As I understand things, most physicists don't give much thought to which interpretation is correct, since any experiments to distinguish between the various interpretations are virtually impossible to do. And most physicists don't care about distinctions for which there will be no experimental evidence.
Among the physicists who do care about the different QM interpretations, it is my understanding that most would go with the Everett (AKA "Many Worlds) Interpretation these days. All other interpretations that I know of are hugely problematic, but there are no significant problems at all with the Everett Interpretation. The only problem is that many people consider it to be "creepy". But not liking the best theory because it is "creepy" isn't very good science, if you ask me.
Regarding there being no single-world interpretation that is logically self-consistent, I'm not convinced about this: The Bohm Interpretation, for instance, is experimentally indistinguishable from the Everett Interpretation. I.e., no matter what incredible technology and powers of QM experimentation we might develop in the future, we will never be able to do an experiment, even in theory, that tells us which of these interpretations is the right one.
Consequently, it would seem that the Bohm Interpretation is logically self-consistent. The problem with the Bohm Interpretation is that it's very ad hoc and violates Occam's Razor. It only exists in order to calm our feelings about the universe being "creepy".
It should be noted, however, that the Everett interpretation does have one issue: it's not clear why probabilities should work the way they do. There are different approaches to deriving the laws of probabilities under Everettian physics, but things very easily get metaphysical once you try to go down that road.
As you point out, the Bohm Interpretation works as a single world interpretation, although it relies on reifying particles embedded in waves to essentially select a single world, which is rather ad-hoc. However, it does give us the probabilities for free, assuming any reasonable initial setup for the particles.
One of the corollaries/interpretations of Sanov's theorem is that, generally speaking, when faced with an astonishingly improbable outcome (e.g. flipping 9,000 heads and 1.000 tails out of 10,000 independent coin flips), no statistical test can differentiate between "that improbable occurence with a fair coin" and "an unfair coin" - the fair coin, when it does something improbable, with have (with overwhelming probability) a specific tilted distribution that looks unfair.
TL;DR By grouping states together (human choice), certain arrangements seem more probable than others.
It would be nice to say that there’s a 50% chance that I measured 0, but how exactly do you get that in a rigorous way from the state vector above?
To make everything complicated, the answer should not treat the experimenter part of the universe specially.
As for why 50%, why not the Born rule? Or are you asking how we derive the Born rule?
Not true in a many-worlds model. The “I measured” part is intended to account for the environment, at least initially.
> Or are you asking how we derive the Born rule?
More or less. In a many-worlds interpretation, there is no Born rule per se. I’m saying it’s not entirely trivial to recover the statistics that the Born rule would give.
Is the mathematical formalism actually more unwieldy, or is it just this interpretation of what it's doing? The 'select a single world' sounds like taking some of the conceptual framework from Everett and trying to paste it on here, rather than giving the Bohm interpretation its own conceptual framework which could possibly be more elegant?
Once we settle on stuff with position, then we have to ask how that stuff changes. One option is that we specify accelerations; that's Newton's way.
Another option is to specify velocities. That is the Bohm way. Specifically, the velocity is derived from the wave function of quantum mechanics. It is basically the derivative of the wave function, normalized and made real. Done. You can see a simple derivation of the equations here: https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivat... The first one derives Bohm's equation very quickly and simply from the starting wave relation equations of Einstein and de Broglie.
The complication is that the wave function is a function of the configurations of all the particles. Thus, to get the velocity, one technically needs the positions of all of the particles of the universe. Practically, one only needs the positions of entangled particles, but still. It is a non-trivial setup though the most basic, natural setup one could possibly have given particles and a wave function. Also, the particle positions do not influence the wave function evolution. This is rather unusual.
For the Dirac wave function, it is even simpler. That object directly gives the velocity of the particles; no derivative needed.
Contrast this with MW which says, I guess, that the fundamental thing that we are concerned with is the wave function. It does not seem that particles exist in any meaningful sense in that theory. It is as if we are machines able to track a singular aspect of the change of an abstract vector in Hilbert space. It is not clear why this vector is often represented as a function on configuration space when there is no configuration of stuff. The theory essentially says that actual reality is nothing at all like what we perceive. I would think an honest account of a theory which only has a wave function would be to formulate the theory on an abstract Hilbert space and derive configuration space and, thus, configurations from that. Not very likely, by the way.
Reality may be deceptive, but I certainly prefer to start with theories in which our experience is explained in a pretty simple and straightforward way: it looks like stuff is over there because there is stuff over there. We have singular experiences because a single experience is what actually happens.
Also note that in Bohmian mechanics, we specify the initial wave function and the initial particles and then evolve the system using differential equations. All of the operator stuff, collapse, etc., comes out of that evolution; we don't need to have any special considerations about them. The quantum formalism becomes analogous to thermodynamics, not a fundamental theory, but a useful practical one replacing the individual evolutions with some useful shorthand. In MW, there is this question of how to model an experimental situation. Where are the measurement operators coming from? What is a subsystem? In BM, these things arise essentially by conditioning on the configuration of the environment. In certain situations, this will give rise to roughly an isolated system evolving according to its own Bohmian dynamics. The measurement interaction is then represented by an operator, or its generalization, depending. But all of that emerges from the basic differential equations evolving the universe.
It is not clear to me how easy it is to do that kind of analysis in MW. After all, there is no singular experience to break it down to, there is no subsystem, there is no definitive experiment being done. It is not really clear how one would falsify a theory which, more or less, assumes everything happens.
This assertion does not make sense to me. The Everett Interpretation and the Bohm Interpretation are experimentally indistinguishable from each other, as I understand things. Consequently, there is no mystery at all with the Everett Interpretation as to why things appear to us the way that they do.
Since the Everett Interpretation is a significantly simpler theory than Bohm's, we should prefer it due to Occam's Razor. On the other hand, since they are experimentally indistinguishable from each other, we can never scientifically assert which of the two is correct, no matter how much evidence we have.
The "indistinguishable" part happens because, according to Everett, there is some version of the experimenter that will have the same experience as the single experimenter in the Bohmian world.
This is not simpler. I have no reason to believe that there are infinitely many copies of me out there. Everett's theory says that there are. Fine. I can't disprove it. I also can't disprove that every instant of my experience is being carefully orchestrated by a thousand angels. It is experimentally indistinguishable from any theory you care to posit.
But I prefer theories where my actual experience is supposed to be a reasonable reflection of reality. I experience a single me and therefore I would prefer a theory in which there is a single me. Bohmian mechanics provides that and in a completely natural and reasonable way.
Everett categorically disputes my experience as being reflective of reality. There are infinitely many copies of me and my experience of being singular is an illusion. I can't dissuade people from embracing that, but it certainly strikes me as peculiar.
Also, in terms of experiments, Everett has infinitely many copies of the universe where all of the statistics of the experiments come out wrong. There are infinitely many that come out right. Is that experimentally indistinguishable? I don't know. Kind of a strange question in the context of "most everything happens".
And that's fine, but the idea that this is simpler than a theory which says my experience is a reasonable reflection of reality, is not. Occam's razor is not about number of equations, it is about what is simplest. I experience a single "me". A theory which supports that experience directly and obviously is simpler than a theory which does not.
This is particularly true when the "extra" equations are simple and obviously a part of the other equations.
The reason why this all gets so convoluted is simply because it exposes how much we rely on terms and concepts that are defined very fuzzily, and often aren't even defined at all, but just accepted for granted as if everyone means the same by them. And then it turns out that we don't, which should really come as no surprise.
This is referencing the nature of the measure and the difficulty of deriving the Born rule. Why should the outcome of measurements be proportional to the square of the wave function? That's indeed a problem in MW.
But even if that's solved in some way, there's an even more foundational issue of how non-determinism can arise at all in a deterministic theory. The MW reply is that there is no non-determinism, but then has trouble explaining observed reality - which is not a good position for a theory to be in.
Yes, back when I studied this topic seriously, this was an issue. E.g., if you toss a quantum coin that has a 1/3 chance of coming up heads and 2/3 chance of coming up tails, this seems to result in only two "worlds". And if there are two worlds, why are the observed probabilities then not .5/.5 rather than .3333/.6667?
I didn't mention this in my OP because (1) that would have been something of a deep-dive for a summary post, and (2) there were ideas being floated about to solve this problem back when I was studying this, but I don't know how these ideas ultimately panned out.
I'm surely curious as to what the current best ideas are about this issue.
At some point this debate becomes a bit too confusing for me. All I can report is that the experts fretted over this.
The relevant probabilities are not derived by number of "worlds". Pick some particular moment and correlated history, look backwards (what is recorded in the current "configuration") at experiments, and one should see the proper statistics appearing in the "vast majority" of experiences.
However, there will be plenty of experimenters who see wrong statistics. Everett predicts this with certainty. There is a "world", according to this, that just split from the moment I am writing this, in which all future experiments have spin up coming up 100% of the time from that moment on. Over time, we all end up correlated with this as the experimenters report their fantastical findings.
If they truly believe in Everett's theory, they would accept that they just happen to be in the branch where this happens. In Bohmian mechanics, they would say something else is going on. The odds of seeing something like that in Bohmian mechanics are so vastly, incomprehensibly small, that it is more likely to see cracked eggs reassembling themselves from random thermal motions. But in Everett, it happens with certainty to some universe.
This is the difference. Bohmian mechanics can be readily falsified based on statistical outcomes of experiments. Perhaps not with 100% certainty, but certainly with 100% practical certainty. Everett can never be falsified based on statistics. It could be falsified if something that was supposed to happen with a literal 100% certainty failed to happen, but with anything statistical, it simply can't because the theory says it does happen.
One could modify the theory to cut out the "outlier" worlds. This is, in some sense, what GRW with a mass density ontology does.
In the Bohm Interpretation, that coin could always come up heads too, but again with a vanishingly small probability.
So they seem equivalent experimentally to me. (And to the experts who have written entire books on the subject.)
Max Tegmark came up with a way to experimentally determine if the Everett Interpretation is correct. (I believe it was Tegmark who came up with this.) It has a high cost for the experimenter, though!
What you do, is rig a gun to a fair quantum coin, so when you pull the trigger, the gun fires 50% of the time. Now shoot yourself in the head with it many, many times. If you end up surviving many rounds of this, you can be pretty darn certain that the Everett Interpretation is correct.
Never mind the billions of other versions of yourself that you murdered to discover the truth!
Hence, in the Everett Interpretation, if you shoot yourself using such a quantum gun, every time you pull the trigger, there will end up being one "world" in which the gun didn't go off and one world in which you put a bullet in your head.
Edit: the most significant problem with the MWI, apart from the "creepy" metaphysical aspects, is the meaning and quantification of probabilities. In particular being able to derive Born's rule, which works so well in practice.
The "Many Worlds Interpretation" is actually something of a misnomer. This is why many people prefer to call it the Everett Interpretation.
It doesn't actually posit many worlds. It posits one very big complex world with very complex superpositions of state. But since your brain ends up in a superposition of states, different facets of this superposition of your brain state perceive this one big complex world, as smaller, simpler "worlds".
And the term for why different pieces of this superposition of states stop having an effect on each other is called "decoherence".
As for how the math works out in terms of probabilities, that is beyond me.
When I studied this, the discussion was usually simplified down to a quantum coin that when flipped would come up heads 1/3 of the time and tails 2/3 of the time.
This only results in two "worlds" though. A heads world and a tails world. So there was an issue that people debated at the time: Why do we perceive the .3333/.66667 probability for these two "worlds", rather than a .5/.5 probability?
I must admit that I am ignorant about the current state of this debate.
There are various interpretations that attempt to define "measurement" in various ways, but those are not the Copenhagen Intepretation.
As for whether you can give a scientific account of how data is processed by a brain in a superposition of states, you most certainly can. (Ever heard of "quantum computing"?) It's just complicated.
Edit: I’ve never heard of any treatment of “quantum computing” which doesn’t include the concept of measurement, the Born rule and the projection postulate. Have you?
Edit2: it was maybe not fair to say that the probability of events is not defined in the Everett interpretation because many-world interpretations have addressed this issue since the original paper from Everett in 1957. But as far as I know they have not succeed. Measurement has also been addressed in countless papers and books for almost a century, for what it’s worth.
In a small poll at a conference on the foundations of quantum mechanics in 2011, the Copenhagen interpretation was the most popular. This could differ from your definition of "these days" I suppose.
https://arxiv.org/pdf/1301.1069.pdf
Update: a 2016 survey by different authors found similar popularity for the Copenhagen interpretation.
Paradoxical traps or thought experiments filled with holes?
MW is even more undefined in terms that we cannot even construct a measurement/singular interaction... (it is always derivative of total system state)
I mean it builds the term "measurement", which is an undefined and unscientific concept, right into the laws of physics. Personally, I find this to be virtually nonsensical.
Both surveys are fascinating reads. They clearly give a sense that despite of the spectacular success of QM how far we still are from the final word in that field.
The paper on which this is based states in the abstract that this fails for Bohmiam Mechanics:
> This conclusion extends to deterministic hidden-variable theories, such as Bohmian mechanics, for they impose a single-world interpretation.
That seems like an unfair characterization. The issue many have with the Everett Interpretation is that it relies on a fundamentally untestable existence of every possible universe in every possible state of being for the sake of conceptual tidiness. It's not unreasonable to apply Occam's razor and hold a measure of skepticism about this.
The Everett Interpretation is clearly the simplest theory because the deep mystery of what would cause probability waves to collapse is made completely irrelevant. There is no wave collapse to worry about or to explain.
Then why is it being taught everywhere? It's been driving me crazy since forever.
If you take away any sensient beings, or whatever it is that is required to make one of these "measurements", then copoenhagen is the same as the many world interpretation. Wave functions go on evolving and there is no collapse. For example, an electron can be in spin up or spin down. It is not in both states. In one "world" it is spin up. In another "world" it is spin down. That is strange enough for all of us. But for some reason people have trouble extending this idea to people, so that a person can be in mulitiple states at the same time (in the different "worlds", in the same sense as the electron being in different "worlds".)
What made this strike home to me was when I was in graduate school and my advisor told me "There are no magic external observers. The observer is subject to quantum mechanics too. He is part of the experiment."
To describe the correspondance between copenhagen and "many worlds", suppose an observer measures if an electron is spin up or spin down. In "many worlds" case his memory of the outcome is correlated with the measured state of the electron. So in the "world" where the electron is spin up (that portion of the wave function) the observer also thinks the electron was measured as spin up. And in the "world" where the electron is spin down, the observer thinks the electron was measured as spin down.
In this "many worlds" case, The observer who measures the electron as spin up will not interact with the observer that measured it as spin down. For all intents in purposes, it is as if that other observer never existed. In the copenhagen case, that other observer does _not_ exist. In this interpretation, the wave function collapsed to only include the part with a single observer.
In effect the observed outcome of the two interpretations is the same. The difference being one of them, the copenhagen interpretation, postulates a magical change in the wave function of the universe.
(Aside - The fact that those observers will not interact is just in a practical sense, to my knowledge. I don't know if it is impossible for them to interact in theory. I don't think it is. Maybe someone else knows the answer to that.)
And the MWI postulates a magical branching into different "worlds", doesn't it?
If the universe is an isolated quantum system evolving unitarily, how does the MWI help to understand the laws of physics that we observe?
It definitively answers the question of when wave collapse occurs and what causes it.
The answer given by the Everett Interpretation is simply that there is no wave collapse, and what we observe is the result of our brains being in a superposition of multiple states.
1) we have a one-particle system that has been prepared into a pure state by measuring the spin along the x-axis
2) we are going to measure the spin along the z-axis
3) the quantum state before is a superposition of the |up> and |down> states (in the basis corresponding to the Sz operator)
4) the theory predicts that we are going to find either |up> or |down> with equal probability
5) immediately after the measurement the quantum state will be either |up> or |down>, depending on the outcome
What is the answer given by the Everett Interpretation? What is the description of the initial conditions? What is the prediction of theory? What is description of the end state?
I hope the answer is not just handwaving and mumbling about "superposition".
I don't understand why this would be difficult to understand.
If you cannot say that the particle is in a well defined up or down state after the measurement then you cannot say either that it remains in a superposition of up and down states. Because that original state was the result of a previous measurement. You cannot even say that the particle (or you, for that matter) does actually exist. The universe is a superposition of states where it does and states where it doesn't. (Does the universe exist at all?)
The standard interpretation of QM:
- we want to explain the physical world that we experience
- we come up with a theory based on a mathematical description of physical states and the equation describing its evolution
- the theory allows for superpositions of states, incompatible with the physical world where we observe only definite states
- why do we observe only definite states?
- we postulate that when we measure the wave function changes becomes and becomes consistent with the observation
- we also postulate the Born rule to compute the probability of observing each potential outcome
- everything is experimentally verified, there are open questions (what is a "measurement"?) but the theory works fine in practice
- we know that this is not a complete description of the world (gravity!)
The Everett interpretation:
- let's assume that the physical world that we experience is just one aspect of a larger, out-of-reach thing
- what is real is the mathematical description (nevermind that it's incomplete), evolving according to the Schroedinger equation
- why do we observe only definite states?
- because this is the way our brains experience the physical world! (see how easily we solved the issue with measurement?)
- what is the probability of observing each outcome?
- ... (but, hey, did you notice how elegantly did we skipped, I mean, solved the measurement problem?)
- we have a collapse-free interpretation of QM! (but remember that if you want to study the physical world that we experience you have to use the projection postulate, because this is the way our brains experience the physical world)
I find interesting that the MWI is so popular among cosmologist, given that QM doesn't handle cosmological issues well. But of course this interpretation "solves" the problem of why the observed universe is precisely the one that we observe.
Everett's theory is interesting, but not a panacea. Maybe decoherence is the key to explaining "collapse", maybe gravity is the key, maybe the answer is somewhere else...
Are you saying they are "now" in a superposition, meaning they were not before the observation?
If so then how can the act of us observing the thing cause us, our brains to go into super-position? And is it just our brain that goes into super-position? Why not the rest of my body too? And what if I'm holding the hand of another person, does she too go into super-position?
I don't think most MWIers would agree with this. Normally they consider worlds to have split only once (irreversible, or approximately irreversible) decoherence has set in. An electron in the coherent state |z+> + |z-> = |x+> wouldn't qualify.
In fact, this seems to be one of the biggest difficulties of the interpretation. Nobody knows whether there even is such a thing as in-principle irreversible decoherence, and if there's not, then the point at which it is "approximately irreversible" is arbitrary.
Edit: Add the state change in the measurement
(|z+> + |z->)|obs> => |z+,obs+> + |z-,obs->
First there is an electron in one of two states, and the observer is uncorrelated. After the measurement, the observer becomes correlated with the electron.
For your unentangled state on the left, Sean Carroll explicitly describes it as a state that doesn't have two worlds yet. I can find the post if you like, or maybe we already agree and I'm misunderstanding.
In what I am describing, the two "worlds" don't really separate. It is possible that they can interact, theoretically. However, you can't construct an experiment to detect the different parts of the wavefunction interacting because of decoherence. You just can not make a coherent quantum system that invovles real people (to my knowledge). So in practice you can not do the experiment.In anything we observe, the two resulting observers (in a measurement with two choices) are effectively isolated.
In other words, decoherence is automatic. Also, it is inherently irreversible.
But, I am sure he (or whoever wrote that post) is saying something sensible so I would be interested in seeing it.
"We wouldn’t think of our pre-measurement state (1) as describing two different worlds; it’s just one world, in which the particle is in a superposition. But (2) has two worlds in it. The difference is that we can imagine undoing the superposition in (1) by carefully manipulating the particle, but in (2) the difference between the two branches has diffused into the environment and is lost there forever."
(State 1 is when the particle is in a superposition by itself and state 2 is when it's entangled with a macroscopic apparatus.)
My issue is that he uses words like "forever" and "impossible." These convey a sense of finality, but the decision of where to draw the boundary is subjective. The worlds can in principle (and under certain cosmological models, must) recohere.
See, for example: https://arxiv.org/abs/1105.3796
"Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment"."
See in particular Section 3.2 (Failure to irreversibly decohere: A limitation of finite systems)
(Edit: I should mention that I am not a physicist, by a long shot. Just a curious amateur.)
No, measurement is just a poor choice of name for a type of interaction some matter can have with other matter. I'm a wave function, and sometimes I have a measurement interaction with other wave functions and that causes collapse. When wave functions of random environment particles do the measurement and cause (seemingly) spontaneous collapse, we call it decoherence and its a serious drag on building quantum computers.
I'm not advocating for Copenhagen, but it is not inconsistent for the reasons you stated. Outside the paper linked here, I'm unaware of any inconsistency in the Copenhagen interpretation.
That's not the Copenhagen Interpretation. Interpretations that claim this are called "Objective-collapse" theories. Back when I cared a lot about this, the most popular Objective-collapse theory was GRW:
Nature's headline does a terrible job at conveying this, really. I would have expected better from the people who edit headlines there.
For example, what if time does not necessarily flow in a single direction at the quantum scale; what if instead, the ground level of physical reality is a timeless information graph / equation that is 'solved by the universe'?
I'm no physicist and no nearly nothing about the real math of QM, but every time I read these lay-explanations of "quantum weirdness" and "wave function collapse", I get this strange feeling that we're thinking about time all wrong: What if unidirectional time is an illusion? What if causality (and inference) is an illusion (thus explaining how hard it is to capture it mathematically)?
Iterated experiment presumes creating fully known fixed same state psi.
Wiener Friends experiment makes the F1 magically know (memorize) state of quantum RNG without measuring it and without being entangled.
Both experiments require cloning which is forbidden.
You may want to check David Hume.
Does pilot wave theory fit the bill?
Bohmian mechanics violates it by not applying to arbitrary subsystems, but only to the universe as a whole (i.e. parts of the universe cannot be treated as quantum-mechanical systems themselves, because they don't have their own pilot waves)
“The etymology of the word ‘universe’ can be traced back to the use of the Old French univers, in the twelfth century, which derives from the earlier Latin universum. This word is created from unus, meaning ‘one’, and ‘versus’, the past participle of the verb vertere, meaning ‘to turn, rotate, roll or change’. So we have a literal meaning of everything ‘turned into one’ or ‘rolled into one’.” from John D. Barrow’s “The Book of Universes.”
Sounds like Bohm is taking the 'uni' in universe seriously, while the paper starts by assuming there is no fundamental unity in the universe.
You just need to have proper error correction. You are right - of course - if QM is completely noisy, or you can't have proper error correction (due to some physical limitation for example).
E.g. for quatum computation some people believes so: https://www.quantamagazine.org/gil-kalais-argument-against-q...