Sean Carroll continues to abuse his blog to promote his pseudoscientific would-be research:



ESP: The credence one should assign to being any one of several observers having identical experiences is independent of features of the environment that aren’t affecting the observers.



ESP (partially fixed): If you measure some quantity \(X\), the result is independent of some completely different quantities \(Y\) that you don't measure.



The article advertises his May 2014 preprint written along with a philosophy student, Charles Sebens. I have already discussed a text by these two authors in Measure for Measure... in May 2014. It turns out that they have written two very similar preprints . Yes, Sebens wrote another earlier paper – the title "Quantum Mechanics As Classical Physics" shows that this guy is hopeless, indeed.First, sociologically, I think it is very unfortunate if the blogosphere is used for this self-promotion. The scientific community and the scientific public should evaluate the papers and ideas according to their quality and not according to the number of times when they are promoted in distorted blogs on the Internet. The Carroll-Sebens preprints are pure trash which is why, in an ideal world, they would immediately drop into the cesspool and no one would try to extract them again. We don't live in the ideal world. We live in a world where people are massively fed the objects from the cesspools by feeders such as Sean Carroll. The claim is that they may derive Born's rule (that the probability is the squared absolute value of the inner product) from something deeper, namely from the many worlds fairy tale.It doesn't make any sense whatsoever. I have discussed the numerous dimensions of why these claims are preposterous many times.You can't really derive the probability rules from "anything deeper" because they're the most elementary part of a theory that makes fundamentally probabilistic predictions.The actual reason behind Born's rule – the gem – was explained at the end of my May 2014 blog post and it has surely nothing to do with many worlds.The point is that any physical theory, classical, quantum, or otherwise, has to define how its mathematical formalism expresses the fact that two states are mutually exclusive. In classical physics, two different points in the phase space are always mutually exclusive. In quantum mechanics, the mutual exclusiveness of two states is simply the orthogonality. For example, in the basis of eigenstates of an operator such as \(L_z\), the different coordinates (probability amplitudes) directly represent the mutually exclusive values \(L_z=-\ell\), \(L_z=-\ell+1\), and so on, up to \(L_z=+\ell\).I don't have to explain to you that \((1,0,0,\dots)\) is orthogonal to \((0,1,0,\dots)\), do I?Now, we need to know that the probability is a function of the length of the vector in the Hilbert space. This fact has to be assumed in one way or another. It may be argued to be necessary for any interesting theory. Unitary transformations form an interesting class of transformations and they are defined by keeping the length of a complex vector constant. One may eliminate other "alternative theories" that wouldn't represent transformations by unitary transformations, and so on. In all these cases, one would have to assume some extra things because one can't really cover all theories of unknown types. But surely among all the theories that have been proposed, the unitarity of the linear transformations may be shown to be necessary.Again, we need to know that mutually exclusive states are orthogonal and the probability has something to do with the length of a state vector (or its projection to a subspace).That's everything we need to assume if we want to prove Born's rule. The rest of Born's rule – I mean the choice of the second power – follows from the Pythagorean theorem. If you want me to be really specific and use my example (of course that it may be said completely generally), the probability that \(L_z\) is either \(m\) or \(m-1\) is equal to some function of the complex amplitudes \(c_m,c_{m-1}\).On one hand, the probability of the "or" proposition merging two mutually exclusive possibilities has to be the sum of the probabilities of each and these individual probabilities are written as functions of the lengths of the projected vectors\[P_{\rm or} = f[|c_m|]+f[|c_{m-1}|].\] On the other hand, we should be able to calculate the probability of the "or" proposition directly from the length of the whole vector,\[P_{\rm or} = f(\sqrt{|c_m|^2+|c_{m-1}|^2}).\] You may see that the two formulae for \(P_{\rm or}\) are only equal if\[f(c) = \alpha\cdot |c|^2\] because the Pythagorean theorem implies that only the second powers behave "additively". The extra arbitrary parameter \(\alpha\) plays no role and one may set it to \(\alpha=1\).That's the real reason why Born's rule works. The probabilities and mutual exclusiveness has to be expressed as a mathematical function or property of state vectors and the totally general rules for probabilities (like the additive behavior of probabilities under "or") heavily constrain what the map between the "human language" (probability, mutual exclusiveness) and the "mathematical properties" can be. The solution to these constraints is basically unique. The probabilities have to be given by the second powers of the moduli of the complex probability amplitudes. It's because only such "quadratic" formulae for the probabilities obey the general additive rules, thanks to the Pythagorean theorem.(The derivation may be reverted, of course. If we know Born's rule – that the probabilities are given by the second power of the length – we may prove that mutually exclusive states are orthogonal because only orthogonal vectors and their hypotenuse are those that obey the Pythagorean theorem; much like the mutually exclusive options obey the additivity of probabilities under "or".)Once we know the simple (a priori counterintuitive, maybe, but extremely important and universal) rule, it becomes meaningless to talk about its "origin" again. Shut up and calculate. There can't be anything that would be "deeper" yet "clearly independent" from the Born's axiom. The axiom, schematically \(P=|\psi|^2\), really has six characters and is based on some simplest concepts in linear algebra. You may hardly imagine a more concise, simpler, or more fundamental starting point! Such an even simpler starting point would have to be something like "OM". ;-) People who have a trouble with the fact that something like Born's rule is fundamental and true must clearly have different reasons than the "lack of simplicity" to invent non-existing problems.Many of Carroll's readers manage to see through the cheap tricks. Carroll and Sebens aren't really deriving anything. One can't derive Born's rule from anything much deeper. You see that the proof above only used modest assumptions – no "second power" was directly included in any assumption – but it had to assume something. It is totally OK in science to assume something. Science is about formulating ("guessing", as Feynman would put it) competing hypotheses and deciding which of them is right by looking at the empirical evidence and thinking about it carefully enough. Quantum mechanics with its postulates was "guessed" and it has won the battle of science (against its proposed or just dreamed-about competitors) more clearly than any other general theory in the history of science.An example of Carroll-Sebens circular reasonining is that they assume that small off-diagonal entries of a density matrix may be neglected – they assume it before they derive or admit that the small entries correspond to probabilities. That's, of course, illegitimate. If you want to replace a small quantity by zero, and to be able to see whether the replacement is really justified, you have to know what the quantity actually is. Moreover, these things are only negligible if classical physics becomes OK, so whatever you do with this approximation is clearly saying nothing whatsoever about the intrinsic, truly quantum, properties of quantum mechanics in the quantum regime!Moshe Rozali and others re-emphasize that the "film with cats" illustration of the "splitting worlds" only works for a binary spectrum but many other observables have many eigenvalues and in many cases, the spectrum is actually continuous. Carroll never says how the worlds are split to a continuum of worlds and how e.g. the mutual exclusiveness is counted over there. He can't because there can't be any sensible answer. He doesn't ever answer whether the number of worlds today is higher than the number of worlds yesterday. He can't because there can't be any sensible answer. He never answers questions about the possibility for the "split branches" to reinterfere again in the future. He can't answer because there is no sensible answer: they clearly can reinterfere in the future in principle, quantum mechanics implies, while the very point of the "many worlds paradigm" is to make a major mistake and argue that the "splitting" is absolutely irreversible. It's never absolutely irreversible.Incidentally, Moshe Rozali also says that the many worlds paradigm doesn't define – and, well, cannot really define – how often the splitting occurs. Rozali uses the example of particle collisions.When two protons collide, they may be described as protons. But they may also be described with a higher resolution, as bound states of many quarks and gluons. The collision may produce a Higgs boson for a little while which decays to two tau leptons (yes, the Kaggle contest causes a professional deformation). Those later decay.Now, we may ask whether the worlds split already when the taus are produced, or only when the taus decay to the final products, and so on. In all these cases, the answer of a correct quantum mechanical calculation is unequivocal: the most accurate quantum calculation doesn't allow any splitting whatsoever, at least not before the measurement is made. The Higgs boson and taus are strictly speaking virtual and the histories with these virtual particles interfere with other histories without Higgses or without taus (I am just saying that to calculate cross sections, you have to sum over Feynman diagrams with different, all allowed intermediate particles: every particle physicist who is not completely hopelessly incompetent knows that). It's just wrong to imagine that in a particular collision, the existence of a Higgs or the taus is a "strictly well-defined" piece of classical information. It's not. Saying that we're on a branch that either had this Higgs or didn't have the Higgs is a major mistake – which may only be harmless because the virtual particles are nearly on-shell (so that a particular Feynman diagram with a virtual particle is much greater than some other diagrams) and because the classical approximation is tolerable. But the virtual particles are never exactly on-shell and classical physics is never the exact description of the reality, so the "many worlds" description is always at least partially wrong.Similar questions apply to the question whether the "splitting of the worlds" applies to the initial protons or initial gluons etc. In all cases, a "splitting" is just something that makes the calculation conceptually wrong, something that adds errors which may be small if classical physics is an OK approximation but which are very large and of order 100% in the strict quantum mechanical regime.The mushy and sloppy reasoning doesn't appear just in some places of the Carroll-Sebens paper. Virtually every "idea" or sentence is flawed, illogical, or vacuous. For example, a principle is called "ESP":"ESP" isn't "extrasensorial perception", or at least Carroll and Sebens don't want to admit that it is. Instead, it is the "Epistemic Separability Principle". Pompous phrases is something that pompous fools enjoy.There are problems with the "principle" at every level. First, the probability is interpreted as the "credence" which is a deliberately vague version of the "Bayesian probability". The problem is that at least in the world with many repetitions of the same experiment, the probability has to manifest itself in the frequentist way, too (the ratio of repetitions/worlds that have some property and those that don't). But in their picture, the frequentist picture never emerges. So they are actually assuming a "Bayesian" interpretation of the probability when they are claiming to derive that they can live without it, and so on.The other obvious problem with the ESP quote above is that it says what the "credence" is independent of. But a usable theory should actually say what it does depend upon. Ideally, one should have a formula. If one has a formula, one immediately sees what it depends upon and what it doesn't depend upon. A person who actually has a theory would never try to make these unnecessarily weak statements that something does not depend on something else. Isn't it far more sensible and satisfactory to say what the quantity does depend upon – and what it's really equal to? Quantum mechanics answers all these questions very explicitly, Carroll and Sebens don't.The statement is not only weak to the extent that it is useless. It is really intrinsically ill-defined. If we say that \(S\) is independent of \(T\), then we must say what other variables are kept fixed while we are testing the (in)dependence of \(S\) on \(T\). Do we keep \(p\) fixed or do we keep \(V\) fixed? I deliberately chose these letters because you should know this exact problem from thermodynamics. The entropy \(S(V,T)\) written in terms of the volume and the temperature may be independent of the temperature, but the entropy \(S(p,T)\) written in terms of the pressure and the temperature may depend on the temperature!So without saying what are the other observables that \(S\) (or, in the quantum wars case, the probability) may depend upon, saying what they don't depend upon is absolutely vacuous and ill-defined.If you want to strip the ESP proposition of all the nonsense, ill-defined words, and everything else, it really says:Nice but it's a completely worthless tautology. Yes, if you're looking at a cat, you're not looking at a dog. The pompous language may prevent one from seeing that the original ESP sentence is the very same crap but if you think about it at least for a minute, you must be able to see that it is the same crap.Moreover, even the partiually fixed version of ESP is wrong in quantum mechanics, in certain important respects. What's important is that if you also measure \(Y\), you do this measurement first, and if \(X,Y\) don't commute with each other, then the result for \(Y\) will influence the outcome for \(X\). More precisely, the best prediction for the \(X\) measurement must take the result of the \(Y\) measurement into account even if they are different quantities. They may really be thought of as "truly independent" if they commute with each other. (This "independent observables have to be mutually commuting" is some sort of an operator counterpart of the statement for states that "truly mutually exclusive, different states must be orthogonal to one another".)I am really annoyed by the proliferation of this trash and I am annoyed by the fact that this trash is being repetitively pumped into the public discourse by the media and blogs run by narcissist crackpots like Sean Carroll, building upon Goebbels' claim that a lie repeated 100 times becomes the truth. At the end, the reason why I am so annoyed is that people don't have time to appreciate the clever, precious, consistent, and complete way how Nature fundamentally describes phenomena, and the people – like Heisenberg et al. – who have found those gems. These people are the true heroes of the human civilization. Instead, we're flooded by junk by Carroll-style crackpots whose writings don't make any sense and who are effectively spitting on Heisenberg et al.The Carroll-Sebens papers are meaningless zero-citation crackpot tirades , if we exclude self-citations (something that certain crackpots love to collect). Every genuine physicist knows that but Carroll abuses the traffic on his blog and misleads the thousands of people who visit it into thinking that he is something else than a crank. I think that it is immoral.