, t2, t3, t4... is not v(t1), v(t2), v(t3), v(t4)..., it is something like v(t1), v2(t2), v2b(t3), v2b1(t4),... and so on. Obviously this sequence of worlds is not evolving in a unitary way (viewed by itself), but the point is that the projections from the universal wave function V(t) (which IS evolving in a unitary way) down to each of these instantaneous worlds cannot be going to the same subspace s, they must be projections to a sequence of sub-spaces s, s2, s2b, s2b1,... so in order to place the terms of the MWI model into explicit correspondence with the measures of our experience in accord with quantum mechanics, we need more than just the Schrodinger rule for evolving isolated systems, we also need the rule for evolving the projection subspaces... and this is MUCH more than just the Born rule for assigning probailities, we need the rule to define the (approximate) subspaces to which the Born rule is applied. Explicitly defining this sequence of subspaces is what the projection postulate in ordinary quantum mechanics does, on a piece-meal basis.

I don't see where MWI is missing that, it uses the projection postulate just like it uses the Born rule, just like someone who doesn't think gravity is really a force can still write F=mg without making themselves some kind of liar! All they are doing is parsing between what they know is an effective theory, and what they think is "actually happening", and that is almost always a purely philosophical distinction.

Now, I personally don't think CI is free of conceptual difficulties either. But I would say that CI comes closer to being a legitimate interpretation of quantum mechanics than does MWI, probably because CI is really not too far removed from just shutting up and calculating.

That is also why I prefer CI. Note where you have identified your own philosophical priority in making that statement of why you consider CI to be "more legitimate"-- that it is closer to shutting up and calculating. Note that someone who really does prefer shutting up and calculating (I've met many who claimed that, none who ever actually did) could easily claim CI is not legitimate either, on grounds that it is not close enough to shutting up and calculating!

 

[Samshorn]

What is the cause of decoherence? Interactions with the environment.

No, just the opposite. Interactions with the environment lead to entanglement and coherence (not decoherence) of the elements of an individual sub-world. Each projection of some entity becomes inextricably entangled with it's own environment (including a version of the scientists that observed it), so we get these islands of coherence, and these islands tend to quickly DEcohere from each other, meaning they do NOT interact with each other, but of course they are all still just components of a single unitarily evolving universal wavefunction.

Thus in isolation, there is no splitting. If v splits it is not isolated.

That's completely wrong. The unvierse is an isolated system, so according to you there is no splitting, and MWI is impossible. Is this the point you are trying to make?

Also note that Schrödinger's equation does hold in QFT. See for example this wikipedia entry, where the free-field Hamiltonian is given.

QFT is relativistic, the Schrodinger equation is not. Ironically, Schrodinger actually first discovered the relativistic version, which we call the Klein-Gordon equation, but discarded it, before arriving at what we call the Schrodinger equation of non-relativistic quantum mechanics. The fact that a wiki article on second quantization refers to the Schrodinger equation is neither here nor there.

 

[Samshorn]

You are saying that anyone who claims to have an interpretation must make a demonstrable link from their interpretation to the equations they are using...

Yes, in order for a conceptual model to qualify as an interpretation of a theory, we must establish a clear correspondence between the elements and features of the model and the empirical content of the theory, which is generally expressed in mathematical terms. I wouldn’t have thought this was controversial.

I actually don't think any interpretation in the history of physics can satisfy that demand... If I interpret forces as real but action as a mathematical trick, according to your stated criteria, I could never use a Lagrangian approach to calculate a constraint force...

My criterion didn't say anything about "real" or "mathematical tricks". The issue isn't about ontology. We're free to use whatever mathematical tricks we wish... but they must correspond in some definite way to the features of our conceptual model in order for that model to qualify as an interpretation of the theory. For example, there is no difficulty translating between a force/vector formulation of mechanics to a Lagrangian formulation. This is a perfectly well defined correspondence. No problem at all.

But there is a problem with an advocate of MWI using the von Neumann recipe for quantum mechanics, because he lacks a well-defined correspondence between the features of the conceptual model and the mathematical methods. Now, there is a mathematical formalism based on the axioms of MWI, and it consists of the Schrodinger equation applied to a universal wavefunction with some universal Hamiltonian and initial conditions. So hopefully we agree that an advocate of MWI is entitled to make that kind of calculation. But they never do. Instead, they use the von Neumann recipe, and they justify this use by claiming that the mathematics associated with their model reduces to the von Neumann recipe (at least for all practical purposes). But does it?

We have two mathematical formalisms, and a claim that one entails the other. This is easy to confirm in the case of force/vectors versus Lagrangian, but not nearly so easy to confirm for the mathematics of MWI and CI. We lack any demonstration that the axioms of MWI (whichever version you prefer) actually do lead to the von Neumann recipe, even just "for all practical purposes". This is why so many volumes have been filled by people striving to establish that correspondence, or at least to make it more plausible. I get the impression that you would advise them to stop wasting their time, because you think it has already been sufficiently established. But I suspect that even most advocates of MWI would not agree with that, and certainly the critics would not agree.

I feel the actual standard we should hold interpretations to needs to be much looser-- they need to give us a sense that we understand the meaning of the operations we are carrying out.

Actually I agree with your standard, i.e., an interpretation needs to "give us a sense that we understand the meanings of the operations we are carrying out". That's essentially a paraphrase of my criterion. I think we differ only in having different ideas about what it takes to "give us a sense that we understand" something. For me, I don't have that sense unless I can see how the terms of my equations correspond to the features of the conceptual model in some definite way. You, on the other hand, get the sense that you understand the meanings of the operations in terms of the model, even in the absence of a clear correspondence between those terms and the model. To me, that’s a contradiction.

But it certainly isn't fair to drop any of those things on the doorstep of MWI, because they all fall on the doorstep of any interpretation of nonrelativistic quantum mechanics.

Yes, I only mention it to emphasize that the task of reconciling the MWI model with our actual computational physics is even more challenging than just the non-relativistic version might suggest, so we are very far from being able to really justify MWI as a viable model. Also, the transition to relativistic theory has important implications for the arrow-of-time problem that besets MWI, and it can’t really even be addressed in a non-relativistic context.

Actually, I don't think there is a requirement for the subsystem v to not interact with anything else, the sole requirement is that it not interact with anything else in a way that leaves a signature or trace.

So if v does not interact with anything in a way that leaves a signature or trace, is that a strong enough condition to say that v(t) evolves in accord with Schrodinger’s equation? If not, wouldn’t the deviation itself constitute a signature?

The fundamental connection between the worlds is the maintenance of unitarity of the whole, and that might require all kinds of "interactions" between the systems, much like entanglements in the EPR paradox.

True, and if we can’t regard branches as isolated systems, this tends to support the idea that the only really isolated system (containing any significant complexity), to which the hypothesis of pure Schrodinger evolution is strictly applicable, is the entire universe. This makes the task of demonstrating the correspondence with von Neumann recipes even more problematic.

I don't see where MWI is missing that, it uses the projection postulate just like it uses the Born rule, just like someone who doesn't think gravity is really a force can still write F=mg without making themselves some kind of liar!

Well, if someone like William Kingdon Clifford, who vaguely imagined that gravity might be interpreted as curvature of space, had written F=mg and claimed that this equation was consistent with his conceptual model of gravity, he would indeed have been lying, because he could not establish that correspondence. It was Einstein’s great achievement to show – explicitly – precisely how the 4-dimensional tensor equations of his metrical theory of spacetime curvature actually do reduce to the simple Newtonian scalar equations in the lowest order approximation. Only by doing so was he able to claim that the spacetime curvature interpretation is consistent (approximately) with those simple equations.

That’s exactly what I’m saying is needed for MWI to justify the use of the simple von Neumann recipe for quantum mechanical calculations. You need to start with the wave function and Hamiltonian and initial conditions of the entire universe (none of which are knowable), and then show how the Schrodinger evolution of this wave function, taking decoherence into account, leads (at least approximately) to the time-asymmetrical behavior and empirical content represented by the von Neumann recipe.

All they are doing is parsing between what they know is an effective theory, and what they think is "actually happening"…

But surely we’re entitled to distinguish between actual “parsing” and mere wishful thinking. If I tell you I can parse the equations of quantum mechanics from contemplation of my dog Smithers, you would dismiss my claim out of hand – and rightly so. So you can’t maintain the position that you will accept any claim that any model represents a legitimate interpretation of any theory. You do have standards, i.e., you require some rational basis for thinking the model really is a representation of the theory.

It all comes down to what you said above, about what it takes “to give us a sense that we understand the meaning of the operations we are carrying out”. You are convinced that if someone actually could make sense of the Hilbert space and Hamiltonian of the entire universe, and if they could somehow divine the initial conditions of a universal wavefunction, such that, subject to the Hamiltonian under the Schrodinger equation (or, better, it’s relativistic counterpart) it leads to suitable time-asymmetric evolution, and that the result, taking decoherence into account, would yield something whose components or projections into some suitable sub-spaces, selected, combined, and arranged in some suitable order, would reduce in some approximation to the usual equations of quantum mechanics. To you this is sufficiently self-evident that you’re willing to take it as given. It isn’t that self-evident to me.

 

[kith]

That's completely wrong. The unvierse is an isolated system, so according to you there is no splitting, and MWI is impossible. Is this the point you are trying to make?

If you omit the "and MWI is impossible" yes, this is one of the points I'm trying to make. Maybe this seems nonsensical to you, but we should really finish the decoherence discussion first.

Since you agree, that decoherence is responsible for the "splitting", but not that it is caused by interactions with the environment, I'd like to ask three questions:
1) What do you think is the cause of decoherence?
2) Do you think decoherence doesn't occur in the CI?
3) Do you know how decoherence works mathematically?

 

[Samshorn]

If you omit the "and MWI is impossible" yes, this is one of the points I'm trying to make. Maybe this seems nonsensical to you...

Yes, I'm afraid it does. According to the "many worlds interpretation", the overall universal wave function is continually evolving into more and more proliferating self-consistent "worlds". You've stated that, since the universe is an isolated system, no such "splitting" of the overall universe into self-consistent sub-worlds can possibly occur. The obvious implication is that MWI is impossible, but you deny this implication... so I don't understand you at all.

 

[Ken G]

Yes, in order for a conceptual model to qualify as an interpretation of a theory, we must establish a clear correspondence between the elements and features of the model and the empirical content of the theory, which is generally expressed in mathematical terms. I wouldn’t have thought this was controversial.

What is controversial is what you mean by a "clear link." Who decides what forms this link must take, and when is it clear versus murky? I would say that MWI does have a clear link-- they say closed systems (and systems whose only external interactions can be treated as specified rather than self-consistently evolving, as with a potential function) evolve by the Schroedinger equation, and that when an observer (or apparatus) becomes part of that system in ways that are not being tracked in detail, the Born rule applies for attributing the measure of the various outcomes the apparatus might be considered to follow when all that missing information is not being tracked. That seems like a clear link to me, even though it doesn't explain the Born rule any better than CI does. If MWI users want a better explanation of the Born rule, it's not because they have to have one to make MWI a valid interpretation, it's that they need one to make MWI a new theory that could potentially make different predictions and guide us into seeing how to test those differences. Successful testing would then make MWI a clearly superior theory, rather than just an alternate interpretation.

The point is, only better predictions are demonstrable, not better interpretations. I would argue that anyone who sees a link, and uses it when they write down the equations, is following their interpretation without any need to demonstrate that their interpretation leads to those equations because interpretations always fall short of doing that. Interpretations are fundamentally subjective, and fundamentally ad hoc.

For example, there is no difficulty translating between a force/vector formulation of mechanics to a Lagrangian formulation. This is a perfectly well defined correspondence. No problem at all.

Sure, but those are formulations, meaning they are equations. We can all agree on the equations of quantum mechanics, they're in the textbooks. What you are saying is that a valid interpretation of a given formulation must demonstrate a correspondence with that formulation. You are in effect asking for the postulates of the formulation to follow from the interpretation! That never happens, it would be backward. We don't interpret Newton's laws as forces on particles, and that gives us F=ma, we start with the formulation (F=ma) and interpret the meaning of the letters. The interpretation gives us a sense of cognitive resonance when we write those letters down, that's all it does. People who use the MWI interpretation get that sense of cognitive resonance when they write the equations of quantum mechanics, so they are using an interpretation-- they can no longer demonstrate that the equations they are writing down somehow follow from that interpretation than you can demonstrate that F=ma follows from the concept of pushing on particles.

To elaborate, let's say I am a strict "shut up and calculate" empiricist. I say that F=ma is just some mathematical symbols used to translate between the outcomes of experiments. I have my initial data, and my calculated prediction, and I compare that to some final data. That's it, no forces, no particles, nothing-- just letters and data. Further, I claim that this is all anyone can ever demonstrate that the physicist is actually doing. The rest is just some kind of self-delusion they carry in their minds, a bunch of interpretations that fail the very test you have put to them-- that they must establish a clear correspondence to the letters in the formulae. If I say that no such clear correspondence is possible because there's no such thing as any of those make-believe notions like forces or electrons, there is not a single thing you can do to demonstrate that I am wrong. If physics really stuck to what is demonstrable, then it would involve no interpretations of any kind. That's what "shut up and calculate" really means-- all interpretations are invalid at the level of demonstrability. So we either stick to that, or we take the alternate approach of recognizing from the start that interpretations are not demonstrable, and use them to get that sense of cognitive resonance that we crave.

So hopefully we agree that an advocate of MWI is entitled to make that kind of calculation. But they never do. Instead, they use the von Neumann recipe, and they justify this use by claiming that the mathematics associated with their model reduces to the von Neumann recipe (at least for all practical purposes). But does it?

There is no other mathematics associated with their model-- they don't have a model. They have an interpretation of the exact same mathematics. If they had any different mathematics, or anything that was demonstrably a different model, then it would be a different theory. If it makes all the same testable predictions, then it is the same theory, and any differences in how it is imagined is just an ontological difference, a purely philosophical difference. This is the only way to enforce a line between science and philosophy.

We have two mathematical formalisms, and a claim that one entails the other. This is easy to confirm in the case of force/vectors versus Lagrangian, but not nearly so easy to confirm for the mathematics of MWI and CI.

If those mathematics are different, then what is the difference? I think we agree that if you look over the shoulder of an MWI proponent as they solve some problem on a quantum mechanics final exam, you are not going to have the slightest idea if they are an MWI proponent or a CI proponent. So I reject the idea that there is a "mathematics of MWI", if there were you could point out on their paper "that's where they used the mathematics of MWI." There won't be such a place.

So you are claiming that the reason for this is they were really using CI, not MWI, they only deluded themself into thinking they were using MWI, but in fact the mathematics they did use is only consistent with CI. CI has now claimed the quantum mechanics theory, from your perspective, so of course MWI must be wrong if it isn't allowed to use quantum mechanics. But then you have to point to the place where they used an equation that was not consistent with MWI. That would have to be the Born rule-- you are claiming MWI has no Born rule. But it does-- it just uses the Born rule postulate to determine the measure of the probabilities that associate with the fragmented "worlds."

Note that is just exactly what CI would do, and for no better reason, the only difference would be that the CI user would be imagining in their head, when they write down the Born rule, that this corresponds to the entire reality. The MWI user imagines it corresponds to a "world." The answer to the final exam question, the "empirical content", is exactly the same either way-- nowhere in that correct solution will we ever see what is going on in the imagination of the testtaker, we just don't get to see the interpretation because it was never anything but a source of cognitive resonance that might have helped them imagine what the letters they were writing down mean. Since the letters are the same, they translate immediately across interpretations, and no one is the wiser. Much like the word "red" we use when we are describing our experience of color.

We lack any demonstration that the axioms of MWI (whichever version you prefer) actually do lead to the von Neumann recipe, even just "for all practical purposes".

The von Neumann recipe is a postulate of MWI just like it is a postulate of CI, all that is different is what that is imagined to mean. The MWI user thinks the Born rule means something different, and might someday yield to some deeper derivation as a result, but they still use it all the same-- begrudgingly. Just like how someone might use F=ma begrudgingly even if they believe the real ontology is least action-- they know that F=ma makes equivalent predictions to any approach that would fit in their ontology, so they use it, even though it is not in their ontology. Same for the Born rule.

This is why so many volumes have been filled by people striving to establish that correspondence, or at least to make it more plausible. I get the impression that you would advise them to stop wasting their time, because you think it has already been sufficiently established. But I suspect that even most advocates of MWI would not agree with that, and certainly the critics would not agree.

I believe that is because they are talking about something different from what you are. They want something more from MWI than just another valid interpretation of QM! They want it to guide them to some deeper message that QM is trying to tell them, something CI is not hearing, but there's no way to demonstrate it is really doing that, until MWI (or CI) inspires some new theory that is actually different from QM and makes some testable prediction that has been verified.

Actually I agree with your standard, i.e., an interpretation needs to "give us a sense that we understand the meanings of the operations we are carrying out". That's essentially a paraphrase of my criterion.

It includes a very important change-- I have stricken out your objective requirement for "demonstrably clear connection" in favor of the purely subjective criterion that it "uses the same mathematics but imagines that it means something different." Sort of like how, if you watch someone solve an F=ma problem, you never have any idea what they imagine that "F" means.

I think we differ only in having different ideas about what it takes to "give us a sense that we understand" something. For me, I don't have that sense unless I can see how the terms of my equations correspond to the features of the conceptual model in some definite way.

Yes, we differ on what requirements we need to satisfy to claim we have an understanding. Let me give an example. Let's say someone back in the day of Newton, let's call him Jim, was told about F=ma and how great it works, and Jim said he will be happy to use F=ma, but he just can't interpret it as forces that are pushing on things. Jim has a philosophical objection to the idea that objects can really have that kind of power over each other, they are just dumb inanimate objects. Instead, all agency must stem from nature herself, and nature must create in some sense the "best of possible worlds". So Jim imagines that objects follow F=ma not because there really are forces on them, but because nature is finding some kind of extremum in some quantity that has not yet been discovered. Jim interprets the "F" as just an illusion of the presence of a force, he feels the F is emergent from some effort by nature to find an extremum. It doesn't matter that Jim cannot say what that extremum is, it's just an interpretation of the meaning of F, based on his philosophical priority that everything that happens must trickle down from nature herself, nothing can be what one object is doing to another because objects don't have that ability.

So then, you come along and say Jim's interpretation is not valid because he can't say what is being minimized. But he says he doesn't need to, it's just what he's imagining when he writes down "F". All the same, he's motivated to try and figure out an extremum principle that could generate the same equation, and he eventually finds action, and then he goes on to use that in deriving relativity and quantum mechanics-- which actually are new theories in which minimizing action has some greater importance than just F=ma. You can say that only then has his interpretation become valid, but he says no, that was only when it became powerful. That's what MWI proponents are trying to do (and similarly for some CI proponents, like Fra)-- they are trying to make the interpretation powerful instead of just passively valid. Power is the only thing that is demonstrable.

Yes, I only mention it to emphasize that the task of reconciling the MWI model with our actual computational physics is even more challenging than just the non-relativistic version might suggest, so we are very far from being able to really justify MWI as a viable model.

MWI isn't really a model, but I agree that these are obstacles for MWI to become powerful. Still, shouldn't we look under every stone? You don't need to put your own stock in that avenue, but it's best if someone tries it.

So if v does not interact with anything in a way that leaves a signature or trace, is that a strong enough condition to say that v(t) evolves in accord with Schrodinger’s equation? If not, wouldn’t the deviation itself constitute a signature?

Yes, the deviation does constitute a signature, collapse constitutes a signature that the observer (or his proxies) have become part of the system and the Schroedinger equation only applies when no measurement is occurring (in CI, where the truth must result from that interaction, rather than preside in spite of it).

Well, if someone like William Kingdon Clifford, who vaguely imagined that gravity might be interpreted as curvature of space, had written F=mg and claimed that this equation was consistent with his conceptual model of gravity, he would indeed have been lying, because he could not establish that correspondence.

You are asking Clifford to have a new theory of gravity, not an interpretation of Newton's gravity. An interpretation would go like "the reason all objects follow the same paths in space and time under gravity is because gravity is nothing but a redefinition of the meaning of an inertial path." That's it, that's all one would need to say, it's an interpretation of mg = ma by cancelling the m's and writing it a-g=0. There is no requirement to provide any equation to support that interpretation other than that.

It was Einstein’s great achievement to show – explicitly – precisely how the 4-dimensional tensor equations of his metrical theory of spacetime curvature actually do reduce to the simple Newtonian scalar equations in the lowest order approximation.

True, but Einstein was not credited with finding a new interpretation, he found a new theory. I would say a better analogy to a new interpretation was D'Alembert's. He replaced F=ma by F-ma=0 and interpreted ma as some kind of inertial force, then he said that the principle is that all forces always balance. He never provided any reason that there ought to be some inertial force called ma, he just asserted that one could look at Newton's laws that way.

That's all MWI is doing-- saying you can look a different way at the postulates of QM, and even though you still use the same postulates, you think they carry a different message (like D'Alembert thinking the message is that forces are always in balance, we live in a balanced universe). It is only the ontology that is different, not the mathematics. When the mathematics is demonstrably different, you have a new theory.

You need to start with the wave function and Hamiltonian and initial conditions of the entire universe (none of which are knowable), and then show how the Schrodinger evolution of this wave function, taking decoherence into account, leads (at least approximately) to the time-asymmetrical behavior and empirical content represented by the von Neumann recipe.

Then why doesn't CI have to start with the observer and show how making an observation collapses into an eigenstate? If CI is allowed to assert the Born rule by fiat and interpret what is real is what happens on the observer end of that mathematical description, then MWI is allowed to assert the Born rule by fiat and interpret whas is real is what happens on the wavefunction end of that mathematical description. It is only if someone wants to argue that MWI is a different theory, or a superior interpretation at least, that they would need to do what you ask. They would like to do it, no doubt, but failing to do so does not render the interpretation invalid, and more than failing to account for why the Schroedinger equation applies to unobserved wave functions if it is their collapse that is real renders CI invalid (which anti-CI people claim all the time).

If I tell you I can parse the equations of quantum mechanics from contemplation of my dog Smithers, you would dismiss my claim out of hand – and rightly so.

Not quite, what I would do is say that I see no personal value for me in the interpretation that you suggest. But if a thousand theoretical physicists interpreted quantum mechanics the way you were describing, and achieved some cognitive resonance by doing so, I would probably have to conclude I couldn't find any value because I simply didn't understand the interpretation you were suggesting.

So you can’t maintain the position that you will accept any claim that any model represents a legitimate interpretation of any theory. You do have standards, i.e., you require some rational basis for thinking the model really is a representation of the theory.

I have to to use it myself, but I don't have to convince others. One can point to a problem with an interpretation without concluding that the interpretation is invalid, because validity of an interpretation is not demonstrable, it is highly subjective.

You are convinced that if someone actually could make sense of the Hilbert space and Hamiltonian of the entire universe, and if they could somehow divine the initial conditions of a universal wavefunction, such that, subject to the Hamiltonian under the Schrodinger equation (or, better, it’s relativistic counterpart) it leads to suitable time-asymmetric evolution, and that the result, taking decoherence into account, would yield something whose components or projections into some suitable sub-spaces, selected, combined, and arranged in some suitable order, would reduce in some approximation to the usual equations of quantum mechanics. To you this is sufficiently self-evident that you’re willing to take it as given. It isn’t that self-evident to me.

That means the interpretation doesn't work for you-- you see those conditions as a stretch. Others don't think quantum mechanics could work as well as it does if those things weren't true. Myself, I'm agnostic about it-- I don't see the point in building a world view that involves those things being true, but I don't think interpretations are for building world views. I think an interpretation is nothing other than a way of thinking about a theory, a way to get the theory to show you a different angle of itself.

 

[Len M]

I would like to make a few comments regarding Samshorn’s position from my philosophical perspective. They don’t add anything at all of substance to the discussion between Samshorn and Ken G, but it is a topic that I find very interesting and I do often wonder (and puzzle) about the relationship between a descriptive model (or interpretation) and a corresponding mathematical predictive model.

I do wonder if Samshorn perhaps places too much emphasis on the validity of an interpretation, (what I would describe as a descriptive model). As far as I can understand, Samshorn considers a descriptive model should have a “scientific linkage” to a mathematical predictive model in order for that interpretation to have some “proper” scientific validity. I would tend to say this linkage happens because generally it is essential to the thought process of the physicists – physicists could not possibly construct predictive mathematical models without the pictures of interpretation (the descriptive models). But I would place no more “proper” scientific validity other than that process of the physicist to the descriptive models, the real physics (for me) is the verified predictive mathematical model which represents our attempts at discerning objective patterns within our reality, not that which lay outside of our mindset and our reality – the ultimate “real thing” if you like. I can actually readily foresee a time (way in the future) when our mathematical models are generated by computers crunching massive amounts of empirical data – then there will be no descriptive models (interpretation) involved.

But I obviously make the above statement from a philosophical perspective of idealism (though with a hint of a scientifically unknowable realism). From the philosophical perspective of strong realism, the above is unpalatable – from a strongly realist perspective, the descriptive model is describing nature as it exists outside of our involvement (at least that’s the intended inference) provided the mathematical predictive model of that descriptive model is verified. Thus a realist would place much more emphasis on the descriptive model than I ever would. For them, if there were no “scientific linkage” (and from my perspective, I question the usage of the word science here because I don’t see descriptive models as being science, but realists would disagree with me here) of an interpretation to a mathematical model, then that is not science. But note that this stance is a philosophical stance with a philosophical premise that states our descriptive models and predictive mathematical models correspond closely to mind independent reality (or will get closer and closer, if not actually reaching that goal). Whatever access we may have to mind independent reality, it is not through the scientific method because we have no means in which to scientifically prove that we can step outside of our involvement, thus rendering an objective investigation of mind independent reality impossible. Any exploration of mind independent reality is going to be philosophical in nature, not scientific. I’m not at all suggesting that Samshorn is a realist in this sense; I only mention it because I think the issue of philosophical perspectives is at the heart of topics like this.

From my perspective, all descriptive models (and hence interpretations) are philosophical, even those most macroscopic of models involving (say) a trajectory of an object. The involvement of space and time that we link to a trajectory of a ball is intuitive, but I consider it to be an interpretation of an underlying “explanation”. That underlying “explanation” I consider to lie outside of our involvement and outside of space and time (which I consider to be constructs of our minds) – it resides within mind independent reality. We have no means in which to step outside of our minds, consciousness, and anything else deemed to be part of us, therefore the scientific premise of objectivity fails when attempting to extrapolate to mind independent reality. The fundamental “explanation” (for want of a better word) that “explains” the trajectory of the ball lay within mind independent reality – all we can do is to interpret the descriptive model of a trajectory as a moving ball, (that interpretation tells us nothing about what a moving ball really is) and construct a mathematical predictive model. The success of the latter within our reality does not give any kind of firm “scientific” validity to our interpretation and does not signify that an interpretation with no mathematical predictive model is invalid. Rather we should remove the word “science” from this context and say that interpretations (and I emphasise that I consider descriptive models to be interpretations) are philosophical, and if looked at in that light, gives a clear distinction between the actual science (which are the predictive mathematical models) and the interpretations. I would have no qualms in accepting a verified mathematical model derived by a physicist via a very ad hoc descriptive model that didn’t make any sense or have any kind of “proper” linkage to the mathematical model. I would instead see it as a physicist making use of pictures in a way that helps their creative process in deriving a very powerful predictive mathematical statement about our reality, not of a reality that lay outside of our involvement.

Of course this is open to ridicule if I say my dog is a descriptive model of the mathematical model of gravitational attraction – the argument that my dog is as valid a descriptive model as an imaginary force between objects is obviously ridiculous. But that is not really my point, my point is that I question the emphasis placed on descriptive models as being science – I would rather describe them as purely philosophical with a hierarchy of “validity”. My dog would be out of sight on this hierarchal scale, but the MWI would certainly be on the list.

 

[kith]

Yes, I'm afraid it does. According to the "many worlds interpretation", the overall universal wave function is continually evolving into more and more proliferating self-consistent "worlds".

A "world" in the MWI doesn't refer to the universe as a whole but rather to a "world of our experience" (see for example Everett's first paper). To allow for experience, the universe must be divided at least into two interacting parts: observer + rest. In a typical measurement situation, it is divided into observer + subsystem of interest + measuring apparatus + uninteresting rest.

So a "world" in the MWI is always a subsystem of the universe. In the theory of open quantum systems, interactions with an environment (like the one given by the measurement apparatus) typically cause decoherence, which leads an initial superposition state of the subsystem to an incoherent mixture. This is interpreted as "splitting of worlds" in the MWI.

Since we agree on the "splitting"-part but not on the mechanism, again the question: what do you think does cause decoherence? This really seems to be the crucial point in the discussion, which is why I asked you some related questions in my last post.

 

[Samshorn]

If those mathematics are different, then what is the difference?

The projection postulate. According to ordinary non-relativistic quantum mechanics, a system in isolation (subject to a specified potential, etc) evolves according to the Schrodinger equation with a suitable Hamiltonian, and then a measurement of the system by an observer (say) yields an eigenvalue of the measurement operator, and the measured system jumps [projection postulate] to the corresponding eigenstate of that operator, and the probabilities of the various possible eigenvalues are given by the Born rule. Now, according to MWI, approximately this same behavior would appear to an observer if we combine the original system and the observer into a single isolated system (with suitable initial conditions, subject to specified constraints, and with the appropriate Hamiltonian) and this combined system evolves according to the Schrodinger equation, plus some form of the Born rule. But please note the word approximately, or, as Bell put it, “for all practical purposes” (FAPP). Decoherence is never complete or perfect in the unitary evolution of a wave function, whereas the von Neumann projection postulate doesn’t entail any fuzziness; it says the state after the measurement is nothing but one of the eigenstates of the measurement operator, and hence the Born rule has sharp applicability to just those precise eigenstates. This is not true in MWI, so the mathematics of MWI are not literally the same as the mathematics of ordinary quantum mechanics. The advocate of MWI just says it is close enough for all practical purposes. In other words, he is arguing that his mathematical model, consisting of applying Schrodinger’s equation to the combined system of observer & observed with suitable Hamiltonian and initial conditions, taking decoherence into account, etc., leads to predictions for the expectations of an observer that are sufficiently similar to the predictions yielded by the von Neuman recipe and the projection postulate so that we wouldn’t expect to be able to tell the difference – at least not in normal circumstances. On this basis, the believer in MWI claims the right to use the mathematical recipe of von Neumann rather than the recipe actually prescribed by MWI (which is convenient, because the latter is utterly impossible to apply in any realistic circumstance).

But there are obvious problems with the claim that the mathematics arising from the MWI model really are (even approximately) consistent with observation and ordinary quantum mechanics. It is only supported by rather vague and incomplete plausibility arguments, and references to putatuve isolated systems involving observers, even though any such system can hardly be smaller than the entire universe, which then leads to its own set of ambiguities. It’s far from clear that the MWI calculational prescription (the one that is actually manifest in the interpretation) could ever be carried out, even in principle. The plausibility arguments depend on viewing things within the context of some definite conditions, and then considering one little incremental (and time-asymmetrical) step being carried out according to the Schrodinger equation, and arguing that over this incremental step the divergence from ordinary quantum mechanics evident to some conception of an observer is too small to be noticed. This is already debatable, but even if one accepts this, it doesn't come close to substantiating the viability of the MWI model as a whole, because that ultimately involves the wave function of the entire universe, and needs to address all the ambiguities arising from that.

As I understand it, you deny that MWI entails any mathematical formulation distinct from ordinary quantum mechanics, but I don’t think that position is tenable (and I don’t think even the advocates of MWI would agree with you). The mathematics of MWI are clearly stated to be nothing but unitary evolution of the universal wave function, augmented if you like with something approximating the Born rule (it can’t be exactly the Born rule, for the reason explained above), but it definitely does NOT include the projection postulate, as explained above. Hence the mathematics of MWI are fundamentally different... but it is argued that, if we correctly account for decoherence, something closely approximating (but not identical to) the projection postulate emerges (for some suitable model of a conscious observer) from the unitary evolution of the universal wave function. But the mathematics are definitely not the same.

It really is very similar to the case of general relativity, where the metrical spacetime curvature interpretation of gravity consists of the proposition that isolated systems simply undergo geodesic motion through the spacetime manifold. People could ask “How can simple unforced geodesic motion possibly be consistent with anything resembling the observed phenomena of forced trajectories described by Newton’s laws!?”, and the task was to show that, in fact, Newton’s laws and all the observed behavior that they describe really do emerge [approximately enough for empirical viability] from the four-dimensional tensor equations describing the curved spacetime representation of events. The empirically accessible differences are so small as to be almost imperceptible in normal circumstances, so GR is deemed consistent with all the empirical success of Newton’s theory. The same task faces MWI. It needs to show that the ordinary equations of quantum mechanics really do emerge [approximately enough for empirical viability] from the Schrodinger equation description of the unitary evolution of the universal wave function. But this has never been shown, so MWI doesn’t really (at present) qualify as an interpretation of quantum mechanics. At best, it is an idea for an interpretation of quantum mechanics.

 

[Samshorn]

Since we agree on the "splitting"-part...

I'm still not following. You began by objecting to one of my statements on the grounds that you believe there can be no "splitting" in an isolated system. Now you seem to be saying that splitting does occur within an isolated system (e.g., the universe), and yet you still seem to be maintaining the objection that was based on the opposite view. So I'm still not understanding you.

 

[kith]

You began by objecting to one of my statements on the grounds that you believe there can be no "splitting" in an isolated system.

Not "in" but "of". The isolated system as a whole doesn't split. Let's return to your original phrasing. Saying that an isolated system v splits into v1, v2, v3... remains wrong. What does split are open subsystems of isolated systems.

/edit: Probably it's time to use a more precise language. Initially, the isolated system is in state |ψ(0)>. For every time t>0, you can express it's state as U(t)|ψ(0)>. So where's the splitting?

 

[Dmytry]

The way I see it, CI is a recipe for calculating what observer (a big, highly complicated system) will see.
MWI (potentially) provides a derivation of such recipe from basic laws by considering evolution of the big, highly complicated system that is observer.
The CI is shut up and calculate, then midway just square the amplitudes and stop calculating, the MWI is shut up and calculate all the way into observer itself. The value of trying to calculate things about observer is that: if we indeed fail to derive Born probability in MWI we will know there is some extra fundamental physics leading up to Born's probability. The approach of sticking to CI is just a case of giving up, using a magical formula for magical 'observer' without ever figuring out how it works. It's like having the gas law and not trying to figure out kinetic theory or thermodynamics.

Regarding a single photon hitting you on forehead, even a single photon will over time fork you into a very huge number of yous due to how thermodynamics works and due to how thermal noise influences the thought. One has to wonder if a digital observer may see different probability laws.
Anyhow, what I believe is that the thermodynamics should be reworked for quantum mechanics, and then from that thermodynamics the Born probability will naturally arise for systems like brains where the thermal noise affects what you think (and what you will think). It may also turn out that the probabilities arise in repeat experiments due to effect on the e.g. source of the photons.

 

[Ken G]

The CI is shut up and calculate, then midway just square the amplitudes and stop calculating, the MWI is shut up and calculate all the way into observer itself.

Here's the problem though. Physics is not a purely rationalistic endeavor-- we don't just introspect the mathematical aesthetics that we like. Instead, we must check our theories against experiment, and MWI simply provides no accounting for the nonunitarity of what we actually perceive. MWI in effect subjugates the action of the observer to the theory about the observer, rather than using the action of the observer to substantiate the theory. The result is that MWI only requires itself to not contradict observations, but physics is built on something deeper than just not contradicting observations, it is built on receiving evidence from observations. Any number of pseudoscientific claims from ghost stories to UFO landings are based on the weak requirement of merely not contradicting observations, and while MWI certainly has a much more scientific footprint than these, it shares this fundamental problem.

The value of trying to calculate things about observer is that: if we indeed fail to derive Born probability in MWI we will know there is some extra fundamental physics leading up to Born's probability.

But we always know that, it is the default assumption. The sticky problem is how to use the approaches of science to get at a principle that underlies the whole structure of how science is done. Some reworking of what we even mean by science is going to be needed to do that, and it must be done so as not to throw out what is good about science, and what separates it from pseudoscience. Faith that MWI will lead us to that principle is fine for an individual to have, but it is hardly some kind of arguable benefit of MWI.

The approach of sticking to CI is just a case of giving up, using a magical formula for magical 'observer' without ever figuring out how it works.

I think this stems from a common misconception about CI. When Bohr says "there is no quantum world", he means "there is no need to continue to advance physics to try to go deeper than quantum mechanics." I don't think Bohr would ever have suggested such a non-scientific idea. What he really meant, I believe, is that the problem of using physics to describe the observer/system interaction encounters a fundamental difficulty that is independent of quantum mechanics or any particular theory-- the act of observation is a kind of filter, and whatever does not come through that filter is not going to be able to be put into a physics theory. This problem was with us all along, but quantum mechanics is the place where we smacked right into it. MWI is essentially what you get when you try to ignore this problem and hope that it will go away, but the bizarre and almost mystical elements of MWI are the consequence of that attitude. It is really the place where science meets pseudoscience, and all Bohr was trying to do was retain the firewall between them.

 

[kith]

Instead, we must check our theories against experiment, and MWI simply provides no accounting for the nonunitarity of what we actually perceive.

We can explicitly see how nonunitary dynamics emerges from unitary dynamics for certain model systems. So if one agress, that there is no good reason to assume that measurement devices obey different laws than electrons (which is based on the fact that the classical laws can be derived from QM), the assumption that collapse could be explained in principle by decoherence seems reasonable. Don't you agree?

This doens't lead directly to MWI, however.

 

[Ken G]

We can explicitly see how nonunitary dynamics emerges from unitary dynamics for certain model systems. So if one agress, that there is no good reason to assume that measurement devices obey different laws than electrons (which is based on the fact that the classical laws can be derived from QM), the assumption that collapse could be explained in principle by decoherence seems reasonable. Don't you agree?

No, I don't think collapse will ever be explained in an unambiguous way by decoherence, but we need to distinguish two very different types of collapse that are easily confused. Decoherence is very good at getting a superposition state involving a subsystem to "collapse" that subsystem into a mixed state of eigenvectors of the decoherence. That's just exactly what decoherence does. But that type of collapse never presented any problems, because it is still perfectly unitary on the whole system, and projections onto subspaces never had to be unitary, even in formal Schroedinger evolution.

The collapse that is at the heart of "the measurement problem" is something different-- it is the nonunitary collapse that occurs when you interpret a mixed state as not a projection from a decohered superposition, but as a particular outcome that has occurred even if you don't know it yet. Scientific predictions are moot on that difference, but interpretations of quantum mechanics are not. Since the predictions are moot on the issue, no experimental test can ever distinguish them, and so no theory that leads to predictions (like decoherence) can suggest how to test that difference either. It is a purely philosophical difference, but what is clear is that the experience of a particular outcome is nonunitary.

 

[bohm2]

This is way too long of a thread to go through all of it and a quick search of the first author of the paper below didn't bring up anything...here is a fairly recent paper arguing against Everett interpretation:

In other words: POD (Parallel Occurrence of Decoherence) points out the existence of not only one, but two mutually independent and irreducible Brownian particles that are subsystems of the same composite system. As long as this is a consistent quantum mechanical picture, we show that this makes for the apparent inconsistency in the very foundations of the Everett Interpretation. In Section 5 we show that the inconsistency can be removed if there is a privileged spatial structure of the model-universe (only one Brownian particle is physically realistic). The absence of a particular rule/prescription or a criteria for choosing the preferred structure forces us to conclude that the highlighted inconsistency is not removed.

We demonstrate that the Everett Interpretation is not consistent with the universally valid quantum mechanics, as long as the Everett-worlds are considered physically realistic. This inconsistency follows from the recent results of Entanglement Relativity and the Parallel occurrence of decoherence (provided for the Quantum Brownian Motion-like models) as corollaries of the universally valid quantum mechanics. In simplified terms: the Everett worlds splitting (branching) is not allowed for the realistic Everett worlds. Thus, we conclude: Unless there is a privileged, spatial structure (decomposition into subsystems) of the model-universe, Everett Interpretation appears either to be not correct or the Everett-worlds (the Everett ”branches”) are not physically real. The interpretational consequences as well as some ramifications of our findings are yet to be explored.

http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.6424v1.pdf

 

[juanrga]

We can explicitly see how nonunitary dynamics emerges from unitary dynamics for certain model systems. So if one agress, that there is no good reason to assume that measurement devices obey different laws than electrons (which is based on the fact that the classical laws can be derived from QM), the assumption that collapse could be explained in principle by decoherence seems reasonable. Don't you agree?

This doens't lead directly to MWI, however.

Collapse is not derivable from decoherence. Neither decoherence has solved the measurement problem

http://arxiv.org/abs/quant-ph/0112095

The key point is that nonunitary dynamics are irreducible (i.e., are not derivable from) unitary dynamics.

 

[kith]

But that type of collapse never presented any problems, because it is still perfectly unitary on the whole system, and projections onto subspaces never had to be unitary, even in formal Schroedinger evolution.

For me, the important point is that decoherence shifts the measurement problem from pure states to mixed states. Decoherence explains how a system with a well-defined property (beeing the eigenstate of an observable) evolves into a system about which we can make only statistical statements. This can be interpreted in the way that the state of the system doesn't contain enough information to determine a unique outcome. And this is a something classical.

Maybe the crucial point is that the CI assumes reductionism?

The collapse that is at the heart of "the measurement problem" is something different-- it is the nonunitary collapse that occurs when you interpret a mixed state as not a projection from a decohered superposition, but as a particular outcome that has occurred even if you don't know it yet.

How can a mixed state be a particular outcome? Do you use outcome in a different meaning than outcome of a single experiment?

It is a purely philosophical difference, [...]

Yes, I agree. But a proponent of the Lorentz ether theory can use the same argument to claim that his view should be treated equal to SRT. Yet the overwhelming majority of physicists thinks SRT is the better interpretation. We agree that interpretations can't be proven, but still some are more plausible than others. And if there's an unambiguous reasonable way to motivate the appearance of collapse from the other axioms, most people are probably willing to adopt this view.

 

[juanrga]

This is way too long of a thread to go through all of it and a quick search of the first author of the paper below didn't bring up anything...here is a fairly recent paper arguing against Everett interpretation:http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.6424v1.pdf

Thanks by the link.

What I do not understand is why it is needed to show that the Everett interpretation is internally inconsistent and does not agree with experiments when this has been done in the past in many occasions.

That is so weird for me as if it was needed to prove today that the ancient Weber electrodynamics suffers from the same kind of defects. If you look to Goldstein textbook, in some footnote page he merely says that Weber electrodynamics is inconsistent but he does not need to prove this (neither its failure to explain experiments) because it was already done in the past.

 

[kith]

juanrga, I think our views are quite incompatible when it comes to interpretations of QM, because you don't seem to acknowledge any other interpretation than the orthodox one. So I don't see the point in discussing with you here.

However, thanks for the paper. I have saved it, but there are other decoherence-related paper's I am going to read first.