...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.”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.
Hopefully, their temperature is not around 0 Kelvin.
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.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.
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.
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).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.
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.
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! ;-)