Ghirardi, Rimini, Weber: a collapsed pseudoscience

Many people are incapable of understanding that the experimental as well as theoretical evidence shows that quantum mechanics is right.

They can't see or don't want to see that the world is described by state vectors that inevitably have a probabilistic interpretation, that evolve according to linear equations and satisfy the superposition principle, that all measurable properties of the physical systems are described by linear Hermitian operators, and that probabilities are the only predictable things that always arise from squared magnitudes of some complex probability amplitudes.



Various people who dream about the resuscitation of classical physics and a reversal of the last 85 years of physics have done pretty much all the conceivable mistakes and have proposed lots of diverse, deluded, and fundamentally flawed schemes whose only purpose is to hide the most important insight of the 20th century science, the framework of quantum mechanics, from the authors' eyesight.




Bohmian pseudoscience

I have spent lots of time with explaining why various major frameworks designed to deny quantum mechanics are deeply flawed. The de Broglie-Bohm pilot wave theory claims that there exist both particles and waves. The waves are guiding the motion of particles in a manifestly non-local, non-relativistic way (when there are at least two particles). There are other aspects that make it incompatible with relativity and quantum field theory - e.g. its impossible coherent description of the spin and quantum fields.

But much more generally, what is flawed about the approach is that it is imagining that there are some "preferred" observables - usually positions - that have well-defined values at a given moment (a particle is really there) while other observables such as the spin with respect to an axis are "not real" because there's no way how to describe them consistently in the Bohmian framework - and moreover, the authors of the scheme must kind of understand that different observables don't commute with each other in the proper physics, so it is fundamentally misguided to try to define all of them at a given moment.

This separation of observables to the real "primitive" observables or beables and the "contextual" or unreal ones that still have to obey quantum mechanics in some sense is completely spurious and artificial. As a result, the approach totally disagrees with the insights about decoherence. Decoherence shows that the physical quantities that "behave approximately classically" after some time in a given environment are fully determined by the Hamiltonian, by the dynamical laws of the theory. There's absolutely no freedom for you to pre-decide which quantities should behave classically (or be "primitive") and which observables shouldn't (and remain "contextual") because the Hamiltonian has the responsibility for this decision: see TRF.

Decoherence really kills the very basic pillars of the de Broglie-Bohm paradigm and I am amazed that some people still haven't noticed.

Everetian pseudoscience

Recently, I have also discussed the many worlds pseudoscience initiated by Hugh Everett III. In that picture, one is imagining that the other alternative outcomes of the experiments are "real worlds somewhere". Except that this picture, while it depends on the real existence of "other worlds", can't provide us with any mechanism how and when the worlds really split so that the possibility of a later interference is not destroyed. (And 0.1 microns is already too long a distance for a good "classical description" - because even distances 10^{-15} meters are known to behave perfectly classically, so GRW really don't solve what they wanted solve.)

Also, this picture can't really give any interpretation to the main set of numbers that every quantum mechanical theory is all about - the probability amplitudes - because the different alternatives are "equally real worlds". Again, it is strikingly obvious that the whole paradigm is incorrect because there is never any exact "splitting of the worlds". Different histories or different outcomes of a measurement only become "mutually exclusive" in the classical sense because of decoherence which is never quite complete. Classical physics only emerges in a limit and always stays approximate - and this is also true for the strict classical logic and classical probability theory that emerge from another approximate description of a phenomenon in terms of decoherence. The world fundamentally remains quantum mechanical.

In principle, there's always some possibility for different terms in the state vector to interfere with each other at some later moment. This possibility is just becoming very unlikely because the off-diagonal elements of the density matrix for observable degrees of freedom expo-exponentially rapidly converge to zero. But it's fundamentally flawed to imagine that there is any moment in which the different outcomes have been objectively and "strictly split".

Ghirardi, Rimini, Weber: a real collapse

But I want to discuss another approach that hasn't been described on this blog yet: the GRW approach. The basic 1986 paper in PRD has 1217 citations as of today which is just gigantic if you realize that the paper is complete crackpottery:

Unified dynamics for microscopic and macroscopic systems (PDF full)

Much like in the other anti-quantum approaches, this approach is trying to make some "classical reality". Unlike the Bohmian pseudoscience, it doesn't add any sharp positions of the particles. Instead, it keeps Schrödinger's equation only and adds some nonlinear "flashes" into the evolution that are meant to squeeze the state vector in the mantinels that the authors consider "appropriate".

It's very easy to describe what their proposal is - even though you may have a hard time to extract this basic point from the dozens of useless pages of the paper above. Imagine Schrödinger's equation for N non-relativistic particles - like the Bohmian pseudoscience, the formalism is linked to particles of the non-relativistic type, so all attempts to apply it to fields are inevitably awkward.

It is evolving according to Schrödinger's equation but GRW don't like that it's spreading because they want to imagine that the wave function is a "real object" and "real macroscopic objects" are not spreading - a classical misinterpretation of the wave function by all the anti-quantum "thinkers". Well, it obviously is spreading and there are many outcomes that have various probabilities - which doesn't hurt - but GRW just don't like it. So they decide that the wave function shouldn't freely spread! How do they ban the spreading? Well, that's easy for GRW.

They say that every 10^{15} seconds, which is a randomly chosen new bureaucratic constant of Nature (whose value is of course completely fabricated and has nothing to do with any justifiable laws of physics or any observations) each particle is obliged to prove to the census officials that it has a rather well-defined location. So there is a Poisson process running for each particle that once per 10^{15} seconds in average, it says "flash" to each particle. The more particles you have, the more flashes you obtain.

Each flash is associated with a particle label "J" - pretend that the particles are distinguishable. The flash is also characterized by a position in the real space, R = (x,y,z). What does the flash do? It changes the wave function discontinuously. How? The wave function Psi(r1,r2, ... rn,t-epsilon) before the flash is changed to a new

# Psi(r1,r2, ... rn) exp(-(rJ - R)²/2a²)

The factor # is chosen to preserve the normalization of the wave function - you surely know how to calculate it as the square root of an integral to guarantee that the new wave function is normalized if the old one is. The whole Gaussian profile is randomly invented. Different functions would produce different theories. Clearly, there's not a glimpse of a justification for a particular function.

The flash is associated with the point in space, R. You see that the wave function for the J-th particle is modified so that the J-th particle will suddenly be more concentrated around the point R (while its finer patterns remain unchanged - it just eliminates the portions of the wave function that is too far from R). You don't want the particles to jump to random locations, so R is chosen randomly from the distribution that coincides with the probability distribution for the J-th particle before the flash - the integral of Psi*Psi over all the other particles' positions.

So it's more likely for the position of the J-th particle to collapse to the place where its wave function is concentrated. Needless to say, the distance parameter "a" is another awkward unjustified bureaucratic dumb parameter that the GRW theory needs to add.

So you see that these particular "physicists" are obsessed with the idea that quantum mechanics, including the superposition principle and the freedom of wave functions to spread freely, has to be bureaucratically suppressed, so they invent a random time scale 10^{15} seconds and a random new width of a wave function for a particle, 0.1 microns, that force individual particles to keep a rather well-defined citizenship. Every 10^{15} seconds, each particle has to undergo a census in which it has to fill its position with the accuracy of 0.1 microns. Because the relative positions between particles are kind of constrained in the bound states, a flash acting on a single particle affects other particles that share a macroscopic object with the flashed particle - so all of them become "localized".

Now, this doubly artificial prescription - depending on two new and totally unphysical bogus parameters (the only genuinely universal parameter that decides about the validity of the classical approximation to quantum mechanics is hbar!) - may seemingly have the "right impact" that makes the world "look like" it does in the proper quantum mechanics. Morever, we've added some perturbation to the system. Does it hurt?

Of course, the bureaucratic values of the timing and the width of the the collapsed packet are chosen to express the feelings of the authors about "what is microscopic" and "what is macroscopic". The collapse is meant to make large objects behave classically. Only if you have 10^{15} particles or more - a macroscopic object - you get a collapse every second. But doesn't it hurt the quantum properties of the objects?

You bet. While the "accuracy of the citizenship" is chosen to be 0.1 microns - which is very high relatively to the size of the atom - it is still vastly smaller than the distance scales at which real particles in the real world may be delocalized according to the wave functions. The latter is, of course, infinite. There is no limit. Particles may have delocalized wave functions. It's a basic point of quantum mechanics.

Consider a large crystal or metal, e.g. a cube whose side is 10 meters. You can buy those. It's 1,000 cubic meters and the weight could be almost 10^7 kilograms or 10,000 tons. Now, does the squeezing of the wave functions of the electrons affect them in a measurable way? You bet.

The linear size is 10 meters which is 10^{11} times the atomic radius. So there are about 10^{33} atoms in it so that 10^{33-15} = 10^{18} flashes appear each second. Obviously, the census officials will keep the position of the crystal "classical". But will they also preserve the internal integrity of this bound state of many nuclei and electrons?

If an electron has a wavelength that is longer than those GRW 10^{-7} meters, then the flash will substantially change its energy. It means that the electron's wave number "k" should be smaller than 10^{7} inverse meters. The spacing of "k" in each direction is 0.1 inverse meters (the inverse size of the crystal), so there are 10^{8} possible values of "kx" as well as "ky" and "kz" for which the electron has a lower energy before the flash. Consequently, there are 10^{24} electrons in our crystal that satisfy the condition. Each 10^{24-15} = 10^{-9} seconds (one nanosecond), the GRW flash will substantially kick an electron so that it has a very different energy.

Similar "flashes" will also destroy the coherence of laser beams (which may have much more than 10^{15} photons that are coherent at distances much longer than 0.1 microns) and do many other nasty things. Every time you have a flash, you really shift the position of the whole system by 0.1 microns. Do you think it couldn't be seen? Don't be silly. Interferometers may measure positions of their arms with the accuracy of 10^{-15} meters or so.

Now, you may try to observe those "predictions" and be sure, you will never see any of these pathological GRW effects because they're just completely unsubstantiated violations of basic principles of quantum physics such as the superposition principle. You may try to slow down the frequency of the flashes or make the post-flash packets wider, so that the predicted pathological effects of the GRW flashes are diminished. And indeed, when you do so, you will restore quantum mechanics in the ultimate limit because the GRW additions will become inconsequential.

If you go to the limit, i.e. if you send the GRW time scale to infinity and/or you send the GRW distance scale to infinity, will you get a valid theory that agrees with the observations of microscopic as well as macroscopic objects in the real world? You bet. In the limit I described, you obtain proper quantum mechanics and you can be damn sure that the predictions of unmutated untwisted unmessed-up-with quantum mechanics agree with the observed behavior of all systems in the world, despite the attempts of anti-quantum zealots to claim otherwise. They surely agree with the behavior of the microscopic objects - that's what GRW agreed with which is why they chose quantum mechanics as their starting point. But quantum mechanics also agrees with the behavior of the large objects: in particular, it predicts that one will never observe a large object "at two points simultaneously". The sign "+" in the wave function or density matrix doesn't mean "AND": it means "OR". If you want a symbol for "AND", you need "x", multiplication.

Quantum mechanics works perfectly well for any kind of objects which is the first thing that people should try to understand before they start to spend years with completely unjustifiable and thoroughly idiotic attempts to mess up with quantum mechanics.

Don't mess up with quantum mechanics.

And that's the memo.

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By the way, I had to write this rant because I had to go through the end notes of The Hidden Reality supplementing the chapter on quantum mechanics. I am pretty much sure that all other popular books on quantum mechanics look similar if not worse but it just drives me up the wall! Pretty much every sentence is fundamentally wrong, usually upside down. Ten years ago, I wouldn't believe that I could say anything like that about the author's text on quantum mechanics.

Density matrix and its classical counterpart

I decided that a reason contributing to the people's misunderstanding of the meaning and validity of quantum mechanics is the prevailing focus on Schrödinger's equation as the basic dynamical law.



Felix Bloch (picture) is, together with Lev Landau and perhaps also John von Neumann, credited with the 1927 discovery or invention of the density matrix.

This equation helps to mislead the people into thinking that the wave function is analogous to a classical wave - an electromagnetic wave, for example. In fact, Erwin Schrödinger himself has never quite understood the meaning of his own wave function.

In my current opinion, each of the three alternative dynamical equations

• equation for the density matrix
• Heisenberg equations for the operators
• Feynman's path integral

is more pedagogical when it comes to the understanding of the actual relationship between quantum mechanics and classical physics. In this text, I will give an overview of such an equation focusing on the density matrix. In particular, I will formulate a new interpretation of quantum mechanics that will allow moderate anti-quantum zealots to collapse the wave function whenever they like, in some sense. ;-)




However, first, let me note that Schrödinger is getting way too much credit while Heisenberg who should be credited for dynamics is being screwed. Schrödinger found his equation in 1926. Heisenberg found his equations, that were later shown equivalent to Schrödinger's picture by Dirac, in 1925. So Heisenberg was earlier.

Moreover, Heisenberg understood what quantum mechanics meant, unlike Schrödinger. Clearly, people talk about Schrödinger's equation because they are able to understand a partial differential equation - not too different from Maxwell's equations, right? - they actively want to mislead themselves into thinking that the wave function is a classical wave of a sort. It's not.

Heisenberg's equations for the operator are more direct a quantum counterpart of Newton's equations of motion. In this picture, the only novelty are the nonzero commutators between the observables - the Heisenberg uncertainty principle etc.

Classical phase space

Fine. Let me now return to the topic I promised in the title - the density-matrix-centered interpretation of the classical-quantum relationship.

We may formulate classical mechanics by the differential equations for x(t), p(t), or whatever degrees of freedom we have. They obey Newton's equations or their generalizations for other degrees of freedom such as Maxwell's equations, and so on. I hope you're still with me.

But in reality, we can't know all these observables with complete accuracy and certainty. Measurements of positions and velocities have nonzero error margins; the detailed motion of molecules in some gas is chaotic and we don't know it; the evolution brings a lot of extra uncertainty. The uncertainty grows bigger.

For all those and other reasons, it's more realistic to assume that even in classical physics, we don't know the exact x(t), p(t). Instead, we know some probability distribution on the phase space (the space of all initial states, or states defining where the system is at any moment):

rho(x,p)

In this text, x and p will be shortcuts for many coordinates on the phase space. The interpretation of the phase space probability distribution is that

dP = rho(x_i,p_i) d^Nx d^Np, i = 1...N

is the infinitesimal probability dP that the system is found around the point given by the x and p coordinates, within a small hypercube of volume given by the measure factor. OK?

Of course, if we know how x and p would evolve, we may also determine how the probability distribution would evolve. It would evolve according to Liouville's equation for the Hamiltonian system. It can be written as

∂ rho / ∂t = {H,rho}

where the curly brackets are the Poisson brackets. You will find everything on that Wikipedia page if you need to refresh your memory.

Now, I want to emphasize that in theory, the description by rho also contains the case in which x,p are known accurately and with certainty: in that case, rho is a delta function located on the point x(t), p(t) of the phase space. In classical physics, a strictly sharp delta-function will remain strictly sharp. Its location is moving as a function of t just like x,p would.

However, the more general, "widely spread" form of rho is much more realistic and universal in its applications. Even when it's spread, in classical physics, you could always imagine that there existed an actual x(t), p(t) at each moment - you just didn't know what it was. However, this thesis has several problems: you can't really prove it because classical physics that uses rho(x,p) as the fundamental object, and encourages you to calculate the probabilities from it, is totally consistent as well.

Moreover, you can't learn anything - make any new predictions or explanations - out of the purely ideological opinion that sharp values of x(t), p(t) existed - if you don't actually know what those x(t), p(t) exactly were. So the idea that a sharp x(t), p(t) exists in classical physics is pure philosophy - there is no physics behind it. This assumption isn't needed for physics to work (physics is consistent with its negation as well); and it's not useful to learn anything (which is why the physical laws without this assumption of "realism" are complete according to any operational definition of the word "complete").

Quantum mechanics: density matrix

Now, the object rho(x,p) is replaced by an operator rho in quantum mechanics. You may write a general operator acting on your quantum mechanical space as a function of x,p - the "generating" operators of your Hilbert space that know about all your degrees of freedom. If you worked with spins, you would have to add spins; if you worked with field theory, you would have to put the fields instead, and so on.

It's obvious how the classical Liouville equation for rho(x,p) is generalized in quantum mechanics: the Poisson bracket is simply replaced by the commutator with the right normalization. The equation for the operator rho becomes:

iħ ∂ rho / ∂t = [H,rho] := H rho - rho H

This is easily obtained from Schrödinger equation for psi if you substitute

rho = |psi> <psi|

and use the Leibniz rule for the derivative of the product, the ordinary Schrödinger equation for psi, and the complex conjugate Schrödinger equation for the bra-vector psi*. In general, rho is a combination of such products, as we will mention, but the equation is linear so the equation works for the combinations as well.

If you think about it for a while, we have made a truly minimalistic change, indeed. In classical physics, the probabilities of different states were given by rho(x,p) which was a function of c-numbers x,p, the coordinates on the phase space. In quantum mechanics, rho is still a general operator, but it's a function of the operators x,p that don't commute with each other. But you may still imagine particular functional prescriptions for rho such as

rho = exp(-(x-x0)² - (p-p0)²)

which is a packet concentrated near x0,p0. Of course, three constants should be added in front of the exponential (to make it normalized) as well as both terms in the exponent (to determine the width and obey the dimensional analysis). But I want to keep the formulae simple and comprehensible. It's important to realize that the definition of rho could work for operators rho,x,p, too. In some sense, the number of operators on the Hilbert space is equal to the number of functions on the classical phase space - there exist natural one-to-one maps based on various "orderings" of the operators.

The trace of rho is equal to one - it's the total probability. This is the quantum counterpart of the fact that the integral of rho(x,p) over the phase space is one. The corresponding equations - Liouville's equation and the rho-Schrödinger equation - preserve this normalization of rho.

The difference between the classical and quantum dynamical equations is just hidden in the fact that rho,x,p are operators in quantum theory and they generally don't commute with each other. But otherwise, the interpretation from classical physics may be pretty much directly extended to the quantum theory!

In particular, just like the values of rho(x,p) determine the probabilities as we announced in the definition of rho at the beginning, the operator rho in quantum mechanics determines the probabilities of any states. How does it work?

Well, if you pick a particular state in the Hilbert space, it has a well-defined probability if it's an eigenstate of the density matrix. This is an unusual operation that's not usually talked about - because the density matrix isn't an "observable" in the usual sense - like positions or momenta etc. But it's still an operator on the Hilbert space. I will formality treat the density matrix rho as the "operator for the probability".

Pure states

Imagine that you have a pure state psi. In that case, the density matrix rho is just the tensor product psi.psi* we wrote some time ago. Can you say what is the probability that the system described by this rho is finding itself in a particular state of the Hilbert space such as chi?

Yes, but using the analogy between observables and density matrix, you can say such a thing only if chi is an eigenstate of rho. When is chi an eigenstate of the "tensor square" psi.psi*? Well, it's easy. It is if chi is either proportional to psi, or it's orthogonal to psi. In the former case, the eigenvalue of rho is 1 (Yes) and in the latter case, the eigenvalue of rho is 0 (No).

It's this simple. Of course, it's not hard to see that the eigenvalues of rho=psi.psi* are (1,0,0,0,0...). Just choose am orthonormal basis of the Hilbert space whose first basis vector is psi itself.

So I would like you to adopt the following restricted description: you can only "sharply" say what is the probability that the state described by psi - or by rho = psi.psi* - is finding itself in the state chi either if psi,chi are proportional to each other, in which case the probability is 100%, or if they're orthogonal, in which case the probability is 0%. No other linear superpositions have well-defined probabilities because they're not eigenvalues of rho.

This is different from the conventional treatment that talks about probabilities for any state to be in any other state. But what this conventional treatment really means is the "expectation value of the probability", chi*.rho.chi, or |(psi*.chi)|^2. However, because chi is not an eigenstate of rho for a general chi, you shouldn't say that the probability is sharply defined! ;-)

You may also allow a collapse of the wave function onto any of the eigenvectors of such a rho. Why? Because it doesn't do anything at all! ;-) The state psi or its density matrix rho = psi.psi* may collapse into some eigenstates chi of rho with the prescribed probabilities (the eigenvalues of rho in those states). The probabilities are 100% for chi = psi (up to a normalization) and 0% for the orthogonal choices. So the state psi will collapse to psi with probability 100% and nothing changes!

The collapse to the orthogonal vector has a vanishing probability and the collapse to generic linear superposition isn't allowed because they are not eigenstates of the "probability operator" rho, the density matrix.

Decoherence

Now, in general, you don't want rho to describe a pure state psi. In general, rho is a combination of the type

rho = sum_i=1...N p_i |psi_i> < psi_i|

where the states psi_i don't have to be orthogonal but the density matrix is still required to have its trace equal to one. In general, the density matrix is still a Hermitian operator. It follows that it can be diagonalized.

Now, the eigenvalues of rho pick a privileged basis of states that have well-defined probabilities - it's the corresponding eigenvalues of rho - and they can be measured. In fact, you may always imagine that at any moment t, someone in the Heavens or elsewhere "made" rho collapse so that it was reduced to the form chi.chi* where chi is an eigenvector of rho before the collapse. The probability that the collapse picked a particular rho is the corresponding eigenvalue of rho in this state chi.

Most people including many physics PhDs are obsessed with the collapse and because they find the spreading wave function too complicated while their brains are inadequate to deal with quantum mechanics, they're impatiently waiting for the right to make the wave function collapse, referring to their consciousness as the ultimate justification of this right to finally kill the spreading wave function. They're also interested in the other creatures who have consciousness and the same glorious rights to collapse "waves" as they do. ;-)

I have good news for you! You're allowed to make the the density matrix rho, the generalized state vector, collapse at any moment you wish, without compromising the predictions (e.g. without destroying any interference) whatsoever! The only condition is that you must collapse it to one of the eigenstates of rho at the moment, and the probability imagined by you that the collapse took you to a particular eigenstate chi of the matrix rho has to be given by the eigenvalue of rho in chi.

Isn't it great? This erases all your psychological problems with subjectivity etc. In fact, all "realist" observers may agree that the collapse is taking place all the time. (Well, because of relativity, "at a given moment" will still mean different things for differently moving observers, but staunch "realists" don't care about relativity much.)

In practice, this may fail to satisfy the emotions of the staunchest anti-quantum zealots. Why? Well, we have already mentioned one reason. If you study the evolution of a pure quantum system that is remaining pure and coherent, the eigenvalues of rho remain (0,0,0...., 0,1,0,. ...0,0,0), which means that the collapse doesn't do anything. You're never allowed to collapse into a wrong basis - a pure state may only be collapsed onto itself. So the wave function continues to spread as time goes - the genuine anti-quantum zealots won't like it.

Even if rho has many nonzero eigenstates, they're not necessarily the states that are easy to imagine for the anti-quantum zealots - the eigenstates of rho are typically different than the "intuitively natural" (wrong) states into which the anti-quantum zealots would like to collapse things.

However, if you describe a subsystem by its density matrix that has been traced over the other, environmental degrees of freedom, decoherence guarantees that rho for this system will have many nonzero entries. The corresponding eigenstates of rho will be close to some intuitively "classical" states and in that case, the collapse does something nontrivial.

Collapse is just in your mind

I have formulated my interpretatino of quantum mechanics as allowing you to collapse rho into one of its eigenstates, with probabilities given by the corresponding eigenvalues of rho. The essential property of this rule is that if you insert these collapses with a random outcome obeying this rule to arbitrary moments of your time, your predictions won't change at all.

So the collapse is completely subjective.

In the past, you could have thought that when I say that the collapse is just a subjective change of knowledge, it was a philosophical assumption. However, in this case, it is actually a provable theorem! What I mean is that when you insert the collapse of rho onto the rho eigenstates as described above, you will get identical predictions for anything you calculate. Why?

Well, it's simple. When you decompose rho into the eigenstates

rho = sum_i=1...N p_i |psi_i> < psi_i|

but in this case, you require that you use the right basis of rho eigenstates (which always exist) psi_i, each of the terms will be evolving independently and the different states psi_i which are orthogonal at the beginning will stay orthogonal in the future as well, because of the unitarity of the evolution.

So if you later, at time T, make a measurement of something, which means that you decompose rho(T) into the eigenstates according to the same formula as the last displayed one, and you will ask about the probabilities of different outcomes, it's clear that each individual term in the decomposition of rho(T) has to come from at most one term in the decomposition of rho(t).

To calculate the probability, you will only need p_i extracted from rho(t) while all the other terms will contribute nothing to this evolution and you may forget them. So it doesn't matter whether you will calculate the particular probability of an outcome encoded in the decomposition of rho(T) from the full evolution, or whether you insert the imagined collapse at time t; in both cases, the evolution up to the time t will just add a factor p_i from the decomposition of rho(t).

The density matrix rho is gaining an ever larger number of nonzero eigenvalues - you may view this process, resulting from decoherence (=the loss of a realistic chance of different outcomes to interfere with each other in the future, i.e. the loss of the information about the relative phase of their amplitudes), as the "splitting of the many worlds". However, it's very clear that you only have one world in the prescription above.

Moreover, the very point of this proof was just the opposite - to show that the collapse, when properly defined, is completely subjective and has no detectable consequences. I guess that MWI bigots want to use some related thinking exactly for the opposite cause - to claim that there objectively exist some thing that don't objectively exist.

In this picture, the procedures used to obtain predictions from quantum mechanics are pretty much identical to the predictions obtained from the classical phase space distribution function in classical physics. The only thing is that things including rho are operators and they only have well-defined quantities (such as probabilities in the case of rho) when acting on their eigenstates. The operators don't commute.

Collapse to a bigger subspace

In the text above, the possibility of a nontrivial collapse was only possible because we were tracing over the environment, thus obtaining a density matrix with an increasing number of independent eigenstates with nonzero eigenvalues.

Can we do it without this tracing over? Yes. In this case, the density matrix will stay pure if it was pure. As discussed above, a collapse to a pure state is not doing anything. Instead, you may consider a collapse to a set of projection operators P_1...P_K that sum to one.

Analogously to the collapse into a pure state, a collapse into projectors may be freely inserted at any moment whenever all the operators P_1...P_K are chosen to commute with the density matrix rho. If that's so, you may imagine that after the collapse, the density matrix becomes rho.P_j = P_j.rho with probability - well, whatever the normalization of the "reduced magnitude" density matrix has to be divided by to normalize it again.

The relationship between the projection operator and pure states that would appear in the "pure collapse" in the previous formalism may be imagined so that e.g. the projection operator is the projection operator on all microstates with a fixed state of the observer system and any state of what we used to call the environment.

Again, in this case, one may show that such a collapse - describing a measurement of "a subset of degrees of freedom" - will have no impact on future predictions; it is a purely subjective trick.

Needless to say, when I get to this formulation based on projectors that sum up to one, I am "almost" formulating quantum mechanics via the "consistent histories" approach. It's almost the same thing at this moment. Except that I am using a simpler and more explicit rule for the consistency - vanishing of the commutator between the projection operators and the density matrix rho. Note that the eigenvalues of rho which survive the collapse don't have to be equal to each other - the only condition is that you're collapsing onto a subspace of the Hilbert space spanned by rho eigenstates.

Every observer also has the right to use projection operators whose commutator [P_i,rho] is not exactly zero but a small nonzero number. In that case, he will introduce errors and inconsistencies and it's up to her what is tolerable. That's analogous to small violations of the "consistency condition" in the usual consistent histories approach.

Copenhagen interpretation of quantum mechanics

I have considered myself a champion of the Consistent Histories interpretation of quantum mechanics for almost 20 years - Roland Omnes' 1992 article just erased all my doubts about the statement that the foundations of quantum mechanics have been fully understood.

However, I have always realized that the "improvements" that this interpretation brings relatively to the Copenhagen interpretation are very subtle and it has been annoying to see that pretty much everyone misunderstands the basic points of the Copenhagen interpretation.



Bohr, Heisenberg, and Pauli. Am I the only one who thinks that Pauli looks like good soldier Švejk here?

There's a lot of misunderstandings being spread about the Copenhagen interpretation - and I would say that some of them should better be classified as deliberately propagated lies and propaganda. In this text, I would like to clarify some of them.




People in Copenhagen

First, let's ask which people are "fathers" of the Copenhagen interpretation. Well, the name indicates that they have something to do with the Danish capital. Clearly, we mean Niels Bohr - a natural leader of the group - and the people who worked with him and/or visited him in Copenhagen in the mid 1920s - especially Werner Heisenberg.

Max Born is of course a key co-author of the Copenhagen interpretation - after all, he supplied the probabilistic interpretation and received a Nobel prize for that. Wolfgang Pauli has also spent some time over there and he would also sign to the principles of the Copenhagen interpretation. The number of top physicists who may be considered parts of the Copenhagen school of thought is much larger - although some of them worked on topics that were further from the "foundations". Let me mention Lise Meitner and Carl Friedrich von Weizsäcker as two "nuclear" examples. I am also confident that people such as Paul Dirac would essentially subscribe to the Copenhagen interpretation.

There was no fundamental disagreement about the meaning of quantum mechanics among those people. Obviously, many other people such as Albert Einstein, Erwin Schrödinger, or Louis de Broglie didn't ever accept the Copenhagen interpretation but they didn't have any alternative. The Copenhagen interpretation works well and we don't need another hero.



Gabriela Gunčíková - Tina Turner: We Don't Need Another Hero. Czech Slovak Superstar II. Yes, all Czech girls and women between 17 and 71 years of age look just like her.

Subjectivity of the wave function

The first major confusion - or propagandistic distortion - is linked to the interpretation of the wave function. The Copenhagen folks were very carefully applying positivism. That means that they refused to talk about properties of physical systems that can't be measured unless some observations or consistency of the predictions make it necessary to talk about them - which is an attitude that became essential with the birth of quantum mechanics. In this sense, they uniformly rejected the assumption of "realism". If the observations are described by a framework that doesn't contain any "real and objective" things or properties before the measurement but if the measurement may be predicted, then it is how the things should be.

Lots of fringe stuff, garbage, and crackpottery was later written by various people who weren't really part of the Copenhagen school of thought but who found it convenient to abuse the famous brand. That's why one can also hear that the Copenhagen school may (or even must) interpret the wave function as a real wave that collapses much like a skyscraper when it's hit by an aircraft on 9/11.

But nothing like that has ever been a part of the Copenhagen school of thought. If you open any complete enough description of the Copenhagen interpretation or if you look at Bohr's or Heisenberg's own texts, you will invariably see something like the following six principles:

1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)

Note that the very first point says that the wave function is a collection of numbers describing subjective knowledge. That doesn't mean that in practice, everything will be always subjective - or whatever the spiritual people have attributed to quantum mechanics. Of course that constant interactions between parts of the world - and different people - pretty much guarantee that they have to agree about many "objective properties". But as a matter of principle, this rule is important for quantum mechanics and Werner Heisenberg has never left any doubts that this is how one had to interpret it.

Heisenberg would often describe his interpretation of the wave function using a story about a guy who fled the city and we don't know where he is but when they tell us at the airport they saw him 10 minutes ago, our wave function describing his position immediately collapses to a smaller volume, and so on. This "collapse" may occur faster than light because no real object is "collapsing": it's just a state of our knowledge in our brain.

In practice, everyone can use pretty much the same wave function. But in principle, the wave function is subjective. If the observer A looks at a quantum system S in the lab, he will use a wave function where S has a well-defined sharp spin eigenstate as soon as the spin of S is measured by A. However, B who studies the whole system A+S confined in a lab won't "make" any collapse, and he evolves both S and A into linear superpositions until B measures the system. So A and B will have different wave functions during much of the experiment. It's consistent for B to imagine that A had seen a well-defined property of S before it was measured by B - but B won't increase his knowledge in any way by this assumption, so it is useless. If he applied this "collapsed" assumption to purely coherent quantum systems, he would obtain totally wrong predictions.

So the wave function is surely subjective if one wants to obtain a universal description of the world. It's a collection of probability amplitudes that may be combined in various ways, before the squared absolute values of the combinations are interpretated as probabilities. All probabilities of physically meaningful events may be calculated in this way - as the squared absolute value of some linear combination of the probability amplitudes.

No collapse in the principles of the interpretation

A widely propagated myth is that the Copenhagen interpretation is all about the "collapse". However, if you look at the six principles above, there is not even a glimpse of a comment about a "collapse" because it's not needed. The notion of an objective collapse was introduced by John von Neumann in 1932 and he was clearly not a part of the Copenhagen school of thought anymore. Comments that Heisenberg later switched to an "objective wave function" or an "objective collapse" are untrue, and even if these legends were true, these new opinions wouldn't be a part of the Copenhagen interpretation and, more importantly, they wouldn't be valid.

Because the wave function is subjective, see rule 1, everything that happens with the wave function has to be subjective as well.

Consider a cat. You will evolve a wave function and the final state is "0.6 alive + 0.8i dead." (The fact that the actual state is not pure in any useful sense will be discussed later.) When you observe the cat, it's - unexpectedly - alive. Once you know that the cat is alive, it becomes a fact. You have to use this new knowledge in all your subsequent predictions and retrodictions if they're supposed to be any accurate. Or valid, for that matter. I think that the previous statement is totally obvious.

However, people invent lots of nonsensical gibberish in order to obscure what's actually going on even though it is fundamentally very clear.

For example, you will hear all the time that it is so difficult to get a "collapse" and there must be some complicated gadget or mechanism that does so. But if you realize that those things are probability amplitudes rather than potatoes, you must see that absolutely nothing has to be supplemented to "get" the collapse.

The laws of physics predict that with the state above, there is a 36% probability that we will measure the cat to be alive and 64% probability that it is dead. Just to be sure, there is a 0% probability that there will be both an alive cat and a dead cat. The last sentence, while totally obvious, is once again being obscured and crippled pretty much by everyone who has every said that he sees a problem with the Copenhagen interpretation.

Once decoherence eliminates the off-diagonal elements, the density matrix for the cat is

rho = 0.36 |alive> <alive| + 0.64 |dead> <dead|

The diagonal entries of the density matrix, 0.36 and 0.64, are the probabilities that we will get either of the results. But the result "we will have both types of a cat" isn't among the options with nonzero probabilities at all, so it will certainly not occur. Only one of the options with the nonzero entries, "dead" or "alive", will occur, and the probabilities are 64% and 36%, respectively.

So one of them has to occur and the "symmetry" between them surely has to be broken. That's what the formulae imply. There is no possible answer of the form "half-dead, half-alive", so the latter result can't be observed. If you used another basis where a "half-dead, half-alive" state would be one of the basis vectors, the off-diagonal elements of the density matrix wouldn't ever go to zero and the interpretation of the diagonal elements of the density matrix as "probabilities" would be illegitimate.

In this sense, while the density matrix (also a subjective tool to predict and explain!) isn't an "observable", it's still true that you may compute its eigenvalues - the allowed probabilities of observable microstates - and the corresponding eigenstates of the density matrix are those that can actually be observed with well-defined probabilities. If a state is not an eigenstate of the density matrix, it's not possible to imagine that this state will be realized after a measurement. The Hamiltonian evolves the density matrix and dictates which states are "observable" in the classical sense.

So when you realize that the numbers 36% and 64% are not piles of potatoes but probabilities, it's very clear that once we learn that the cat is alive, even though the chance was just 36%, the number 64% has to be replaced by 0% while 36% jumps to 100%. We know that the cat is alive so for us, it's a fact. It's nonsensical to try to "preserve" the dead option because the dead option was not realized.

It makes no sense to claim that it's "predetermined" that the cat would be seen as alive. The free-will theorem, among other, morally equivalent results, shows that the actual decision whether the cat is seen alive or dead has to be made at the very point of the spacetime where the event (measurement) takes place; it can't be a functional of the data (any data) in the past light cone.

One more comment, linked to the recent discussions about Everett's "many words", is the following. People often say that is unfair that some terms disappear. And they say that the disappeared terms should exist in separate worlds, and all this crap. But it is the very meaning of probability that only one of the options occurs and the others just disappear once we know that they were not realized. The actual event we were trying to predict breaks any "democracy" between the different possible results that were "on equal footing" prior to the actual event.

Even more importantly, people often say that "rho = rho1 + rho2" decomposition of the density matrix means that there are "two worlds", one that is described by "rho1" AND one that is described by "rho2". (Similarly for "psi", but for "rho", the comments are more clear.) But this is a complete misunderstanding of what the density matrix and addition means. The density matrix is an operator encoding probabilities - its eigenvalues are predicted probabilities. And we're just adding probabilities, not potatoes.

What does it mean to add probabilities? It doesn't mean "AND" at all! If "P(A and B)" vanishes i.e. if A and B are mutually exclusive, then "P(A) + P(B) = P(A or B)". You see the "or" word over there? It's always "OR"! So whenever you ADD terms in the density matrix - and similarly the state vector - it always means "OR" rather than "AND"! So the existence of the two terms can in no way imply that there should exist both options or both worlds. It's complete rubbish. People who say that the two terms in the wave function imply that there have to exist two real objects somewhere in the "multiverse" are making an error that is as childish as confusing addition and multiplication. Literally. They're just confused about basic school-level maths. And you can't just confuse the words "and" and/or "or" because if you do, your whole framework for logic becomes flawed.

Let me rephrase a point of the "Lumo interpretation" clearly: you describe the system by a density matrix evolving according to the right equation and it is always legitimate to imagine that the world collapsed to an eigenstate of the density matrix and the probabilities of different eigenstates are given by the corresponding eigenvalues of the density matrix. Incidentally, this also works for pure states for which "rho = psi.psi". In that case, "psi" is the only eigenstate of "rho" with the eigenvalue of "1", so you may collapse into "psi" with 100% probability which leaves "rho" completely unchanged. ;-) The only illegitimate thing to imagine is that the world has collapsed into a state which is not an eigenstate of "rho".

Uncertainty principle

The third rule is the uncertainty principle. It means that generic pairs of properties, such as "x" and "p" or "J_x" and "J_z" - but pairs of projection operators describing various Yes/No properties of a system could be even better examples - can't have well-defined values at the same moment. Especially John von Neumann, before he began to say silly things, liked to emphasize that the nonzero commutators and the Heisenberg uncertainty principle is the actual main difference between classical physics and quantum physics. If the commutators were zero, the evolution of the density matrix would be equivalent to the evolution of the classical probabilistic distribution on the phase space.



Because the projection operators P and Q corresponding to two Yes/No questions about a physical system typically don't commute with one another, it is totally illegitimate to imagine that during its evolution, a quantum system had well-defined both Yes/No properties, P and Q. It just couldn't have had because P and Q don't commute and they don't usually have any common eigenvectors (unless there are eigenvectors of the commutator [P,Q] with the vanishing eigenvalue).

This main principle is the main "underlying reason" why the GHZM experiment or Hardy's experiment produce results that are totally incompatible with the classical or pre-classical reasoning. The classical reasoning is wrong, the quantum reasoning is right - and the nonzero commutators in the real world are the main reason why the classical reasoning can't agree with the observations.

Complementarity principle

Bohr's favorite principle shows that the systems exhibit both particle-like and wave-like properties, but the more clearly you can observe the latter, the more obscure has to be the latter, and vice versa. In some sense, this principle just follows from the uncertainty principle for "x" and "p" because particle-like behavior occurs for measurable states that are close to eigenstates of "x" while the wave-like properties are seen when the measurable states are close to eigenstates of "p" - with long enough wavelength (more precisely, long enough "any" features of the wave) so that the wave properties may be seen.

In some sense, the complementarity principle is totally uncontroversial - unless you are Shahriar Afshar, of course. ;-) So I won't spend more time with that.

Measurement devices are classical

The fifth rule says that the measurement devices follow the rules of classical physics. This is another source of misunderstandings.

The Copenhagen school surely didn't want to say that quantum mechanics couldn't be applied to large systems. Indeed, many people from the Copenhagen school were key researchers who helped to show that quantum mechanics works for large systems including molecules, bubble chambers, solids, and anything else you can think of.

Instead, this rule was meant as a phenomenological rule. If you measure something, you may assume that the apparatus behaves as a classical object. So in particular, you may assume that these classical objects - especially your brain, but you don't have to go up to your brain - won't ever evolve into unnatural superpositions of macroscopically distinct states.

Is that true? Is that a sign of a problem of the Copenhagen interpretation?

It is surely true. It's how the world works. However, one may also say that this was a point in which the Copenhagen interpretation was incomplete. They didn't quite understand decoherence - or at least, Bohr who probably "morally" understood what was going on failed in his attempts to comprehensibly and quantitatively describe what he "knew".

However, once we understand decoherence, we should view it as an explicit proof of this fifth principle of the Copenhagen interpretation. Decoherence shows that the states of macroscopic (or otherwise classical-like) objects whose probabilities are well-defined are exactly those that we could identify with the "classical states" - they're eigenstates of the density matrix. The corresponding eigenvalues - diagonal entries of the density matrix in the right basis - are the predicted probabilities.

Because the calculus of decoherence wasn't fully developed in the 1920s, the Copenhagen school couldn't have exactly identified the point at which the classical logic becomes applicable for large enough objects. However, they were saying that there is such a boundary at which the quantum subtleties may be forgotten for certain purposes and they were damn right. There is such a (fuzzy) boundary and we may calculate it with the decoherence calculus today. The loss of the information about the relative phase of the probability amplitudes between several basis vectors is the only new "thing" that occurs near the boundary.

Again, this point was the only principle of the Copenhagen interpretation that was arguably "incomplete" but their proposition was definitely right! To make this point complete, one didn't have to add anything new to quantum mechanics or distort it in any way. One only needs to make the right calculation of the evolution of the density matrix in a complicated setup. In that way, one proves that they always treated the measuring devices in the right way even though they couldn't fully formulate a fully quantum proof why it was the right way.

Correspondence principle

Both Bohr and Heisenberg also emphasized the correspondence principle, e.g. that the quantum equations reduce to the classical ones in the appropriate limit. If you study e.g. the evolution of the expectation value of "x" and "p", they will evolve according to the classical equations. It's the Ehrenfest theorem.

As discussed in the previous point, it is not enough to show that the world of classical perceptions will occur in the limit as well: we also need to know that the right "basis" will become relevant in the classical limit. Nevertheless, with the extra additions that had been demonstrated in recent decades, I mean decoherence, we know that it is true that the classical perception and choice of states does occur in the appropriate classical limit.

So all the points of the Copenhagen interpretation were right and they were only incomplete because they didn't explicitly calculate where the classical-quantum boundary really is. I need to emphasize that this boundary is fuzzy. And this boundary doesn't mean that quantum mechanical laws ever break down. They never break down. What's true is that for large enough systems, one may use - and should use - the approximate classical scheme (the word "approximate" sounds too scary but in reality, these approximations are super excellent for all practical and even most of the impractical purposes) of asking questions because one may show that it becomes legitimate.

Well, I surely don't expect that people will stop being hysterically angry about the Copenhagen interpretation and its alleged flaws - which don't exist. But at least, I would like to see the chronic Copenhagen haters to acknowledge that the Copenhagen interpretation says what it says and that it clearly doesn't have any demonstrable flaws. It has no internal inconsistencies and it is not in contradiction to any observation done as of today.

And that's the memo.

Hugh Everett's many worlds interpretation of QM

Among many other things, Brian Greene's new book, The Hidden Reality, shows very clearly that the author is kind of obsessed, to put it mildly, with Hugh Everett's interpretation of quantum mechanics.

Everett's adviser was John Wheeler. By 1957, Everett completed his PhD thesis. It was considered wrong and worthless by Bohr and pretty much everyone else - with John Wheeler playing the natural role of a loving boss - so he left research and became a key figure defining the U.S. nuclear weapons policies behind the scenes. Scientific American described his personal life as tragic - silence, disconnect from the family, alcohol etc. Fine, let's stop this irrelevant stuff.

I wanted to know what the thesis was actually saying so I began to read it:

• Dissertation (via PBS)
• Paper-like version (in Reviews of Modern Physics)

To summarize my impressions in two short sentences: I noticed that Brian Greene was affected much more than I could have thought - even his description of a physical theory being a bound state of a formal part and a physical part is taken from this thesis; second, Everett's thesis is much more obvious gibberish than I thought.




As far as I can say, the ideas that Everett was a forefather of decoherence or consistent histories are just full-fledged misconceptions. For some time, I was happy to realize that gibberish was being written at all times. However, my optimism about the current situation was quickly replaced by pessimism because the difference between the 1950s and the 2010s is that in the latter decade, this gibberish would be - and, in fact, is - being promoted via lots of official channels. Everett was at least original and his prose was very clear. Of course, he may deserve to have been a top philosopher of science if we accept that such a field may exist. But as I will argue below, his thesis wasn't a good science.

Now, Brian is a good person and I can't get rid of the impression that he's partly trying to revive some of Everett's stuff because of some kind of compassion. But if that's the case, I don't think it belongs to physics. Right is right and wrong is wrong and redefining those words by some emotional criteria means to give up science.

Looking at the dissertation

In the introduction, Hugh Everett III complains about quantum mechanics with the help of a two-observer experiment I will discuss momentarily. But even before this portion of the thesis, there is his picture what he considered conventional quantum mechanics he wants to challenge. He also says:

The state function "psi" is thought of as objectively characterizing the physical system, i.e., at all times an isolated system is thought of as possessing a state function, independently of our state of knowledge of it.

It is not only wrong; I believe that it was flagrantly dishonest for him to write it. Everett had to know that this wasn't what the true founding fathers of quantum mechanics were saying. In particular, Werner Heisenberg was always emphasizing that the wave function is not an objectively existing wave but rather a description of our subjective state of knowledge.

Niels Bohr, John von Neumann, Max Born, and probably also Wolfgang Pauli, Paul Dirac, and others would agree. But even if it were just Bohr and Heisenberg, it's just not possible to imagine that Everett had been unaware of their actual perspective on these matters. And it is unforgivable that Everett has actually tried to deny that this "school of thought" actually existed. It follows that he was fighting a strawman. Everett's even more confused classmates could have been saying that "psi" was a classical wave - but even if that's the case, one shouldn't write a PhD thesis based on classmates' confusions.

Observer B observing observer A observing system S

Fine. So Everett hasn't honestly described the theory or interpretation he was actually trying to challenge. But his treatment gets more detailed. The main "paradox" he wants to solve is the following situation (which is not really his invention, it's essentially the well-known Wigner's friend which is just an extension of Schrödinger's cat):

Observer A measures and studies the evolution of a microscopic system S in a lab. Observer B measures and studies the evolution of the whole composite system A+S. According to A, the measured properties of S become a reality as soon as they are measured. According to B, things only become sharp once B looks inside the lab; before that, even A is found in a linear superposition of states with different properties. Because A,B have different answers to the question when did the properties of A became real facts, there is a contradiction.

That's what he says. Now, to make his demagogy look "powerful", he offers - and debunks - four alternative solutions and chooses the fifth one that, as he claims later, makes the many worlds inevitable. The only problem is that none of the four alternative solutions is the correct quantum mechanical solution. So by accumulating four piles of junk, he believes that the reader will feel lost and accept whatever he will offer them. Lee Smolin has extended this demagogic technique to stunning dimensions.

So that's why Lee Smolin often tells you that there are e.g. 12 or 144 theories of quantum gravity - 11 or 143 mutations of some completely idiotic crackpot papers plus string theory - so string theory is meant to be diluted by this "argument" and 11/12 or 143/144 of the physicists are supposed to study the Smolin-like shit.

Fine. What were Everett's alternative answers?

1. Solipsism - there's only one observer in the Universe.
2. QM fails when acting on apparatuses or observers.
3. B cannot measure the state of A+S without killing A, or stripping him of the ability to observe.
4. Add hidden variables.
5. Apply QM everywhere - but, as Everettt says, it means that it has to be non-probabilistic.

Now, 1) is wrong because many of us are qualitatively similar and all of us may use quantum mechanics to predict things. If I were the only person who can use it, that's fine but I would still have no explanation why other people look so qualitatively similar and apparently share common ancestry with me. ;-)

The point 2) is wrong because QM applies to arbitrarily large systems, geometrically speaking.

The point 3) is wrong because we may create a computer with some artificial intelligence that should be admitted to behave qualitatively similarly to us - and all the important properties of the computer may be measured.

Hidden variables 4) don't exist because of various reasons, inequalities, tests.

The first part of Everett's answer 5) is correct - the previous 4 alternative solutions are wrong - but everything he adds to it is wrong, too. In particular, it's not true that quantum mechanics should or can work without the notion of probability built into its basic framework.

But in his answer 5), he hasn't really solved the "paradox" yet. The correct solution - one that he doesn't even mention as one of five alternatives - is the following:

Indeed, the correct way for observer A to use quantum mechanics is to consider the measured properties of S to be facts as soon as A measured them. And indeed, the canonical correct way for B to treat the system A+S is to evolve it into the relevant superpositions and only accept the properties of A+S as facts once B measures them. Indeed, A,B have different ideas about "what is real". But this can lead to no contradictions. In particular, "what is real" only means "what is already known", and no surprise that this question is subjective and has different answers for A,B. The particular proof of the absence of demonstrable contradictions also depends on the fact that A could have only perceived properties that had decohered, and because decoherence is irreversible, B won't be able recohere them. So it is up to B whether he imagines that some properties of A+S were behaving "classically" even before B measured them; he doesn't have to make this assumption.

Whether "something is real before it was measured" cannot be measured :-), because of a logical tautology, so it is obvious that this question can lead to no physical contradictions, and that's totally enough for physics to work as it should.

Trying to make physics "more consistent than needed" and "overshoot" by claiming that it must also have answers to all questions that can't be measured is just a totally misguided recipe. Physics isn't obliged to answer physically meaningless questions and indeed, one may use quantum phenomena to show that all such questions whether "something was real before it was seen" are meaningless and can't have objective answers.

Whether "something was known" before it was measured is clearly subjective, so A and B have different answers. And this is indeed reflected by their different "psi" at different times because "psi" is the state of their knowledge. In practice, when you care whether you may run into contradictions by assuming that there was a real reality - some objectively real property - before it was seen, the answer is that as long as the property had decohered from its alternatives, you may always assume that it was objectively real.

But incidentally, this philosophical assumption won't help you to learn a single damn thing. It's just a physically worthless philosophical dogma, and indeed, this dogma will cause you trouble when you try to study the detailed behavior of coherent enough quantum systems because in those systems, the objective reality cannot be assumed to exist before the measurements - otherwise you really get wrong predictions.

Correct interpretation of predictions

In quantum mechanics, one learns something about the system and constructs the initial "psi", the state vector, or its tensor second power "rho", the density matrix. It can be evolved in time via the equations everyone agrees with. And when we want to ask any physical Yes/No question, and every question in physics may be divided to a collection of Yes/No questions, we compute the expectation value of a corresponding linear projection operator in that state - "psi" or "rho" (in the latter case, it's Tr(rho.P). We obtain the probability that the answer will be Yes. This is a recipe to answer all questions.

In practice, we may also ask questions about whole histories, so "P" may be replaced by some product of projection operators at different times, according to the detailed rules of the Consistent Histories. I view this is a problem-free extension of the single measurement with a single set of projection operators.

Anyone who is trying to answer some physical questions by something else than by looking at expectation values of linear operators in the quantum states is simply not doing quantum physics, or not doing it correctly.

Splitting to many worlds

When an observer observes something, Everett must say that the world splits into worlds where different alternative outcomes occur. Now, this is demonstrably at least as problematic as the "materialist collapse" of a "real wave". Why? Because he must be careful that the worlds don't split into sharply defined alternative worlds before the properties decohere - otherwise he would spoil the interference patterns etc. and everything that is quantum about quantum mechanics.

On the other hand, he must make sure that the splitting of the worlds occurs as soon as decoherence is over. But the "moment" when decoherence is over isn't sharply defined. Decoherence is never "absolute". Decoherence is a continuous process that becomes "almost totally complete" after a certain time scale but it is never complete.

The defenders of the many worlds such as Brian Greene complain about Bohr's phenomenological rule urging you to "collapse the wave function" when you measure something. The rule is creating an arbitrary boundary between the microscopic world and the macroscopic world, they complain.

But it's totally obvious that Everett's picture needs this boundary as well. The boundary tells you when the worlds actually split. They don't split when a microscopic particle remains coherent. They only split when something decoheres. (I am using the modern arguments with the full knowledge of decoherence because I want to judge the validity of the interpretations according to everything we understand today. Of course that some of these issues were misunderstood by everyone in the 1950s.)

So Everett's picture does need a boundary between the microscopic and macroscopic world. And indeed, decoherence is a way to show that there is a boundary. At some moment, the quantum processes - such as interference between different alternatives - become impossible. Decoherence exactly calculates the time scale when this occurs for a given system. It depends on the system, its Hamiltonian, and the parameters. It's a fully dynamical question.

It's very clear from the wording that Everett - and even his disciples today - find it unacceptable to claim that there is a boundary between the microscopic and macroscopic world. That was really a major driver of Everett's efforts. He didn't like that Bohr's interpretation depended on a different treatment of the small and large objects.

But decoherence has definitively demonstrated that Bohr was right on this point. There is a boundary. There is something different about the behavior of the large systems. But the difference doesn't mean that Schrödinger's equation doesn't apply to them. It always applies to all systems - including the system A+S studied by B. What's different for the large systems is that one may use an approximation scheme that restores some notions from classical physics. It's analogous to the fact that for large enough systems, you may approximate (statistical) physics of the building blocks by the macroscopic thermodynamic description.

But you don't have to.

When Bohr et al. were telling you that you should use a different logic for the small observed systems and the large objects such as observers, they were correctly saying that there's something about the large objects that isn't true for the small ones. But they were not saying that Schrödinger's equation can't be applied to large bound states of many particles. Of course that it can and many of the same people close to the founding fathers of QM were investigating exactly those issues.

Bohr couldn't crisply formulate and quantify how decoherence acts but it is very clear that he understood that there is some real statistical argument that follows from proper quantum mechanics that justifies his different phenomenological treatment of large objects - the fact that they often behave similarly to objects in classical physics.

Assigning probabilities to many worlds

Brian Greene is well aware of this problem. But it is such a huge problem of the many-worlds scenario that I can't believe that someone could disagree that the problem really kills the MWI picture.

Everything we learn in theoretical physics is about taking some usually quantitative information about the system and its state, and predicting the state at another time - usually a later time. So "physics" is all about the numerical values of things such as the S-matrix elements - the scattering amplitudes for incoming and outgoing particles of given types, momenta, and spins. In the quantum context, all the detailed information that the theory actually spits is about the probabilities of different things.

So you would think that an interpretation of quantum mechanics will be able to say where those numbers - everything we know and we can calculate about a quantum mechanical theory - enter the interpretation. But they really don't enter the MWI interpretation at all!

MWI is just a way to visualize that there could have been other outcomes of a measurement. You just declare that they live in "separate worlds". Of course, by definition, all those worlds with different outcomes are inaccessible. They will never affect you again - even in principle - which is why they're unphysical according to the standard interpretation of the word "physical".

Fine. You visualize the qualitative fact that there could have been other outcomes. The visualization is totally useless for any prediction because everything you will do will be constrained by the outcomes that you have already learned to be facts in your world - because you have measured it.

But is there a room for the actual numbers? Take a wave function that says that a particle has a 64% probability to be at C and 36% probability to be at D. There are two "many worlds", C and D. Now, if there are really just two, it's clear that the very philosophy should tell you that C and D are predicted to be equally likely. You can't hide the numbers 64%, 36% anywhere in the theory. That's a big problem because all of our knowledge of any quantum system is composed out of such numbers! All of physics is in these numbers. Qualitative visual aids involving outcomes that have been ruled out may be fine for someone but they have nothing to do with the actual calculations and predictions in physics.

An alternative is that you split the world to 64,000 worlds where you measure C and 36,000 worlds where you measure D. Well, it's awkward because if the 64,000 worlds are really identical, they're really one of them - because such a symmetry must be a gauge symmetry in quantum gravity, and so on.

But just accept that there are 64,000 parallel worlds where the observer measures C and 36,000 worlds where he measures D. Does it prove that the odds will be 64% and 36%? The answer is, of course, that it doesn't. And those who say "it does" suffer from the same basic confusion about all of physics and all of rational thinking as the advocates of a natural high-entropy beginning of the Universe; and as the most hardcore defenders of the "mediocrity principle" version of the anthropic principle on steroids. I will call it

The egalitarian misconception

To say that the 64,000 worlds of C-type and 36,000 worlds of D-type will lead to odds that are 64% vs 36%, you have to assume that it's "equally likely" for you to be in any of these worlds. But where does this assumption come from?

Of course, it doesn't come from anywhere. It's just a dogma, and a totally wrong and irrational one. Those people believe that some states or objects are "created equal". The believers that the entropy of the early Universe is predicted to be high believe that all microstates are always equal - like in an egalitarian society. Those who believe that we're the "typical observers" think that every observer in the Universe, every skunk who lives on Jupiter or Gliese 5835235bcz or anywhere has the same democratic rights and weight as a U.S. citizen. In the many-worlds context, the same believe leads Brian Greene and others to think that the multiplicity of the worlds would imply that the odds will be proportional to the ratios of the number of Universes.

But in all three cases, the conclusion is just completely wrong.

Egalitarian or uniform distributions are just one distribution among infinitely many. In fact, I can show that the egalitarian assumptions are totally inconsistent. There are infinitely many (infinity to the infinite power, in fact) different distributions of the strength of the vote on Earth. And egalitarianism is just one of them. Using the egalitarian principle, all distributions should be treated as equal. Because the egalitarian distribution has a negligible vote - measure zero in the set of distributions - it follows that it is not realized.

This sounds like an argument of a witty child but it is true. There is absolutely no self-consistent reason why you could assume that the egalitarian treatment of the "microstates"; "copies of you in many worlds"; "different observers in the inflating multiverse" should be justified.

In fact, every time we see something "equal" in physics, there has to be a rather nontrivial enforcement mechanism that explains the inequality. In other words, the default state of the affairs is that the different objects in large sets are totally unequal. If you want to say that something is equal about them, it is a bold and nontrivial assertion and you must do hard work to prove it. In an overwhelming majority of cases, you will fail because your statement is just incorrect.

The case in which egalitarianism works is a totalitarian society that restricts or kills everyone who differs from the average. With the help of a few Gulags, a society may come pretty close to the "ideal" of egalitarianism - the despicable idea that people and their lives should look equal. Well, it just happens that there usually has to be a person or a group who controls this unhuman experiment with the humans and who remains damn "unequal" to them - a kind of Stalin or Hitler or Gore dictating people how to reduce their dark skin, ownership of factories, or carbon footprint or something of the sort.

Egalitarianism of elements of a random large set is never natural in Nature - and in a properly functioning society.

Another exception is thermal equilibrium. If you achieve it, all microstates with the same values of conserved quantities become equally likely; the logarithm of their number is known as the entropy. But the equal number is not due to some a priori egalitarianism that applies to the microstates. It's a result of a mechanism we may describe - thermalization.

If a classical system evolves in a sufficiently chaotic way, it will randomly try all places within a slice of the phase space (the quantum discussion is analogous but uses very different mathematical objects to describe what's going on). So by the ergodic hypothesis, at a random moment in the future, you will get a random state on the slice - a random microstate.

But it takes some time to "enforce" this inequality. The microstates must be intensely mixed with each other. Such an equality between the microstates only occurs in the future - after some time spent by thermalization. This equality surely doesn't hod for the Big Bang because there was no thermalization prior to the Big Bang. And indeed, the entropy of the Universe at the beginning is correctly predicted - by Bayesian inference that reformulates the usual proofs of the second law - to be low.

The thermalization plays the analogous role as Hitler's liquidation of the people in extermination camps or Stalin's Gulags. There is a mechanism that does something. If you understand how it works, you will see that it makes the set more uniform. But if you have no argument like that, the set is almost certainly not uniform.

Of course, I kind of think that all the people who assume the "egaitarian misconception" are kind of driven by the fact that deeply inside their souls, they're fanatical Marxists. But Marxism is not compatible with all the details of the way how Nature works - much like most other ideologies.

When those Marxist people try to prove something, they think that it's the "default state" that X=Y for any two objects X,Y that look kind of qualitatively similar. They think that if they say X=Y, they don't need to prove anything. On the contrary, if someone says that X isn't equal to Y, they attack him - sometimes, they send him to the Gulag - because he dared to say that things are not equal.

But the matter of fact is that in maths or science or anything else, saying that X is equal to Y is a much bolder and less likely proposition than the statement that X is not equal to Y. There are many more ways how X may be unequal to Y. ;-) So the default assumption is that X is almost certainly not equal to Y. If you want to prove that X=Y, you need some argument - symmetry, ergodic hypothesis, Gulag, or something like that. But it is never "automatic". Every rational person knows that saying X=Y is, in most cases how to randomly choose X,Y, crazy. The Marxists just don't get this simple point. The Marxist ideology has so hopelessly eaten a big portion of their brains that they don't even realize that they're making an unjustified assumption.

But they are making nontrivial, crazy, and in all the cases above, fundamentally wrong assumptions, indeed. In the case of the many worlds, one of the consequences is that they totally revert what is fundamental and what is not. They want some "unjustified egalitarianism" between Universe - that couldn't undergo any thermalization via ergodic hypothesis; and whose inhabitants didn't face the threat of a Gulag - to be the assumption that implies the right probabilistic predictions.

It can't work in this way. The real world works exactly in the opposite way. The probabilities are computed from the quantum mechanical formulae are the main tools that allow us to derive things about the real world. In particular, if some things are equal in the real world, we have to reduce the proof of the equality to some calculation that ultimately deals with the probabilities because the probabilities as calculated from the laws of physics are fundamental, and all their macroscopic or political "corollaries" are just emergent and derived facts.

For example, one may derive that after some time spent with thermalization, all microstates will be approximately equally likely. One may calculate this thing by a correct calculation based on quantum mechanics. In the same way, one may prove that after some time spent by shooting rich or skillful people, a communist nation becomes a nearly uniform conglomerate of mediocre citizens, with the exception of a Stalin who is of course different in some respects.

But one cannot find a similar proof that the microstates were equally likely during the Big Bang; or that inhabitants of different planets have the same vote in the global political elections deciding who of them is us :-); or that copies of you in Everett's "many worlds" have the same odds to be thinking that they are you. It's not only true that there's no proof of such things as of today. In fact, none of these things can be proved - and the reason is that none of these things is really true.

I can't believe that these simple points may be controversial.

The Bousso-Susskind hypermultiverse

Leonard Susskind and Raphael Bousso are creative guys and famous physicists. Both of them are well-known for some papers about holography, too. Of course, the first scientist is still a bit more famous. They have just released a preprint to show that they're on crack and they are greatly enjoying it:

The Multiverse Interpretation of Quantum Mechanics

The ordinary multiverse with its infinitely many bubbles whose possible vacuum states are located in 10^{500} different stationary points of the stringy configuration space was way too small for them. So they invented a better and bigger multiverse, one that unifies the "inflationary multiverse", the "quantum multiverse", and the "holographic multiverse" from Brian Greene's newest popular book, The Hidden Reality.

Yes, their very first bold statement is that parallel universes in an inflating universe are the same thing as Everett's many worlds in quantum mechanics! ;-)

Sorry to say but the paper looks like the authors want to stand next to Lee Smolin whose recent paper - as much crackpottish as any paper he has written in his life so far - is about "a real ensemble interpretation" of quantum mechanics. Bousso and Susskind don't cite Smolin - but maybe they should! And in their next paper, they should acknowledge me for pointing out an equally sensible and similar paper by Smolin to them. ;-)




Just like your humble correspondent would always emphasize that the "many worlds" in Everett's interpretation of quantum mechanics are completely different "parallel worlds" than those in eternal inflation or those in the braneworlds, these famous physicists say - On the contrary, they're the same thing!

However, at least after a quick review of the paper, the drugs seem to be the only tool that you can find in the paper or in between its lines to convince you that it's the case. ;-)

It's a modern paper involving conceptual issues of quantum mechanics, so it treats decoherence as the main mechanism to address many questions that used to be considered puzzles. Good. However, everything that they actually say about decoherence is a little bit wrong, so their attempts to combine those new "insights" with similar "insights" resulting from similar misunderstandings of the multiverse - and especially the way how outcomes of measurements should be statistically treated in a multiverse - inevitably end up being double gibberish that is cooked from two totally unrelated components such as stinky fish and rotten strawberries.

In what sense decoherence is subjective

One of the first starting points for them to unify the "inflationary multiverse" and the "many worlds" of quantum mechanics is the following thesis about decoherence:

Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment".

That's a loaded statement, for many reasons. First of all, decoherence isn't really a version of the collapse. Decoherence is an approximate description of the disappearing "purity" of a state in macroscopic setups with various consequences; one of them is that there is no collapse. The probabilities corresponding to different outcomes continue to be nonzero so nothing collapses. They're nonzero up to the moment when we actually learn - experimentally - what the outcome is. At that point, we must update the probabilities according to the measurement. Decoherence restricts which properties may be included in well-defined questions - for example, insane linear superpositions of macroscopically different states are not good "basis vectors" to create Yes/No questions.

As first emphasized by Werner Heisenberg and then by anyone who understood the basic meaning of proper quantum mechanics, this "collapse" is just about the change of our knowledge, not a real process "anywhere in the reality". Even in classical physics, dice may have probabilities 1/6 for each number, but once we see "6", we update the probabilities to (0,0,0,0,0,1). No real object has "collapsed". The only difference in quantum physics is that the probabilities are not "elementary" but they're constructed as squared absolute values of complex amplitudes - which may interfere etc.; and in classical physics, we may imagine that the dice had the state before we learned it - in quantum physics, this assumption is invalid.

It may help many people confused by the foundations of quantum mechanics to formulate quantum mechanics in terms of a density matrix "rho" instead of the state vector "psi". Such a "rho" is a direct generalization of the classical distribution function on the phase space "rho" - it only receives the extra off-diagonal elements (many of which go quickly to zero because of decoherence), so that it's promoted to a Hermitian matrix (and the opposite side of the coin is that the indices of "psi" may only involve positions or only momenta but not both - the complementary information is included in some phases). But otherwise the interpretation of "rho" in quantum mechanics and "rho" in classical statistical physics is analogous. They're just gadgets that summarize our knowledge about the system via probabilities. Now, "psi" is just a kind of a square root of "rho" so you should give it the same qualitative interpretation as to "rho" which is similar to "rho" in classical statistical physics.

Second, is decoherence "subjective"? This is a totally equivalent question to the question whether "friction", "viscosity" (or other processes that dissipate energy) is subjective. In fact, both of these phenomena involve a large number of degrees of freedom and in both of them, it's important that many interactions occur and lead to many consequences that quickly become de facto irreversible. So both of these processes (or their classes) share the same arrow of time that is ultimately derived from the logical arrow of time, too.

First, let's ask: Is friction or viscosity subjective?

Well, a sliding object on a flat floor or quickly circulating tea in a teacup will ultimately stop. Everyone will see it. So in practice, it's surely objective. But is it subjective "in principle"? Do the details depend on some subjective choices? You bet.

Focusing on the tea, there will always be some thermal motion of the individual molecules in the tea. But what ultimately stops is the uniform motion of bigger chunks of the fluid. Obviously, to decide "when" it stops, we need to divide the degrees of freedom in the tea to those that we consider a part of the macroscopic motion of the fluid and those that are just some microscopic details.

The separation into these two groups isn't God-given. This calculation always involves some choices that depend on the intuition. The dependence is weak. After all, everyone agrees that the macroscopic motion of the tea ultimately stops. In the same way, the information about the relative phase "dissipates" into a bigger system, a larger collection of degrees of freedom - the environment - during decoherence. The qualitative analogy between the two processes is very tight, indeed.

But a punch line I want to make is that decoherence, much like viscosity, isn't an extra mechanism or an additional term that we have to add to quantum mechanics in order to reproduce the observations. Instead, decoherence is an approximate method to calculate the evolution in many situations that ultimately boils down to ordinary quantum mechanics and nothing else. It's meant to simplify our life, not to add some extra complications. Decoherence justifies the "classical intuition" about some degrees of freedom - what it really means is that interference phenomena may be forgotten - much like the derivation of equations of hydrodynamics justifies a "continuum description" of the molecules of the fluid.

Clearly, the same comment would be true about friction or viscosity. While the deceleration of the car or the tea is usefully described by a simplified macroscopic model with a few degrees of freedom, in principle, we could do the full calculation involving all the atoms etc. if we wanted to answer any particular question about the atoms or their collective properties. However, we should still ask the right questions.

When Bousso and Susskind say that there is an ambiguity in the choice of the environment, they misunderstand one key thing: the removal of this ambiguity is a part of a well-defined question! The person who asks the question must make sure that it is well-defined; it's not a job for the laws of physics. Returning to the teacup example, I may ask when the macroscopic motion of the fluid reduces to 1/2 of its speed but I must define which degrees of freedom are considered macroscopic. When I do so, and I don't have to explain that there are lots of subtleties to be refined, the question will become a fully calculable, well-defined question about all the molecules in the teacup and quantum mechanics offers a prescription to calculate the probabilities.

The case of decoherence is completely analogous. We treat certain degrees of freedom as the environment because the state of these degrees of freedom isn't included in the precise wording of our question! So when Bousso and Susskind say that "decoherence is subjective", it is true in some sense but this sense is totally self-evident and vacuous. The correct interpretation of this statement is that "the precise calculation [of decoherence] depends on the exact question". What a surprise!

In practice, the exact choice of the degrees of freedom we're interested in - and the rest is the environment - doesn't matter much. However, we must obviously choose properties whose values don't change frantically because of the interactions with the environment. That's why the amplitude in front of the state "0.6 dead + 0.8i alive" isn't a good observable to measure - the interactions with the environment make the relative phase terribly wildly evolving. Decoherence thus also helps to tell us which questions are meaningful. Only questions about properties that are able to "copy themselves to the environment" may be asked about. This effectively chooses a preferred basis of the Hilbert space, one that depends on the Hamiltonian - because decoherence does.

To summarize this discussion, at least in this particular paper, Bousso and Susskind suffer from the same misconceptions as the typical people who deny quantum mechanics and want to reduce it to some classical physics. In this paper's case, this fact is reflected by the authors' desire to interpret decoherence as a version of the "nice good classical collapse" that used to be added in the QM framework as an extra building block. But decoherence is nothing like that. Decoherence doesn't add anything. It's just a simplifying approximate calculation that properly neglects lots of the irrelevant microscopic stuff and tells us which parts of classical thinking (namely the vanishing of the interference between 2 outcomes) become approximately OK in a certain context.

Let's move on. They also write:

In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event.

If you think about it, the purpose of this statement is inevitably elusive, too. Decoherence is not just "the decoherence" without adjectives. Decoherence is the separation of some particular eigenstates of a particular variable and to specify it, one must determine which variable and which outcomes we expect to decohere. In the real world which is approximately local at low energies, particular variables are connected with points or regions in spacetime. What decoheres are the individual possible eigenvalues of such a chosen observable.

But the observable really has to live in "one region" of spacetime only - it's the same observable. The metric in this region may be dynamical and have different shapes as well but as long as we talk about eigenvalues of a single variable, and in the case of decoherence, we have to, it's clear that we also talk about one region only. Decoherence between the different outcomes will only occur if there's enough interactions, space, and time in the region for all the processes that dissipate the information about the relative phase to occur.

So it's completely meaningless to talk about "decoherence in spacelike separated regions". Decoherence is a process in spacetime and it is linked to a single observable that is defined from the fundamental degrees of freedom in a particular region. Of course, the region B of spacetime may only be helpful for the decoherence of different eigenvalues of another quantity in region A if it is causally connected with A. What a surprise. The information and matter can't propagate faster than light.

However, if one restricts to the causal diamond - the largest region that can be causally probed - then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment.

This is just nonsense. Even inside a solid light cone, some degrees of freedom are the interesting non-environmental degrees of freedom we're trying to study - if there were no such degrees of freedom, we wouldn't be talking about the solid light cone at all. We're only talking about a region because we want to say something about the observables in that region.

At the same moment, for the decoherence to run, there must be some environmental degrees of freedom in the very same region, too. Also, as argued a minute ago - by me and by the very authors, too - the spatially separated pieces of spacetime are completely useless when it comes to decoherence. It's because the measurement event won't affect the degrees of freedom in those causally inaccessible regions of spacetime. Clearly, this means that those regions can't affect decoherence.

(A special discussion would be needed for the tiny nonlocalities that exist e.g. to preserve the black hole information.)

If you look at the light sheet surrounding the solid light cone and decode a hologram, you will find out that the separation of the bulk degrees of freedom to the interesting and environmental ones doesn't follow any pattern: they're totally mixed up in the hologram. It's nontrivial to extract the values of "interesting" degrees of freedom from a hologram where they're mixed with all the irrelevant Planckian microscopic "environmental" degrees of freedom.

They seem to link decoherence with the "holographic" degrees of freedom that lives on the light sheets - and a huge black-hole-like entropy of A/4G may be associated with these light sheets. But those numerous Planckian degrees of freedom don't interact with the observables we're able to study inside the light cone, so they can't possibly contribute to decoherence. Indeed, if 10^{70} degrees of freedom were contributing to decoherence, everything, including the position of an electron in an atom, would be decohering all the time. This is of course not happening. If you associate many degrees of freedom with light sheets, be my guest, it's probably true at some moral level that the local physics can be embedded into physics of the huge Bekenstein-Hawking-like entropy on the light sheet - but you must still accept (more precisely, prove) that the detailed Planckian degrees of freedom won't affect the nicely coherent approximate local physics that may be described by a local effective field theory - otherwise your picture is just wrong.

The abstract - and correspondingly the paper - is getting increasingly more crazy.

We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry.

This is a huge unification claim. Unfortunately, there's not any evidence, as far as I can see, that the many worlds may be "geometrized" in this way. Even Brian Greene in his popular popular book admits that there is no "cloning machine". You can't imagine that the new "many worlds" have a particular position "out there". The alternative histories are totally disconnected from ours geometrically. They live in a totally separate "gedanken" space of possible histories. By construction, the other alternative histories can't affect ours, so they're unphysical. All these things are very different from ordinary "branes" in the same universe and even from other "bubbles" in an inflating one. I don't know why many people feel any urge to imagine that these - by construction - unphysical regions (Everett's many worlds) are "real" but at any rate, I think that they agree that they cannot influence physics in our history.

We propose that it must be possible in principle to verify quantum-mechanical predictions exactly.

Nice but it's surely not possible. We can only repeat the same measurement a finite number of times and in a few googols of years, or much earlier, our civilization will find out it's dying. We won't be able to tunnel our knowledge elsewhere. The number of repetitions of any experiment is finite and it is not just a technical limitation.

There are many things we only observe once. Nature can't guarantee that everything may be tested infinitely many times - and it doesn't guarantee that.

This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite.

In de Sitter space, the observables are probably not exactly defined at all. Even in other contexts, this is the case. Observers can't survive their death, or thermal death of their surrounding Universe, and outcomes of most experiments can't be completely definite. Our accuracy will always remain finite, much like the number of repetitions and our lifetimes.

In the next sentence, they agree that the assumptions fail - but because of the holographic principle. One doesn't need a holographic principle to show such things. After all, the holographic principle is an equivalence of a bulk description and the boundary description so any physically meaningful statement holds on both sides.

At the end, they define "hats" - flat regions with unbroken supersymmetry - and link their exact observables to some approximate observables elsewhere. Except that this new "complementarity principle" isn't supported by any evidence I could find in the paper and it isn't well-defined, not even partially. In the quantum mechanical case, complementarity means something specific - that ultimately allows you to write "P" as "-i.hbar.d/dx" - a very specific construction that is well-defined and established. In the black hole, complementarity allows you to explain why there's no xeroxing; the map between the degrees of freedom isn't expressed by a formula but there is evidence. But what about this complementarity involving hats? There's neither definition nor evidence or justification (unless you view the satisfaction of manifestly invalid and surely unjustified, ad hoc assumptions to be a justification).

If you read the paper, it is unfortunately motivated by misunderstandings of the conceptual foundations of quantum mechanics. In the introduction, they ask:

But at what point, precisely, do the virtual realities described by a quantum mechanical wave function turn into objective realities?

Well, when we measure the observables. Things that we haven't measured will never become "realities" in any sense. If the question is about the classical-quantum boundary, there is obviously no sharp boundary. Classical physics is just a limit of quantum physics but quantum physics fundamentally works everywhere in the multiverse. The numerical (and qualitative) errors we make if we use a particular "classical scheme" to discuss a situation may be quantified - decoherence is one of the calculations that quantifies such things. But classical physics never fully takes over.

This question is not about philosophy. Without a precise form of decoherence, one cannot claim that anything really "happened", including the specific outcomes of experiments.

Oh, really? When I say that it's mostly sunny today, it's not because I preach a precise form of decoherence. It's because I have made the measurement. Of course, the observation can't be 100% accurate because "sunny" and "cloudy" haven't "fully" decohered from each other - but their overlap is just insanely negligible. Nevertheless, the overlap never becomes exactly zero. It can't. For more subtle questions - about electrons etc. - the measurements are more subtle, and indeed, if no measurement has been done, one cannot talk about any "reality" of the property because none of them could have existed. The very assumption that properties - especially non-commuting ones - had some well-defined properties leads to contradictions and wrong predictions.

Decoherence cannot be precise. Decoherence, by its very definition, is an approximate description of the reality that becomes arbitrarily good as the number of the environmental degrees of freedom, their interaction strength, and the time I wait become arbitrarily large. I think that none of the things I say are speculative in any way; they consider the very basic content and meaning of decoherence and I think that whoever disagrees has just fundamentally misunderstood what decoherence is and is not. But the accuracy of this emergent macroscopic description of what's happening with the probabilities is never perfect, just like macroscopic equations of hydrodynamics never exactly describe the molecules of tea in a teacup.

And without the ability to causally access an infinite number of precisely decohered outcomes, one cannot reliably verify the probabilistic predictions of a quantum-mechanical theory.

Indeed, one can't verify many predictions of quantum mechanical properties, especially about cosmological-size properties that we can only measure once. If you don't like the fact that our multiverse denies you this basic "human right" to know everything totally accurately, you will have to apply for asylum in a totally different multiverse, one that isn't constrained by logic and science.

The purpose of this paper is to argue that these questions may be resolved by cosmology.

You know, I think that there are deep questions about the information linked between causally inaccessible regions - whether black hole complementarity tells you something about the multiverse etc. But this paper seems to address none of it. It seems to claim that the cosmological issues influence even basic facts about low-energy quantum mechanics and the information that is moving in it. That's surely not possible. It's just a generic paper based on misunderstandings of quantum mechanics and on desperate attempts to return the world under the umbrella of classical physics where there was a well-defined reality where everything was in principle 100% accurate.

But the people who are not on crack will never return to the era before the 1920s because the insights of quantum mechanics, the most revolutionary insights of the 20th century, are irreversible. Classical physics, despite its successes as an approximate theory, was ruled out many decades ago.

I have only read a few pages that I considered relevant and quickly looked at the remaining ones. It seems like they haven't found or calculated anything that makes any sense. The paper just defends the abstract and the introduction that they have apparently pre-decided to be true. But the abstract and and introduction are wrong.

You see that those would-be "revolutionary" papers start to share lots of bad yet fashionable features - such as the misunderstanding of the conceptual issues of quantum mechanics and the flawed idea that all such general and basic misunderstandings of quantum physics (or statistical physics and thermodynamics) must be linked to cosmology if not the multiverse.

However, cosmology has nothing to do with these issues. If you haven't understood a double-slit experiment in your lab or the observation of Schrödinger's cat in your living room and what science actually predicts about any of these things, by using the degrees of freedom in that room only, or if you haven't understood why eggs break but don't unbreak, including the degrees of freedom of the egg only, be sure that the huge multiverse, regardless of its giant size, won't help you to cure the misunderstanding of the basics of quantum mechanics and statistical physics.

The right degrees of freedom and concepts that are linked to the proper understanding of a breaking egg or decohering tea are simply not located far away in the multiverse. They're here and a sensible scientist shouldn't escape to distant realms that are manifestly irrelevant for these particular questions.

And that's the memo.