Why Probability in Quantum Mechanics is Given by the Wave Function SquaredThe 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: 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" 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:

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

You are doing such important work exposing this. Of course Carroll can never win the war with his twisted MW interpretation since nature trumps will always ultimately trump trash. But over time he and his buddies can cause a shitload of confusion that will take years to clean up. He should have stuck to GR.

ReplyDeleteHello. Your proof of the Born rule with Pythagoras is a little bit similar in spirit to Gleason's theorem. Do you think Gleason's theorem alone is enough to justify the Born rule?

ReplyDeleteUs simple civil/sanitary engineers from a previous generation thought that physics was the ultimate science, the high church of (empirical) reason, with actual saints like Bohr and Einstein. It makes us afraid, lost on a darkling plain, to realize there are lunatics even that cloister.

ReplyDeleteDear Andrew, it is a little bit similar, perhaps, but I find such an assertion to be too vague if you want to elaborate upon it. It's similar but it's also different. Gleason's theorem is about the formula for probabilities of P using density matrices, Prob=Tr(P.rho). There is no additional "squaring" in this formula.

ReplyDeleteBut the general approach to prove that the quantum formulae are the only consistent ones is the same. The assumptions are also additive properties of the probability, and so on.

I wasn't constructing my argument based on Gleason's theorem because I have never considered such results to be important. Gleason's theorem is another case of too much ado about nothing. The content of it was surely clear to the founders of quantum mechanics. In the same way, i don't really claim any inevitable originality, anyway. I am sure that everyone who understands QM decently enough could write down such an argument. It's just that unfortunately, almost no one is doing such things so the public discourse is drowning in nonsense which is emitted by very many people, indeed.

In the local right-wing newspaper the headlines are comedy gold.

ReplyDeleteThe Friday edition features ITS GONE PEAR SHAPED, AND NOW PUTIN HAS HIS BACK TO THE WALL (in which Putin is claimed to fear not the West but his own people) followed by (in the same edition) PUTIN'S VORACIOUS APPETITE IS NOT SATED (in which it is claimed that the Russian people will circle the wagons around their embattled hero and cry foul at foreign attempts to denounce him)

Other headlines include STRONGMAN AIMS TO SHOOT DOWN QUEST FOR JUSTICE and PUTIN'S LIMITLESS AMBITION FEEDS HIS INTEREST IN DRAGGING MATTERS OUT.

The PM Abbott, in the style of the true venal pollie, has jumped on the bandwagon of international self-aggrandisement with unaccustomed alacrity in order to distract attention away from his troubles at home. Like a true Aussie hero he's leading the pack for truth and justice against no less an enemy than Satan himself.

Its all gone off rather well, the Saturday edition features an in-depth article from the paper's in-house nutter G. Sheridan entitled ABBOTT ACCRUES DIPLOMATIC CAPITAL FOR CRISIS LEADERSHIP, followed by PURER VIEW OF CHARACTER ON DISPLAY AS POLITICS LAID ASIDE (in which the various aspects of the PM's greatness of personality is discussed).

And in order to make sure we've got the message heading the letters page is ABBOTT'S APPROACH TO PUTIN SHOWS WEST THE WAY.

The whole effect of this relentless and absurd beat-up is like watching a cartoon. It's clear that the printed media is now nothing more than an outlet for the favoured political views of whoever controls them. As sources of rational information they are completely worthless. I gave up reading the left-wing newspaper decades ago. It looks like its time to give up reading the right-wing newspaper as well.

Lubos, you’re unending battles with these QM interpreters is becoming reminiscent of those WWI guys going over the top to charge entrenched defenders - a very nobel effort indeed. It’s a mystery to me how a CalTech professor of physics can get away with babbling obvious BS about multiple universes, but it sure looks like he can and in doing so even acquire more prestige, at least among the uninitiated.

ReplyDeleteHave you ever seen a formulation of QM based on the quaternions? I’ve long wondered about that and after reading the Dirac interview you posted the other day I was happy to see Dirac did also. Like he said, the quaternions provide the simplest example of a non-communative field and so seem natural for QM given the centrality of commutators.

I wish Sheldon would go around to his office and explain how QM actually works ;-)

ReplyDeleteGreat points. You touched on this in the post but to me the issue is really even more fundamental than the details of the argument. The entire strategy doesn't constitute a "derivation" from the beginning. Basically, what all of these arguments do is find some reasonable assumptions and then show that the Born rule is the unique choice for probabilities consistent with these assumptions. Then, I'm supposed to believe that this means that unitary evolution implies the Born rule.

ReplyDeleteOf course, there is another option, which is that the entire exercise is pointless because there is no sensible probabilistic interpretation of many worlds to begin with. Thus, it doesn't matter that there is a unique rule that this nonexistent probabilistic interpretation hypothetically must obey.

To me, it's like arguing that the basic postulates of gauge theory imply that there can be no anomalies. You "derive" this factoid by demonstrating that if there was an anomaly with a non-zero coefficient it would destroy unitarity and render the theory inconsistent. Therefore, the only consistent possibility for the coefficient of any anomaly is 0, so we've proven that gauge theories can never be anomalous! Of course, we've neglected the option that maybe some gauge theories are just not well-behaved physical theories at the quantum level. The "derivations" of the Born rule are equally absurd in my mind.

To Caroll issues like "how and when branching happens" are "relatively tractable technical challenges"

ReplyDeleteOnce Wolfgang Pauli drew a blank rectangle and said that this proved he could paint like Titian "Only technical details are missing".

Pauli was joking. Carroll isn't. That is unfortunate. Lubos is as usual excellent in pointing out that the "technical details" are that the theory is DOA ... the usual meaning.

We are the thin strong thread, for our scientific method. The rest is drama, art, and poetry.

ReplyDeleteIt used to be eminent physicists would get letters and documents by mail from cranks, scribblings and rantings using diagrams and pictures and grade school math. Now they sit next to you on the faculty. Now they publish alongside you in peer reviewed journals. Next you will be in the audience politely applauding as they accept an award your work deserves. Finally, Physics itself will be rewritten in crankery.

ReplyDelete"

ReplyDeleteBut Obama was elected, Lubos. That’s democracy!"Yes, so were Bliar, and Cameron, and any other number of complete shits. Just because all the alternatives to democracy are far worse doesn't mean it doesn't suck. Not that you claimed it didn't though.

The Zeroth Axiom of GovernanceAll governments, however constituted, are run by irredeemably traitorous scum who should at best be regarded as extremely dangerous recidivists let out on parole by mistake.Much follows from this. In particular, institutions of governance which in their construction do not fully reflect all the implications of this Axiom for the wellbeing of the people so governed should be regarded as a clear and present danger and eliminated accordingly, i.e. with extreme prejudice, and pronto.

Now, since there are NO institutions of governance anywhere in the world which in their construction fully reflect all the implications of this Axiom for the wellbeing of their respective peoples, they should all therefore be immediately eliminated with extreme prejudice and replaced forthwith.

OK, that's the plan in a nutshell. I leave it as an exercise for others to flesh out the details and put it into execution.

Talking of executions, I hope to see Bliar, Brown and Cameron hanged one day for sapping and impurifying all of our precious bodily fluids, but mostly of course for filling the country with all those hideous turd-world aliens.

I am confused. AFAIK there is no standard theory(but many conjectures, see references below) the derives Schrodinger equation, so how is it that people try to "explain" the Born rule and yet SE itself has not been explained.

ReplyDeletefrom introduction, see also the references(4,5,6,7)

http://arxiv.org/pdf/physics/0610121.pdf

"Most students and professors will

tell you that the Schr¨odinger equation cannot be derived. Beyond the standard approaches

in modern textbooks there have been several noteworthy attempts to derive the Schr¨odinger

equation from diﬀerent principles 4,5,6,7, including a very compelling stochastic method8

, as well as useful historical expositions9."

Such fundamental equations obviously can't be derived "out of nothing". At most, one may show that they are not independent,. that some subset of these fundamental rules or equations is enough to derive others. But if some others follow from the first ones, anyway, it's not terribly important - it is a pure human convention - to decide which of the claims and equations are fundamental axioms and which of them are derived. It's only the whole structure that has a physical meaning.

ReplyDeleteAside from deriving from nothing which is impossible and deriving from some other, comparably fundamental propositions and equations, one may also do what Schrodinger did and "induce" the equation from its desired consequences - the empirical observations and logical necessities. In this sense, Schrodinger "derived" it by working to combine de Broglie's wave with some equations that make packets move similarly as particles move in the external potential. That was his specific non-relativistic equation at the end. But it's not really a derivation of the general Schrodinger equation for any Hilbert space, not necessarily one non-relativistic particle; it is not really a derivation in the mathematical sense. It's just a way to make the right guess look like less shocking a victory in a lottery and more unavoidable. None of these "derivations" may ever be rock-solid because right theories in general can't be "uniquely" extracted from the observations. If this were possible, Newton would have derived quantum mechanics himself.

LOL, right. Now people - often without such affiliations - are bombarded by letters and blog posts by cranks who often sit on faculties.

ReplyDeleteYes, Obama was elected, Gene, and so was Putin and most others.

ReplyDeleteAccidentally, I just got this video

https://www.youtube.com/watch?v=YfRtbIQ1kTw

where Obama says that individuals are too small insects who have to surrender all their rights in the name of the New World Order. Is that video genuine? I can't believe it. I've been listening it 10 times, trying to see some discontinuity proving it's fake, but so far I failed!

Who is brainwashed? Go to Donbass, open eyes. I have many family there. My father was teacher of math physics for all his life then go retired and had a shop in home village. Now the shop is robbed by separatists and he is called a jew, even if he is not a jew. All jew properties will be nationalised - they say. Poroshenko is the jew, they write it on the internet, on posters, they say it on gatherings. American jews, european jews, banker jews, ukrainian jews want to destroy ukraine. nazi-jews - sepraratist live in paranoia. Jews everywhere but there are rally almost no jews in ukraine (really very few) -only in mind of separatists. Jews pay for nazis - they scare people with Azov Batalion, but if i were jew i would be scare more of separatist that want take all from businessman, they fight capitalism, not the Azov Batalion nobody never not saw. They live in fantasy world, all enemies are controled by USA jews, Poland has military bases in Odessa, Sweden has special soldiers sent, CIA control ukrainian army, ukraine shot areaoplane on Malaysia to kill Putin, capitalist fight agaisnt Russia last bastion of freedom from jewish bankers, they pin hammer and sickles to saint George ribbons -this all is insane. All is fighting against them, Americans, Poles, Lithuanians, Latvians, Estonians, Swedes Canadians. But for them its ok that they have Serbians, Bulgarians or even Chechens. They supported by nazi skinheads from Russia, Poland, Hungary. Nazis proud to fight nazis.. Deep, deep, deep paranoia. Come do Donetsk. I was there already. See with your own eyes and then respond how you can support all of this mindless amok with no sense. Go, buy ticket, I want to see you there. I want to know if after talking with these people your mind and intelligence wont feel ofended by their bullshit, and propaganda. Did you saw russian national tv. Are you not offended by this? They treat people like morons and you clap them? It so easy to write all those thing if you were not there, so buy a ticket and please go! Or come to Russia if you afraide of coming to Donetsk. Come to Moscow. See what people say like that Poland, Hungaria and Romania are anexing west ukraine - so many people believe this sick bullshit. Come see this, and then say if you are not offended.

ReplyDeleteAs a Canadian I'm a bit sensitive to U.S. extraterritoriality. I would have thought the European's would have had bigger ballz though. With a little foresight I think the French could have owned a U.S. bank or two. Simply hedge against the Euro big time and then destroy it's value (i.e. trade war, piss the Germans off). From this position of strength they could have sued the U.S. for economic peace. Perhaps have the dollar cleared in a DMZ. Too clever?

ReplyDeleteYou dont have to be the Russian President, because he's clearly following your line of thinking - he's bringing Russia down with the idea of preserving its "greatness" - a task worthy of a true ayatollah. If he was truly peaceful, reasonable and even smart, there would be no rockets in the separatist's hands - only trade agreements. But things are not simple, right? One have to consider the mass stupidity and ignorance of the population a.k.a national interests and use it to some advantage. There are also clever people dreaming of war glory, invasions and empires (which all fell due to economic reasons - the last colonial country in Europe - Portugal - is one of the poorest states now). The good leader will try to find the balance, while the bad one will run for the popularity. Russia would have invaded Ukraine if only it was capable of doing so, and obviously it's not (otherwise it would be fact), contrary to the sport-level of euphoria in some people.

ReplyDeleteWell, anyone is free to choose a side to defend and I guess someone has to take care of the Third World's interests. As the proud son of Mother Russia Sergey Brin has puted it: Russia is Nigeria with snow. Of course, he was not correct. In Index of Economic Freedom (very informative indicator) Nigeria is higher than Russia, which shares place with Burundi. So if we hear from a source, that the world have arrived at a time when a backward state is loaded with the mission of saving the world from the leading, developed nations, maybe we have to check the credibility of the source. Putin makes all efforts to keep Russia at the level of its well-deserved fame. He is making exactly the opposite of what he actually tries to achieve - he is bringing NATO to its borders. That's the only result from his actions, besides the increasing financial isolation - another sife effect of his cop-turned-thug level of thinking.

Nobody would benefit from severed relationships with Russia, it must be noted. But this statement alone is serving the Russian madness. Russia is the one which will lose the most from any form of isolation. Lets look at some numbers from the period 2011-2013. The Russian export for EU is twice the size of the EU export - about 230 billions. Fifty-five percents of all Russian export is to the EU. The european investments in Russia constitutes about 80% of all investments (almost 190 bil), while Russian investments are 76 bil and represents a negligible part of all investments in the EU. Europe imports 45% of its gas and 33% of its oil from Russia, while Russia exports 88% oil and 70% gas to Europe and so on... Lets have the data in mind when we praise the wild lands at East, lest they enlight our non-brainwashed minds with their darkness.

Luboš M. I'm fully with you. But what I learned from the commentators is that all logic is not enough if somebody is growing up intolerant.

ReplyDeleteNot sure if I am on the right track here - but is it not possible to derive Einstein's field equations from a small set of fundamental assumptions (like equivalence principle, invariance of the speed of light in vacuum)?. Obviously not its source term (the energy momentum tensor) which needs input from the physical setup of the system, but pretty much all the rest of the equations are derived from something more fundamental. Einstein set up his equations, then he extracted predictions like gravity waves, light deflection which were subsequently found in corresponding measurements.

ReplyDeleteThat would be different from the Schrödinger equation, which had been designed to yield numbers in agreement with existing spectra. In this sense: Is not the Schrödinger equation a rather empirical product, while Einstein's equations are from first principles?

A historical aside: Some time ago I had a look at Born's original paper "Quantenmechanik der Stoßvorgänge" which is in German. I realized, that interestingly he first got "his" rule wrong, he considered Φ instead of |Φ|^2. But then he corrected it by adding a footnote:

ReplyDelete"Anmerkung bei der Korrektur: Genauere Überlegung zeigt, daß die Wahrscheinlichkeit dem Quadrat der Größe Φ proportional ist."

Accepting that America supported Maidan, and accepting that shooting down MH17 was a mistake, there is still only one warmonger here. Russians are taking over key positions in the "separatist" movement, as Putin moves to take by force that which he could not win any other way. No matter how much justification he may feel, there is only one way to see what is happening - Russia is taking territory from neighboring countries by use of force. The fig leaf of a native separatist movement has been pushed aside in recent days. Maybe Europe needs a good bloodletting, a new war to focus their attention, but I fear that any attempt to soft pedal what Mr. Putin is doing will be seen as apology for a coming mass murder, and, no matter how lofty or justified his goals, he is the bad guy, now.

ReplyDeleteYou totally miss the real reason for Putin’s actions in accepting the dogma of his megalomania. I urge you to try and look at things from his point of view on the assumption that he is a reasonable and, perhaps, even a kind man. Even if you do not believe this, give it a try.

ReplyDeletePutin’s world is vastly different from yours in that he has to worry about internal stability in mother Russia. It has been true for centuries that Russia has needed secure, stable and friendly neighbors in order to preserve its own, internal, national integrity. He is not “the bad guy” but just a leader doing the best in the position he occupies. I do not envy him.

Europe certainly does not need a good bloodletting; they have enough of that and western interference can only serve to increase that likelihood.

The "sphere of influence” serves the vital need to increase Russia’s internal cohesiveness/stability. Russia does not enjoy the huge geographical advantages of my own country, the US.

ReplyDeleteI’m sure you know that Winston Churchill said that the best argument against democracy is a five minute conversation with the average voter but that all other forms of governance are worse.

ReplyDeleteIt is not an ideal world.

This is little bit off topic for this blog post. But mention of quaternion, by Dirac and you, reminded me of a paper by my colleague. He (Horia Petrache) is professionally an experimental biophysicist but he is very good mathematician. He likes to do such things in his spare time after he is done with biophysics and physics teaching! The paper is pedagogical. It discusses how hyper complex numbers can be arrived at from simple group theory. He thinks that this may be known to mathematicians but may be possibly new and interesting to physicists. He would like to get comments from anyone who is interested in such stuff. His e-mail

ReplyDeleteaddress is given in the paper.

http://www.mdpi.com/2073-8994/6/3/578

The US, from about 1991 until about 2008, was unarguably the world's dominant power. After the banker-created financial crash of 2008 - and the $16 trillion bank bailout - the economic pieces on BigZ's grand chessboard of power began to crumble and fall, and by 2013 China had become the dominant world economy. So the US had its generation of unchallenged supremacy, but the US neoliberalcon kleptocrats drove the US ship of state aground with ill considered, expensive wars; incessant bank bailouts which continue to the tune of some $50 billion per month; trade policies which exported US jobs to India and China; and economic policies that funneled 95% of income gains into the pockets of the 1%. What is happening now in Ukraine (and Africa as well) is a last ditch attempt to finish looting the world before the whole crumbling US edifice collapses. Putin is demonized because he has failed to cooperate with that grand plan.

ReplyDeleteDear Holger, I am convinced it's right to say that the postulates of quantum mechanics deserve the label "fundamental principles" much more than Einstein's equations - and in this sense, they are analogous to the "equivalence principle" from which the equations of GR are deduced.

ReplyDeleteBut the particular simple form of Einstein's equations, just with the Einstein tensor, and a stress-energy tensor, isn't fundamental or exact in any way. General equations obeying all the good principles also contain arbitrary higher-derivative terms (higher order in the Riemann tensor and its derivatives, with proper contractions), and may be coupled to many forms of matter including extended objects and things not described by fields at all.

So the simplicity of Einstein's equations - the fact that only the Einstein tensor appears on the lef hand side - is nothing fundamental at all. It's really a consequence of approximations. At long enough distances, all the more complicated terms that are *exactly* equally justified, symmetric, and beautiful become negligible.

On the other hand, the form of Schrodinger's equations or other universal laws of quantum mechanics is *exact* and *undeformable*, so it's much more fundamental.

Schrodinger's equation itself is just one among numerous ways - not exactly the deepest one - to describe dynamics in quantum mechanics - the equation behind Schrodinger's picture (there's also the Heisenberg picture and the Feynman approach to QM, not to mention the Dirac interaction picture and other pictures).

The wisdom inside Schrodinger's equation may perhaps be divided to several more "elementary" principles and insights. The wave function, when its evolution carries the dynamical information, is evolving unitarily with time. And the generator of the unitary transformations is the Hamiltonian. These two pieces combine to Schrodinger's equation.

The unitarity of all transformations as represented in QM is a very general principle that could again be called a universal postulate, or it's derivable from other closely related principles that are the postulates. It holds for all transformations, including rotations etc., not just for the time translations generated by the Hamiltonian.

The map between the evolution in time and the Hamiltonian is really due to Emmy Noether, so the Hamiltonian's appearance in this equation in QM is due to the quantum mechanical reincarnation of Noether's theorem. The theorem is very deep by itself, even in classical physics.

Again, I am not saying that the principles behind GR aren't deep. But Einstein's equations *are not* these principles. They're just a random product obeying some principles and its simplicity is only due to people's laziness, not because this simplified form would be fundamentally exact. It's not. The postulates of quantum mechanics however *are* and have to be exact. I feel that you get these things upside down.

Thanks for that paper.

ReplyDeleteI agree completely even if I am only a dinosaur physicist. It has been fifty years since I learned any new math but it seems to me that there are only two fundamental things in physics, quantum mechanics and statistical mechanics. Both have to be inviolate else reason itself has no meaning.

ReplyDeleteI’m sue these two must be connected at some very deep level as well.

Thanks Kashyap.

ReplyDeleteSort of similar to Dirac's "derivation" of his equation. He derived it by playing around with equations and matrices.

ReplyDeleteESP--- sounds like apartheid to me :)

ReplyDeleteAlso it sounds like a good sound bite for Alan Sokal to use in his next paper for Social Context mag.

Thanks very much for this articulate rebuttal. At the end of Carroll's latest post, I notice he sounds like some fervent devotee -- a regular True Believer. He's all filled with parallel universes evangelical fervor. Sigh.

ReplyDeleteHi Gene, I am still not seeing why relativity would not be regarded fundamental. Historically, QM was initially non-relativistic, and it worked OK to explain the spectrum of hydrogen on the accuracy level available at that time. Once the measurements turned more accurate, physicists had to sit down again and modify QM to include relativistic corrections. This procedure was then repeated a few times until they could finally reproduce effects like the Lamb shift. On the other hand, Einstein did not derive relativity from QM as a limit case. It was the opposite, relativity was there first, and the founders of QM were forced to incorporate its mechanisms into their equations.

ReplyDeleteImagine, spectroscopy had not been invented by the 1920s - would the Schrödinger equation have been set up nonetheless? Or QED, without the availability of precision measurements like Lamb shift or the gyromagnetic ratio of the electron? I don't think so, because the formalisms first had to be tweaked for quite some time to bring theory in close agreement with those measurements (see also the book of Schweber about "QED and the men who made it").

Einstein, however, derived his equations essentially through thought experiments, based on very basic principles. They were available prior to those precision experiments, which subsequently verified his ideas to an incredible level of accuracy (an obvious exception was the invariance of the speed of light, which was known at that time and taken by Einstein as a building block of his theory). Nobody had ever been thinking about gravity waves before Einstein presented his equations. Now, their indirect measurement through the Hulse-Taylor binary pulsar represents one of the most precise agreements between experiment and theory ever observed in physics - without any prior fine tuning of the theory. Einstein himself could have done the corresponding calculations using his original formalism.

That is why I would regard relativity truly fundamental.

Well there are many schools of thought. I subscribe to the one that believes that nervous countries on the perimeter of Russia, "the country that does not know where it ends" in the words of Vaclav Havel, actively seek any kind of protection available. Without the comfort of geographical separation that we Czechs now enjoy, I can imagine why they run under the NATO umbrella. And given the NATO history and doctrine, peaceful and non-expansionist Russia has nothing to worry about.

ReplyDeleteNATO is an attractive club for the nervous countries on Russian perimeter. And there would be nothing wrong if every former Eastern bloc countries were in it. I do not recall any "faux outrage", if anything the butchering of separatist Chechens together with their civilians would have deserved even more attention than it got at that time.

ReplyDeleteI have to admit being out of my depth here. It’s just that I cannot imagine a non-quantum world; it is absurd to think there could be such a thing and statistical mechanics/thermodynamics amounts only to careful counting.

ReplyDeleteI can envision violations of GR but QM and SM seem as inviolate as logic itself.

Hi Lubos, have you seen this recent preprint (http://arxiv.org/abs/1407.6833), which aims to derive the rules of quantum mechanics from string interactions (instead of the other way around as you have explained in past blog posts)?

ReplyDeleteYes, I did, and was tempted to write about it, too - but was busy with some things.

ReplyDeleteNote that Itzhak Bars is the persistent advocate of physical theories with two time coordinates. He is also a conservative to some extent.

:)

ReplyDeleteYes, I'd heard that one. I don't know what the setting was but presumably clearly it reflects his rather dim view of the average voter.

I say he was absolutely right of course. Indeed, I take the effective dimness of voters

en masseas a given — the evidence is stunningly overwhelming. Moreover it is highly unlikely that things will ever change in that respect. Incidentally, how much of this dimness one should attribute to apathy, ignorance, gullibility, pre-occupation with more immediate concerns etc, or just plain intellectual incapacity is a separate issue. Dunno.But there's a flip side to all this, one that maybe Churchill would naturally prefer to downplay, namely treacherous governors — and it's those whom I prefer to concentrate on. By way of contrast, I believe

a lotcan be done about them. Or preferablytothem. At least I know what I'd like to do to them, some of them anyway. :)That was really my point.

BTW, WC, though a great man and just what we needed at the time, was certainly not without a giant streak of shit running down his back. He was quite happy for instance to have Londoners locked out of the tube stations during the Blitz. Yes, the little people could just f##king well cower in those useless Anderson shelters—if they could build them, that is—or under the fcuking stairs. Well, the mob thought otherwise and smashed their way through, plod or no plod. So that was the end of that load of nonsense.

You don't hear much about it though. It doesn't fit the 'disciplined' (i.e. fquit) plucky-Londoner characterisation of the officially endorsed 'narrative' (a word I have come to despise).

Still, the lesson remains: king or no king, don't push your luck, because we'll cut your f##king head off if you do, so be nice.

GR is a classical theory that works for large distances. If you go to very small distances it is clear that you will be in the QM realm and it is obvious that gravity cannot vanish into the thin air at small distances, so that makes it clear that gravity is quantum mechanical in origin. Then QM must be the more fundamental. At least that is my simple minded conclusion.

ReplyDeleteMaybe I said that wrong. Europe does not so much need a bloodletting as much as they deserve it. All this crap about making warfare illegal, followed by substantial disarmament, relying on America for a defense-on-the-cheap. Well like Spock famously said, that was never gonna work as long as humans were involved. Now America has been driven into some neo-isolationist cocoon and western Europe stands alone. Whatever happens, they did it to themselves. Putin is following a perfectly good rule book. So are all the militias, warlords, proxies, and whatever else. Gonna be fun to watch - from far away.

ReplyDeleteBoth, GR and QM, break down at distances of the Planck length. There has to be a theory replacing them, and at lower energies that theory has to cover properties of both. It will also cover the origin of gravity, but it is impossible to tell off hand how exactly that would look like. Sure such a gravity would share properties with quantum mechanics, but it has to be more than that. Otherwise one could simply quantize gravity and carry everything over to distances below the Planck length, but it doesn't work out, because the so called "classical " gravity, with its rampaging curvature, is spoiling the party at these length scales.

ReplyDeleteNo, Holger, you are totally wrong. All evidence makes it overwhelmingly clear that QM never breaks down, not even at the Planck scale. We can do perfectly consistent calculations of quantum gravity physical phenomena at the Planck scale and the postulates of QM are 100% valid.

ReplyDeletePutin played it shrewdly. Had he quickly invaded the rest of Ukraine, little NATO could have done, but would have bankrupted Russia (Steve Piechenik analysis) -- As it is, NATO is stuck with financial support. Front door closed, back door trading with the BRICS is increasing. To protect the Rotschild dollar, war is needed.

ReplyDelete9 veteran US intelligence officers now confirm, that Kerry is not telling the truth (again).

ReplyDelete"We are hearing indirectly from some of our former colleagues

that what Secretary Kerry is peddling does not square with the real intelligence."

http://consortiumnews.com/2014/07/29/obama-should-release-ukraine-evidence/

This corresponds with a previous posting on that website from investigative journalist Robert Parry (probably relying on the same source), that US satellite photos show the fatal missile fired from a launcher which appeared to be controlled by Ukrainian soldiers in Ukrainian uniforms.

Hmmm, Vladimir should appoint her Foreign Affairs Secretary---

ReplyDeletegiven her pic, Kerry would be so flummoxed, Vlad could do what he liked :)

not me, another Gordon.

ReplyDeleteI am the real Gordon!

ReplyDeleteRussia's character comes from 1000 years of bloodletting of it's own people.

ReplyDelete