If we use the same rules to answer the question "Do many worlds exist?" as we use for answering questions about the electrons' spins and other questions "obviously accessible to the experiments", the answer of quantum mechanics is a resounding No. There can't be any "multiple worlds". After all, the splitting of the worlds would correspond to a quantum xeroxing machine and that's prohibited by the linearity of the evolution operators in quantum mechanics. Also, the conservation laws would be violated whenever the worlds split, assuming that they were not split before the "measurement" or another critical moment. And if they were split in advance, the interpretation would violate causality because the "Everett multiverse" would have know about the measurements in advance.
Quantum mechanics unambiguously says that the linear superposition of orthogonal states, \(\ket\alpha+\ket\beta\), doesn't mean that "both the things described by \(\ket\alpha\) and \(\ket\beta\) exist at the same time". Instead, the plus sign means "OR", not "AND". The state says "only \(\ket\alpha\) is possible AND only \(\ket\beta\) is possible" but when we want to omit the words "possible", the only right translation is "Nature realized \(\ket\alpha\) OR \(\ket\beta\)". It's the usual probabilistic mixture. Well, there is a difference: in quantum mechanics, we first add the complex probability amplitudes, and then we square the absolute values of the results (the probabilities). In classical statistical physics, we sum up the probabilities directly so the "mixed" or "interference" terms would be absent.
So the "many worlds" are obviously prohibited when the rules of quantum mechanics are being used for all physical questions, including the questions that some people could be religiously prejudiced about. (I really think it's analogous to religious beliefs because many otherwise rational people abandon all rational thinking when it comes to questions that have the potential to unseat or otherwise disturb their God. Their boundary behind which rational thinking is prohibited is as arbitrary and surprising as it is for those who love to refuse the quantum character of quantum mechanics.) In the following text, I will discuss another part of this issue and explain that if you wanted to use some non-quantum, more classical rules in which quantum mechanics would be embedded, you would be forced to defend an indefensible theoretical framework, too.
When Shannon met Brian Greene a few months ago, he mentioned that he had a "little disagreement" with your humble correspondent about the foundations of quantum mechanics. It surely sounds nice and diplomatic and I endorse the diplomatic content of the quote. However, when it comes to the actual beef, I must say: A little disagreement? Galileo and the Pope had a little disagreement. ;-)
Let me discuss several points related to the indefensibility of the types of "many-worlds interpretation" that try to construct a "more realist model" into which quantum mechanics is embedded as an approximation:
- it opens a previously non-existent question, "Which events may be classified as a good enough measurement so that they have the right to split the world?", one that can't have an objectively meaningful answer; while the Copenhagen quantum mechanics avoids such problematic questions because the presence of a measurement (or "collapse") is purely a subjective matter, any "realist intepretation" makes the conflict included in this question sharp, and therefore requires a qualitatively different treatment of "quantum objects" and "classical objects"
- too finely grained a tree of the "many worlds" violates the uncertainty principle
- the very existence of the "other worlds" violates the positivist, empirical approach to science
- the Lorentz symmetry is inevitably violated in any "explicitly enough well-defined model" of the splitting of the Universe
- none of the problems or signs of incompleteness of the probabilistic Copenhagen-like interpretation exists.
Proper QM doesn't need an objective definition of what a measurement is; MWI does
Three weeks ago, I argued that quantum mechanics is a tool to probabilistically answer questions that may be "subjectively" asked by observers, not a tool to describe the objective state of reality (which doesn't exist). Despite this fundamental rejection of quantum mechanics, this theory is fully compatible with objective science. It's because the subjective nature of knowledge adds no inconsistency to science – and because the equations of quantum mechanics guarantee correlations in the results that multiple observers obtain when all of them ask the same question.
But the key feature of the fundamentally subjective theory called quantum mechanics is that if no questions are being asked, no questions need to be answered. If the objects in our environments aren't asking any questions for us, we don't need to answer them and we don't need to imagine that the world is doing anything else than evolving the probability amplitudes according to the continuous Schrödinger's equation (or equivalent equations in other pictures). In particular, there's no "collapse" if there's no subject asking questions and learning answers! What is often called the "collapse" is the process of learning and it is a fundamentally subjective process.
In particular, quantum mechanics is compatible with numerous "theories" about the question "who possesses consciousness and is allowed to perceive things". As long as "consciousness" is a totally immaterial, spiritual process (i.e. as long as we don't talk about its measurable, material manifestations, which are clearly as accessible to science – especially neuroscience – as any other material processes), the difference between these different philosophical theories is unphysical. There's no experiment, even principle, that could answer this question. So one may give any answer to the question. In particular, solipsism is fully compatible with quantum mechanics (much like totally opposite philosophies, e.g. one in which you are "one soul" with all the macroscopic objects on Earth and your unified body perceives anything, it just doesn't allow the information to be sent from one part of the body to another). You may consider the whole external world – including other people – to be a collection of "dead machines" that just obediently evolve according to Schrödinger's equation.
Let me emphasize that quantum mechanics doesn't force you to believe that other people are "qualitatively different from you". Clearly, science – especially Darwin's evolution – makes it clear that there's no such qualitative difference between two people as all people share their ancestry. Instead, it allows you to dismiss questions about other people's consciousness – in a purely "spiritual", operationally inconsequential interpretation of the word – as unphysical questions.
The alternative may look more "materialist" which is intriguing for many people but it is a source of a terrible problem. Everett's interpretation suffers from this terrible problem just like any other "realist interpretation" of quantum mechanics, any other theory that tries to present the probabilistic, subjective, non-realist character of quantum mechanics as an illusion following from a hypothetical "realist [classical] theory".
Why is it a terrible problem? Because if you assume that the world is objectively found in a state, you need to prevent it from entering (or staying in) "unfamiliar" complex linear superpositions of macroscopically distinct states. If you assume the world possesses "objective reality" at the fundamental level, the process that does this job – "physical collapse", "splitting of the Universe", or anything of this sort – is a process that simply takes place at a given moment or it doesn't. In principle, all good physicists should ultimately agree whether this process has occurred or not.
But that means a catastrophe. It means that the coherent quantum mechanics has to objectively refuse to hold behind a critical line. One needs to abandon it, modify it, and so on. But such a modification is totally unjustifiable. There doesn't exist a tiniest glimpse of evidence that quantum mechanics could fail to work for some objects larger than \(X\). In fact, it seems obvious that all similar conceivable modifications of quantum mechanics would be either incompatible with the basic observed data or internally inconsistent.
At this point, and in many others, I am flabbergasted how upside-down the explanations by Brian Greene (and others) are. In his book The Hidden Reality, Greene tried to claim that the orthodox probabilistic interpretation of quantum mechanics has to establish an artificial boundary between the world of phenomena described by quantum mechanics and those described by classical physics.
But as we have seen two and three paragraphs above, the orthodox probabilistic interpretation of quantum mechanics is on the contrary the only conceivable explanation that does not have to do anything of the sort. In particular, quantum mechanics is always valid in this approximation. Bohr et al. just correctly said that in addition to quantum physics, the classical picture has to be also (approximately) right for questions whose answers we want to treat as pieces of classical information. But that doesn't mean that there's new physics that invalidates quantum mechanics. It just means that there are two descriptions, quantum and classical, that start to coincide and co-exist for large enough systems.
On the contrary, as I said, the assumption that objective reality exists means that one must believe that Nature has a very particular "critical line" behind which the coherent rules of quantum mechanics that we know from the microscopic world cease to hold. It means that the "objectivist interpretations" of any kind have to assume the existence of new phenomena that isn't observed and that isn't justified by anything whatsoever – except for philosophical prejudices.
When do the worlds split?
The "many worlds interpretation" is a typical attempt to find an objectivist reinterpretation of quantum mechanics – at least that's how e.g. Brian Greene presents it and I totally think that his presentation makes much more sense than any other tirade about Everett's picture (even though it's ultimately totally wrong, too).
It assumes that there must objectively exist "many worlds". In one of them, you measure Stalin to have won the war, in another one, you measure Hitler to have won the war, and so on. How many such universes are there? How finely do you have to divide the universes to make the MWI work? Roughly speaking, you want every small measurement or every small "macroscopic process" to produce new split worlds but what is counted as a measurement or a macroscopic process?
It's a very subtle question and it's easy to see (although some people may prefer not to look) that whatever answer you offer – except for the correct answer, namely that the world never splits – produces insurmountable contradictions. The basic problem is that if you assume that the objective "splitting of the worlds" is the reason why we perceive sharp answers instead of "fuzzy superpositions" (note that the actual reason is that the wave function describes probabilistic distributions with "OR", not a fuzzy shape of objects) and if your "splitting" occurs too rarely (more precisely, less frequently than infinite frequency because any observable may be potentially observed by "someone"), the world will be more fuzzy than the observations indicate. If your splitting will be "too frequent" (more frequent than zero frequency, to be precise), your picture will contradict the uncertainty principle. Note that theories with an "objective collapse of a wave function interpreted as a classical wave" suffer from exactly the same problem. One may say the same things about them.
In the MWI approach, the splitting of the worlds is an objectively important moment. You know, it's not easy to create many new worlds that contain everything that our world does. ;-) An MWI advocate may be tempted to link this splitting to decoherence. However, decoherence is never perfect. In a basis of states we find natural (e.g. because it's local), the density matrix never quite becomes diagonal. There's always a nonzero (although expo-exponentially decreasing) risk of "recoherence" and if you want to avoid this risk, you're never allowed to mechanically divide the worlds.
A related problem – it's actually exactly the same problem – is that when you divide the worlds into "many worlds" too finely, your description will violate the uncertainty principle. Why?
Almost three weeks ago, I discussed consistent histories. Imagine that you observe the trajectory of a particle in a cloud chamber and you decide that the measurement of the position took place every microsecond, at \(t=0.0\), \(t=1.0\times 10^{-3}\), and so on. At each moment, you also measure the momentum of the particle with the best accuracy \(\Delta p\) that is compatible with the uncertainty principle. So far so good.
But the precise moments when the universe splits doesn't seem to be God-given and objective. So another person may think that the splitting occurred \(10^{-16}\) seconds after each splitting according to yourself. Now, there are 10 billion other people who assume the same microsecond spacing but whose "special points" are shifted by multiples of \(10^{-16}\) seconds. Can we reconcile the interpretations of all these people?
You are forced to say that the splitting actually occurs every \(10^{-16}\) seconds. The worlds split every time when at least one person thinks it does. Note that with a larger number of people, I could be forced to accept an arbitrarily fine splitting. But that's a problem because that would imply that in a particular branch of the "many worlds multiverse", the particle's position is measured pretty much at every moment. But if it's so, the uncertainty principle dictates that the momentum can't possibly be determined accurately at all. But each person above actually measured \(p\) rather accurately. By increasing the density of the "split world moments", we violated the uncertainty principle by an arbitrary factor. With 10 billion people, \(\Delta x\cdot \Delta p\) was \(\hbar/10,000,000,000\). Too bad.
So we're allowed to imagine that for macroscopic bodies, the histories are "coarse-grained" and the equivalence classes are treated classically. But we simply can't afford to make the graining too fine. At the same moment, there are clearly no "preferred boundaries" that would separate the space of possible histories into "little cubes" everyone may agree upon (much like the phase space isn't objectively divided to particular "only correct" rectangles of area \(2\pi\hbar\) that everyone must agree upon). It follows that to invent a rule answering the question "When do the worlds split?", you either violate the uncertainty principle or invent some arbtirary rules that contradict the Lorentz symmetry, rotational symmetry, and that simply depend on many totally arbitrary decisions that no one believes may have an objective significance.
Proper quantum mechanics, as pioneered by Heisenberg, Dirac, Pauli, and a few other friends, and as godfathered by Bohr, cleverly avoids all these problems. It doesn't have to divide the phase space to "canonical rectangles with the only right shapes" because it says that such divisions – and the choice of bases – depend on the situation and the questions that an observer asks. They are not objective in character. The same is true for the separation of the "space of possible histories" which is just a harder, infinite-dimensional version of the task to "divide the phase space to the only right rectangular boxes". The reason why we may dismiss the hopeless task of looking for the "precise boundaries in the phase space" is that no objective boundaries exist. They only arise subjectively, in someone's head. But that means that the transition from the linear superpositions to the sharply perceived outcomes of experiments – the "collapse" – is subjective, too.
Positivism
Philosophy is never a good science. But when it comes to philosophies, many laymen in quantum mechanics – and even people not considered laymen in quantum mechanics by the society or by themselves – often think that "realism" is the right philosophy behind modern science. This viewpoint, based on millions of years of our everyday monkey-like experience, has strengthened by the 250 years of successes of classical physics and it was – unfortunately – energized by Marxism that repeated the untrue equation "science = materialist ideology" many times. Marx, Lenin, and related bastards surely belong among those who have encouraged people to never leave the mental framework of classical physics. But it is "positivism" which is the philosophy that is closest to the founders of the modern science, especially relativity and quantum mechanics.
Positivism says that all reliable knowledge – the truth we are allowed to become fans of – has to boil down to empirical observations and mathematical and logical treatments of such empirical data. It sounds uncontroversial among science types but many of them don't realize how dramatically it differs from the "materialist ideology". In particular, positivism assumes nothing about the "existence of objective reality".
I am not going to worship positivism because in the most general sense I have just mentioned, it represents the absence of any knowledge with beef rather than knowledge itself (this absence is important at the beginning of research – which has to begin with a tabula rasa without prejudices – but it's bad if someone's mind stays tabula rasa even a long time after that). That's also why e.g. Werner Heisenberg heavily criticized positivism as a philosophy – it seemed vacuous to him. It's kind of paradoxical because his beliefs in physics were absolutely positivist. But he rightfully criticized people who don't know or believe anything and who make living out of not discovering anything. ;-)
Incidentally, Auguste Comte – despite his being the founder of this "pro-science" positivist philosophy – had crazy opinions about science, too. He once declared that the chemical composition of the stars would forever remain outside science because we couldn't travel to the stars. It took less than a decade after his death before spectroscopy told us everything about the composition of stars (at least their surface). It's fun to be eager to say that "questions such as XY are inevitably outside science" except that many (or most) statements of this kind (but not all of them) are wrong. Whether some question is scientifically meaningful is a subtle question and difficult science research is needed to resolve it (the question is difficult because we don't know all conceivable experiments and all of their conceivable relationships to the "interesting statements" in advance): philosophical prejudices are never enough. They're not enough if your answer is Yes and they're not enough if your answer is No!
But let's return to Everett's picture. It assumes that there objectively exist "other worlds" except that pretty much by definition, the "splitting" is an irreversible process. Because you can't return to the past, you're also unable to return to the "crossroads" from which other worlds originated. But that's the only way to get to the parallel universes, so you can't "get there" (or interact with them) at all.
Now, if this is universally the case, even in principle – and MWI seems to be crucially based on this assumption – then the question whether the other branches exist is outside science, because of the basic positivist definitions of a reliable truth. We can find new ways to study the sunlight but we can't find ways to return to the past or change the facts or events in the past which is why we're sure that the other worlds will remain empirically inaccessible.
It's an OK argument but I still find it more important that there can't be any sensible "set of rules" that would tell you "when the worlds split". Even if we can't observe other worlds, we may still accumulate very strong indirect evidence that they do exist or they don't exist. I need the previous discussions about the "too finely grained histories" and other things to collect data that are relevant for this question whether the other worlds exist. And the answer is No, they can't exist. Whether they're in principle observable or not, the question about their existence turns out to be available to scientific reasoning – one that boils down to the empirical data and their mathematical and logical treatment – and the answer is, inconveniently enough for MWI and other "realist" advocates, that these constructions can't exist.
Lorentz symmetry is doomed in MWI, too
Consider an EPR-style entanglement experiment. We measure properties of two entangled particles. The two events – two measurements – are spacelike-separated. So which of them occurs first depends on the reference frame.
However, if you literally imagine that the number of worlds is increasing at the moment of each measurement and the "tree of parallel worlds" gets ramified, it is possible to find out whether the first measurement occurred first, or the second measurement occurred first. Each measurement is a "vertex" in the branching tree of worlds and one of them has to be closer to the "root" of the tree in the past, so it occurred first. Because the branching of the worlds is an objective processes, all observers should agree about which of the two spacelike-separated measurements occurred first. But relatively implies that different observers won't agree which of the two spacelike-separated events occurred first. That's a contradiction between MWI and relativity.
Again, proper orthodox quantum mechanics cleverly avoids this problem because nothing "objective" is changing during the measurement. The measurement is a change of the subjective knowledge which is why the ordering of the two changes of knowledge may depend on the observer – and on his reference frame. The subjective interpretation of the wave function and the "collapse" (learning) is a property of orthodox quantum mechanics that is necessary for it to agree with relativity in all physically meaningful, operationally answerable questions. This consistency is fully preserved because the "ordering of the collapses" is identified as a question that is only meaningful subjectively which is why different people (in different inertial systems) don't have to agree about the answer. And indeed, they don't agree.
The splitting of the worlds, much like "objective wave function collapses", inevitably leads to contradictions with relativity.
Quantum mechanics is complete and consistent
But the main reason why all the research into hidden variables, de Broglie-Bohm pilot waves, Ghirardi-Rimini-Weber collapses, and many worlds – among a few other, less widespread "realist approaches" – make no scientific sense is that their main motivation, the hypothetical "flaws of the Copenhagen quantum mechanics", is completely invalid.
There is nothing wrong or incomplete about quantum mechanics – the new framework discovered within the Copenhagen school. The intrinsically probabilistic meaning of the wave function and related insight aren't a matter of "interpretations": they're inseparable properties of quantum mechanics, they're general postulates of quantum mechanics, they're really what makes quantum mechanics quantum. The very moment when someone starts to talk about "interpretations" as something that should be built "on top of quantum mechanics", he is already deluding himself and refusing all the insights that are actually summarized by the term "quantum mechanics". Quantum mechanics as a theory doesn't have any other interpretation than the Copenhagen interpretation, with the Born rule, or newer reformulations of pretty much the same thing.
All the other ideas that are called "interpretations of quantum mechanics" are really totally different theories – either toy models that only work as OK descriptions of some extremely limited and special situations but that can't be generalized to "full physics" or, which is more usual, just hypothetical theories whose existence is a wishful thinking many people protect as gold (even though one may easily show that no such theories compatible with the basic empirical data may exist). People who sell "interpretations of quantum mechanics" nearly as a whole new subdiscipline of physics are analogous to people who want to "interpret Darwin's evolution" for a long enough time so that the creator and the events from the Bible reappear again. They just don't like what the theory is saying and be sure that it is saying that the wave function has to have a subjective probabilistic meaning.
As long as one is doing genuine science and not prejudiced ideology, quantum mechanics, a new framework for physics clarified by the Copenhagen school in the 1920s, isn't negotiable. It's as established as evolution, heliocentrism, or any other important pillar of science, and the people who try to relabel basic postulates of quantum mechanics as "illusions" are as deluded as creationists or geocentrists.
Redistribution of probabilities among many worlds
Two paragraphs earlier, I mentioned that most of the theories in the MWI business and related businesses don't really exist: their existence is a wishful thinking. The dreamed about derivation of the Born rule for the probabilities from the MWI framework is a great example of this unlimited, breathtakingly irrational wishful thinking displayed by the MWI advocates and other "realists".
After the quantum revolution, we know that all empirical evidence coming from repeated experiments may be summarized as measured probabilities of various outcomes of diverse experiments. Once again, all the empirical knowledge about the physical processes that we have may be formulated as a collection of probabilities. Probabilities are everything we may calculate from quantum mechanics (and from other parts of science, too). So they're surely not a detail.
Orthodox quantum mechanics promotes probabilities to fundamental concepts and uses the standard probability calculus – which existed a long time before quantum mechanics – to give you rules how to verify whether the probabilistic predictions of a theory are right. The basic laws of quantum mechanics are intrinsically probabilistic. The MWI framework tries to deny this general point. It has many worlds – something we would normally call "a priori possible results" are pretended to be "real new worlds somewhere out there" – but at this moment, we haven't even started to discuss the empirical evidence yet. We only start to discuss the empirical evidence once we start to compare the measured probabilities with the theoretically predicted ones because everything we empirically know are probabilities!
But when it comes to the probabilities, MWI has absolutely nothing coherent to say. If the probabilities of "spin up" and "spin down" are 64% and 36% respectively, the MWI framework just gives you two worlds. How do you actually extract the numbers, 64% and 36%? There doesn't exist any proposed answer that makes any sense. It's clear that there can't exist any answer that makes any sense because probabilities can't be "derived" out of something that has isn't probabilistic.
You may try to say that there are 64 worlds with "spin up" and 36 worlds with "spin down" and all of them are equally likely (or 16 and 9 worlds, or other multiples). Except that almost all probabilities predicted by quantum mechanics (and verified by experiments) are irrational numbers so you would need infinitely many "many worlds" to account for these irrational probabilities: a division to fractions just isn't good enough and all "rational approximations" would look so awkward that no one would believe they're right. Or you may just have two worlds and assign the unequal probabilities to them (and justify it, for example, by saying that the observer doesn't know "in what universe he is", and the right answer is just one that happens to agree with the Born rule). But a new, "deeper" derivation of the quantum mechanical predictions – and all such predictions have the form of probabilities – is what you wanted to achieve. So if you mysteriously assign your fictitious worlds the probabilities by hand, you have clearly derived nothing. You have just invented a childish story compatible with your religion (one that may still be shown incorrect if you try harder).
When someone tries to offer an allegedly "deeper" explanation of the probabilistic rules but he ignores the fact that he doesn't have any remotely conceivable explanation what the probabilities could emerge from, and this is a superserious problem because all the data in science may be formatted as probabilities, it seems to me that the person is so prejudiced that it makes absolutely no sense to discuss these issues with such a person. What drives him is pure bigotry, a metaphysical, quasi-religious fanaticism ready to overlook all empirical evidence we have or we may ever add. Indeed, that's exactly what the anti-quantum zealots are doing all the time.
And that's the memo.
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