Off-topic Nobel news: medicine prize goes to Gurdon (UK) and Yamanaka (JP) for a method to create universal stem cells out of mature cells. Seems like a great choice to me, too bad it's been reduced.
Niels Bohr would celebrate the birthday yesterday, as Google's doodle reminded us. It's interesting to look at the Bohr-Einstein debates again. Wikipedia covers the story rather nicely.Before the quantum revolution
These two Gentlemen liked each other, respected each other, and enjoyed the debates. Einstein was the more famous one and Bohr was right. An interesting twist came before the debates, soon after photons were introduced to physics. These days, we view photons as a hallmark of the quantum theory. So you might expect the pro-quantum guy to be a great champion of photons and the anti-quantum guy to be their foe.
However, the truth was the other way around. Einstein liked photons – after all, he got his Nobel prize for his explanation of the photoelectric effect. He liked them because the discreteness of the energy packets was giving a clear visualization to the numbers behind Planck's calculations.
Bohr originally disliked photons because the discreteness rule was arbitrary. There are many other ways to discretize or perturb the classical electromagnetic theory and one couldn't know why this particular one was chosen. If you think about it, it's really paradoxical that it wasn't Einstein who took this Bohr's position – because Einstein later liked whenever God had no other choice. In the case of discreteness of the electromagnetic quanta, there would be many other rules to introduce the quantization.
Needless to say, \(E=N\cdot \hbar\omega\) was later properly derived from quantum mechanics applied to the electromagnetic field (or another field) so the ambiguity – the reason behind Bohr's original dissatisfaction – has disappeared.
Bohr must have softened his objection in 1913 when he proposed the old quantized Kepler-style model of the atom – something that Einstein approved after some initial hesitation – because this model introduces quantization to the orbits in a way that perhaps looks even more ad hoc than the quantization of the energy carried by the electromagnetic quanta. While the photons survived since 1900 or 1905 almost in their original form, Bohr's old model of the atom didn't. We know that it only works for the Hydrogen atom's spectrum (some of its methods are also similar to some valid insights of the WKB approximation, however, and hold more generally) and this agreement is a matter of an accident, too.
Quantum revolution
When the revolution erupted in the mid 1920s, Einstein started as a full-fledged skeptic. He wouldn't like the Heisenberg uncertainty principle and he disliked Born's probabilistic interpretation, too. That's why he wrote a letter to Born saying the famous quote, "At any rate, I am convinced that God doesn't throw dice."
Well, maybe God doesn't throw dice for various reasons – for example because there is no God and there are no heavenly dice – but the physical implications are exactly identical to the hypothetical world where God throws dice. The results of measurements are generally random and the precise outcomes can't be predicted, not even in principle.
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In the first stage of Einstein's opposition to quantum mechanics, he ambitiously disagreed with the proposition that one can't measure the position and velocity of a particle (or its particle-like and wave-like properties) at the same moment. He would say that one may detect an interference pattern but one may still determine from the screen's momentum which slit the particle went through.
Einstein's proposed method to determine the slit would involve an exact measurement of the vertical component of the momentum of the screen S2. It moves slowly but in principle, you may measure the momentum of the screen with any resolution, Einstein argued, as long as you allow the screen to move for a long enough time. From the magnitude of the kick, you may determine whether the particle was redirected at the slot "b" or "c".
Homework exercise for you: What possible changes of the vertical momentum of S2 can you actually measure in this experiment?
Off-topic: Sputnik 1 was launched on October 4th, 55 years ago. The Soviet cosmic dominance continued for another decade or so.
Bohr already understood those things so he quickly found the bug of Einstein's method: the screen obeys the laws of quantum mechanics, too. So if its vertical position is accurate enough for the experiment to preserve the nice interference pattern, and it usually is, then it has an uncertainty of the vertical momentum, too, and this uncertainty is large enough for us to be unable to determine which slit the electron reflected from.
This part of the debates debunks the widespread criticism against Bohr claiming that Bohr thought that the laws of quantum mechanics don't apply to macroscopic objects such as screens. Of course that he knew that the laws of quantum mechanics did apply to them as well. He has actually critically depended on this fact when he was clarifying Einstein's would-be paradoxes. Let me copy this quote by Bohr:
In particular, it must be very clear that... the unambiguous use of spatiotemporal concepts in the description of atomic phenomena must be limited to the registration of observations which refer to images on a photographic lens or to analogous practically irreversible effects of amplification such as the formation of a drop of water around an ion in a dark room.This says that the result of the measurement may only be considered a "fact" once it gets imprinted to some properties of macroscopic bodies whose appearance is "practically irreversible". This description of the role of macroscopic objects is right on the money and nothing has changed about it since Bohr's years. We can't talk about any "facts" unless they are measured – which means until the observables are entangled with features of complicated enough objects that decohere, using the modern verb.
Bohr understood that these processes affecting the macroscopic apparatuses are "practically irreversible". In my opinion, the word "practically" clearly shows that Bohr knew that in principle, processes involving "large objects" are as reversible and may "recohere" as realistically as processes involving microscopic objects. Just in practice, the probability of a "reversal" or "recoherence" (the latter word was added later but I would claim that Bohr implicitly knew the spirit of it) is so tiny that this possibility may be neglected.
That's why properties of the macroscopic objects may be "practically considered" to be facts analogous to classical facts and their existence is needed for us to talk about events in the classical language (but the actual relationships between the events – the evolution in between – are governed by quantum mechanics). Bohr was simply right. There was nothing "crucial" missing in his description of the measurement process.
Einstein's box and Bohr's triumph
Einstein's second criticism was attacking the "energy-time uncertainty relationship" and I discussed it in March 2012. Again, Einstein thought that he could measure time and energy at the same moment if he used a gravitational field. Bohr's explanation on the following morning was spectacular – it showed the power of key ideas in physics. They are so powerful that they may be used against their discoverers, too. ;-)
Bohr pointed out that the time won't be measured accurately because the vertical position of the weight will have a nonzero uncertainty and this vertical position (and its inaccuracy) will affect the measured proper time (and its inaccuracy) because of the gravitational red shift. Recall that clocks tick slower if they're deeper in the gravitational field (lower altitude).
After the fix – Einstein forgot to include his own general relativistic effect but Bohr restored it – it was possible to see that \(\Delta E \cdot \Delta t\geq \hbar/2\) again.
Second stage of debates: hidden variables
The first stage of the debates ended and sometime in the early 1930s, Einstein would effectively admit defeat. He had been wrong: all his "clever" methods to measure things more accurately than the uncertainty principle allows were failing. So he changed his attitude, accepted that one can't actually measure those things accurately, but there's still some underlying reality, whether it may be measured or not. So he began to argue that quantum mechanics was incomplete:
I have the greatest consideration for the goals which are pursued by the physicists of the latest generation which go under the name of quantum mechanics, and I believe that this theory represents a profound level of truth, but I also believe that the restriction to laws of a statistical nature will turn out to be transitory.... Without doubt quantum mechanics has grasped an important fragment of the truth and will be a paragon for all future fundamental theories, for the fact that it must be deducible as a limiting case from such foundations, just as electrostatics is deducible from Maxwell's equations of the electromagnetic field or as thermodynamics is deducible from statistical mechanics.The evidence that quantum mechanics is actually fundamental and all other theories are its approximations – and not the other way around – continued to grow and became practically irreversible some years after Einstein's death. Nevertheless, some people still believe the same things Einstein believed in the early 1930s and, despite their much weaker current position relatively to Einstein, are often much less generous to the founders of quantum mechanics than Einstein. The wrong proposition above, "quantum mechanics is incomplete, it is just a dirty approximation to a more glorious underlying theory", became a driver behind the de Broglie-Bohm pilot wave theory and other failed developments.
Third stage of debates: EPR
Einstein, Podolsky, and Rosen published their paper in 1935. They were able to realize that quantum mechanics seems to be able to produce stronger and more diverse correlations than a classical picture could. They consider a two-photon entangled state\[
\ket\Psi = \frac{1}{\sqrt{2}} \zav{ \ket{VV} + \ket{HH} }.
\] I would become a picky historian of science if I tried to reconstruct the 1935 paper exactly, without all the things that were added or clarified later – e.g. in an Aharonov-Bohm paper in 1957. However, EPR clearly realized that quantum mechanics is incompatible with the idea that the two entangled photons "objectively possess" properties that are independent of each other and the classically inevitable idea that any measurement of the photon #1 will only depend on properties of the photon #1 and similarly for the photon #2. Instead, quantum mechanics allows entanglement – correlations that depend on the type of measurement done in the other lab – and this violated locality in the opinion of EPR. A general state in the Hilbert space \(\HH_1\otimes \HH_2\) depends on \(n_1 n_2\) complex amplitudes (\(n_i={\rm dim}(\HH_i)\)) while EPR were feeling "certain" that the two subsystems had to be described by "actual classical data" so the number of these classical numbers for a composite system should be \(n_1+n_2\) rather than \(n_1n_2\).
Well, as clarified later, the main thing that was violated by quantum mechanics was realism, not locality: locality may hold exactly and in quantum field theory, it does. (I am talking about locality of actual influences that may be in principle used to send information; I don't consider the very existence of the entanglement to be nonlocal in any sense. It's mostly a terminological issue that some other sensible people could disagree with.)
Einstein would always consider "realism" for granted. Bohr replied to EPR by a paper that some folks, such as John Bell, considered "almost unintelligible" and I must admit I see where they're coming from:
Bohr: the statement of the criterion in question is ambiguous with regard to the expression "without disturbing the system in any way". Naturally, in this case no mechanical disturbance of the system under examination can take place in the crucial stage of the process of measurement. But even in this stage there arises the essential problem of an influence on the precise conditions which define the possible types of prediction which regard the subsequent behaviour of the system... their arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete... This description can be characterized as a rational use of the possibilities of an unambiguous interpretation of the process of measurement compatible with the finite and uncontrollable interaction between the object and the instrument of measurement in the context of quantum theory.At the beginning of the quote, Bohr agrees that the polarization states of the photons aren't affected by any subtle features of the apparatus – and there's no influence on the "other lab". Concerning the rest, it surely reads like a cryptic text but I think that the "precise conditions which define..." simply means what kind of a measurement (circular vs linear polarization, which axes) of the photons' polarization was chosen. And Bohr clearly believes – in agreement with observations, but without giving any clearer explanation – that it is OK for quantum mechanics to yield combined predictions that depend on the "type of measurement" chosen by the two labs and this property of quantum mechanics is a feature, not a bug, and it doesn't imply any incompleteness of quantum mechanics.
The phrase "uncontrollable interaction with the apparatus" meant that one shouldn't try to imagine that the measured particle and the apparatus are in a particular state before the measurement and they participate in a particular classical process or "interaction" that leads to a particular outcome: they should be allowed to be in a state that is uncertain, described by the state vector, and therefore not admitting any detailed visualization of the interactions that decide about the outcome. That's why the interaction must be considered "uncontrollable"; the word "uncontrollable" really means "possibly violating the assumption of realism".
In that particular somewhat incomprehensible paper, Bohr didn't state clearly enough that "realism" was the incorrect assumption behind EPR (although he arguably said an equivalent thing with "realism" renamed as "full controllability") and he probably didn't prove that the entanglement didn't allow any faster-than-light communication and that it was compatible with special relativity (i.e. that there existed Lorentz-invariant, special relativistic quantum theories that still allowed entanglement). At any rate, one may understand that Bohr understood that the predictions of quantum mechanics for the EPR experiment were right and he was proved correct by the experiments although I would give him a D for detailed pedagogical skills displayed in that particular paper.
Well, maybe the usage of the word "uncontrollable" instead of "unrealist" does indicate that Bohr didn't fully appreciate the power of the argument which unmasks the huge gap between classical physics and quantum mechanics. The phrase "uncontrollable interactions" still suggests that in principle, one (a bold physicist such as Einstein) could try to search for a "controllable" description, the only one that Einstein would consider "complete".
In this case, much of the fog was caused by the ambiguous interpretation of the word "uncontrollable". It meant "unrealist" or "incomplete" to different people. For Einstein, the assumption that quantum mechanics made that some processes must be considered "uncontrollable" was equivalent to the assertion that quantum mechanics was "incomplete". However, Bohr used "uncontrollable" in the sense of "making no assumptions about realism". And because quantum processes are known to violate realism, we may replace "making no assumptions about realism" by "dismissing realism at the fundamental level". Of course, Einstein believed that being "realist" was a necessary condition for a theory to be "complete", so he wouldn't care about the terminological ambiguity – but this lack of care was a reason why he was wrong.
Incidentally, analogously ambiguous terminology that becomes ill-defined or murky in the quantum world was also affecting the validity of some statements Einstein made when Born proposed his probabilistic interpretation in 1926. Wikipedia says:
Einstein rejects the probabilistic interpretation of Born and insists that quantum probabilities are epistemic and not ontological in nature.Well, are the quantum mechanical probabilities "epistemic" (related to subjective knowledge) or "ontological" (related to objective existence) in Nature? This is an example in which the number of meaningful terms shrinks, not expands. In the previous paragraphs, I said that quantum mechanics forces you to admit that Bohr's "uncontrollable" may have two meanings – "the theory is incomplete" (false for QM) or "the theory doesn't assume realism" (true for QM). Here, we see the opposite effect: the words "epistemic" and "ontological" (which had strict and separated meanings in the classical world) get merged in their quantum symbiosis. The quantum probabilities are epistemic – they describe the observer's knowledge before the measurement (and the previously mentioned number \(n_1n_2\) of probability amplitudes for a composite system also resembles the behavior of "epistemic" probability distributions) – but they're also "as ontological as you can get". They're both epistemic and maximally ontological: there's just no "more ontological underlying description" and there can't be one! Equally importantly, the quantum probabilities are neither "epistemic" nor "ontological" in the exact classical sense (with all the detailed implications) simply because quantum mechanics isn't classical physics, stupid.
It looks to me like Bohr wasn't too interested whether or not a realist description was possible in principle. He was interested in the valid description of observations. That's a noble goal but if it were something Bohr would really be satisfied with and care about, then I would agree with the EPR's posthumous children who could say that Bohr wasn't able to disprove Einstein's claim that quantum mechanics was incomplete. He was only able to point out that the EPR's proof that quantum mechanics was incomplete was invalid because it assumed "controllability" i.e. "realism" – and we know that the assumptions that EPR actually believed in 1935 disagree with the observations.
I remain a bit uncertain on whether or not Bohr was actually able to prove that all realist descriptions of Nature had to be wrong. His sometimes incomprehensible prose leaves this question open. But he was the boss of the gang of physicists who had the right theory, who knew it had to be right, and who could definitely find errors in all particular attempts to show that there was something wrong with quantum mechanics. Bohr was more of a "defender", I would say. He didn't spend much time with unpromising attempts to explain Nature – wrong theories that others tried to construct. You might say that it's a legitimate attitude of a physicist. But if such misguided "alternative theories" flourish and spread even 80 years later, maybe a physicist should be expected to know something about the wrong theories filling our environment – and why they're wrong – as well.
P.S.: Bohr was very kind, patient, and constructive. In the blog entry above, you will find a link to a 5-star amazon.com book about the Bohr-Einstein debates. Here's a story from that book:
After the exchange of pleasantries, battle began almost at once, and according to Heisenberg, `continued daily from early morning until late at night'... During one discussion Schrödinger called `the whole idea of quantum jumps a sheer fantasy'. `But it does not prove there are no quantum jumps,' Bohr countered. All it proved, he continued, was that `we cannot imagine them'. Emotions soon ran high... Schrödinger finally snapped. `If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.' `But the rest of us are extremely grateful that you did,' Bohr replied, `your wave mechanics has contributed so much to mathematical clarity and simplicity that it represents a gigantic advance over all previous forms of quantum mechanics.'Bohr was right and he still appreciated the contributions by his friends who were wrong and was eager to explain quantum mechanics to them even when they were ill, treacherous, prejudiced, and stubborn. ;-) This is a fairer picture of Bohr than Brian Greene's "Bohr was a nasty limited bully who forced a brilliant and independent student Everett to humiliate himself." (It's not an exact quote but it is a rather accurate summary of the Everett chapter in Brian's recent book.)
After a few days of these relentless discussions, Schrödinger fell ill and took to his bed. Even as his wife did all she could to nurse their house-guest, Bohr sat on the edge of the bed and continued the argument. `But surely Schrödinger, you must see...' He did see, but only through the glasses he had long worn, and he was not about to change them for ones prescribed by Bohr.
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