Saturday, June 15, 2013

There is no classical world

...even Sean Carroll may say true things about the foundations of physics...

How is it possible? Well, quantum mechanics implies that if a process isn't prohibited by some absolute laws such as symmetries and conservation laws, it may happen even though the probability may be very tiny (like in quantum tunneling; or in Carroll's authorship of valid sentences about quantum or statistical physics).

Sean Carroll decided to promote an animated cartoon film on quantum mechanics, previously embedded in John Preskill's blog – it's nicely done but you may ultimately think that it's missing a Wow factor – and he said some correct things.

The most important one appears in the title: there is no classical world. Carroll correctly states a self-evident fact – that is nevertheless underappreciated by many – that classical physics is just an approximation for certain phenomena. It becomes increasingly more relevant or accurate when objects and processes become more classical (which usually means bigger) but it never becomes exactly true.

Let me admit that whenever Carroll writes such a thing, one that contradicts Carroll's hardwired emotions and sentiments, I can't get rid of the impression that he was just persuaded by John Preskill to do so. It seems somewhat implausible to me that after all these passionate posts he wrote about the need for realism and the extensive space he has given to "philosophers" i.e. crackpots who try to interpret quantum mechanics as an illusion ultimately boiling down to a classical model, he would voluntarily write what he wrote now. But good that he did it, anyway.

It was sort of courageous because a vast majority of the readers of similar blogs – probably including this one – is controlled by uncontrollable anti-quantum instincts. Carroll's comment section shows it's the case. Let's look at it.

In the first comment, Ted J. Vlamis writes
I notice your careful choice of words that “there is no classical world”, as opposed to “the entire universe is quantum mechanical”. Any thoughts on reconciling the contradictions between Quantum Mechanics and Relativity.
Carroll said that "there is no classical world" but according to a somewhat intimidating body of evidence, the proposition "the entire universe is quantum mechanical" is a valid and important proposition, too.

Moreover, there is no contradiction between quantum mechanics and relativity. Their union is even more constraining than each of these two foundations of modern physics separately but the constraints admit solutions, anyway, and they're beautifully consistent. In fact, the full-fledged quantum (probabilistic, non-realist, and so on) character of the laws of physics is the only way how to reconcile the empirically verified violations of Bell-like inequalities with the principles of relativity. The principles of (special) relativity, which were extracted from many experimental situations, along with several additional very specific experimental facts (about entanglement etc.), may be used to directly prove some postulates of quantum mechanics.

In the second comment, Carroll replies to Vlamis as follows:
There are no contradictions between quantum mechanics and relativity; quantum field theory reconciles them beautifully. We’re still looking for a complete quantum theory of gravity (whose classical theory is general relativity), but that’s another issue.
Right, there are no contradictions between (special) relativity and quantum mechanics and quantum field theories (and string theory) are explicit proofs of that.

Carroll doesn't directly say whether quantum mechanics is compatible with general relativity although he mentions it. So this question deserves a few sentences. General relativity can't be used as a starting point to construct a quantum theory of gravity following any straightforward standardized process of "quantization". So general relativity may be said to be incompatible with the procedures of "quantization" that work for other theories.

However, in contrast with claims in the popular literature, it's really misleading to say that the principles of a relativistic description of gravity (which boil down to general relativity in the classical limit) are incompatible with quantum mechanics. They're surely not incompatible. After all, we know that the string theory vacua flawlessly reconcile the principles from both pillars.

The correct statement is that classical general relativity and general quantum mechanics don't immediately tell us what phenomena occur in extreme conditions, such as the Planckian distance scales, where both quantum mechanics and strong gravitational fields become relevant. When it comes to the principles themselves, those of quantum mechanics and those of general relativity aren't incompatible. Their union is just subtle enough so that we can't immediately derive their implications for the world in which the quantum phenomena and strong-gravity GR phenomena overlap. But that's it. The overlapping region ultimately is described by a consistent theory; and the regimes controlled by GR only or QM only can even be described by a theory that was understood before people started to reconcile GR and QM.

The third comment by Joe focuses on the experiment from the animated film that I decided to embed above this very sentence:
The video shows how there is only a red shift of the reflected laser light when the mirror is in its ground state, because no energy can be extracted from zero-point energy of the ground state. At first I thought this was amazing but then I wondered how this differed from the classical prediction. In a classical picture, the mirror in its ground state would be completely motionless. The laser still cannot be blue shifted because the mirror is motionless but red shift is possible because the laser can impart energy to the mirror. Can someone explain how this experiment demonstrates a quantum phenomenon? (BTW, I’m not a quantum denier, I just can’t wrap my head around the experimental results.)
The movie starts with a few general comments on particles and waves and the uncertainty principle. Then it discusses the experiment with a small but not atomic-scale mirror that contains billions of atoms (30 microns times 30 microns or something like that). Laser light is sent to the mirror and reflected. Using helium, the mirror is cooled down almost to the absolute zero and they're ready to measure the blue shift or the red shift.

Classically, the mirror sits at \(x=0\) with \(p=0\). The red shift would have to be zero. Quantum mechanically, this is not allowed as it would violate the uncertainty principle. In quantum mechanics, one may derive that this ground state implies \(\Delta x\) of order one femtometer. The reflected light can't carry a higher frequency/energy because it would have to steal some energy from the mirror but there's no lower-energy state than the ground state. So only red shift is possible.

In the real-world experiment, one doesn't have \(T=0\) exactly so the blue shift won't be absent completely. But quantum mechanics still predicts a different behavior than classical physics. Classical physics predicts that when the mirror is slightly moving before the collision, and at \(T\neq 0\), it is indeed moving, blue and red shift are equally likely because the mirror is equally likely to move against the laser beam as it is to move away from the laser beam.

I suspect that unusually enough, Joe misidentified the reason for the red shift or blue shift in classical physics. The right (Compton-like) description in classical physics is in terms of a photon-mirror collision that simply gives the reflected photon an extra positive or negative momentum depending on the previous motion of the mirror. You won't be able to say much if you only look at the energy of the mirror because the energy conservation law isn't enough to determine the momenta of the mirror and the photon after the collision. However, if you add the momentum conservation law, you may watch the whole collision e.g. from the center-of-mass inertial system and in this frame, the final photon's energy is clearly the same as the initial one. The blue shift or red shift in the lab frame is then derived from the Doppler shift – from the relative motion of the lab frame with respect to the center-of-mass frame. This Doppler shift depends on the initial velocity of the mirror and both signs are clearly equally likely. (We don't have to talk about individual photons; an analysis of classical electromagnetic waves reflected from a moving mirror will lead to the same prediction for the blue shift and red shift.)

OK, so classical physics makes blue shift and red shift pretty much equally likely. However, what they observed is that the blue shifted photons start to disappear much more quickly than the red shifted ones, thus confirming a prediction of quantum mechanics and clashing with the prediction of classical physics.

In the fourth comment, Vlamis thanks Carroll for a clarification concerning the compatibility of QM and SR. However, look at this fifth comment by Doc C:
That’s like saying a grain of salt is sodium and chloride. It’s not, it’s sodium chloride. Quantum behavior describes the foundations of our world, but our world is not its quantum foundations. Perhaps there are constraints on the classical manifestations of the quantum foundations, but the classical world emerges from its quantum foundations. The quantum foundations are not isomorphic with our classical world.
Well, this is the kind of a completely incoherent babbling by a layman who thinks he's very smart and philosophical but the babbling really makes no sense whatsoever.

The relationship between quantum mechanics and classical physics has nothing to do with sodium, chlorine (the element is not called chloride!), or sodium chloride – except that quantum mechanics is clearly needed for a realistic understanding of the reason why sodium and chlorine bind to produce salt.

I won't accuse Doc C of thinking that the quantum-classical relationship is equivalent to the appearance of a molecule of salt. He clearly wanted to say that the "whole is different from the union or the sum of the components". Well, in some aspects it is different, in some aspects it is the same thing. However, the slogan "the whole is different from the sum of the components" has nothing to do with the classical-quantum relationship, either. The sentences by Doc C are just memorized slogans that have nothing to do with each other.

The sentence "Perhaps there are constraints on the classical manifestations of the quantum foundations, but the classical world emerges from its quantum foundations." proves, I believe, that Doc C doesn't understand that quantum mechanics isn't just a "constrained classical physics". It's a totally different theory. The predictions of the right theory, quantum mechanics, aren't a special case of predictions of a classical theory. Instead, they're often predicting things that no classical theory could ever predict. The violation of Bell's inequalities is an example.

His final sentence "The quantum foundations are not isomorphic with our classical world." makes it even more clear that he misses the whole point – starting from Carroll's title "There is no classical world". It is true that quantum mechanics isn't isomorphic to classical physics but what's totally wrong is the word "our". Our world is simply not classical so every sentence about the foundations using the sequence of words "our classical world" proves that the author of the sentence is a moron.

Moreover, while we may distinguish the real world from its description, it is true that the real world is isomorphic to quantum mechanics (or a particular quantum mechanical theory) in the sense that every question about the real world is isomorphic to a question about the quantum mechanical theory and the answers agree.

In the sixth comment, Bob wrote:
How does the ground state survive the laser? And, like Joe above, why isn't the energy lost by the red-shifted light enough to allow the blue-shift in both the quantum and classical cases?
Well, the ground state doesn't necessarily remain the state of the mirror at all times. The mirror can get excited. But just like an atom, it will eventually (quickly) fall back to the ground state unless any conservation law forbids such a process. At zero absolute temperature, everything wants to be in the ground state. At a higher temperature, the vibrations of all the degrees of freedom yield some kind of a thermal equilibrium and a nonzero probability of non-ground states, too.

The mirror is mechanically attached to a structure. In classical physics, its position therefore oscillates back and forth as a harmonic oscillator, spending the same time in the motion against the photons and away from the photons. I have already discussed it. In quantum mechanics, the position of the mirror is a position in a quantum harmonic oscillator and the energy carried by this quantum harmonic oscillator is quantized. Only certain transitions are possible. Transitions between discrete energy levels (like in atoms) is what quantum mechanics gives us instead of the mirror-photon classical collision. (The classical limit emerges from the interference between many energy levels when they become dense enough.)

The cooler the system is, the more correct it is to assume that everything sits in the ground state most of the time. When a degree of freedom is excited so that the system is no longer in the ground state, the excess energy is going to be communicated to a random (probably different) place or places, and the system (the mirror) will return to the ground state.

Concerning the second question, the probability (calculated in quantum mechanics, i.e. one in the real world) that the mirror finds itself in a particular (e.g. the first) excited state and delivers the extra energy to the incoming photon that would become blueshifted is very tiny. It's much more likely that the extra energy is thrown away by a separate photon (which has a much lower frequency than the incoming photon).

In the seventh comment, mlilom replies to some sentences in Carroll's article
“Nevertheless, you can still meet people (the wrong-minded ones) who are willing to believe that electrons and photons are governed by quantum mechanics, but not that they are governed by quantum mechanics.”

Hopefully, their temperature is not around 0 Kelvin.

Just saying.
Well, nice, but the human beings – and all other objects – are governed by quantum mechanics even when the temperature is higher than 0 kelvins. It is not true that quantum mechanics – the correct theory – modifies the predictions at very low temperatures only. Quantum mechanics modifies everything. For example, it eliminates the Maxwell-Boltzmann distribution for a temperature and replaces it with the Bose-Einstein or Fermi-Dirac distribution. This is a phenomenon at a nonzero temperature.

While a low temperature is good to preserve some coherence which is a good condition for some of the quantum effects to be easily visible (and yes, the quantum distributions materially deviate from the classical ones especially at low temperatures, too), the quantum mechanical theory doesn't cease to hold for higher temperatures, either. And the deviations from classical physics may be manifest at room or higher temperatures, too. For example, the white dwarfs have a high density which means that even at very high temperatures, the Maxwell-Boltzmann (classical) distribution is inapplicable.

And needless to say, at any temperature, we still need quantum mechanics to understand the atomic and molecular composition of the matter around us. Even at the room temperature, the atoms in everything we see are governed by the laws of quantum mechanics.

The eighth comment by Brett:
Good videos. Cool experiment. I don’t want to be banished, but maybe Laurent Nottale deserves a little more attention. I’m honestly all-in on the idea that everything can be described by an increasingly chaotic wave function with increasing scale and vice verse. That’s how every system in nature seems to work.

Doc C,
I would be so pleased to find out you are a professional physicist. My ego would go through the roof.

[Addition in the 9th comment]
By that, I mean I would be pleased that I understood the video and you didn’t. aw snap grrrl.
Brett is right that the comment by Doc C wasn't exactly high-brow but Laurent Nottale's concepts are preposterous, too. You really can't derive quantum mechanics from a classical theory, not even a fractal one. Fractals may be "cool in some sense" but it is not enough to be "cool in some sense" if you want to solve a particular problem, e.g. a problem of classical physics in its efforts to describe some microscopic experiments. Fractals aren't cool enough for that; their coolness has really nothing to do with the paradigm shift that the quantum revolution imposed upon us.

Finally, the tenth comment was authored by Bill Bunting:
I was wondering about the electron, which in my imaginings is an energy surplus consequence of the overlap of the proton and the neutron which pops out upon union and rotates around the cleavage of the nucleus. The fact that it stays in proximity of the PN pair suggests that it is being both repelled and attracted, and the fact that it is rotating around the nucleus (if indeed it does) suggests further that the forces working on the electron are changing position at a speed sufficient to cause the electron to reposition very rapidly as it moves through the Higgs field (which will act to limit that speed).

I plan to collect every PhDComic that is put out and I am hoping that some of them will work backwards to explain how all of this serves to drive chemistry.

I am making sure that our local high schools are aware of this wonderful adventure.
An electron isn't an energy surplus of a nucleus. It is as independent a particle as a proton or a neutron and virtually all aspects of its motion are independent from the mass or energy of the nuclei or the nucleons. This is really the point of atomic physics that governs all of chemistry (and therefore biology and most of the engineering): the nuclei don't participate in the quantum motion that decides about the birth of atoms and molecules. Only electrons do – because they are the lightest ones.

The forces between the electron and the nuclei may be approximated just as the ordinary electrostatic Coulomb force. In particular, the mass of the nuclei (the number of neutrons) doesn't really matter for chemistry (and biology); that's why the different isotopes of an element are virtually equivalent for chemistry (and biology) while they may still be employed as useful markers to trace the fate of atoms (using the methods of nuclear physics). The agreement between such a theory and experiments shows that pretty much everything else may be neglected. We also know lots of corrections that modify the energy of the states by small amounts etc. but since the mid 1920s, physicists could unequivocally exclude any theory that would try to deny that the main force governing the motion of electrons in atoms and molecules is the \(Q_1Q_2/4\pi\epsilon_0r^2\) Coulomb force.

The existence and good behavior of atoms does in no way depend on the pairing between protons and neutrons (PN?). After all, most of the hydrogen atoms only possess a proton. Everything else that Bill Bunting says about physics is rubbish as well but at least it's good that he will try to redirect high school students towards animated cartoons on physics. Hopefully not his movies, however. ;-)

New Iranian president

Off-topic but I don't want to dedicate a special article to this comment. There are presidential elections in Iran and they seem to be genuine. If you asked me yesterday, I would have answered that Jalili was likely to win because his image was carefully nurtured by the official Iranian media as I followed them over the years.

But holy cow, Hassan Rouhani seems to have grabbed over 50% (52.5% of valid votes, 50.8% of all votes – big inefficiencies, it seems) right now so that he could win right away, well above the 15% of the runnerup. If he drops below 50%, there will be a second round involving the two top candidates. Needless to say, Rouhani's "conservative" competitor would probably accumulate a greater support in the second round as he would collect most of the votes from other "conservative" candidates' supporters.

This is rather incredible. While he's been Khamenei's voice in certain institutions, he's the opposition-backed candidate and I would say that this trained lawyer, diversely certified theologian, and a former nuclear negotiator is a pro-peace-with-West, free-market advocate who wants to free up the Persian Internet, radio, and newspapers which, he believes, could suppress the corruption. He's probably more libertarian than many politicians we have in the West! ;-) Given these comparisons, and assuming that his behavior in the office would match this rosy picture, I can't imagine how someone justifies continuing sanctions against Persia.

If this guy is allowed to win, I think that claims could be made that Iran is becoming a democracy as we know it. His current frontrunner status is even more amazing for Czechs because we spell/transliterate his last name as "Rouhání". Do you know what's the Czech word for a blasphemy? It's "rouhání" – the words agree including the diacritical marks! ;-)


  1. It was sort of courageous because a vast majority of the readers of
    similar blogs – probably including this one – is controlled by
    uncontrollable anti-quantum instincts.

    Lubos - I'm skeptical of your idea of anti-quantum instincts because I can't find any such instinct in myself now or in the past. I went through a period decades ago when I thought "There is no classical world" was wrong, but this was from reading some writers who argued so, not any instinct. I simply don't have any gut-level problem with the statement. I don't care if the world isn't classical! Why should I?

    I know that generalizing from myself doesn't prove anything, but my idea is more than that. I think these people are some mixture of being mistaken in one way or another about implications of the statement, and feeling threatened by anything they don't understand.

  2. A good way to demonstrate to people that indeed there is no classical world and what we preserve as classical world is just an approximation which may or may not exist, is to point to inherently QM theories like (2,0) SCFT. In this theory the Planck constant is ‘h’ is fixed to one.

    This means that we can’t go to the classical h=0 limit to approximate the classical theory (then for small h we can perturb around it). In fact even the notion of moduli space of vacua and thus of target space time is not well defined.

    And this theory is not a construction; it is the CFT dual of M theory on AdS7xS4.

    I wonder what these people would say when they face this simple truth via a concrete example…

  3. Marcel van VelzenJun 15, 2013, 12:17:00 PM

    I'm afraid it is getting more and more clear that part of accepting
    relativity and quantum mechanics as the foundations of modern science
    also implies accepting the consequences of the Coleman-Mandula and Weinberg-Witten theorems, as nature seems to do.

  4. You must be an exception, Smoking Frog! If someone reads an article whose very title is "there is no classical world" and, after having ignored all the content, he writes a would-be authoritative assertion about "our classical world" that clearly plays an important, ruling role in the assertion, then he simply has to be governed by hardwired anti-quantum instincts those that make him completely blind when it comes to any claims or evidence that could suggest that classical physics isn't the right theory. It must be emotional, automatized, it is an animal instinct of a sort.

  5. I barely have an understanding of classical mechanics! All I have is an ill-assorted assemblage of innate intuition, things learned in high school and mostly forgotten, and a few things revisited in adult life. It's mostly gaps.

    As for QM, I could not begin to claim an intuition for it. I think that could come after having worked through the algebra, but I am a long way from that.

    What I have learned from TRF is to be extremely suspicious of my prejudices, and wary of snake-oil salesmen eager to exploit my natural tendency to accept "simple", "common-sense" scenarios.

  6. Lubos, I wish I could think of a really intelligent defense of what I'm claiming. :-) But I do think I'm right.

    I don't think I'm an exception. I think some very considerable percentage of people who are ignorant of QM, on being informed, would not strongly reject it but would say, "My God, that's amazing! Are you sure you're telling it right?"

  7. Eugene - I myself am not terribly well informed - more than you, but not by a country mile, say.

    I think Special Relativity is harder to believe than QM (not that I disbelieve SR, of course).

  8. LOL, in all those classical tirades about or against QM, I only see "are you sure you're telling it right, you must have made an error, you are a heretic, or a liar, and I don't want to hear that again" but I don't see any "my God, that's amazing" in any positive or transformative sense, ever, at most "amazing" in the sense of (literally) "unbelievable" which means that the screaming person will act as he hasn't heard anything and he won't ever believe it, anyway. ;-)

  9. That's because those are people who make tirades. Not many people are like that.

  10. Consider all comments threads, not only in blogs but below news articles. They're heavy with bigots and nuts. How f-ing crazy does a person have to be to post some of that stuff? A lot more crazy than most people you know in real life.

  11. Exactly, the existence of a classical limit isn't something universally valid or guaranteed and we know counterexamples. I suppose that those people would say that the (2,0) SCFT is a mathematical curiosity and the words just can't resemble the dynamics of any such a theory that would be fundamentally non-classical.

  12. "uncontrollable anti-quantum instincts" - I have the all the time, but it's no a hatred towards QM. It's just a mistake I catch myself repeating over and over.

  13. Yes, anti-quantum instincts are in a sense "hard-wired". The brain does not "see" a picture of what is out there. All the inflow of sensory information is compressed and winnowed, and then the brain "constructs" a virtual representation to impose a pattern on the information--a result of evolution by natural selection. IMO, the classical world picture is sort of like this---picture a TV screen--examined close up, the picture is made up of pixels, but from a distance, it is a familiar picture without gaps and defects. The picture is in a sense, a virtual representation of the pixels
    BTW, the "classical" view of molecules etc in chemistry was jolted into reality largely by Linus Pauling. His book on QM in chemistry seems excellent.

  14. Hmmm, peace-in-the-making between Sean and Lubos :) All Sean has to do is to renounce his views on time and its arrow, and I can start drafting a peace treaty. Now LS is another animal :) (I hesitate to even mention his name because google-bots seize on this and push ads in my face promoting his latest crappy book, even on TRF (and, God, the latest one seems trashy).

  15. About the red-shift vs. blue-shift discussion - I suspect that the energy that is imparted in a blue shift is lost to the cooling mechanism. That is, that the cooling has a minimum attainable temperature very close to 0K, say, 1nK. And when a photon [packet of photons] is [are] redshifted, it increases slightly to say 1.1nK, but then the extra thermal energy is subtracted off to the cooling mechanism.


  16. Marcel van VelzenJun 15, 2013, 7:43:00 PM

    "which seems real only because we are so damn big." The same applies to
    gravity which is only obvious after you build a Planck scale probing
    machine like the Sun or the Earth!

  17. Marcel van VelzenJun 15, 2013, 7:59:00 PM

    Although Sean is making progress on QM, his understanding of relativity is still rather weak:

    “I can look at the tomato and instantly infer what the carrot is doing, without ever looking at it.”

  18. I appreciate a beauty of a consistent theory - and apparently Mother Nature does, too. Other than such philosophical considerations, is there an experimental result indicating that gravity is quantized?

  19. What do you mean by "quantized" here?

    The world is quantum so everything in it has to be quantum, too. By the adjective "quantum", I mean "obeying the general postulates of quantum mechanics".

  20. Lubos,
    I can’t help but feel that I have seen this show before. Another reform-minded candidate, Mohammad Khatami, was elected in 1997 with almost 70% of the vote. Khatami did succeed in a few reforms but he was totally squelched by the clergy before he could do very much toward reforming Iran.

    I hope history does not repeat but Rouhani will have to tread very carefully. Corruption is rampant in Iran and that is the root cause of her ongoing economic failures. There are just too many people on the take and not enough doing productive work. I doubt that we are going to see Iran’s Glasnost very soon.

  21. Gordon,
    As I have said before, the only thing that makes the classical view more palatable than the QM perspective is familiarity. The human brain is every bit as capable of thinking quantum mechanically as classically.
    Remarkable thing, the human brain. Pauling surely had one of the best ones, didn’t he?

  22. Thanks, Gene, and it's strange but I consider neither corruption nor economic unproductivity to be among the greatest problems of or threats posed by Iran.

  23. Does everything have to be quantum? Does the curvature of space-time obey the laws of quantum mechanics? Do gravitons exist? How do we know there are NO non-quantum phenomena?

    I agree with you that "everything has to be quantum" is a very reasonable working assumption. Is it more than a working assumption?

  24. My Iranian friends don’t think much of either Rouhani or Khatami but they are generally bitter about what has happened to them personally as a result of the clergy’s ascendance. My sources may not be very objective.
    Certainly Iran is mis-managed and serves mainly the interests of the Revolutionary Guards and, of course, the mullahs, both of whom are still solidly entrenched.
    Neither they nor I view Iran as much of a threat to its neighbors nor to the US or israel. Iran is supportive, generally, of Shiite movements outside the country but, so far, has not acted aggressively and probably won’t. Of course they are a principal supplier to Hezbollah and don’t want to see Assad fall.
    People, including you, have been claiming for years that Israel would attack Iran but it hasn’t happened and likely won’t.

  25. The sun and the earth are Planck-scale probing machines? I don’t think so.

  26. and that's probably the best reason why animations aimed at school
    children - introducing these concepts - is IMHO the right thing to do...

  27. I really enjoyed being told the Czech meaning of the new Iranian president! ;-]

  28. When talking to a child would it be incorrect or misleading to say that the classical world is a sort of "optical illusion" in the same way that the continuous motion on a movie screen is, which in reality is 24 frames flashing a second? I mean an illusion which is tightly constrained by the laws of quantum mechanics and the law of large numbers (or whatever you call it when macroscopic objects are observed with zillions of particles)?

  29. Yes, Jiří, haven't I already said it? The spacetime curvature much like everything that can be measured by a "device" is and has to be a Hermitian linear operator on a complex Hilbert space so that the complex coefficients in front of the eigenstate in a decomposition to eigenstates express - after squaring the absolute value - the probabilities that the corresponding eigenvalue is realized.

    The spacetime curvature much like everything else in the Universe has to obey the laws of quantum mechanics. Gravitons have to exist. I have given the proof of all these statements - via contradiction - several times on this blog. If you missed or misunderstood the proofs, maybe you did, but that changes nothing about the fact that physics has established these things.

    There can be no fundamentally and accurately classical objects or phenomena in our quantum world. No, it is not a working assumption. It is, on the contrary, an *outcome* of the scientific process.

  30. Dear Gene, we almost always agree but sometimes we seem to be far from it.

    Looking at Syria whose Assad is supported by Iran and where chemical weapons were used and where 60,000 people died in a civil war, not to mention the terror and deaths in many other countries in the region, I really can't understand what you may mean by saying that Iran causes no harm by supporting its allies in the region.

    Clergy would surely suck for us - or me - but in that region, pretty much everyone has been trained to be a believer so the election of people who are more-than-average-people believers is sort of a natural product of democracy even if there's one. But just someone's being or not being in clergy isn't the last thing that may decide about the evolution of a country.

    I think that Israel's odds of attacking Iran will drop substantially unless they do so rather quickly because things are changing. It may be much more awkward to attack a country whose president claims he wants to peace with everyone. I agree with you that people in such nations use enemies to advance internal agendas but when such enemies were historically talked about in this way, an actual conflict erupted in a big fraction of the situations so it would be silly and irresponsible to assume that every violent talk about enemies has to end up with no event.

  31. Nice, Luke, it's clearly a metaphor but I would personally endorse it. While not perfect, it is appropriate in many respects, and if you meant particular optical illusions we know, the analogy could become really close and quantitative.

  32. I would like to ask a naive question concerning the consistency of GR and QM in ST. The difficulty noted by Penrose about any consistent solution keeping both sets of fundamental principles resides, as I understood, in the fact that time is a parameter in QM (the unitary evolution operator maps states between time slices). With SR, this is solved in QFT because it so happens that you still keep unitarity no matter what set of time slices you use (so it remains frame independent). However, in GR you have the problem that the time slicing becomes dependent on the evolution itself.
    You could do a monster-Schroedinger-cat experiment in principle by having a huge nuclear explosion being triggered by a photo-detector detecting or not a photon reflected from a half-permeable mirror, and that nuclear explosion will push a big amount of mass just enough to have it plunge into a neutron star to form a black hole (say).

    So you end up with a superposition of a black hole and a neutron star in the end (entangled with all the rest but that doesn't matter). Now how does ST or whatever unification of GR and QM handle the fact that the time slicing itself, determining the unitary evolution, is different in different branches (the one with the black hole and the one with the neutron star will clearly have different behaviors of whatever we call the time parameter near the star/hole ?

  33. But *no* quantum theory has a "classical limit". At most you have a decoherence in several almost non-interfering classically-looking branches. But there's no way to pick only one single branch, which would be the true classical approximation. There's in other words, no way to deduce the Born rule from unitary quantum physics. The Born rule is simply an effect of our subjective perception (the strange happening that I perceive only one branch).

  34. Sorry, Patrick, but the Born rule is one of the universal postulates of quantum mechanics so it's preposterous to say that one "can't deduce it from unitary quantum mechanics".

    I don't know why you say that quantum theories don't have classical limits. A classical particle moving in a potential V(x) is the classical limit of a quantum particle moving in V(x).

  35. Dear Patrick, the "problem" with time's being a variable is just an illusion. There is no problem. A theory is Lorentz-covariant - produces Lorentz-symmetric predictions - if one can find the Lorentz or Poincare generators as operators acting on the HIlbert space of the given theory. Whether the Lorentz symmetry is manifest in a particular formalism is a different question from the question whether the Lorentz symmetry is obeyed.

    I have discussed the "monstrous Schrodinger cat" experiment many times on this blog. Indeed, the Hilbert space contains (and will typically evolve) into states that are linear superpositions of macroscopically different states - in the case of astrophysics, this includes superpositions of a neutron star state and a black hole state. The existence of these superpositions in the Hilbert space is an inevitable implication of universal principles of quantum mechanics that have been known for 85 years so string theory obviously won't change anything about them.

    Yes, the metric is a dynamical variable (operators, probabilistic predictions) in a gravitating theory as well and yes, it's a bit subtle to define what unitarity means when the spacetime background itself is a quantum variable. Well, as you formulated it, it's not a really difficult problem in most contexts - assuming a scheme for the Hilbert space by describing all states as excitations of a particular background, the unitarity works just like in a QFT and boils down to the Hermiticity of the stress-energy tensor. Here, I was assuming a gauge-fixed version of GR or its extension. In this picture, a black hole state may be constructed as an excitation or a neutron star background or vice versa - or both of them may be viewed as excitations of a third background (more vacuum-like).

    The further the two microstates are, the more awkward it is to assume that decoherence doesn't reduce the superposition into ordinary classical probabilistic alternatives but even if you imagine that you have the credentials to write down the accurate description without a decoherence, it can be done. In particular, light-cone-gauge superstring field theory is a theory that contains gravitons, black holes, and neutron stars, but it is manifestly unitary.

    A definition of quantum GR-like theory that is not gauge-fixed is less understood and requires things like the Wheeler-DeWitt equation which remain vaguely known. But there is no guarantee that looking for such a manifestly covariant description is a promising path. There's no guarantee that this is how the correct theory may be described.

  36. Marcel van VelzenJun 16, 2013, 9:25:00 AM

    Gravity is a force suppressed by an energy scale of the
    order of the Planck-scale. A bunch of electrons and protons would only
    know about the strong, weak and electromagnetic forces until "they" decide to
    build the Large Planck Machine of the order of the Sun or the Earth,
    exploding the fact that gravity always adds up. But even then they would
    only probe the classical description of gravity. For a quantum
    mechanical Planck-scale probing machine they would have to build a black

  37. Marcel van VelzenJun 16, 2013, 10:02:00 AM

    Dear Lubos, I saw you endorse my statement but I meant accepting these
    theorems without trying to evade them by introducing supercharges which
    will probably make you less happy but maybe that's what we have to accept from the LEP and LHC results.

  38. Natural sciences IS all about extracting a finite set of data from nature (that you can map to natural numbers or 0's and 1's if you like).

    These serve for building (mathematical) models of nature, be they classical or quantum, that's all there IS !

    Forget about philosophizing about the "IS" in this context, it's a complete waste of time.

    It's pretty much an old hat and thus I'll stop here with an appropriate quote by Bohr (although it IS tautological as IS all what I am saying):

    "There IS no quantum world. There IS only an abstract physical description. It IS wrong to think that the task of physics is to find out how nature IS. Physics concerns what we can say about nature..."


  39. Sorry off topic:

    It seems that Mike Duff (one of few people who do that) is fighting the anti-string zealots again.

    Sometimes I think these guys should not be left unchallenged and other times I think that if people like Mike Duff debate as equals with such people, they legitimate them.

    Again an almost unmistakable measure of crackpotism is how often Einstein’s name is brought up; this guy seems to prove it…

  40. The Sunnis are being used in Syria like they were used in Afghanistan to fight the Soviet-supported regime of "leftist-secular," monarchy
    connected, Afghan ruling class, who called in the Soviet army when the going got hot, just as Assad is doing today.

    There is a direct parallel between Kabul 1979 and Damascus 2012/2013.

    And the US is behind the same cabal here that produced bin Laden,
    Mullah Omar and the Talibans in Afghanistan, ten-fifteen years down that
    road post 1979.

    It's totally Machiavellian, aka the enemy of my enemy is my friend.

    Remember, the US did the same thing in Iran 1953 and paid for it in Iran 1979!

    With friends like that once installed and in place it leads to: Cairotoday, Benghazi tomorrow and Mali the day after that in the MENA, like
    it did Iran before and maybe Pakistan tomorrow.

    What we sow now we then reap afterwards.

  41. If you place yourself in the paradigm of NR QM (to keep it simple) and you return to von Neumann, then there are 2 state evolutions: process 2, the hamiltonian-driven unitary evolution, and process 1, the projection and the Born rule.

    Now, *that* only makes sense if we take the somewhat schizzophrenic assumption that nature "jumps" from classical state to classical state with in between them some unitary evolution. It is the switching from a quantum evolution (process 2) to a "classical instant" (process 1) that involves the Born rule. The unitary evolution itself doesn't contain it. State projection is not unitary.

    It is this difficulty which has given rise to the positivist view (there's no ontology to the mathematical structures of quantum theory) and in general, to the "measurement problem".

    The more traditional way of doing physics, where the formalism describes an objective reality and is not just a calculational trick to link observations without any ontological contents, automatically leads to Many-World like interpretations. That is, if you take quantum theory seriously, you cannot avoid postulating universal unitarity "all the time", and you cannot avoid the world to end up in a huge decohered superposition, in which every term remains (these terms are what are colloquially called the "many worlds"). However, there's no room at all in this for the Born rule, except for the matter of subjective experience. There's no way to DEDUCE the Born rule from just process 2. The reason why a conscious (?) observer has experiences in agreement with (only) ONE branch of all these terms is not explained, but it has to be postulated that this is drawn according to the Born rule. But it has nothing to do anymore with the "ontological" or objective physics, but only with subjective experience (of which branch you happen to experience).

    So in as much as unitarity is kept as a fundamental physical principle (and hence process 1 is not ontologically, but only subjectively possible because not unitary), there's no Born rule in the objective physics.

    To come to your remark, it is true that in toy systems there exist coherent states which are full quantum solutions which continue to remain in approximate relationship with the equivalent classical problem.

    But most decohered solutions are SUPERPOSITIONS of coherent states, and hence superpositions of near-classical states. These are exactly the "many worlds" or the "branches". The particular case of a coherent solution in a potential is a very special case where there is, and remains, only one branch. Real-world systems are not like this. They give rise to several branches.

    So there is no classical limit. The branches look a bit like several classical states, but they split in several branches most of the time. There is not a *single* classically-looking solution which remains classically-looking, because it almost always ends up spitting in a superposition of SEVERAL classically-looking terms. Only very special cases, like coherent solutions to certain potentials, are an exception to this.

    This is exactly the whole Schroedinger-cat issue.

    There's no interference between the dead cat and the live cat, but both classically-looking branches are present. Through the Born rule, we only subjectively experience one of these branches, but if you adhere to strict unitarity, there's no way to get rid of the other.

    A superposition (even non-interfering) of a dead cat and a live cat is NOT a classical state, but TWO distinct classical states.

    That we only experience one of these branches, and that the probability for experiencing a particular branch is given by the Born rule, is then not part of the physics proper.

  42. Dear Patrick, quantum mechanics *does* predict the objective values of probabilities of outcomes or perceptions that *are* perceived subjectively. That's what any quantum mechanical theory does; that's how a particular quantum mechanical theory is compared to the observations.

    Every quantum mechanical theory uses a Born rule.

    Your references to von Neumann seem to be deliberately obscuring the situation, too. Von Neumann was "almost" a member of the inner ring of the fathers of quantum mechanics but he wasn't a full-fledged member. His opinions and interpretations aren't representative of what we call the Copenhagen interpretation.

    His proclamations about these conceptual things were always a bit different from the proclamations by the true fathers of QM - Bohr, Heisenberg, Dirac, Pauli, and perhaps a few others - and I would say that a bit wrong.

    The Copenhagen or any viable interpretation always includes some form of the Born rule - squared absolute values of complex amplitudes are interpreted as probabilities - because it's totally essential to connect the maths to observations.

  43. I hope you realize that the Copenhagen view (what I called the positivist view) was a kind of trick to couple quantum theory to classical physics. It is all right if you take on 2 possible stances, but I thought I understood that neither is yours, maybe I'm wrong.

    The first stance is that quantum theory is not fundamental. That the whole trick with quantum states, wave functions and so on is just a calculational tool but that there is "really" an underlying physical mechanism, of which one can one day show that it results in similar or identical statistical results with quantum calculations. That was essentially Einstein's view, and many others have tried so. I would call THIS the "classical view". There is some classical physics that mimicks statistically as calculated by quantum theory, but quantum theory is just a happy trick that has nothing to do with "nature" except cranking out the right numbers for god knows what funny mathematical coincidence.

    The other stance is a truly positivist vision, but if you apply it totally, you will end up in a form of solipsism. If quantum theory *is* fundamental, and there is only observation, and no ontology outside of raw observation, then you will end up only keeping your own subjective observations. There is no objective ontology that is not observed, and "other observers" don't exist either: if you think you have seen other observers sharing observations with you, then that is only because you have an observation of those observers. Those observers then don't exist but are an unessential construct - only your observation of the observers exists - like everything else in quantum mechanics apart from your subjective observations.

    However, if you want to posit any form of objective reality as described by a fundamental quantum formalism that is universal, I don't see how you can get around taking the quantum state or any equivalent for "real" (not OBSERVABLE, just ontologically real). And then you necessarily end up in some or other Everettian vision.

    It is a bit strange to work on "a theory of nature" when you posit that no nature exists, isn't it ? That "nature" is just the set of your own personal subjective experiences, and that's it.

    Because, again, you can only take the probabilistic vision of quantum theory (denying any kind of ontology to the mathematical objects in the quantum formalism - it is just a trick to calculate probabilities and that's it), if you accept some kind of classical background ontology (which is exactly what the Kopenhagen interpretation posits). This completely fails if you postulate (as I thought you did), that quantum theory is universal and fundamental.

  44. Dear Patrick, as always, there is no objective reality at the fnudamental level but all your sentiments you try to attach to quantum mechanics, including labels like solipsism etc., are demagogy.

    Quantum mechanics doesn't support any solipsism because one may derive, using QM rules only, that different observers will agree whenever they agree and none of the observers is more fundamental than others. Still, quantum mechanics is a tool for computing observations of a particular observer, probabilities chosen from a well-defined subjective framework, which isn't unique.

    See texts like

  45. Dear Patrick, it's strange when you say that we're in agreement about most things. When I read your comments, I don't agree with a word, at least I haven't found such a word yet.

    There is no objective reality at the fundamental level, 90% of your comments are all about some theories based on the assumption that the reality is fundamentally classical, so they're waste of time and crackpotterty. If there's something in your comment that isn't self-evidently wrong and a waste of time, could you please extract it and post it separately? Thanks.

  46. " it's strange when you say that we're in agreement about most things.
    When I read your comments, I don't agree with a word, at least I haven't
    found such a word yet."

    When I read what you write about how you read what I write, I don't recognize my writings either. One of us, or both, has thus a serious comprehensive reading problem :-)

    To give you just a few examples, I *do* consider the option that there is no objective reality at the fundamental level, contrary to what you claim I do. Only, that amounts to solipsism, and at the same time, that there's nothing to say about the non-existent objective reality and its fundamentals. So I do not claim that there has to be an objective reality... only then you have to face the consequences of your working hypothesis.

    Another example where you don't seem to read what I write, is that you keep repeating that I claim a classical paradigm while MWI is NOT a classical paradigm. You confuse the paradigm of objective reality with the classical paradigm, and put that confusion on my side.

    Finally, you seem to deify the godfathers of quantum mechanics with their Copenhagen interpretation and then accuse others of religious fanaticism.

    It is not because these people did important work and merit fully all the admiration for that work, that they have to be the sole possessors of the philosophical view on their new ideas. Galileo can be considered the founder of the concept of space-time relativity, but when you read his texts there were still quite some interpretational issues he had which have been corrected only much later. For instance, for him, the principle of inertia only concerned *circular* motion. Even Newton thought he needed some kind of absolute space to define force.

    So the brilliant originators of an idea are not always the people who have the clearest view on things - which is normal, they only just discovered it, and they didn't have all the other, later views on it.

    So in as much as I respect the originators of quantum theory, I do maintain that their interpretations were still garbled. Which is understandable. It was so strange that they had to say *something*. I don't deify them. You do.

  47. Dear Patrick, the fact that the quantum revolution ended an era of physics in which the physical theories were constructing a model of "objective reality" is not an "option to consider" but a scientific fact.

    I have already explained why quantum mechanics - with its predictive scheme rejecting the existence of objective reality - does not imply solipsism and I have disproved all your other idiotic claims, too. Could you please stop flooding my blog's comment sections with this garbage? You probably have enough time to waste - but I don't - and you may think that 100 times repeated lie becomes the truth but I am one who won't tolerate this Goebbelsian spamming and I will ban you after you repeat one of your idiocies once again.



    Shows that among purports experts there is much disagreement. I don't know why. You like many of them, in spite much thinking, obviously have not understood yet that one cannot require reality to be one size fits all. Rather well developed ground. I think LM earlier suggestion that you consider the prior postings and the directions they lead would be useful.