A vast majority of the people who write popular books, blogs, and comments at discussion forums about the foundations of quantum mechanics are peers of the stupid monkeys.
A week ago, Scott Aaronson wrote that he is a champion of the "Many Worlds Interpretation" (MWI) even though MWI is slightly more frail than heliocentrism. That's what I call an understatement on steroids.
The term "MWI" is notoriously illdefined, it may mean everything or nothing or something in between and there is no actual theory of physics that would deserve this name and that would work. But let's assume that the proponents of MWI mean that there exist many worlds and different mutually exclusive properties of a physical system are realized simultaneously.
In the following 40 seconds, let's see that it ain't the case.
Let's take an electron and measure its spin component \(j_z\) via the SternGerlach apparatus i.e. via a magnetic field.
The initial state of the electron is prepared to be "up" with respect to a particular tilted axis – every state of the spin in 3 dimensions is "up" with respect to a semiaxis – so that we have\[
\ket\psi = 0.6 \ket{\rm up} + 0.8 \ket{\rm down}.
\] So the electron will have a 36% chance to have the spin "up" and 64% chance to have the spin "down". Note that it's not just the absolute values of the amplitudes that matter. The relative phase matters, too. If we changed the relative phase of the two terms by the factor of \(\exp(i\alpha)\), it would mean that the axis with respect to which the electron is polarized "up" would rotate by the angle \(\alpha\). Such a rotation may be inconsequential for our measurement of \(j_z\) but it would matter for the measurement of all other components of the spin.
Now, let's ask the key MWI question: will there be an electron with spin "up" as well as an electron with spin "down"?
The MWI proponents say "Yes". They imagine that different possibilities "really occur" in different universes, and so on. So this is the main question that decides about the validity of the MWI. Stupid monkeys are obsessed by questions whether MWI and other things are "not even wrong", "politically correct", "obeying Occam's razor", "pretty", and all such irrational adjectives, but no one seems to care about the question whether it is scientifically false or true.
Quantum mechanics offers a universal rule to answer all Yes/No questions that have any physical meaning, that are in principle observable. For the given question, we identify the projection operator \(P\), i.e. a Hermitian operator \(P=P^\dagger\) obeying \(P^2=P\) (which is why its eigenvalue have to obey \(p^2=p\) as well and they must belong to the set \(\{0,1\}\) i.e. {No, Yes}). The expectation value\[
{\rm Prob} = \bra \psi P \ket \psi
\] is interpreted as the probability that the answer is Yes. Quantum mechanics doesn't allow us to predict anything else than probabilities. So there's always some uncertainty about the answer to the question. The only exceptions are projection operators whose expectation values are equal to \(0\) or \(1\): these values correspond to "certainly No" or "certainly Yes" and there's no uncertainty left.
We will see that the "key question of MWI" is of this sort. The projection operator for a question "A and B" is constructed as\[
P = P_A \cdot P_B.
\] When it comes to operators, "and" is multiplication. That's why Logical AND i.e. conjunction is also known as "binary multiplication". And that's also why the probabilities of two independent questions' having answers "Yes" is equal to the product of probabilities.
Fine, what are \(P_A\) and \(P_B\)? They are projection operators on the subspaces for which the answers to questions A and B are "Yes". In particular, we have\[
P_A = \ket{\rm up}\bra{\rm up}, \quad P_B=\ket{\rm down}\bra{\rm down}.
\] They're projection operators on the "up" and "down" states of the electron, respectively. There are just no other states in the Hilbert space for which the statement "there is an isolated electron with the spin up" or similarly "...down" would be valid. Now,\[
\braket{\rm up}{\rm down} = 0
\] and therefore\[
P = P_A P_B = \ket{\rm up}\bra{\rm up}\cdot \ket{\rm down}\bra{\rm down} = 0.
\] Therefore, the probability that there will be both an electron "up" and an electron "down" is\[
\bra\psi P \ket \psi = \bra \psi 0 \ket\psi = 0 \braket\psi\psi = 0.
\] I've written the derivation really, really slowly so that at least 10% of the stupid monkeys have a chance to follow it. At any rate, we may prove that the probability that the electron exists in both mutually exclusive states simultaneously is zero. It can't happen. The derivation is identical for any other mutually excluding alternative properties of any physical system.
Note that the operators \(P_A,P_B\) commute with one another, i.e. \(P_A P_B=P_B P_A=0\), which means that both questions may have an answer at the same moment (the uncertainty principle adds no extra hassle). That allows us to avoid some discussions.
The simple conclusion is that there aren't many worlds. QED. Get used to it, monkeys. ;)
Let me now spend some time by discussing how indefensible various "loopholes" would be and why there are many other ways to see that the answer to the question "Are there many worlds?" had to be "No". And I want to mention several likely fundamental and rudimentary errors that prevent MWI advocates from deriving the right answer to this simple question and from seeing that this is truly a kindergarten stuff and not something that they should be confused by for days, weeks, months, years, decades, or centuries.
First, let me discuss the interpretation of the "plus" sign.
As I already suggested, it's important to distinguish addition and multiplication. (If you don't know what multiplication is, watch 0:400:45 Miss USA on maths.) The key fact is that the wave function composed of several mutually exclusive pieces such as\[
\ket\psi = 0.6 \ket{\rm up} + 0.8 \ket{\rm down}
\] has a plus sign that roughly means "OR", not "AND" as many people apparently think. When we care about the \(j_z\) component of the spin, the formula above says that the state \(\ket\psi\) allows the electron to be either "up" OR "down". It doesn't say that there is both a spin "up" AND a spin "down".
If we need to say "AND" in quantum mechanics, either "one proposition/question AND another proposition/question" (as discussed with the \(P=P_A P_B\) relationship above) or "one object added on top of another object", we need multiplication, not addition. For the case of the two propositions, we have already discussed an example, the \(P=P_A P_B\) relationship above. If we discussed physical systems composed of several pieces, e.g. a group of 2 apples and a group of 3 apples, we would need another kind of a product, the tensor product,\[
\ket{\text{5 apples}} = \ket{\text{2 apples here}} \otimes \ket{\text{3 apples there}}.
\] The matrix elements extracted from similar "tensor products" are products of the matrix elements for the individual subsystems and the same thing therefore holds for the probabilities, too.
Some people may be thinking that it almost looks like I am suggesting that the MWI advocates are complete idiots with the IQ of a retarded thirdgrader because they can't distinguish addition from multiplication. The reason why it looks so is that this is exactly what I am trying to say. In fact, it's pretty obvious that my attempts to say such a thing are successful and I am actually saying this thing. ;)
Why is there so much confusion about the meaning of addition and multiplication here?
Because people with common sense – as it evolved for millions of years – and no genuine knowledge of the pillars of modern physics (which includes the MWI advocates) always think in terms of objects, e.g. apples. So when you're adding two apples and three apples, place the two groups next to one another, you're adding apples. Similar addition more or less applies to lengths of sticks, momenta and other conserved quantities, and even quantities such as voltages, currents, charges, and many others.
But this "combining objects that exist simultaneously is addition" is fundamentally and completely wrong for wave functions in quantum mechanics. In quantum mechanics, addition of wave functions or density matrices roughly corresponds to "OR", not "AND", and "AND" must be expressed by multiplication. How can we understand the origin of this flagrant difference between the classical thinking and quantum mechanics?
The primary reason is that quantum mechanics just isn't describing the objects themselves. It describes propositions we can make about objects. As Niels Bohr used to say, Physics is not a tool to describe how the reality is. Physics is a tool to say right things about what we can see. The basic building blocks such as the wave functions and projection operators don't describe and count objects but encode propositions, knowledge, information.
For propositions and their probabilities (expectation values of the projection operators), addition is simply not "AND", addition is "OR". The right mathematical expression for "AND" is another operation, namely multiplication rather than addition.
An MWI advocate could start to spread fog. It may be debatable which one it is, the difference between "AND" and "OR" isn't that important, anyway, and it may be up to centennial deep philosophical discussions which way it goes. Well, all these statements are pure rubbish. There isn't any ambiguity, confusion, or room for modifications. Addition and multiplication are completely different operations so you should better not confuse them. The right theory that is tested is the theory that says the same thing about the interpretation of addition and multiplication as I did. Be sure that if you modify its rules, the rules of quantum mechanics, by randomly replacing addition by multiplication and vice versa at various places, you will get a completely, qualitatively different theory that will yield a totally different description of the reality and it will disagree with almost all observations, including some extremely elementary ones.
There just isn't any room for confusions and debates. Just like a 7yearold schoolkid who invents arrogant excuses why she cannot learn the difference between the addition and multiplication (note that I am politically correct so I sometimes include "she" in similar sentences, especially if it increases the degree of realism), the MWI proponents should be given a failing grade and should be spanked.
Be sure that any "technical" modification of my proof that there aren't many worlds will damage the theory so that it will become totally incompatible with the experimental tests. For example, if you suggested that the projection operator for "A and B" should be \(P_A+P_B\) rather than \(P_A P_B\), you will easily find out that the same rule used for any experimentally testable situation will lead to wrong predictions. In fact, pure thinking is enough to see that "AND" must be expressed by the product of the projection operators and not the sum.
Using charge conservation to prove there aren't many worlds
The fact that one electron can't suddenly be split to two electrons so that it would be both "here" and "there" may also be derived from charge conservation, angular momentum conservation, mass conservation, or other conservation laws. In quantum mechanics, such laws still hold.
If the initial state \(\ket\psi\) is an eigenstate of the electric charge operator \(Q\),\[
Q\ket\psi = q\ket\psi,
\] then, because \(QH=HQ\) i.e. the charge is conserved i.e. the symmetry generated by it is a symmetry of the Hamiltonian i.e. of the laws of physics, the final state will obey the same relationship with the same value of \(q\). But if there were an electron on both places, the electric charge could be shown to be doubled and different than the original one. That would conflict with the conservation law.
Inflating the Hilbert space along the way
Some people could say that my derivations are missing the point that there is an "Everett multiverse". I should have increased the size of the Hilbert space before the measurement etc.
There are many wrong things about such a potential objection.
First, the constancy of the dimension of the Hilbert space is a mathematical necessity. Especially because some MWI proponents including Brian Greene say that they want to be led by the most natural interpretation of the equations of quantum mechanics, it's totally indefensible to actually change the dimension of the Hilbert space along the way. It's surely not what quantum mechanics tells us to do. In fact, one may easily show that such a proliferation of the degrees of freedom couldn't lead to an internally consistent theory.
It may be explained in many ways, e.g. by the quantum xerox nogo theorem. There can't be any evolution of a state in \({\mathcal H}\) to a state in a larger Hilbert space such as \({\mathcal H}\otimes {\mathcal H}\) because the evolution of the state vector in quantum mechanics is linear while the map \[
\ket\psi\to \ket\psi\otimes \ket\psi
\] is not linear; it is bilinear or quadratic. If \(\ket x\) and \(\ket y\) were evolving to \(\ket{xx}\) and \(\ket{yy}\), respectively, then linearity would dictate that \(\ket{x+y}\) evolves to \(\ket{xx+yy}\) while the universal squaring formula would say that it should evolve to \(\ket{(x+y)^2}=\ket{xx+xy+yx+yy}\). These are different ket vectors on the larger Hilbert space because there are extra mixed terms. At any rate, it's a contradiction: in a quantum world, there can't be any gadget that creates two exact copies out of the arbitrary initial state.
Another problem with the objection is that I actually haven't done any assumption about the nonexistence of the "Everett multiverse". For example, in the fast "charge conservation" proof, \(Q\) could have meant the total electric charge in "all branches" of the world you could ever hypothesize. Clearly, if the number of worlds is being multiplied, the charge won't be conserved. That will be a problem because the symmetry generated by \(Q\) won't be a symmetry of the laws that control the "Everett multiverse" anymore. It won't be able to be exact at a fundamental level, you won't be able to use it to constrain the laws of physics, and so on. This "demise" will be fate of all the symmetries in physics (translations, rotations, Lorentz boost, parity, etc.) because all symmetries are related to a conservation law.
One more problem with the "splitting of the Universes along the way" is that there can't possibly exist any justifiable rule about "when this splitting takes place". There aren't any sharp qualitative boundaries between phenomena in Nature. It's clear that there can't be any splitting during a sensitive interference experiment – because such an "elephant in china" converting the fuzzy quantum information into the classical one would surely destroy the interference pattern.
The problem is that in principle, we may say the same thing about 2 particles, 3 particles, 100 particles, or \(10^{26}\) particles. In principle, the interference pattern involving an arbitrarily large system may be measured so the Universe is just not allowed to "split" into possibilities where different classical outcomes are realized because such a splitting would make the "reinterference" permanently impossible while it is arguably always possible in principle.
In practice, there's a lot of irreversibility, "decoherence", but this process always depends on our inability to manipulate with the elementary building blocks of information too finely. Decoherence is an emergent phenomenon and it isn't sharp, either. There is no point during the decoherence process when you could say "now it's the right time for the universes to split into many worlds". Decoherence is just a continuous process in which the offdiagonal elements of the density matrix gradually decrease. They decrease faster and faster but they're never "quite" zero.
Shannon told us that Brian Greene thinks that he and your humble correspondent have a "little disagreement" about a physics question. ;)
The little disagreement is about the existence of a paradigm shift in the 20th century science that would invalidate the previous framework of classical physics. I am sure it has happened in the 1920s; Brian Greene thinks that it hasn't happened so it is still possible to think about Nature in the "realist" way. Of course, I could also be saying it is a little disagreement, I have also been taught how to be diplomatic, polite, hypocritical, and dishonest. But I just don't think it's right to behave in this way. The disagreement is clearly about a major question, about the very existence of modern physics as something that is outside the box of classical physics. Brian Greene is really denying the existence of quantum mechanics; instead, he is suggesting that what we need are new theories (e.g. nonlocal ones or multiverse ones) within classical physics (although he and others prefer more obscure ways to describe the very same thing, ways that make the naked Emperor's new clothes look more fashionable and decent).
The MWI chapter of The Hidden Reality by Brian Greene (whose Czech translation by me will be in the bookstores on Monday) really drove me up the wall many times because most of it is literally upside down. One repeatedly "learns" that if we want to describe the whole world in a uniform fashion, we must adopt the MWI ideology. Bohr et al. were incapable of doing so, so they preferred to live in their messy, marginally inconsistent system of ideas, and use behindthescene tricks to fight against the true messengers of the truth such as Hugh Everett III.
This uses the right words except that the content is exactly the opposite of the truth.
Bohr et al. always used legitimate, official, and transparent channels to discuss similar physics questions – e.g. in the BohrEinstein debates – and it is the MWI advocates who are using nonstandard channels such as popular books to spread misconceptions. Equally importantly, the "universal validity of the laws for small and large objects" is an important consideration, indeed. But it unambiguously says that MWI is wrong and QM as understood by Bohr et al. and the followers – modern physicists – is the only plausible right answer.
I have already mentioned why it is so. There just can't be any splitting of the worlds when one quantum particle is coherently and peacefully propagating through an experimental apparatus. The same comment applies to 2 or 3 particles so if we're using the laws of physics coherently for small as well as large systems, there can't ever be any "splitting of the Universes".
An impressive song about the Higgs, a new genre of music.
There is one more aspect of the unity that could be violated by the MWI advocates to defend the indefensible. They could say that the question "is there an electron here as well as an electron there", the question whose probability we calculated to be zero, shouldn't be answered by the rules of quantum mechanics i.e. by identifying the right projection operator and by computing its expectation value (interpreted as the probability of "Yes"). They could say that this is a question "above the system" that should be answered by some philosophical dogmas.
But that's not how physics works or should work. Quantum mechanics has a way to answer all physically meaningful i.e. in principle observable questions and it is the same way for all the questions. In fact, there is nothing unusual about asking whether there are electrons at two places. This is the kind of questions that all of physics is composed of. If you were free (or even eager) to abandon your standardized theory and methodology to answer such questions and if you switched to some metaphysical dogmas just because this question about the many worlds is "ideologically sensitive", it would prove that the theory you may still be using for other questions isn't something you are taking seriously, isn't something to answer really important questions in physics. It would surely show that you have double standards and the technical theory you're using isn't universal and uniformly applicable because you often replace it by metaphysical dogmas.
Your attitude would be completely analogous to the attitude of a fundamentalist Christian physicist who just chooses to believe that Jesus Christ could walk on the sea because the laws of gravity and hydrodynamics didn't have to apply and the nonnuclear conservation of carbon atoms could have been invalidated when he was converting water into wine. And I don't mention many other Jesus' hypothetical crimes against the laws of physics that such a physicist could be eager to overlook for political reasons. ;)
The MWI advocates prefer metaphysical dogmas and their naive classical intuition over the standardized quantum mechanical "shut up and calculate" approach to answer such questions about the electron on two places (or pretty much any other question in physics) because they haven't started to think in the quantum way yet. To think in the quantum way is to be deciding about the validity of propositions (or the probabilities of their being valid) and the procedure is always the same. One constructs the projection operator related to the proposition and calculates its expectation value in the quantum state. It's the probability and if the result is \(0\) or \(1\), we may be certain that the answer is "No" or "Yes", respectively.
(The detailed arguments or calculations may proceed differently and avoid concepts such as "projection operators" but they must still agree with the general rules of quantum mechanics.)
When we follow this totally universal quantum procedure – valid for questions about microscopic systems as well as macroscopic systems – carefully and rigorously, we will find out that quantum mechanics as it stands, in the same Copenhagen form as it has been known since the 1920s, answers all questions, including those that "look philosophically tainted", correctly i.e. in agreement with the experiments. Sidney Coleman gave many examples in his lecture Quantum Mechanics In Your Face.
For example, it's often vaguely suggested by the MWI champions and other "Copenhagen deniers" that the experimenter could feel "both outcomes at the same moment". However, by the correct quantum procedure whose essence is absolutely identical to my discussion of the two positions of the electron at the beginning, we may actually find the answer to the question "whether the experimenter feels both outcomes at the same moment". We will convert the proposition to a projection operator, it has the form \(P=P_AP_B\) again, and because its expectation value is zero for totally analogous reasons as those at the top, it follows that according to quantum mechanics, the experimenter doesn't perceive both outcomes at the same moment. This is a completely physical question, not a metaphysical one, and quantum mechanics allows one to calculate the answer. It's just not the answer that the antiCopenhagen bigots would like to see.
Quantum mechanics doesn't predict "unambiguously" which of the outcomes will be perceived by the experimenter (spin is "up" or "down"?) but this uncertainty is something totally different than saying that he will perceive two outcomes. The number of outcomes he will perceive may be calculated unambiguously by the standard rules of quantum mechanics and the number is one. There is no room for "two worlds" or "two perceptions at the same moment". Which outcome will be felt has probabilities strictly between 0 and 100 percent so the answer isn't unequivocal.
When the MWIlike folks are discussing these matters, they are constantly making lots of other totally rudimentary errors – and perhaps "deliberate errors" – aside from the confusion of addition and multiplication I mentioned above. A frequent one is to totally forget or deny that quantum mechanics predicts and remembers correlations (in their most general form known as entanglement) between any pairs, triplets, or larger groups of degrees of freedom and properties that may coexist in the real world.
For example, Coleman mentioned the cloud chamber example by Nevill Mott. A particle leaves the source in the cloud chamber. It is in the \(s\)wave: its wave function is spherically symmetric so it has the same chance to move to each direction. So why does it create a straight line of bubbles in one direction rather than a spherically symmetric array of bubbles?
Again, this may be interpreted as some superdeep metaphysical question that goes well beyond quantum mechanics and the Copenhagen interpretation may be claimed to be incapable of answering such questions. Except that there is nothing hard or metaphysical about this question at all. It is completely physical, quantum mechanics allows us to answer it using a very simple calculation, and the answer is right. There will be a straight line of bubbles because one may prove that due to some demonstrable entanglement between properties of the supersaturated water or alcohol at various points that the propagation of the charged particle causes, the direction of two newly created bubbles as seen from the source is always essentially the same.
(One may prove that the charged particle only creates bubbles in a small region around its location; and one may prove that the position of the charged particle goes like \(\vec x = \vec p \cdot t / m\) where the momentum \(\vec p\) is essentially conserved. That's enough to see that the bubbles will be aligned.)
So again, while quantum mechanics gives ambiguous predictions about the direction in which the "bubbly path" will be seen – all directions are equally likely – it actually does unambiguously predict that the bubbles will have a linear shape, they will only emerge along a straight semiinfinite track. There is absolutely no inconsistency between these two assertions. Any wrong idea that QM has to predict that the distribution of the bubbles is spherically symmetric boils down to a trivial error: the omission of the fact that the existence or absence of bubbles at a point is correlated with the existence or absence of bubbles at other points. In fact, the correlation is so tight that for each semiinfinite line, there are either bubbles everywhere along the line or there are no bubbles on it. And there is only one semiinfinite line.
As I said many times, the people who have trouble with proper, i.e. Copenhagen or neoCopenhagen laws of quantum mechanics, are always "eager" to simplify the quantum rules of the game prematurely and convert the situation to some "real physical object" way too early (well, one should really never do so but if one does it too early it may be more damaging). But Nature never does such mistakes. It remembers the wave function which knows about all the possible correlations between all the degrees of freedom, which knows about all the relative phases because they could matter, and only when an observable question has to be answered, it just calculates the right answer. The right calculation looks very different than any kind of reasoning in a classical world but it isn't too hard; it's really straightforward and in all situations in which classical physics used to work, it still gives the same answer (with tiny corrections).
When the initial wave function for the charged particle in a cloud chamber is spherically symmetric, it doesn't imply that spherically asymmetric configurations of the bubbles at the end are forbidden i.e. predicted to have vanishing probabilities. On the contrary, we may prove (the right verb really is "calculate" because the proof boils down to the calculation of an expectation value of a projection operator) that the distribution of the bubbles will be spherically asymmetric – a semiinfinite line in a direction. There is no contradiction because the initial wave function isn't a real object such as a classical field, stupid. It's a quantumgeneralized probabilistic distribution. A spherically symmetric probabilistic distribution (on a sphere) doesn't mean that the actual objects such as the particles (or, later, the bubbles they will create) are spherically symmetric. Instead, it means that the probability that the objects are found in one direction is the same as it is for another direction. But because the particle may be shown to be in a direction, we know that the actual measurements of positions will inevitably be spherically asymmetric.
Is that really so hard to understand that the wave function in quantum mechanics is a generalization of a probability distribution – and not a generalization of a classical field? It encodes the information about the physical system, not the shape of the object itself. It is not really difficult to learn these things but some people just don't want to.
And that's the memo.
Friday, August 24, 2012 ... /////
Simple proof QM implies many worlds don't exist
Posted by
Luboš Motl
at
2:42 PM



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snail feedback (106) :
I now fully understand your frustration when translating The Hidden Reality. Brian Greene seems to defend this Many Worlds approach saying it is "the most conservative framework for defining Quantum Physics".
Have you seen this hilarious video? A Capella Science  Rolling in the Higgs (Adele Parody)
http://www.youtube.com/watch?v=VtItBX1l1VY&feature=share
Right, Shannon. It's about 30 pages of this stuff that keeps on going and it's repeated and repeated and everything is upside down. From the viewpoint of the history, I find it demoralizing and demotivating. Be smart and lucky enough to be one of 35 key people who realize the most important revolution of the 20th century science. It ain't easy. Is it worth it?
Almost 90 years later, there will still be "mainstream" books published that you haven't really discovered anything, just muddled the waters, and you were a thug who was bullying brave original thinkers (proper word: crackpots of your age), and your theory is unable to do all the things (that it is actually totally able to do), and the original thinker's theory is surely better and more unified (although it isn't even welldefined, it doesn't describe anything correctly whatsoever, and is nothing else than defense of the intellectual inability, laziness, and dogmatism).
Imagine you discover the most important thing of the 21st century now, looking at the Universe from a much more farreaching, accurate, abstract, and unified perspective. Some people won't be able to get it so you will explain them why it's wrong. In 2100, there will be popular books sold to millions of people that you were a bully who used political tricks to modify inconvenient theses, and so on. It's terrible. I don't really know whether, if history is a good guide, I would like to discover the 21stcentury counterpart of quantum mechanics. The hassle  not just hassle in your life but apparently also hassle in your "afterlife"  may be just too intense.
The "conservative" label is particularly silly for the MWI, indeed. Speculations about splitting worlds according to ad hoc rules no one has really meaningfully formulated, ever, because it's not really possible, are the least conservative thing one may imagine. Quantum mechanics is radical but it also preserves the basic scheme and collection of observables and their properties in physics more or less without change. One could say that quantum mechanics only differs from classical physics by having xppx = i.hbar instead of xppx=0. The commutator is just a little bit different, a tiny number called Planck's constant times i which must be there because the commutator is antiHermitian, and that's it. It's a very modest deformation of the particular laws of physics for the particular classical system we used to have (the classical limit of the quantum theory); one must just learn what it means to work with a theory where xppx isn't zero but the classical physicists could still be told they were "approximately right" in the observable sense of approximations because their assumption xppx=0 had an "approximately right results".
Adding infinitely many randomly and vaguely fucking and reproducing universes just in order to deny that xppx isn't zero i.e. x and p (or any observable pair) can't have welldefined properties at the same moment is just the maximally ad hoc, uncontrollable, "progressive", degenerative, irrational thing one can do. Such a framework isn't "approximately equal" to any previous theory, it's not building on anything. It's very clear that it's just a messy attempt to fake the correct theory by some unjustifiable building blocks.
Thanks, Victor, it's really impressive. The music genre is just like the Yellow Sisters but it also has the extra Higgs bonus points. ;)
I have never read a clearer explanation of the basic idea of QM, Lubos. Those folks who claim that Schroedinger's cat is half alive and half dead need only to read the + sign as "or". It's so very simple.
Regarding your small disagreement with Greene, I recall Sheldon's famous retort regarding LQG, "Small disagreement!! The Pope and Galileo had a small disagreement!".
Hahaha I knew you couldn't leave that mumbo jumbo on Scott's blog go unanswered. Yesterday I skimmed though all 100+ comments and was disappointed not to find yours ... does Scott have you on his "ignore" list?
Ha ha, that rocks :))) !
And now I want to hear this particular parody of "Bohemian Rhapsody" they announced in the last few seconds, LOL :D
Thanks, Gene, for your professionally loaded synergy. The quote from TBBT is of course a memorable one, LOL. ;)
I find this article curious. I'm a believer in the EverettWheeler interpretation, and yet I agree with all the physics you describe here. And I don't recognise much of the version of EWI you present. Odd...
The EWI is really about the quantum state of the observer, rather than the system being observed. The 'Copenhagen' view it is set up in opposition to is that you have a quantum system obeying quantum physics which is observed by a classical observer obeying classical physics  the transition from one to the other occuring through these projection operators and wavefunction collapse.
The EWI view is that the system observed and the observer are both quantum systems, and that the process of observation is simply a temporary coupling of the two systems.
It's similar to the way coupled oscillators give rise to normal modes. When coupling is introduced, the modes of vibration of the components become correlated, and turn out to be the eigenvectors of the interaction matrix. If one system starts in a superposition of eigenstates, and is observed by (interacts with) another system, the observer enters a superposition of correlated eigenstates, each state corresponding to an observer observing a particular state.
EWI is 'conservative' in the sense that it simply extends without modification the postulates of quantum physics to the observer. It agrees absolutely regarding the physics of the system being observed.
The 'many worlds' label comes from an attempt to explain to the lay public what such a quantum observer would experience. Because the different eigenstates are orthogonal, they don't interact, and thus each eigenstate of the superposition would be unaware of all the others. It would be *as if* there were multiple observers in multiple worlds, each seeing one outcome.
Thus, if you want to prove EWI wrong, you need to show how conventional QM handles the quantum state of *observers* without them ever entering superpositions. Or to say how else you would interpret the experience of a quantum observer in a superposed state.
I haven't tried it for quite some time whether my comments would be censored now. The odds are always O(50%) for all such leftwing blogs. ;) That's high enough a risk not to waste time. After all, my blog has a somewhat larger traffic than his blog so I am sure that a blog entry here is more visible than a comment at his blog.
Song about higgs is not completely new genre. Bjork did the whole album out of vocals only.
It seems to me that you only proved that the spin cannot be both up and down in the same world, but a multipleworld theory would say that the up and down occur in different worlds. So if we let Ua mean up in world A, and Db mean down in world B, then P(Ua) = P(Db) = P(Ua and Db). Of course P(Ua and Da) = 0. Similarly with charge conservation, the MWI is that the conservation law is that the charge is equal across worlds, not that the sum across worlds is equal to one world.
Sorry, Jonathan, I haven't made any assumption about the number of worlds so it applies to any number of "components".
It is also complete nonsense that the charge conservation could mean something else than the conservation of the total charge  of the sum of all the contributions. If there exist many components of the universe, in the usual sense of the word "exist", then the total charge is indisputably the sum over them.
The charge can't really mean anything else. The U(1) symmetry generated by the charge has to transform all the charged fields in all components of the Universe so the value of the charge as the quantity has to be the sum. There is no way to escape these facts. The only thing you can achieve by denying these facts is that you completely misunderstand Noether's relationship between charges and symmetries, too.
My impression was that Everett was groping towards the idea of decoherence but not really getting there in a comprehensible way. i.e. you don't need a "special rule" to "collapse" the wave function. Bohr et al. might never have believed that, but perhaps lesser minds who came after them did.
"I haven't presented "EWI" because I've never heard any theory that was claiming to be called "EWI". This is a totally bizarre term."
That's the EverettWheeler Interpretation, which is the correct name for it. 'Many worlds' is a misnomer.
"It's good that you explicitly say that "EWI" treats observers differently than the "observed system" because this was one of my primary "accusations", one that disagrees"
I haven't said that.
Observers and the observed are treated identically, and observation as a physical process is no different to any other sort of coupling or interaction.
"The Copenhagen school was talking about observers in isolation but it never meant that such large bound states didn't follow the laws of quantum mechanics"
No, it was an attempt to invent laws of quantum mechanics that would explain why a quantum reality *appeared* to observers to be classical. This was the 'wavefunction collapse'. The idea was that the physics proceeded according to reversible QM until it was 'observed', at which point it would collapse down to a single eigenstate according to some projection.
But it was unclear what physically distinguished 'observation' from any other sort of interaction of systems, and all sorts of crazy ideas related to consciousness, gravity, size, complexity, and thermodynamics have been proposed. Everett's thesis was to simply say these devices were unecessary. If a quantum observer interacted with a quantum system, it would enter a superposition of mutually noninteracting states, each corresponding to the observation of one outcome. That is to say, unitaryevolution, reversible QM already fully explained our classical experience with no need to posit a nonreversible 'collapse'.
Everett's physics had absolutely no new content  it was simply (a subset of) ordinary and already widelyaccepted QM  it just applied it to the observer problem and found there was nothing difficult to explain.
"Quantum states *always* enter superpositions. In the cloud chamber example, the whole system evolves into a superposition of states of a charged particle and bubbles in the same direction  superposition over all directions."
Agreed. But the question is about the quantum state of the *observer* who observes the particle, which is a sphericallysymmetric superposition of observers each seeing a particle in one direction.
Having explained carefully that the issue was over the quantum state of the *observer*, and whether it was a superposition, I'm surprised to see you again point to the state of the *system being observed*.
You need to address the question of whether the *observer* of the decaying particle, or Schrodinger's cat enters a superposition of observer states. What is the quantum state of the detection apparatus? Of the scientist? Can they ever be in superposition?
Dear Lubos, Even though I couldn't say exactly why, as a layman I intuitively felt the many worlds interpretation was inherently absurd the moment I heard. It struck me as the sort of thing a nottobright nerdy sciencefiction fantasist smartypants would go for, like the idea of a technological singularity.
If I remember it correctly MWI is used to explain the different "worlds" in "Sliders" ... :D
Jonathan is absolutely right. You should read his point again slowly and try to understand it.
All these things are completely untrue.
You and your fellow manyworld cranks may be using the term "EverettWheeler Interpretation" but it is a nonsensical term because Wheeler hasn't contributed anything to it aside from the deliberately obscuring title "relative state".
It's nonsense that Bohr et al. wanted to "explain why things look classical" by assuming a demarcation line. And it's nonsense that the Copenhagen school ever assumed any "collapse".
You need to address the question of whether the *observer* of the decaying particle, or Schrodinger's cat enters a superposition of observer states. What is the quantum state of the detection apparatus? Of the scientist? Can they ever be in superposition?
I have addressed this question about 500 times already, and so did Heisenberg, Bohr, Dirac, and others 85 years earlier. Yes, states always evolve into very general complex linear superpositions of any basis vectors one may choose. As I predicted, you would still be unable to notice in your new comment, and I just added you on the blacklist because your degree of idiocy is something I just won't suffer through again.
The whole point of MWI is to redefine what exists means. Also, by stating P⟨updown⟩=0 you are assuming one world, which I assume you are calling component. I've never seen Noether's theorem reformulated to work for multiple worlds, but you definitely can't just take the one world formulation and apply it as is to a multiple world situation. Whether MWI is true or not is different from correctly representing the concept mathematically. My own opinion is that whether MWI is true or not is not knowable by us, if it has been correctly formulated. A misformulated version of it will definitely be false.
The fact that lesser minds  such as Everett himself  said lot of rubbish after 1925 is surely not a good reason to deny that the foundations of quantum mechanics, the framework of modern physics, was built correctly by Bohr, Heisenberg, Dirac, Pauli, and a few others, is it?
The whole point of MWI is to redefine what exists means.
The only problem is that no one has ever seen such a point. You may dream about "redefining the existence" except that there isn't any "new" definition of existence. It's just a sequence of lies. If you disagree, could you tell me what your new definition and the new derivation of the dynamics of charge etc. is supposed to be? To offer a legitimate counterevidence, you will have to rediscuss all these elementary derivations I did and offer your "alternative" derivation of all the experimentally tested conclusions for which the MWI discussion is inequivalent to proper quantum mechanics. You know very well that no such an alternative theory may exist.
It's very obvious that there can't be any "intermediate" or "third way" of existence that would allow one to have one's cake and eat it, too. It doesn't matter whether the spin exists in another component of the Universe or not. If there is an extra electron anywhere, it carries an electric charge and the conserved quantity has to be the sum of the charges, and similarly for other quantities. Whether the universe is connected or not is an absolute detail, an irrelevant technicality. There isn't any "different kind of existence" in which the conserved quantities wouldn't have contributions from all pieces of the Universe.
Also, it's not true that I was assuming one world for the orthogonality. The states are orthogonal whenever they're differenteigenvalue eigenstates of a Hermitian operator, e.g. J_z in this case; it's a trivial oneline proof in linear algebra. I don't need to make any assumption about the number of components in the Universe, it may be anything you want but the directly experimentally measured value is 1.
you are still stupid, accept it.
paradox: if the MWI were true there would be a universe where instead the MWI is not true.
conclusion: MWI is interpretation is wrong! :)
sorry for my horrible english.
Luboš,I wonder if you saw following paper: http://xxx.lanl.gov/abs/1111.3328
As ignorant as I am, I still venture to wonder, Are there any physically meaningful tests of the MWI? I note the citations in wiki:
Deutsch, D., (1986) ‘Three experimental implications of the Everett interpretation’, in R. Penrose and C.J. Isham (eds.), Quantum Concepts of Space and Time, Oxford: The Clarendon Press, pp. 204214.
Plaga, R. (1997). "'Proposal for an experimental test of the manyworlds interpretation of quantum mechanics'". Foundations of Physics 27: 559–577.
Are these authors presenting worthy suggestions?
Well, Lubos has argued persuasively that MWI can't be correct, but I don't think this reason can have anything to do with it. if MWI were correct, there couldn't be any universe in which it was not correct. What you are saying is essentially that in MWI any imaginable universe exists  this is not true which is I guess a minor nice thing that one can say about MWI  and that, there must be a universe in which multiple universes do not exist. I'm sorry but what?
There is an interesting philosophical problem with MWI that does make me uncomfortable with the idea, Lubos's reasons aside:
If all probabilities are somehow realized in "other worlds" there must be some worlds in which every event is an unlikely outcome. In such universes, disturbingly enough, quantum mechanics looks wrong from a statistical point of view: It makes predictions about how likely certain things are to happen, which would appear wrong, purely by chance, in a large number of universes. Not only is the idea that as a scientist you could find yourself in a universe where the correct theory makes unreliable predictions abominable, one could make the argument that it is very unlikely we happen to be in a universe where quantum mechanics looks goodwhich might lead into anthropic arguments...
In Wiki they link the plus sign to a "disjoint union"
Is this your meaning or am I on the wrong track.
That one should need prove a theory false although it has no observable consequence and makes no computational advances is still another objection. The burden is on the mwi folk not on those who have so often proven that qm works. Mwi in all formulations add no new useful prediction. If one could not although you demonstrate one can demolish it, it would at best be a philosophical construct.
If Fred, or anyone can point us to a consistent modification on Noether that would conserve any property such that we could at least retain the explanatory power of symmetry then only would Mwi even rise to not even wrong stature.
It's a simple statement about how to calculate probabilities. The probability that A or B occurs if the two events are mutually exclusive, is the sum of their probabilities P(A) +P(B) (if they aren't mutually exclusive you must subtract their joint probability (ie "and")). If you want to calculate the the probability that both events occur, well, actually they are mutually exclusive so their joint probability should be zero. But if they are independent it would be the product of their probabilities.
This URL is in response to the smoking monkey!
Enjoy: http://www.youtube.com/watch?v=B70ZOrY8BYo
How is MWI explained in The Hidden Reality? I have some layman questions and I have a hard time googling any layman explanations, e.g., if the electron will have a 36% chance to have the spin "up" and 64% chance to have the spin "down" and both happen how exactly do the probabilities manifest themselves in this deterministic situation?
So, your own opinion is that the truth of MWI is not knowable by us. What the shit does that mean?
Again, physics is not about existence; it is about what we can observe! Jesus!
The prejudice might get worse and worse as time passes but Nature always recognizes the truth. The bad thing though is that humanity will waste a lot of time with these MWI and other crackpots theories. That's the frustrating part.
Still I'm here "interneting" with Dr Motl and just last month I spoke with Brian Greene. It feels like I'm close to the Gods'Fight.
Cool :)
In the past I used to shrug my shoulders and thought people persuing just wrong ideas (without trolling against others) are mostly harmless...
But now I think if too many physicists keep doing things that can too obviously not work, this could cast a damning light on the whole field (of fundamental or theoretical physics for example) which would be dangerous ... :/
Sorry, I have to disagree with the and/or discussion. Schrodinger's cat isn't "alive or dead". That would be a hidden variables "interpretation". The point of the cat experiment is that sentences like "the cat " don't make sense, QM only gives probabilities for the result of measurements.
In the case of "0.6up> + 0.8down>" , we could say: "The result of a measurement will be either up> OR down>", but we could just as validly say "The eigenvectors are up> AND down>".
This is just a language issue, not an issue of understanding.
Hi Lubos
You speak as if an MWI "split" happens when a photon hits a halfsilvered mirror, for example . That's not what the theory says though; a "split" may only happen at the same time that an observation is made. Quantum states in linear superposition still exist in MWI and the mathematics is the same.
Bohr said that the wavefunction collapses and the state is now an eigenstate of the measurement just made. MWI says that the universe splits into copies when the measurement is made, with one copy for each eigenstate that had a nonzero probability of being found.
The issue of the split maybe occurring over a short period of time, is the same as the issue of Copenhagen wavefunction collapse maybe taking some time.
Of course you may say that decoherence is superior to both of these views, and you may be right. However, Bohr didn't know about decoherence , he rejected MWI in favour of Copenhagen.
So, there is no issue with "split states being unable to reinterfere with themself" or whatever. In the case of a MachZend interferometer, for example, if the probability of detector B triggering is 0%, then MWI says that there is no splitting of universes, in this particular case MWI is just identical to Copenhagen.
Also I am not sure why you bring up charge conservation etc. Each individual universe follows the laws of physics, including charge conservation.
If the universe splits then there's twice as many electrons and twice as many protons.
The Hilbert space that a wavefunction lives on, is something that is just within one universe. When a split occurs, each universe gets its own Hilbert space, the vectors in one space no longer have anything to do with the other space. The different universes, by definition, cannot interact with each other ever again.
NB. I don't adhere to MWI personally, but the thing you refute in this post is not what Everett and his fans do adhere to.
Jorge Luis Borges, the famous Argentinian short story writer, wrote the story, "The Garden of the Forking Paths" in 1941, which suggested the idea of many worlds. David Deutsch has been championing this idea, and, in his popular book, "The Fabric of Reality" and in some papers, claims to have "proved" it using the double slit experiment. He claims that the interference results from passing single photons through a double slit can only be explained by MWI where "shadow photons" from the many worlds are interacting with the photon in this world.really bizarre "proof". It is sort of proof by incredulity or lack of imagination.
I must admit that many worlds is a fun science fiction concept, but isn't plausible.
Also, the brains entertaining it seriously really don't compare with the QM founders'Dirac's 1930 book is extremely clear, and Heisenberg's famous paper is complete magic, if very hard for me to follow.
http://fqxi.org/community/forum/topic/1413
So you both agree that observers themselves can enter into superpositions? (that's pretty much how I understand MWI, that I myself am in some way in a quantum superposition) If so, it's not obvious to me what you're actually disagreeing over other than weather you like the words "many worlds interpretation"...
Those people never clearly say what they actually believe. A vast majority of them never clearly says whether superpositions of macroscopically different states are legitimate states and the minority is as split as the world can never get. ;)
Of course that my answer is Yes, it's the superposition principle. The reason why such superpositions aren't familiar from the "classical" perceptions is explained by decoherence but there is nothing fundamentally wrong about these superpositions.
Dear Old Wolf, one could perhaps agree that it is a language issue but your claims about the preferred language are still completely wrong.
The sentence "the eigenvectors are up and down" is valid but it has nothing to do with the state vector "psi" itself so it is not equivalent to my original sentence. It only describes a priori possible choices. The sentence I mentioned was meant to only describe possible states whose coefficients are nonzero so it carries some information. Your sentence carries none.
There are no "hidden variables" in the sentence "cat is dead or alive". It's just an ordinary logical statement using the conjunction OR. You surely don't want to prevent physicists from using the word "OR", do you? I assure you that physics or any science would be impossible without words like "OR".
It's also untrue that statements "observable XY has value xy" may be meaningless. All such propositions are valid in general, by the basic rules of quantum mechanics. Histories constructed out of such sentences may fail to be "inconsistent" if I use the GellMannHartle terminology but one surely can't ban any of these sentences at the level of general quantum mechanics, before the dynamics is considered.
So it's not really "just" language. You misunderstand the physics, too.
Dear Old Wolf, when you say that there's a "split" after the measurement, you are back to the question "what is a measurement" (who has enough consciousness or whatever to be allowed to measure: now the same agents have the right to split the worlds!), the same question that was claimed to motivate the whole interpretation because the Copenhagen interpretation is said not to answer such questions.
In reality, there can't of course be any splitting of the world and I have proved so. So it's not true that my description isn't relevant for this question. Some people just don't want to hear things that prove that they believe in wrong things.
In the Copenhagen interpretation, the "measurement" is a somewhat arbitrarily defined threshold/event after which one may treat the information using the laws of classical physics. So one may talk about a "measurement" at a point behind which classical physics becomes an OK approximation, or later than that, but not before that. It's very important that it's a phenomenological theory only; nothing qualitative is actually changing about the world at the "moment of measurement". There isn't any "moment of measurement".
Bohr has never said that the "wave function collapses". All of your comment is just pure bullshit. It's impossible to react to every sentence written by everyone who writes complete bullshit about quantum mechanics, about the way how the world actually works, about the mathematical possibilities how it could work, and about the history of science. All these things are being distorted, rewritten, rotated upside down, and you're a part of the problem, too.
I read The Fabric of Reality, too, when it came out. Deutsch also wrote that quantum computing, when it comes, will owe its power to massively parallel computations being performed on the qubits in many universes simultaneously that differ only by a smidgen. I guess the computer operators in our neighbor universes work for us... or we work for them :)
Deutsch is near the top of my wishlist of people who I would like to see publish a guest blog at TRF, but ONLY if they stay around for the discussion afterward :)
Borges was a genius writer, he surely mined theoretical physics for inspiration.
The Hidden Reality refers to the Garden of the Forking Paths, too, just mentioning it was Brian Greene's favorite literature on related topics. But one could seriously claim that if the "splitting worlds from quantum mechanics" is a legitimate insight in physics, it wasn't done by Everett for the first time but by this book. Everett hasn't made it more meaningful in any detectable sense. He just subtracted the references that make it obvious it is science fiction, and he only removed them because he was advised by Wheeler.
But you have to remember that this is the Copenhagen interpretation;
"that observer is in a superposition" doesn't mean "there are two copies
of that observer and they are in different states". It means "the wavefunction we should use to make predictions about the physical properties of that observer, is the mathematical sum of several other possible wavefunctions".
That is always trivially true, as a mathematical statement; what people
would be interested in, is if coherent superpositions of
"macroscopically distinct" wavefunctions were ever needed to describe
"observers" in the real world. Decoherence prevents this from happening;
but as quantum computers become more advanced, we will get closer to
having superpositions of observerlike cognitive processes.
The danger would be a huge waste of time (like a few centuries)... like religions did in the past (and still do in some part of the world). This would throw our civilisation into the dark ages of science. We are living exciting times with the LHC, space probes etc... I hope physicists won't waste it. They have a huge responsibility on humanity's evolution path.
Yeah that is right.
I am worried too about the fact that even though, due to the advanced knowledge and technologies we have now, we could learn a lot about deep fundamental questions (probably even in the not so far future) this great chance could be gamed away ...
I recently had a serious word with my colleague who borrowed "Vom Urknall zum Durchknall" to me, in order to tell him what I really think about it and the author, his misbehavior in Munich, etc ... :D.
I the course of our lively discussion I learned that he belongs to the sourballs who are of the opinion that it is completely legitimate to cut fundamental physics since it is not important compared to the "real world" problems humanity faces at present etc etc ... His office mate (who I considered to be quite a nice and friendly guy too) is even worse; if he had the power to do it, he would probably turn off the LHC immediately to "save energy" for example, and abolish fundamental physics to save the money for something that is "more useful to humanity".
Boy how did this discussion upset me since I never thought that these two colleagues are among such hardcore sourballs :(((.
At the moment, I hardly manage to look them in the eyes without turning into an angry shadron again when we meet accidentally in our corridor, our small kitchen, or at our weekly group meetings, ect ...
Happily the director of our institute is more reasonable: The day after the higgsindependence day he explicitely pointed out the discovery of the higgs as very important, we all should know about it and we should all learn how the higgs mechanism works by ourself if we do not know it already :))).
The second part of his speech I since then use as a pretext to read TRF even at work ... :P :D :)
Thanks Eugene :)
Your translation sounds very nice in my ears, good for Focus Magazine to talk to real physicists instead of trolls ;). Now after all Prof. Lüst seems to have friends in the media. Maybe Germany has to improve its image after the horrible appearance of our own local troll king in Munich, which leads the science journalists to pull themself together ... :D
Hm, Nicolai wants to directly quantize spacetime ... is he a LQG theorist ? The original German article with the pretty picture I will read as a nice and comforting bedtime story to sleep well and peacefully :)
"The whole point of MWI is to redefine what exists means."
That reminds me of Clinton's famous quote " It depends on what the meaning of the word "is" is."
http://www.youtube.com/watch?v=j4XTl_3y0
Thanks for the translation Eugene.
Funny how these people all look alike to us ;D
(in TBBT Raj's dad confused Leonard with Sheldon and says "oh sorry, you all look alike to us").
LOL, a fun scene. But I have some problems to believe it's genuine and there's this symmetry between the subraces as presented by TBBT. I may be wrong but I surely do believe that the diversity of the appearances between the whites is larger than for other races. Or is it really just because we're not optimized to distinguish other races finely enough and they're similar unequipped by the resolution for the whites in a symmetric way?
You're right. Whites have different hair colours, eyes colours, complexion. Asians and blacks don't have those "striking" differences.
european populations have the smallest genetical variety by far than any of the other mentioned "groups". hair colours yes, there is a big variety dna, no there isn't.
Dear Lubos,
I think that your derivation doesn't show that the MWI is incorrect, because my interpretation of the projectors is a little bit different than yours.
In your proof P_A=up><observes down
and not the pure state you wrote. ( But your derivation doesn't really use the state, that's why I left this to the end. )
What do you think about my position?
I think Lubos has explained this very well, especially with his reference to Mott as well as his proofs. Fundamentally the confusion on this point resides in people's adherence to a notion of objective reality, which must be abandoned in the quantum world. As pointed out we have to think in terms of probabilities. Is there some probability that if you made a different decision in your life you could have been the next einstein? Certainly there is and that has to be factored into the evolving wave function, but does that mean there is some version of yourself leading the life of fame and fortune? No, and that's the point. You AND your doppelganger can not be the outcome of an observation. It has to be you OR your doppleganger. The use of superposition by MWI advocates is misleading. All the superposition preserves is the indeterminancy of an unobserved state. However, the state is NOT you AND your doppelganger. A superposed state is unique in itself. It is a state between mutual exclusive possibilities. This is very important because such states do not have classical analogs. MWI proponents want to change the what exist means before they understand what it means now.
To me, the many worlds interpretation means something like: "The entire universe can be modeled as a quantum system, and the outcomes of experiments can be predicted probabilistically by analyzing the evolving correlations/entanglements". ("Many worlds" comes from the fact that in this model, the whole universe is quantum, and therefore in a superposition of mutually exclusive states.) This seems to be what Fred's saying, and to me the question of weather MWI is valid is basically weather that's true or false. Can you derive the Born rule just by looking at the whole universe's state vector? Can you make a toy model of a quantum mechanical universe containing a scientist measuring the spin of an electron and conclude "he's got a 60% chance of seeing an UP", for example? That's the question I'm curious about.
"The entire universe can be modeled as a quantum system, and the outcomes of experiments can be predicted probabilistically by analyzing the evolving correlations/entanglements."
Well, I would probably call this paragraph "a few words, far from complete words, describing quantum mechanics in its Copenhagen interpretation. This difference in our wording isn't just terminology, it's about the credit and rewriting of the history of physics because your terminology suggests that there is something in your sentence that the Copenhagen school didn't discover. There's nothing of the sort. So if one strips everything that is demonstrably wrong about "MWI" and anything ever connected with MWI, one is back to the Copenhagen quantum mechanics and a movement trying to deny that it was these men who actually made the revolution in the foundations of physics.
I do understand the physics, but we are disagreeing on which English words to use to describe it.
Would you also say that in the doubleslit experiment, the electron goes through one slit or the other?
It's more commonly said that it goes through one slit and the other (i.e. both slits).
No, we are disagreeing on the substance. The propositions "A and B" and "A or B" are two completely different, inequivalent statements.
The statement "the electron exists in slit A or slit B" is valid  with the disclaimer that one must avoid the wrong classical preconception that an objective answer exists. But the statement "an electron exists in the region of slit A *and* an electron exists in the region of slit B" is just wrong.
It may be more common but it's wrong. You can't learn physics or logic or maths properly by choosing "more common" answers and sentences. You must choose more correct ones.
Right  fair enough. So according to you, people like me and Fred are copenhagen advocates, and according to us, you're a many worlds advocate. Well as long as people manage to communicate eventually... Is this maybe not what Brian Greene was referring to all along though? I mean I haven't read the book in question, but I imagine this was what he was angling at, maybe while introducing some slightly dodgy analogies to communicate with a lay audience...... I watched that Sidney Coleman lecture last night actually, and it seemed like he'd got most of the way to making the Born rule come from all the other postulates. Which was quite cool actually... This is doable right? Feel like doing a post on it?
I have no idea what you're talking about. Everything is upside down. I assure you that I have never been a MWI advocate according to myself and you have never grown enough to become a Copenhagen advocate.
Still, the claim that outcomes  with most of the information stored in entanglement/correlation  is predicted probabilistically is what the Copenhagen school brought to the world.
I have done dozens of posts on what you're saying, discussed a lecture on this topic by Sidney Coleman, and this blog post was another one. But you have probably missed *everything*. Probably deliberately so.
Dear Lubos,
of course that + does not mean exactly OR in quantum mechanics because of interference. But for cats it becomes a good enough approximation of OR because of interference.
I just liked the way Sidney Coleman basically explained why an observer would get random results when measuring an electron's spin, without referring to the Born rule at all. He explained reduction of the wavefunction very clearly as well. It's something I'd never seen before, and I found it very interesting. It kind of seemed like you could pretty much the same argument to just totally junk the Born rule and derive it from the other postulates, but I've never seen the full derivation. Not only that, but I've heard people claim that such a derivation is impossible. What's your position on this? Btw I notice Coleman cited Everett in that Quantum Mechanics in your Face lecture.... *grin*
You're just an irrational asshole  sorry if you don't like my terminology: I just watched about 10+ additional episodes of Bullshit of Penn and Teller, wonderful.
What should I do with your junk? All your opinions, priorities, interpretations, methods are just junk.
The Born rule is nothing else than the rule that QM predicts the probabilities and they're equal to c_i^2 where c_i is the complex coefficient of a decomposition of the wave function to a basis of eigenstates. If one uses modern i.e. quantum physics, *every* meaningful question may be reduced to a question about eigenvalues of observables and every such a question may be answered by a calculation of the amplitudes followed by the Born rule. It's the most important fundamental pillar of all of modern science.
The Born rule is exactly true, it is fundamental, it has earned Max Born a welldeserved Nobel prize, and you as well as everyone else who wants to "junk it" is a deranged scumbag and idiotic fuckedup asshole.
Whether one may "derive it" from other postulates is completely irrelevant. One surely has to start with some postulates that are at least as strong and farreaching as the Born rule. The previous sentence is a tautology; the greater strength of the other hypothetical postulates clearly follows from the fact that the Born rule can be derived from it.
Your idiotic ad hominem comments about Coleman are completely distasteful, too. I am sure that there isn't an iota of difference between my comments on QM and his comments, I know that he mentioned Everett and so did I, and I also know that he credits the Copenhagen founding fathers with the discovery of quantum mechanics and all the foundations needed to what he has ever said about the inner workings of quantum mechanics.
Many World Interpretation (as I understand it) assumes in effect that each path under the path integral correspond to a separate reality. Inserting unity in the form 1=Sum >< is interpreted as a sum over different realities. So your argument misses the point, I think. The measuring instrument cannot be simultaneously in the states 1> and 2> (Landau) but Everett assumes it is
(in different realities). I am sorry, I would be only to happy to see the MWI disproved.
Is Fred the same Fred that did silly heat experiments a while back? If so, he doesn’t know a whit of physics.
Luboš Motl wrote:"Is that really so hard to understand that the wave function in quantum mechanics is a generalization of a probability distribution – and not a generalization of a classical field? It encodes the information about the physical system, not the shape of the object itself."
That sums it up.
If I understand you, you are simply removing the process of collapse entirely from the theory (and from the world.) Every interaction results in a superposition, characterized by quantum mechanics, that continues to propagate. End of story. There is a single universe that is much more complex.
The idea of collapse is a crutch to try to explain what we think we experience and is the root of all of the confusion about what an observer is and what constitutes an observation. That is how it was explained to me a long time ago in a private conversation with a mathematical physicist of some renown and it seemed a wonderful simplification with an enormously expanded view. I don't think Lubos' attack is relevant to that view.
I stand ready to be eviscerated, even blacklisted. :)
Andrzej, sloppiness is an important part of this philosophically prejudiced demagogy.
The formula
1=Sum › ‹
must be interpreted as the sum over *possible* realities, not actual realities. There is absolutely no ambiguity about this statement  it may be directly measured. The interpretation of the sum above is exactly the same as
int dp dq / 2.pi.hbar
the integral over the phase space in classical physics. This is not just an analogy; in the classical limit, the sum above reduces to the integral over the phase space. Now, the individual points of the phase space are clearly not realized simultaneously  the phase space is the complete set of possible states in which the physical system *may* be but the number of states in which it actually is is demonstrably equal to one.
The fact that the squared amplitudes c^2 are probabilities isn't one of dozens of possible speculations; it is a completely directly observed experimental fact. We may just associate the wave function with a particular experimental situation and if we measure once, we don't see any wave function in the experiment because the wave function isn't observable  both in the linguistic and technical sense. If we measure many times, we see the probabilistic distributions related to the wave function in the usual QM way, thus proving that the wave function is a semifinished product for (all) probability distributions. This is not a random guess; it is a claim that may be directly observed in experiments.
I am sorry, I would be only to happy to see the MWI disproved.
Maybe you would first have to open your eyes.
There has never been any collapse in the proper, Copenhagen (and physically equivalent, probabilitybased instrumental) interpretation of quantum mechanics. It has always been a crutch, a deeply misleading popular metaphor for newspapers that kind of influenced even those who shouldn't have been influenced and who should know better.
The collapse isn't an actual process; it is just our simplification of our own knowledge, the arbitrary moment of time after which we may just use the conditional probabilities assuming the observed facts and forget about the result of the probability distribution defined for values different from those that were already made known to us.
This is without a doubt the most clearer and simple explanation of the basic idea of QM. I agree that MW theories are hogwash. To start with, how are many world to be tested? Trusting many worlds would be like trusting a person who claims to have been given so called divine message in sleep....
Looking forward for more of your posts
I would say that it is rather just a simplification of our perspective to something we can grasp. That no such moment really exists, just a universe of propagating and expanding superpositions due to prior interactions and leading through subsequent interaction to more of the same. This is the sense in which there are "many worlds." What I perceive as "I" is purely historical and is just a locus through it among which there are many ("many" being an enormous understatement.)
Out of all this our perception of singular events and their probability is mysterious and in some deep way relates to measure, which is the real domain of quantum mechanics.
Back to the armchair where I belong. Thanks for giving me the floor for a moment.
Dear Don, fine, if this simplification or any other simplification helps anyone, he may use it to improve his life. But he shouldn't call it science. Science isn't about simplification at any cost; science only allows simplification as long as the theory remains accurate as a description of all the known and relevant phenomena.
One may simplify the explanation of sex to children by telling them that babies are brought by storks. Such a simplification helps but it is not valid science. There is no genuine stork that is bringing babies  babies are born without any birds whatsoever (except for the bird that the Czech readers are thinking about now)  and in the very same sense, there is no collapse, no many worlds, no hidden variables, and so on. Quantum mechanics just predicts probabilities of outcomes directly, without any of these intermediate storks, and the assumption that there exists one of these storks leads to a direct conflict with experiments as long as one looks at the experiments comprehensively enough.
This is more a technical point I guess and doesn't change the content of the article but I was wondering if since the "multiplications" were direct products are the sums really direct sums? My intuitive interpretation of the two types of products as applied to probabilities in general is that states are like marbles in bags. If you have a product of states then it's like one state is a marble (not necessarily a specific marble) from bag 1 and the other is from bag 2 so you take the direct product of the states to symbolize the fact that the probability to have the state s1(x)s2 is the product of the probability to have s1 and the probability to have s2 whereas for a sum of states you're really saying that the two states are two marbles from the same bag so obviously when you draw you only get one or the other.
I hope I understand you well in which case you're right and it's important.
Two marbles have states that live in the *tensor product* of the singlemarble Hilbert spaces. It's important that the tensor product isn't the direct sum. The dimension of the tensor product is d1*d2 where d1,d2 are the dimensions of the singlemarble Hilbert spaces.
On the other hand, the dimension of the direct sum is d1+d2. The direct sum of two linear spaces may also be "geometrically" described as the Cartesian *product* of the two individual linear spaces. But this Cartesian product is really just a sum. What one needs for two marbles is the tensor product of the Hilbert spaces and the probabilities for conditions "marble 1 does something and marble 2 does something else" reduces to the product of the two individual probabilities if the marbles are unentagled.
And yes, if one talks about one marble e.g. in the double slit experiment, its having more possibilities where it can be corresponds to extending the spaces as direct sum. So if a single marble can sit in one of 15 red holes or 4 blue holes added later, it may sit in one of 19 holes and the Hilbert space is the direct *sum* of the original 15state and 4state Hilbert spaces. The marble is in one of the 15+4 holes, so it's either in the red holes OR the blue holes. This "OR" is what corresponds to the direct *summation* of Hilbert spaces. It doesn't increase the number of objects; it only increases the number of mutually excluding states/properties that the objects may have.
Sorry, I don't know what happened with my previous post. Basically, I wanted to write two things:
1) Since the projectors are related to the observations of an observer, P_A*P_B=0 only means that the same observer cannot observe the electron in both states simultaneously. In the MWI, there are two different observers in two different worlds who observe the different states, so there is no contradiction.
2) I think that the MWI only works after decoherence, so the MW state should be described by a density operator, where the offdiagonal terms are zero. If the decoherence isn't complete (so there are small offdiagonal terms), than the MWI is only an approximate picture.
Dear Rezso, you probably used "smaller than" and "greater than" which you shouldn't in a partly HTMLenabled comment editor.
1) Your attempt to escape the unescapable by "restricting it to an observer in one world" would only be justifiable if you could also create the corresponding mathematical objects that would describe whether a metaobserver in the whole system of worlds may see electrons in both spin states  anywhere. If it is in principle impossible to talk about the observations in the whole "MWI multiverse", then the MWI multiverse obviously doesn't exist.
Needless to say, such an attempt will fail because it's exactly equivalent to the previous problem with the word "observer" replaced by "metaobserver". There can't be any operator that expresses the existence of objects or their properties in the "multiworld" for the reasons I have already demonstrated and your newest "excuse" is just a terminological sleightofhand that tries to redefine the "observer" in such a way that the "multiworld" becomes inaccessible in principle. At any rate, if done correctly, the argument leads to an inescapable conclusion: the other worlds can't exist.
2) Decoherence is a meaningful theory that can be explained and verified by welldefined mathematical formulae but MWI is not. There isn't any "MWI after decoherence". MWI is a philosophical prejudice that was promoted decades *before* decoherence was discovered and it is not really equivalent to decoherence, either. And decoherence doesn't produce any "multiple worlds". It explains why some bases of states are more observable in the real complex world than others. You are talking about a nonexistent combination of MWI (which is an illdefined piece of rubbish) and decoherence (which is a homework exercise and totally indisputable consequence of ordinary quantum mechanics applied to states in which an interesting system is treated separately from the uncontrollable environment).
Dear Lubos, thank you for your answers.
1) I completely agree that we should not introduce extra structure for metaobservers, because in the MWI, we would like to describe the measurement process without the measurement axiom and without adding any extra structure to conventional unitary QM.
2) Do you think that decoherence alone can solve the measurement problem completely? Surely, it can explain why macroscopic objects behave in a classical way. And it is a physical process, no one can deny it's existence. But is it the final answer? The result of decoherence theory is a density operator for the system (after the environment is traced out). The probabilistic interpretation of this object should be put in by hand.
For example, if you take a look at this article: http://arxiv.org/abs/quantph/9908008, Joos concludes that decoherence is not the final answer and that there are only two possibilities for the good interpretation (if hidden variable theories such as pilot wave theory are excluded): 1) we should modify the Schrödinger equation to get a real, objective collapse 2) we should use the MWI. My opinion: I dislike option 1), because the Schrödingerequation is equvialent to unitary time evolution, so even a small modification would lead to a completely different philosophy behind the equation. So, if I were forced to choose I would clearly go with option 2).
What do you think? You clearly dislike option 2) but I suspect that you will say that you dislike option 1) too.
Dear Lubos,
You wrote:
"Also, I feel very uneasy about your sentence "the probabilistic
interpretation of [density matrix] should be put by hand". Which hand?
What is the sentence supposed to mean except for trying to spread some
irrational and totally unjustified doubts by some rhetorical tricks? The
density matrix is *by definition* the quantum version of the
probability distributions on the phase space, so of course that it has a
probabilistic interpretation, by definition."
The meaning of my sentence was the following. In modern decoherence theories, you start with the wavefunction of the system+environment, build an orthogonal projector from it, and then, you trace over the environment to obtain the density operator of the system. So, there are no probabilities in the definition!
First, the decoherence term in the master equation has to kill the offdiagonal matrix elements (in the preferred basis). After that, the remaining diagonal matrix elements can be interpreted as classical probabilities. What I wanted to say above is that this is a new assumption which is needed to connect the theory with experiments. This is why some people think that there is something more in the measurement problem.
Of course, one can argue with this analysis. So now, I'm going to argue with myself. :)
One can say that the properties of the density operator make a probabilistic interpretation natural. Hermicity means that the diagonal matrix elements are real, Tr=1 means that their sum is 1, and positivity means that all of them are positive. So a probabilistic interpretation is natural.
Oh no, today it seems like that I have convinced myself that my previous argument was wrong. :S
Cheers
Rezso
You say "So, there are no probabilities in the definition!". That's a highly bizarre assertion. Whenever you want to interpret the calculations physically, you *need* to use the word probability because it's the only valid interpretation of the matrix elements of the density matrix, of the expectation values of projection operators, and so on.
What I wanted to say above is that this is a new assumption which is needed to connect the theory with experiments.
No, there is absolutely no "new assumption" in decoherence. Decoherence is just ordinary quantum mechanics applied to a particular kind of questions about the coexistence of a system with its environment. The interpretations of all objects such as density matrix are exactly the same as they always are in quantum mechanics. The probabilistic interpretation is not only natural but it's also one that may directly derived from observations and the only one that allows the theory to reduce to the previously known classical limits.
Hi Lubos,
I highly admire your neverending defence, against allcomers, of the probabilistic interpretation and encourage you to never stop, it's clearly how nature is
Problem is, it's a a mix of psychological nonacceptance and miniscule logical loopholes (eg MWI, superdeterminism, crazy godlike pilot waves) that allow the fretting deniers of nature's randomness a corner to fight from, and while you deal superbly well with the logical arguments, you'll never solve the psychiatry problems.
FWIW, I agree with YOU.
Dear Lubos,
okay, you convinced me that you are right. The probabilistic interpretation of the density operator follows naturally from it's mathematics, so nothing more (like MWI or something else) is needed, decoherence alone solves the measurement problem.
But I still maintain that the fundamental definition of the density operator should use the partial trace and not the classical probabilities. And this is a difference between decoherence theory and ordinary QM (=Copenhagen Interpretation).
In ordinary QM, the construction of the theory goes in the following order:
1) Wavefunction, unitary time evolution
2a) Measurement axiom, wavefunction collapse, classical probabilities
3a) Density operator is defined from the probabilities and from the corresponding collapsed wavefunctions
But the decoherence motivated construction of QM goes as:
1) Wavefunction, unitary time evolution
2b) System+Environment, density operator is defined by a partial trace
3b) Classical probabilities emerge from the density operator after decoherence is complete
So, I want to say that 2b) is a better definition for the density operator than 3a), because 3a) relies on the ad hoc wavefunction collapse rule, while 2b) doesn't.
Do you agree with me in this?
http://ca.news.yahoo.com/formeruspresidentbillclintonbacksinterstellarvoyage164714882.html
I want to know what you think of this. Do you think interstellar travel is possible, or science fiction? Hearing from a physicist would be great.
"What I think is that your position is just a linguistically powered rubbish that can't be given any interpretation that makes sense and you are just wasting my time.
In an experiment with one electron, "electron exists with spin up" is exactly the same proposition as "electron has spin up". Trying to create any doubts about this is totally irrational.
Also, if you used the MWI philosophy to arbitrarily insert existential quantifiers ("there exists a universe in which") in front of all propositions, you would totally screw all rules of logic about the propositions. You can't just add quantifiers without totally changing the logic.
In particular, "electron has spin up" is the exact negation of "electron has spin down" but "there exists a universe with electron up" isn't complementary to "there exists a universe with electron down", especially because both propositions would almost certainly be "true" in an MWI. So this is experimentally excluded because we know that they're negations of each other.
In such comments, I see that any discussion is totally hopeless after the first sentence. You say that we have different interpretations of projection operators. Holy fuck. How can you have a different interpretation of a projection operator? It is a very elementary object in principle, both mathematically and physically, and there is only one interpretation that is consistent with observations as well as logic and it's the interpretation of QM.
The interpretation is that a projection operator is P obeying P^2 = P, we also want P^dagger=P, that is identified with the observable having No/Yes i.e. 0/1 eigenvalues answering to a question  namely the question Is the physical system in a state inside the lambda=1 eigenvalue (of P) subspace of the Hilbert space? The expectation value of this P in a pure state or Tr(P.rho) is the probability that the proposition holds. That's it.
What the fuck is your interpretation? You're always promising some other interpretation but there isn't any. Crackpots like you are talking too much. In reality, the MWI babblers haven't even decided whether projection operators play any role in MWI at all. The reason they haven't decided is that none of the two answers makes any sense and they know it.
At any rate, I am waiting for your prescription how to use projection operators to make the calculations in your nonCopenhagen framework, the MWI counterpart of my paragraph two paragraphs above. Before you actually have something of the sort, could you please kindly shut up and stop these meaningless tirades that only show one thing, namely that you're never willing to learn anything and you prefer to spit tons of this vague nonsensical mud over the Internet?
Cheers
LM
Dear Lubos,
the comment you just replied to was my oldest comment in the thread. But it was broken, and I only removed "smaller than" and "greater than" symbols from it to make it work.

"In such comments, I usually see that any discussion is totally hopeless after the first sentence."
Actually, you already convinced me that you are right and the MWI is an incorrect interpretation. :)
"Also, if you used the MWI philosophy to arbitrarily insert existential
quantifiers ("there exists a universe in which") in front of all
propositions, you would totally screw all rules of logic about the
propositions. You can't just add quantifiers without totally changing
the logic."
Yes, you are right. I haven't thought about this, when I wrote my old post.

But the old Copenhagen interpretation is incorrect too because it uses an ad hoc wavefunction collapse rule and the preferred basis is chosen by hand.
Decoherence theory is the correct interpretation of quantum measurements,
where classical probabilities naturally emerge from the density operator after decoherence is complete. But the wavefunction never really collapses.
Previously, I thought that the decoherence interpretation can be naturally merged with the MWI, but you convinced me that I was wrong.
Cheers,
Rezso
Your calculations and logic are both wrong.
You're simply calculating the probability that electrons within the same timeline would exist in multiple states at once to be 0, which would obviously be true. Within the same timeline the probability of existing in different states would be 0, but that doesn't have anything to do with the MWI.
All interpretations of the doubleslit experiment use the same mathematics and quantum theory, the results of doubleslit experiment are just interpreted differently.
In MWI there is no collapse, you see the electron that exists in your timeline.
So your disproof is all wrong.
I'm certain that in the future multiple timelines will be experimentally proven, though I'm not sure about the MWI in particular.
By a timeline, you probably meant a world line, right? ;)
Show me your "correct MWI" calculation of the same trivial thing but before you do so, please accept the fact that your comment is just a laymen's rubbish.
Very nice find, Victor.
Also nice (in my opinion):
Newton's First Law, by the Number Sixes and
the Double Slit Experiment by Future Management Agency.
Both of them Creative Commons licenses so you can't beat the price :D
As far as the proponents of many worlds go, it's not the
laymen and selfproclaimed experts and prophets who just can't get their minds
around the wave function being a subjective probability distribution because it
mathematically looks like a classical wave for one particle, preferably
spinless, that bother me. Most of those people are on the level of the Flat
Earth Society. It's the slightly bigger names that subscribe to this
illconditioned interpretation that freak me out, e.g. DeWitt, Zurek, perhaps
partly Wheeler (he did talk about the wavefunction of the Universe) and I have
a hunch that Sidney Coleman is something more of a fan of many worlds than you
would like to think. The language that he uses in his In Your Face talk is
kinda MWIish, e.g. at about 12:15 he says something like "we were in the
branch that got spin up". Also he never says that he takes the
wavefunction to be nonphysical and his position seems to be
"associated" with Everett, obviously, Yakir "Weak
Measurement" Aharonov, David Albert, and Zurek. Now Zurek did a lot of
great stuff on decoherence, but he subscribes to a modified many worlds
interpretation of QM. Anyway, Sidney says a lot of smart things, but I'm really
worried about these MWIstyle statements. This might not be as serious as I
take it to be, though it's hard to know, and even if it is of course none of
Sidney's opinions reduce the amount of inconsistency of MWI. But it points the
way to a curious psychological phenomenon, or problem, if you will.
And that is that otherwise smart people, very smart even, who can extract
wonders from the mathematics underlying our physical theories, reduce to
complete morons when it comes to interpretational issues, the debating of which
usually consists of very simple and irrelevant mathematics obscured to an
arbitrary degree by metaphysical/sciencephilosophical vocabulary that they
probably aren't really qualified to use. Take the recent work of 't Hooft and
Weinberg for instance. I find that very mystifying.
I find Zurek to be the most curious of these figures. In his paper at http://arxiv.org/abs/0707.2832 he
advocates a variant of the MWI, of course called “relativestate” to make it
more bland. Amongst other things he claims to derive the Born rule
noncircularly (funny how after Deutsch et al’s failures it sounds like this is
a specific type of its derivation :)) with the aid of envariance, a theoretical
aid much in the spirit of the decoherence program. Unfortunately he truly doesn’t
sound like he’s talking complete crap. He might be reaching for the deepest interpretational
layers of quantum mechanics that can be reached without denying the objective
existence of the wavefunction. Of course that might be worse than not reaching
for them at all, since the consistency of the Copenhagen interpretation makes
it completely unnecessary and it’s probably a ton of bullcrap anyway, only neatly
worded and convoluted to the point when it looks convincing. But it does look
convincing. Do you have an opinion on Zurek’s derivation? Especially, do you
think you can identify a point at which possible inconsistencies arise? I tried
debunking it myself but haven’t spotted the obvious problem yet. The only paper
negatively addressing Zurek’s interpretation that I could find was by Ulrich
Mohrhoff, a curious guy who I think is doing a good job in patiently explaining
to the antiquantum zealots why the probabilistic interpretation is the thing.
But while ok, he seems to be doing stuff a bit differently from, say,
consistent historians, so I am very much interested in your opinion.
Cheers,
notallama
Dear notallama, I would endorse a big part of what you write. Just a few comments. The "relative state interpretation" isn't Zurek's renamed stuff. It's the title, perhaps with formulation instead of interpretation, of Everett's 1957 thesis. So Zurek seems to be analyzing the *same* thing. Still, his 2007 paper starts by assuming the probabilistic interpretation, as far as I can read it.
I also agree that Sidney Coleman himself used some MWIlikesounding language. But as far as I can say, it's always just the language. He may have used the word "branch", perhaps because he was inspired to use it, but I don't see any indication that he would actually interpret the squared amplitudes as anything else than the probabilities or that he would try to look for a model where the wave function is "more real".
Many of us have adopted certain phrases, especially because the strongest "proselytizers" when it comes to quantum mechanics are those who don't understand QM properly. (I remember a Czech physicist at my Alma Mater in Prague, Bedrich Velicky who knew very many famous world physicists, who always complained how universities don't teach the "real deal", but when it came to his "real deal", it was some naive "realist model", not remember which one.) So each of us picks a tolerable one among them, Coleman probably picked the Everett language as the most tolerable one but I don't think that it has influenced his thinking.
I agree that those people are smart and brainpowerful when it comes to some technically more demanding questions but they just become complete idiots when the topic switches to interpretation. And I exactly agree with your observation that their technological capabilities suddenly evaporate and the most difficult maths is on the level of "squared amplitudes", and in most cases, they don't even square it right or they don't care whether it should be squared, and so on. It's completely weird. They probably see other "otherwise very smart" people who are doing the same thing so they feel justified to be equally breathtaking idiots. It's an infection of a sort.
The 2007 Zurek paper is full of lots of redundant gibberish but of course I think that it's among the saner papers on the interpretational issues. It explains that MWI can't do almost anything right, as I read it, but one may supplement it with his insights  which are described by 50 different names or metaphors, decoherence, quantum Darwinism, einselection, envariance, and so on, and so on, but the essence is always the same mechanism  to get a sensible "interpretation". Also, if I guess right, the c^2 probabilities are extracted by looking at many states of an entangled complicated system including the environment chosen so large that each microoutcome corresponds to a large number of microstates of the whole big system with the same absolute value of the amplitudes, by symmetries, the probabilities of each are probably claimed to be the same, which allows to "derive" c^2 in general by summing over many terms with the same absolute value.
I think it's silly to think that this is more fundamental than the general rule for the situation in which the amplitudes have different absolute values  because they almost certainly have different absolute values, so it's contrived to assume that they should have the same absolute value. But it's a part of the hatred against everything that is quantum, including the simple Born rule. Some people just don't want it to be fundamental  well, one of the postulates or derived statements that are so closed to postulates by derivations that it makes no sense not to call them fundamental  and Zurek "partially" joins this idiotic movement in the paper.
You're basically just saying that it is impossible to observe an electron that is simultaneously spin up and spin down, and that every observation will confirm that charge is conserved. I doubt any MWI proponent would disagree with either statement or feel that it contradicts their interpretation.
I think there's a valid philosophical objection to an interpretation that talks about the reality of alternate possibilities that can never be observed (if you can't possibly observe them, in what sense do they deserve to be called real?). But I don't see how you'd derive a mathematical contradiction to it, since at its heart it's just a very literal interpretation of the mathematics of the wave function.
Personally, I don't see MWI as being much different than people talking about virtual particles in QFT. You'll never observe them, so are they real, or is it just a convenient way to visualize the math behind your theory? Probably the latter, but I'm not going to go to war over it and call people stupid monkeys if they talk about virtual particles.
MWI proponents may "feel" ;) various things but science is not about feelings and the contradiction is there.
It's not true at all that this multiworld fantasy is a "literal interpretation" of the wave function. It's a wrong interpretation designed as crutches for the stupid people but it has nothing to do with the right probabilistic interpretation and indeed, it contradicts it.
As always, the key point of MWI that makes it incompatible with the real world  and with quantum mechanics  is the idea that there objectively exists some classical information that is independent of the observers and observations. This ain't the case.
Sensible people call about virtual particles but they understand that they are not real physical particles. They're mathematical constructs contributing to probability amplitudes for processes involving real particles. But the point of the many worlds is different. It's the very point of MWI that those worlds are "real" in the classical sense, and this assumption may be shown and has been shown to contradict observations. If you're not getting it, you *are* a stupid ape.
You write:
"But the statement "an electron exists in the region of slit A *and* an electron exists in the region of slit B" is just wrong (...) It's a pointlike particle, there is only one electron (by charge conservation etc.), and it can't be in both slits at the same moment."
But what about deBroigle's waves of matter? An electron can be described as a wave, and waves are certainly not just single points of space. All kinds of waves occuppy a region of space, so a wave can be in both slit A and B at the same time (just like Russia lays in both Europe and Asia, because it's not a point but an area) and there's nothing wrong with it.
It's obvious in the case of double slit experiments performed with waves of water, for many people it's obvoius in the case of light, and I think there is no reason to think different in the case of electrons.
Dear Kmut,
one could say that it was the very main purpose of this statement of mine to emphasize that the electron is *not* a classical wave. Prince de Broglie misunderstood those things much like you do, even after 1924 when he proposed his wave, which is why throwing his name around can't turn your invalid statements into valid ones.
A classical water wave goes through both slits  one may detect "something" by an appropriate detector in both of them. But when an electron goes through the pair of slits, there is *nothing* that could ever be detected in both slits simultaneously. If you use a detector of any kind, call it a detector of waves, particles, disturbances, spirits, whatever, and if these detectors only operate in the regions around the two respective slits, they will never beep simultaneously.
Also, the electron, unlike a classical wave, will always create a single point at the photographic plate.
It's just not true that "there is nothing wrong with electron's being a classical wave". There's a lot of wrong things. A whopping 50% of statements one can make about waves are plain untrue about the electron. Just to be sure, many laymen don't get it: one wrong thing would invalidate your claim. But there are lots of waves to invalidate it, it's just wrong.
A classical wave may be a method to think about the behavior of an electron or a quantum particle in some respects but it's surely not a valid model for all of its behavior. An electron is not a classical wave and the wave function isn't a classical wave, either.
LM
Dear Lubos
I really didnt want to make any ad hominem arguments. It certainly wasn't my purspose.
I'm not a physicist but a person who would like to become one in the future, so my knowledge in this area is basic, especially when compared to yours.
But you must know that it inst an unusual way for the people who teach QM to look on this problem from a differend side than you do.
You say that electrons aren't classical waves because they cannot be measured in a classical way.
But there are people who say that electrons are like classical waves because the Dirac equation, and more basic Schroedinger one describe a classical i.e. deterministic and unique time evolution so the real difference is in the act od measurement.
In the quantum world the measurement is more "drastic" than in classical one. To observe waves on water we only need some light with energy too small to change the pattern in statistically significant way. But in quantum world energy of a wave we need to measure position of the electron is enough big to interfere with it.
I've read recently some words by Wojciech Zurek, and I had an impression that he understads QM in in similar way stating that macroscopic objects are all quantum and the reason for which they dont behave like waves and for which they have unique lociaction, is that they're not enough separated from the environment, which is responsible for all this huge amount of interactions that forbid the macroscopic objects to behave like waves.
Isnt this view just dual to yours? And how can one interprete interfference patternw in double slit experiment with electrons? If electron is pointlike poarticle then what forbids it to behave like classical pointlike particle and forces it to change its momentum?
Is there any book particular where I could find all the answers to theese questions?
Thank you in advance
"But there are people who say that electrons are like classical waves..."
There are many people who say many dumb things and indeed, it's the main purpose of all these blog entries of mine to correct the widespread misconceptions. It's disappointing if you don't appreciate it and it's surprising that you seem to read this blog anyway even though the correction of stupidities said by people, especially if it is many people, is selfevidently the defining driver behind this blog.
The wave functions evolve according to analogous "deterministic" equations as classical fields and waves but their physical interpretation is completely different so the "determinism" of Schrödinger's equation – or the Dirac equation promoted to a quantum equation for an actual system – does *not* translate to classical determinism of the real world which simply doesn't hold.
Interesting post but it appears you don't understand many worlds.
Take your example of an electron in 0.6up> + 0.8down>.
You wouldn't argue that there are "two" electrons there, that there is an electron with spin "up" as well as an electron with spin "down"? Of course not.
Now lets say that electron interacts with an electron that is 1.0up>.
The joint state would be 0.6up>up> + 0.8up>down>.
Similarly, here you wouldn't argue that there are some how four electrons? Of course not.
Now lets say go back to the sterngerlach experiment.
All many worlds says is that if we don't introduce something new to quantum mechanics, scientists and measuring devices are also particles, so if they interact with a spin 1/2 particle:
0.60up> + 0.80down>.
The end state is:
0.60scientist sees up>up> + 0.80scientist sees down>down>.
And like before, there aren't two electrons, and there aren't two scientists. And no scientist is every going to see an electron up and an electron down. And this doesn't violate conservation of charge any more than 0.60up> + 0.80down> does.
That is many worlds.
Sorry, the application of quantum mechanics to arbitrary systems is what conventional orthodox quantum mechanics is all about. It was the Copenhagen school that began to study molecules, metals etc. etc. using quantum mechanics. It is a complete lie that proper quantum mechanics has ever been claimed not to apply to arbitrarily big systems.
If you don't have any two electrons (in total) representing one, you can't call it many worlds because it clearly has nothing to do with many worlds. There aren't many worlds if there is only one.
Unfortunately we do not get to decide what people call things. I agree many worlds is misleading name.
You are right to claim that anyone who believes in what you call "many worlds" is a stupid monkey.
Unfortunately the people who profess in many worlds would not agree that what you call "many worlds" is what they believe. As such when in discussions with those people your post is of little use to me which is disappointing.
Dear James, science is about learning objective laws while being disappointed also depends on your subjective feelings and preferences.
So your being diisappointed, howevever I might prefer another outcome, doesn't imply that there is an iota of inaccuracy in what I wrote.
You may use the phrase "many worlds" in any way you want, for example for "one world", you may twist the terminology in any way you invent, but you won't change anything about the fact that there's no viable modification of quantum mechanics, a theory that was first fully defined by the physicists who were meeting in Copenhagen and no one else.
You are really misinformed here, and you're stubbornness by calling other people monkeys shows that you are not open to the real ideas MWI proponents have.
Since you are considering an isolated electron, first consider a state vector describing an observer measuring the electron. Then we see that
observer neutral x measuring system > observer measures up x electron spin up + observer measures down x electron spin down.
Now what MWI adherents do is realistically interpret the resultant wave function and thus there must be two different equally real worlds. Now why exactly some worlds are more probable than others is a difficult question, but it is no more difficult then the question why probabilities arise in the Copenhagen interpretation. Probabilities can be interpreted as the probability of being in a certain branch.
You're example is wrong because 1. you consider an isolated system without the observer. Decoherence shows us that a superposition of the electron will quickly get entangled with the observer. 2. you seem to be using the projection postulate in the sence of the Copenhagen interpretation that it gives the probability of the electron being in a state up or down. But in the MWI sence the probabilities can be seen as giving the probability of the observer being in a world in which up or a world in which down is measured. Surely being in both worlds (P_A * P_B) has probability zero, but that doesn't imply the MWI is false.
Furthermore, charge and energy conservation are always derived in a single universe framework. And the MWI is pretty much consistent with this, as it can be shown that these quantities are in fact conserved within a single universe. So an observer will do measurements that are in correspondence with the conservation of these quantities.
I think many people here have pointed out your fallacies but you keep on calling them monkeys. Though I myself am not yet convinced that MWI is the key to all our questions about QM, I am convinced that you do not understand the MWI debate correctly.
In the same arguement how can you dismiss manyworlds theory without testing it ? Shot down by your own logic....
jesus christ you are pretentious. the most amusing bit of this whole "proof" is your tendancy to cobble together a mishmash of different forms of math. you prepare an algebraic proof, and then try to convince us that your "proof" invalidated MWI by using binary operations (AND, OR, etc). clearly, as stated below in a more polite manner, you do not understand the fundamentals of what you are trying to discuss.
Interesting & I'm sympathetic but think the quick response would be to say that probabilities only come into play when superposition collapses. So the probabilities are only relevant when it comes to 'discovering which world you are in'. There isn't a specific world where someone would meet both outcomes at once.
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