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.

Brian Greene and anti-quantum zeal

First of all, I received my copy of The Hidden Reality a few weeks ago - which I was asked to translate to my mother tongue - and it is mostly excellent. Recommended.

It covers physics from the viewpoint of parallel worlds. This term may have many different meanings that are related to each other in some cases and that are mostly unrelated (and shouldn't be confused) in other cases. But they still make a nice unifying theme for a book that allows the author to cover many topics.

In the initial chapters, Greene explains the modern cosmology beautifully. Is the Universe finite or infinite? Is the expansion accelerating? In a very large Universe, regions may be causally separated and they form a "quilted multiverse" if the total volume is infinite. He adds inflation with its "inflationary multiverse" and explains how the bubbles expand and how they look infinite from inside and finite from outside.




When the topics get more stringy, there are beautiful explanations of the quantum tunneling, with bubbles inside bubbles (which didn't occur in the pre-stringy inflationary cosmology) and the landscape of the stringy vacua. Greene talks about the "brane multiverse", "cyclic multiverse" (selling its marketing points but admitting that everyone thinks that it's babbling), and "landscape multiverse". Later in the book, he would discuss holography (which isn't really a multiverse, but he uses the word here as well), a Platonic multiverse of all mathematical structures, and a few other things.

The landscape multiverse

Of course, the things get controversial when he turns his attention to the anthropic principle. It's still mostly balanced but I think that he vastly underestimates the extent to which the "principle of mediocrity" is ill-defined and probably incorrect. In the anthropic principle as clearly described by Greene, we should expect the probability "P" that a parameter of Nature has value "X" to be the fraction of the observers "P" in the whole multiverse that see the value "X" of the parameter in their surrounding environment.

Fine. Greene thinks that the only problem with this prescription - aside from the difficulty of the relevant maths - is the problem of "infinity over infinity" (illustrated by the question whether the set of even integers is bigger than the set of all integers). There are infinitely many observers and each subset is infinite as well and infinite numbers can't be canonically divided by each other because you don't know how to order the infinite sets so that they could be compared.

I don't think it's the only problem. I don't even think it's the main difficulty of the "measure problem". Even if the multiverse and its history were finite, there would be serious problems with the anthropic reasoning. The main problem is that one doesn't know and cannot know what he counts as an "observer" - is that just humans, or all their cells? Do smarter observers have a bigger weight? Is their measure multiplied by their lifetime and/or the number of thoughts they can make in one life? Are the basic measures proportional to volume of space (at some time) or the volume of spacetime? And so on.

More importantly, he doesn't really admit the key point that the "mediocrity principle" in any form is almost certainly wrong. It's just one particular measure - an attempt to define uniform priors (which can't exist) - but a valid theory can use any other, non-uniform measure as well and chances are that if a measure on the landscape is relevant, it's a highly non-uniform one, whether you view it as a measure on the universes or the observers. There is absolutely no rational reason why the uniform measure should be the right one (someone's being a Marxist who loves egalitarianism everywhere is only an utterly irrational reason).

I don't want to talk about the anthropic principle too much here. At least, I am happy that as far as I can see, The Hidden Reality contains nothing of the Sean-Carroll-style crackpottery about the duty of the early Universe to have a high entropy that have plagued some chapters in Greene's second book, The Fabric of the Cosmos.

Anti-quantum zeal

But right now I am going through the quantum chapter and I can't believe my eyes. In The Elegant Universe, Chapter 4 was actually my most favorite chapter. In my opinion, Greene did a superb job in explaining basics of quantum mechanics over there. And most importantly, there was nothing conceptually wrong about what he wrote, despite the technical simplifications that were needed in a popular book. (The chapter largely avoided the subtleties of "interpretations".) In fact, as far as I remember, that could be said about the whole book.

In this case, it's much more accurate to say that there is nothing right about what Greene wrote about the interpretation of quantum mechanics. It contains pretty much all the laymen's misconceptions one can routinely hear and read in various popular and sometimes even "not so popular" books. All this stuff is frustrating because as far as I can see, there doesn't exist a single popular book about the interpretation of quantum mechanics that would be basically right. Correct me if I am wrong. (Maybe Zeilinger has written something that makes sense?)

So the chapter about the "quantum" or "many worlds multiverse" is a sequence of dozens of pages filled with irrational criticisms of Niels Bohr - who is painted as a really bad guy - and against conventional quantum mechanics. Pretty much every argument is wrong - it's really upside down. Of course, I am professionally translating exactly what the author wrote which doesn't mean that I don't suffer. ;-)

One may say that Greene is squarely in the camp of anti-quantum zealots (I think that this is what he means the "realist camp"), no doubts about that. How the same physicist could have written a totally OK introduction to quantum mechanics in The Elegant Universe is not clear to me. ;-)

Everett's and other misconceptions

So the reader learns about Hugh Everett III, a grad student who wrote a heroic thesis in which he outlined his opinion that Niels Bohr was an idiot and that the probabilistic interpretation of quantum mechanics had to be replaced by something else. John Wheeler, his adviser, liked it, but Wheeler was bullied by the evil Niels Bohr whom Wheeler had to worship, Greene essentially writes, so Bohr and Wheeler forced poor Everett to censor and dilute his thesis. :-)

The reality is, of course, that Everett's original thesis was full of complete junk about the non-existent problems of proper quantum mechanics and Niels Bohr kindly explained to John Wheeler why this stuff was junk. So Wheeler made it sure that Everett wouldn't write this junk into the final draft of his thesis because no person should get a physics PhD if he thinks, in the 1950s or later, that proper quantum mechanics is inconsistent.

Unfortunately, as of 2011, Brian Greene - and all other authors of popular books about quantum mechanics, to be sure that I am not singling him out - still misunderstands why the criticism of quantum mechanics has always been and remains rubbish.

The "collapse"

The main problem that shows that "Bohr is in trouble" is that one needs to get from the ambiguous wave function to the definite outcomes. But Schrödinger's equation doesn't allow such a collapse, so "Bohr is in trouble", we repeatedly read. Holy cow. It's really Greene et al. who is in trouble because he doesn't want to admit that the wave function is just a probability, not a real wave, even though it's clearly needed to explain the experiments that yield clear outcomes.

Greene constantly uses the term "probability wave" for the wave function but he doesn't mean it. It is clear that from almost every sentence that he doesn't believe that the wave function only contains the information about the probabilities. He is still imagining a classical wave.

This is highlighted by pretty much all the details. For example, in the book's discussion, all particles have their "waves" (plural). However, there's only one state vector - or a wave in a higher-dimensional space - that describes the whole world. This is not really a detail. This is a totally essential thing for the discussion of any interactions in a quantum mechanical theory and the measurements in particular. The wave function remembers and has to remember all the correlations between the individual particles.

All these things were beautifully described by Sidney Coleman in his Quantum Mechanics In Your Face lecture. Around 2005, Brian Greene and his friends at Columbia asked me to make the talk located somewhere in Harvard's archives available to them (they wanted to use it somewhere) - which I/we did, if I remember well - but Greene had to be very disappointed because this talk by Coleman proves very clearly why exactly the opinions about quantum mechanics held by Greene are fundamentally wrong.

Does normal quantum mechanics predict that we will see a "mixed haze" of different outcomes? The answer is a clear No.

As Coleman emphasized, to discuss these questions, we have to describe not only the microscopic particle but also the apparatus - or the humans - in terms of quantum mechanics. When we do so correctly, we may easily prove that the humans always perceive a definite outcome.

The first proof of this kind was pointed out in the early days of quantum mechanics by my English great granduncle Nevill Mott. He considered a bubble chamber and asked why the particles leave clear tracks going in one direction instead of some diluted isotropic fog.

Well, one may prove - and he did prove - that there is a correlation between the bubbles' angular direction. So if the particle creates the first bubble in the Northern direction, one may show that the momentum points into this direction and the second bubble will also be in the Northern direction. This is a statement that can be clearly shown in a quantum mechanical description of the particle plus the whole bubble chamber.

The same thing holds for another basis vector in which the particle moves into another direction, and so on. So if we define the operator "P" that has eigenvalues 1 or 0 if the first two bubbles appear in the same direction or not, respectively, then we can show that for any initial state of the particle in the bubble chamber, the eigenvalue is 1. It follows that the eigenvalue is 1 for any linear superposition, too.

Brian Greene probably uses a nonlinear operator whose eigenvalue is 1 ("sharp track/answer") when acting on basis vectors North or South, but 0 ("fuzzy dizzying track/answer") when acting on any nontrivial linear superposition of North and South. But such a "Greene operator" violates a basic postulate of quantum mechanics that all observables and properties of physical systems (and all perceptions and any other phenomena and questions with answers that may be talked about) are and must be encoded in linear operators. If you're answering questions about physics with something else than linear operators, you're not doing quantum mechanics, at least not correctly!

In other words, particles will leave a clear, straight track regardless of their initial state. The particle may be in an s-wave which is spread all over the sphere. But that won't change the fact that the angular directions of the individual bubbles stay correlated.

In the same way, one may ask whether Schrödinger will have mixed or sharp feelings after he observes his cat. The cat is either alive, in which case Schrödinger will be happy, or dead, in which case he will be sad. Both happy and sad states have eigenvalue of the operator "Schrödinger has a well-defined feeling" equal to 1, i.e. yes. (I could use the same argument for the cat itself but I chose its owner. Brian Greene explicitly contradicts this simple calculation and says that the humans will have "confused feelings" - seeing a display showing "Grant's Tomb" and "Strawberry Fields" at the same moment - which is just unambiguously and demonstrably wrong.) So any linear superposition has the same eigenvalue. It follows that observers always have well-defined feelings about the cat. I don't need any collapse. There is no collapse.

I can just calculate the probability that the answer is Yes according to the probabilistic rules of quantum mechanics and the results is 100 percent. So the debate is over. 100 percent means that the answer is settled. 100 percent is certainty. Saying that something else is needed by quantum mechanics to answer this question is just pure bullshit. Readers (and writers) of popular books love to paint quantum mechanics as a realm where everything is fuzzy and diluted; it's spread everywhere. But that's not the case. Despite the probabilistic character, proper quantum mechanics perfectly remembers all the correlations that exist - and predicted correlations may often be higher than what any classical theory could achieve (as constrained by Bell's inequalities and their generalizations). In this case, predictions of quantum mechanics are often sharper and more certain than predictions of classical physics. In particular, some statements may be calculated to have 100-percent probabilities. Those statements are certain.

A similar discussion holds for the question why the results of the repeated experiments are random. Design any quantity that measures some non-randomness of the sample. For example, repeat the same experiment measuring a spin (up or down) 1 million times and try to find a correlation between the two measurements that follow after each other - that would prove that the sequence isn't quite random. But you may calculate this correlation from quantum mechanics and it's zero in the limit of infinitely many repetitions. Experiments confirm it. The results are random - any other test will also show that - and this fact can be proved by the basic framework of QM; nothing else is needed.

Again, I don't need to talk about any collapse. This has nothing whatsoever to do with collapse. There is no physical process that could be called the collapse. It's about the validity of a proposition and quantum mechanics has a totally well-defined recipe to calculate the probability that a proposition is right. In these textbook cases (Do observers have sharp feelings? Are the results of independent repetitions of the same experiment uncorrelated?), the calculated probability is 100 percent, which means that quantum mechanics unambiguously implies that these things have answers and they're the answers we know.

Also, Coleman has discussed the alleged "nonlocality" of quantum mechanics. There's nothing nonlocal about entanglement - it's just a damn correlation. In the simplest cases, there isn't even an interaction Lagrangian, so the interactions surely can't be nonlocal. Even in interacting theories, we usually have a strict locality - that's why relativistic quantum field theories are also called local quantum field theories. Phenomena's (and especially decisions') impact on spatially separated other phenomena is strictly zero. The idea of a "nonlocality" in EPR setups is always an artifact of the confused person's attempt to imagine that the wave function is an observable that has to be "remotely modified" to avoid problems. But the wave function is not [an] observable.

Saying that quantum mechanics is incomplete (or even invalid) in its answers to any of these questions is clearly and self-evidently incorrect. Pretty much all the authors of popular books on quantum mechanics want to promote these questions to some huge, religion-scale philosophical mysteries that can never be fully grasped or solved and that break Niels Bohr's teeth and render his theory inconsistent or incomplete. In reality, they're easy homework exercises that an undergraduate student who wants an A from quantum mechanics should be able to calculate within minutes.

Now, if someone faces severe psychological problems in accepting that the fundamental laws of physics make probabilistic predictions, he may try to invent silly ways how to "visualize" what's going on - from imagining the wave function as a "classical wave" (that has to "collapse") to imagining many worlds of Everett. But these psychological problems of the person can in no way justify the statement that there is something incomplete or wrong about proper quantum mechanics.

There's nothing wrong or incomplete about quantum mechanics - and on the contrary, there's a lot of wrong things about all the "theories" of "not quite quantum mechanics". In fact, none of them works as a description of all the known things about the world. Also, as Coleman emphasizes, the very notion of a field looking for "interpretation of quantum mechanics" is based on a misunderstanding. Everywhere in the history of physics, only the previous phenomena described by a simpler approximate theory may be interpreted within a more complete theory. So it makes sense to talk about the "interpretation of classical physics" within quantum mechanics - but not in the other way because quantum mechanics is the more correct, complete, and accurate theory while classical physics is the less correct, incomplete, and approximate one!

Anti-quantum zealots and geocentrism

For those who haven't heard the punch line of Sidney Coleman's lecture, I can't resist to recall it.

At the very end, Sidney paraphrases a wise comment by philosopher Ludwig Wittgenstein. People used to believe geocentrism. Wittgenstein asked why people usually considered such a belief in the past "natural". His friend told him that it was because it "looks like" the Sun is revolving around the Earth. Wittgenstein replied with this key point:

Well, how would it look like if it had looked as if the Earth were rotating? :-)

Obviously, it would look exactly like the world around us. ;-)

[It's natural for things to move - and people could have known for quite some time that "free motion" is indistiguishable from the rest (the old principle of relativity, perhaps combined with the equivalence of inertial and gravitational masses).]

In the same way, authors of popular books on quantum phenomena still find it "natural" to think that there is a "realist" or classical picture behind quantum mechanics because it "looks like" there is a "realist" or classical picture in the quantum mechanics. Oh, really?

Well, what would it look like if it looked like that the world is really following the causal laws of quantum physics without any reductions of the wave packets - and not any laws of classical physics - at the fundamental level?

Needless to say, it would look exactly as our ordinary everyday life. Welcome home. :-) And thank you for your patience.

NPR: Brian Greene on The Hidden Reality

Ira Flatow interviews Brian Greene for 17 minutes if you have time (audio). It's not only about Brian's new book.

Somewhat controversial hypotheses but as Brian says, the book is not an uncritical manifesto for the multiverse.

The enigmatic cosmological constant

The cosmological constant remains one of the most mysterious players in the current picture of the world.



A building of the Faculty of Natural Sciences of the Charles University in Albertov. In those buildings, where the Velvet Revolution began on November 17th, 1989, Einstein spent a few years but he (and Mileva) didn't like Prague much. Just to be sure, the place had been called Albertov well before Einstein came there: it's named after Prof Eduard Albert MD (1841-1900), a Czech surgeon and poet.

In 1915, after a decade of intellectual self-torture in Prague and elsewhere, Einstein managed to write down the final form of Einstein's equations:



They're pretty. Please imagine that there is a minus sign in front of "8.pi". The convention above is bad.

When I was 15, I would write them about 50 times in my notebooks, in beautiful fonts. ;-) Both sides describe 4 x 5 / 2 x 1 = 10 functions of space and time - a symmetric tensor field. The left-hand side is the "Einstein tensor", describing some information about the curvature of the spacetime. (The term "R_{mu nu}" itself is called the Ricci tensor.) The right-hand side is proportional to the stress-energy tensor "T_{mu nu}". It encodes the density and flux of mass/energy and momentum - which are the sources of the spacetime curvature.




Einstein quickly realized that there was a price to pay for the dynamically curving spacetime: it wasn't able to sit at rest. Instead, the total size of the Universe - or the typical distance between two galaxies - would behave just like the height of a free apple according to Newton's equations. It can fly up and decelerate; or it can fly down and accelerate. But it can't sit in the middle of the room.

For Einstein, this was unacceptable. Much like everyone else in the (de-Christianized) physics community, he was convinced that the Universe has always existed. It had to be static, he thought. (He could have predicted the expansion of the Universe but he didn't. It had to wait for experimenters such as Edwin Hubble. We will mention this point later.)

In 1917, in order to make the Universe static, he added the term

+ Lambda g_{mu nu}

to the left hand side of his equations. The value of the positive cosmological constant "Lambda" he needed for his static Universe - whose geometry is "S^3 x R" (three-sphere times time) - was

Lambda = 4.pi.G.rho_matter

where "rho_{matter}" was the average mass density of the Universe as envisioned by Einstein. The negative value of the pressure would become more important than the positive energy density, and it would prevent the Universe from collapsing, keeping the curvature radius of the 3-sphere equal to "1/sqrt(Lambda)". (The fixed size would be unstable, much like a pencil standing on its tip, but I won't discuss these extra pathologies of Einstein's "solution" in any detail.)

This value of "Lambda" had the right sign and was actually comparable to the currently believed value of the cosmological constant, as I will clarify below. It's either rather accurate or more accurate, depending on what you substitute for "rho_{matter}". Our Universe is not Einstein's static Universe, so we can't measure the right "rho_{matter}" to substitute to these wrong equations ;-) or more precisely right equations with wrong assumptions about the parameters (driven by desired solutions).

You may also move the cosmological constant term to the right-hand side of Einstein's equations which would become

-8.pi.G.(T_{mu nu} + Lambda/8.pi.G g_{mu nu}) =
= -8.pi.G.(T_{mu nu} + 2.rho_matter.g_{mu nu})

Note that in this way of looking at Einstein's equations with the cosmological constant, the cosmological constant is nothing else than a correction to the stress-energy tensor. This correction is proportional to the metric tensor. A positive cosmological constant is nothing else than an addition of a positive energy density and a negative pressure, "p = -rho".

For Einstein's universe to be static, the required "rho" is actually equal to "2.rho_{matter}" where "rho_{matter}" is the average density of matter (assumed to be approximately dust) in the static Universe. Note that if Einstein had known dark matter and visible matter, and if we neglected that they're not quite dust, "rho_{matter}" would be 4+23=27% of the critical density, and this times two is equal to the 54% of the critical density. That would be needed for our Universe to be static.

Because the actual value of the energy density stored in the cosmological constant is about 73% of the critical density which is more than the figure 54% mentioned above, our Universe is actually accelerating its expansion. But you see that the difference between 54% and 73% is not too high. In fact, it's not a long time ago when the acceleration was zero - when the Universe was gradually switching from decelerating expansion to accelerating expansion.

But in that moment, the Universe wasn't static because it still had a positive value of the "velocity" of the expansion. Just the acceleration - another derivative of the velocity - was zero. If you wonder when was the moment when the acceleration was zero, it was approximately six days before God created the Sun and the Earth, about 4.7 billion years ago. ;-)

I ask the Christian readers not to get carried away. It's a complete coincidence - believe me more than the Bible even though it may be hard :-) - and I admit that the six-day accuracy was a little bit exaggerated. The error margin of the figure 4.7 billion years is below 10 percent, however.

Blunder

Of course, when the expansion of the Universe was found by Hubble in the late 1920s, Einstein was upset that he had failed to predict it. If he had predicted it, he could have become more famous than Isaac Newton if not Juan Maldacena. ;-)

That's why Einstein swiftly identified the addition of the cosmological constant term as the greatest blunder of his life. Of course, this was far from a great blunder. In fact, we currently know that the term is there. The greatest blunder of Einstein's life was that he didn't give a damn about quantum mechanics in particular and empirically based science in general in the last 30 years of his life.

Let's look at the reasoning that led Einstein to think that the addition of the term was the greatest blunder. Of course, Hubble had showed that the term wasn't needed because the Universe was expanding, exactly the possibility that Einstein wanted to avoid rather than to predict. But Einstein surely had an a posteriori theoretical reason to think that the term was bad, hadn't he?

Well, the term was "ugly", he thought. It was spoiling the beautiful simplicity of the original Einstein's equations, Einstein would say.

However, we must be extremely careful about such subjective emotional appraisals of the beauty. They may easily be wrong. The sense of beauty is only a good guide for you if it is perfectly correlated with Nature's own taste. Even Einstein has failed to achieve this perfection correlation at many points of his career.

Do we have a more scientific reason to trust Einstein's equations, instead of saying that they're "pretty"? The "counting of the number of terms on the paper" is surely an obsolete criterion for the beauty, especially because the maximally supersymmetric supergravity has many terms, despite being the prettiest theory in the class. So why would we rationally think that Einstein's equations are "prettier" than similar equations in which we would add e.g. squared curvature terms, among others?

Well, we have understood the reason at least since the 1970s - when the ideas of the renormalization group in particular and the organization of the laws of Nature according to the scale in general became a key pillar of the physics lore. The actual reason why the "squared curvature" and even more complicated terms are "bad" is that these terms only become important at short distances. Each factor of a curvature in each term of such equations is approximately adding a factor of "1/squared_curvature_radius". So to protect the right dimension of the terms, it must be multiplied by a coefficient that goes like "length^2".

What is the "length"? Well, it's some special length scale where the behavior of physics changes - and some new terms become important or negligible, depending on the direction where you go in the length scale. The general experience in particle physics indicates that all such scales "length" are microscopic: the size of the atom, proton, electron. And the Planck length is the shortest one.

So at all distances much longer than this macroscopic "length", all the higher-derivative terms - such as the powers of the Ricci tensor - may be neglected. That's really why Einstein's equations, without those extra terms, are a good approximation for long-distance physics. That's why we shouldn't add the "ugly terms".

What about the cosmological constant term?

Well, it actually has fewer derivatives than the curvature tensor: it is even more important at long distances than the curvature tensor in the original Einstein's equations! So we can't neglect it. According to the modern replacement for the "beauty criterion", you can't eliminate it. Einstein's decision to call the cosmological term "ugly" was an example of his flawed sense of beauty.

Quantum physics

And indeed, as we have known from 1998 or so, the cosmological constant is positive because the expansion of the Universe is actually accelerating (it was a big surprise). In fact, it's bigger than what would be needed for the acceleration of the Universe to vanish - what would be needed for Einstein's static Universe. That's why the expansion of the Universe is accelerating. The greater positive cosmological constant you add, the more capable it will be to accelerate the expansion.

(The term "dark energy" is sometimes used instead of "cosmological constant". Dark energy is whatever drives the accelerating expansion and the nature of "dark energy" is deliberately vague. However, accurate observations indicate that "dark energy" has exactly the same properties as a positive cosmological constant, so you may pretty much identify the two terms.)

The energy density carried by the cosmological constant is about 3 times larger than the energy density carried by dark matter and visible matter combined.

Now, you have to realize that the cosmological constant is the energy density of the vacuum. Use the convention in which the cosmological constant term is moved to the right hand side of Einstein's equations. And define the tensor "T_{mu nu}" in such a way that it vanishes in the vacuum. But there's still an extra term added to "T_{mu nu}" which is, therefore, the stress-energy tensor in/of the vacuum.

Can our theories explain that this energy density of the vacuum is nonzero? Well, they can. Too well, in fact. ;-) They explain it so "well" that their predictions are wrong by 60-123 orders of magnitude. :-)

Needless to say, the value of the cosmological constant can't be calculated from "anything" in a classical theory. You need to assume a value and any value is equally legitimate.

In quantum field theory (at least a non-supersymmetric one), you may decide that the classical value of "Lambda" inserted to the equations is zero. But even if the classical value is zero, the total value of the cosmological constant is not zero.

As you should know, quantum field theory produces quantum effects - temporary episodes in which particle-antiparticle pairs emerge from the vacuum and disappear shortly afterwards. These quantum effects modify the masses and energies of all objects (aside from other properties). They change the mass of the Higgs (that's why there's the hierarchy problem) and everything else; they move energy levels in the atoms (by the Lamb shift and many other shifts), and many other things.

They also change the energy density of the vacuum. In particular, if you consider Feynman diagrams without any external lines, they determine the quantum mechanics' contributions to the vacuum energy density. Because of the Lorentz symmetry of the original theory, this quantum-generated energy density is automatically promoted to a stress-energy tensor that has to be proportional to the metric tensor - the only invariant tensor with two indices - so the pressure is always "p=-rho", just like for the cosmological constant.

The simplest diagrams without external lines are simple loops (circles) with a particle running in it. They contribute to the vacuum energy density by something proportional to

+-mass⁴

where "mass" is the rest mass of the corresponding particle species. The bosons contribute positively; the fermions contribute negatively.

The observed value of the cosmological constant, if expressed as the energy density, is approximately equal to

mass_neutrino⁴,

i.e. the fourth power of the lightest massive particle we know, a neutrino. This relationship is only approximate - as far as I know. It may be a coincidence but it doesn't have to be a coincidence. (In the "c=hbar=1" units I use, the energy density is energy per cubic distance but the distance is inverse energy, so the units are "energy^4" or "energy^d" in "d" spacetime dimensions.)

To get the finite number above, we may have to choose a regularization scheme, and it seems helpful here to assume dimensional regularization. (But the final result is not too compatible with the observations, anyway, so it's questionable whether the method is really helpful. But we will continue to assume that this basic calculation is valid.)

So if the neutrinos were the only particles that would contribute their quantum loops to the cosmological constant, you would get approximately the right vacuum energy density (with a wrong sign because neutrinos, being fermions, contribute a negative amount to the energy density).

However, there are many particle species that are heavier than the neutrinos. In particular, the top quark is approximately 10^{15} times heavier than the lightest neutrino (or the smallest neutrino mass difference; we can't quite measure the absolute neutrino masses today). Because it's the fourth power of the mass that contributes to the vacuum energy density, the top quark loop contributes a negative term that is about 60 orders of magnitude too large.

And then you have all the conceivable contributions to the cosmological constant from the "intermediate" particles between the neutrinos (which are OK) and top quarks (which are 60 orders of magnitude too high). Every effect you may imagine - including confinement, Higgs mechanism, and other things - modifies the value of the cosmological constant.

For the Higgs field, for example, it's important to distinguish the potential energy at the local maximum and the minimum. We live at the minimum but the cosmological constant would be vastly (60 orders of magnitude) higher at the local maximum. And it's just the Higgs field.

And as simple particles as the top quark or the Higgs boson give you contributions that are 60 orders of magnitude too high. In fact, the top quark is almost certainly not the heaviest particle in the world. Particles worth the brand "particle" may exist up to the Planck scale which is 15 orders of magnitude heavier than the top quark. (Particles heavier than the Planck scale are black hole microstates.) Clearly, if you include the heaviest, near-Planckian particle species (e.g. the new particles predicted by grand unified theories), you will get contributions to the cosmological constant that are about 120 orders of magnitude too high.

In fact, the observed cosmological constant is equal to "10^{-123}" in the Planck units - a very unnatural pure number.

How is it possible that the sum of all the effects and loops of particles of diverse masses ends up being so tiny, comparable to the contribution of the lightest neutrino which is ludicrously lighter than the Planck scale?

Supersymmetry

You may have noticed that the contributions of the bosons are positive while the contributions of the fermions are negative. Can you cancel them?

Well, a problem is that the masses of the bosons are some random numbers, and the masses of the fermions are other random numbers. There's no reason for them to cancel exactly or almost exactly. 3-6+9-15+48-98 has a chance to be zero but it's probably not zero.

Things change if you have unbroken supersymmetry. If supersymmetry is unbroken, each boson has a fermionic partner and vice versa. The masses of both partners exactly match. When it's so, it follows that the total quantum correction to the cosmological constant vanishes. (You may still need to be careful about a "classical" term that could have been nonzero to start with. In my opinion, it's rather reasonable to expect or require that the classical term has to be zero in realistic vacua.)

However, supersymmetry in the real world has to be broken. The mass differences between the pairs of superpartners are at least as large as the top quark mass - at least some of them. It follows that you still get an uncanceled contribution that is comparable to the contribution of the top quark we chose as a benchmark. And it's 60 orders of magnitude too high.

At least, you get rid of the larger contributions that could arise from the near-Planckian heavy particles and that would be 120 orders of magnitude too high. With broken supersymmetry, the discrepancy between the measured and "estimated" cosmological constant gets reduced from 120 orders of magnitude to 60 orders of magnitude.

It looks like progress - we have already done 1/2 of the job. While it's true, there is also some sense in which the - smaller - discrepancy obtained in the supersymmetric context (supergravity, in fact, because we want to include gravity as well) is much more "real" than in the non-supersymmetric context.

I still believe that all the physicists are confusing themselves with the "estimates". Particular theories or string vacua - perhaps a bit different than the popular ones; perhaps the same ones with a more correct calculation of the vacuum energy density - could actually lead to a more accurate cancellation than what is suggested by the estimates. The discrepancy of the 60 orders of magnitude could be fake.

There have been many episodes in the history of physics in which people made a very sloppy estimate and they (thought that they) ruled out a correct theory because of this estimate. For example, people would believe that the gauge anomalies in all chiral vacua of string theory (with Yang-Mills fields) had to be nonzero. They believed so until 1984 when Green and Schwarz showed that the complete calculation actually produces an answer equal to zero. That sparked the first superstring revolution.

I find the "generic" estimates of the cosmological constant to be equally sloppy to the arguments in the early 1980s that the gauge anomalies in string theory had to be nonzero. There can also be a contribution from a counterpart of the Green-Schwarz mechanism. The total could be 10^{-120} in Planck units. And much like in the Green-Schwarz anomaly cancellation, there may exist more "profound" and "simpler" ways to show that the cosmological constant cancels much more accurately than people expect.

A big difference is that in the case of the type I string theory's gauge and gravitational (and mixed) anomalies, we know that they cancel. We know the Green-Schwarz mechanism and other things. The "similar" scenario for the cosmological constant remains a speculation or a wishful thinking, if you wish. So we can't say that science has showed that the situations are analogous. I still think that this wishful thinking is relatively likely to be true.

Landscape of possibilities

In quantum field theory, you may adjust the classical value of the cosmological constant to any number you want. So you may adjust it so that when the quantum corrections are added, you get exactly the desired value.

String theory is much more rigid and predictive. You can't adjust anything. Much like quantum field theory, string theory allows you to calculate the quantum corrections to the cosmological constant - and all other low-energy parameters - but unlike quantum field theory, it also allows you to calculate the classical pieces, too. There's no dimensionless continuous static parameter in string theory that would be waiting for your adjustments.

There are only discrete choices you can make - the topology of a Calabi-Yau manifolds; integers encoding the number of branes wrapped on various cycles and magnetic fluxes; and some related discrete data.

If you believe that there's no Green-Schwarz-like miracle waiting for us, then you must probably agree with the anthropic people who say that the most likely prediction of the cosmological constant by a single semi-realistic vacuum is comparable to the Planck scale, about 120 orders of magnitude too high.

If you believe so, then you face a potential contradiction which is "very likely" if the theory produces a small number of candidate vacua. In such a situation, the existence of more than 10^{120} solutions that string theory offers is saving your life. It's saving you from the discrepancy. The large number of solutions de facto allows you to do the same thing that you could do in quantum field theory. In quantum field theory, you could continuously adjust the cosmological constant (and all other parameters). In string theory, you're not allowed to adjust it continuously but the number of solutions is high enough so that you may adjust it "discretely" and "almost continuously".

I still think that one should try not to rely on such mechanisms that are meant to be able to cure any inconsistency by a universal metaphysical trick. (This nearly religious "cure for everything" is common among low-level physicists such as the loop quantum gravitists who think that they can cure "all UV problems" by their spin network aether, without doing any special work. That's too bad because in a consistent framework with a QFT limit, one can prove that e.g. gauge anomalies cannot be cured. So any framework that allows you to argue that even theories with gauge anomalies can be defined is inevitably internally inconsistent.)

There seems to be a disagreement between the observed and estimated value of the cosmological constant so we should work hard to improve our estimates. We should find previously neglected terms and mechanisms that, when accounted for, make our estimates more compatible with the observations.

The opposite, anthropic attitude could have been used to "solve" any puzzle in the history of science. But in every single puzzle we understand (and consider to be solved) today, we have learned that the anthropic solution was wrong. The neutron is "anomalously" long-lived but we don't need a landscape to explain that (even though the longevity could be argued to be important for life); we can calculate the lifetime and it's the "small phase space" of the decay products that makes the neutron more stable than expected.

And I can tell you thousands of such examples of puzzling features of Nature that could have been explained by the anthropic hand-waving but the right explanation turned out to be different and more robust.

Supergravity seems to be rigid when it comes to the calculation of the vacuum energy density and those 60 orders of magnitude of disagreement seem to be real today. But we may be mistreating the vacuum graphs in supergravity. We may be missing the counterpart of the Green-Schwarz anomalous transformation laws. We may be missing some purely quantum effects that only (or primarily) affect the tree-level graphs. We may be missing alternative ways to prove an almost exact cancellation.

The cosmological constant may be linked to

mass_neutrino⁴

as I have suggested above and there may exist a good reason why. For example, the value of Lambda could be running in a bizarre way and the running could stop below the neutrino mass (the mass of the lightest massive particle), guaranteeing that the value of "Lambda" stays comparable to the fourth power of the neutrino mass. (In a similar way, the fine-structure constant doesn't run beneath the mass of the lightest charged particle, the electron.) A value of "Lambda" that is vastly higher than "mass^4" could make the effective (gravitating) field theory defined for the "mass" scale inconsistent for a currently unknown reason.

And because 60 is one half of 120, the observed cosmological constant may also be related to the ratio

m_Planck⁸ / m_Top⁴

where I chose the top quark mass - our previous benchmark - to represent the electroweak scale or the superpartner SUSY-breaking scale which is arguably not far from the electroweak scale. I have about 5 different scenarios how some of these formulae could be shown correct on a sunny day in the future. Needless to say, I realize that none of those scenarios is fully convincing at this point. But people should keep on trying, anyway.

And that's the memo.