Tuesday, April 28, 2015

Heisenberg's Nobel lecture

Two weeks ago, I discussed Max Born's 1954 Nobel lecture about the statistical meaning of the wave function – and the history of quantum mechanics. Many other fathers of quantum mechanics have received their Nobel prizes.

To avoid repeating Heisenberg's photographs, let's include a different hay fever sufferer. ;-)

When it comes to the basic character of quantum mechanics, the most relevant other Nobel prize went to Werner Heisenberg in 1932. Well, he only picked the prize in December 1933 – he was chosen as a winner retroactively because no candidate compatible with Nobel's will was proposed in 1932. OK, let us already look at the lecture
The development of quantum mechanics (PDF, 12 pages)
because I find it much wiser than what almost all people in the "foundations of quantum mechanics" are saying today, 82 years later.

On the first page, Heisenberg makes it clear why Niels Bohr was viewed as the ultimate guru of the quantum community. Heisenberg himself interpreted his own efforts and achievements as refinements of some technical problems in Bohr's old model of the atom.

On one hand, it's legitimate to "discard" this not-quite-correct model of the atom entirely. On the other hand, it has played an extremely important role historically. And people like Heisenberg who went through the era in which Bohr's model of the atom was the "cutting edge of physics" may have captured some fundamentally correct ways of thinking.

On the very same first page, we already see the basic correct philosophy that reduced the rest of his groundbreaking discovery to a sufficiently intense period of mathematical reasoning:
...This circumstance was a fresh argument in support of the assumption that the natural phenomena in which Planck’s constant plays an important part can be understood only by largely foregoing a visual description of them. Classical physics seemed the limiting case of visualization of a fundamentally unvisualizable microphysics, the more accurately realizable the more Planck’s constant vanishes relative to the parameters of the system. This view of classical mechanics as a limiting case...
I've said pretty much the same thing in the past, using slightly different words. But this was a wonderful insight that opened the whole quantum treasure. You know, since the analyses of the blackbody radiation, it was known that the constant \(\hbar\) played a certain role in many related but different phenomena.

People could see that this constant was universally important and whenever it appeared, something was behaving very differently than what classical physics was predicting. In fact, the very visualizability of the physical system – the assumption that there exists an objective state of the physical system at every moment that may be in principle captured by a picture – was breaking down whenever \(\hbar \neq 0\) was affecting the physical predictions.

Whenever \(\hbar\neq 0\), all pictures are inevitable misleading.

They are misleading because the very assumption of classical physics that certain objects objectively possess certain well-defined physical properties breaks down. The constant \(\hbar\) directly measures how much this classical assumption breaks down in Nature.

I have just visited Heisenberg's grave and asked him to record his explanations what was important for his discoveries in the audio form once again. You may also try the 1968 audio in his native tongue or the 85-minute Heisenberg and the reality question (German).

This insight is what is needed to correctly understand all the phenomena that quantum mechanics successfully explains. It is needed instead of many things that are not needed and that are not the point at all – like hidden variables or many worlds (MWI) or sudden discontinuous objective collapses (GRW) or many worlds or classical particles and waves existing simultaneously (like in Bohm's theory). None of the flawed concepts in the previous sentence has anything to do with the new assumptions that are actually needed to correctly understand all formulae with Planck's constant \(\hbar\) in them. Heisenberg et al. were going in this direction because they wanted to explain some observed phenomena. Instead, people promoting the realist pictures are doing so because they want to defend some philosophical prejudices regardless of the empirical data that don't really play an important role in their reasoning. They want to replace fundamentally unvisualizable quantum mechanics by MWI, Bohm, GRW etc. because they think that the "spirit" of their alternatives is similar to the novelties brought by quantum mechanics, but they are more philosophically pleasing. But that shouldn't matter in physics. Quantum mechanics works to predict and explain the actual phenomena, the actual equations that may extracted from the data.

Everyone who is tempted to think that there is something right about hidden variables, MWI, GRW, or Bohm's theory is urged to read Heisenberg's lecture, or at least the first pages of it, at least 12 times.

On the second page, Heisenberg continues by saying that it was understood that one needed a "new theory" that does reduce to classical physics in the right limit – effectively in a similar way that was already sketched by Bohr's principle of correspondence – but whose character before the limit is taken is qualitatively different.

He also said that the need for the new quantum laws to be probabilistic was gradually appreciated – especially when it came to Einstein's coefficient for the emission of radiation. Because the electromagnetic energy has to be emitted in discrete packets, the calculable continuous numbers can't tell us about the "intensity" because the "intensity" is supposed to be discrete. So they have to tell us about something continuous, namely the probability that the emission takes place. Max Born's Nobel lecture conveyed the same story about the initial reasons why people began to understand that the new laws were unavoidably going to be probabilistic in character.

While there was something good about the planetary model of the atom, the non-visualizability was the key to understand the atoms. The classical electron paths had to be abandoned. Some matrix elements between stationary states behaved "like" the intensity of radiation emitted while the atom is switching from one level to another. However, they had to be something else. Later, we would appreciate those things as the probability amplitudes.

On the third page, Heisenberg made us sure that he understood that it was OK to refuse to talk about the precise position of the electron while it's happily orbiting the nucleus. To measure the position accurately, you would need to send a very high-frequency photon, and that would kick the electron and ionize the atom completely. You can't really measure what the electron is doing without totally changing the future. And that's why you are allowed to say that the "exact" position of the electron at a given moment is operationally meaningless.

It was important for Heisenberg to realize that the new description that was emerging in front of his eyes was as complete as the classical trajectory. He had all these amplitudes (including phases) and he was able to see that they would play exactly the same fundamental role as the full classical information was playing in classical physics. The previous sentence doesn't mean that the game is the same. Classical and quantum mechanics are different games. But they need some information about the physical system to be applied and Heisenberg had understood what is the kind of information that has to be inserted to the emerging theory of quantum mechanics.

In classical physics, the radiation was calculable from the knowledge of the immediate state of the atom, a point in the phase space. That was enough to compute the intensity of the radiation at each frequency. In quantum mechanics, one needs to determine both the initial and the final energy eigenstate, and what is calculable is some "amplitude" that tells us something about the intensity of light at any frequency.

Because in quantum mechanics, one needs to specify both the initial and final state before we calculate anything (there are no preferred "infinitesimally adjacent" states to the given state of the atom, so all pairs are as good as others), the quantities analogous to the "intensities" actually become a matrix – the object we know from linear algebra (that Heisenberg re-discovered). Because the intensities etc. are calculable like matrices, Heisenberg was suddenly able to realize that all observables – ordinary \(c\)-numbers in classical physics – have to be promoted to matrices.

Note that in all these early investigations, he was thinking in terms of matrices expressed relatively to a basis of energy eigenstates: that's where he was led by thinking about the atomic levels. It took some time before people learned to switch from one basis to another all the time and to realize that all of them are equally good to formulate the physical theory. Heisenberg credits Dirac and Jordan for this "transformation theory".

Heisenberg "knew" that each observable was linked to a matrix. But it would be just a table – and not a full-fledged algebraic matrix – if one operation were not taking place, namely the matrix multiplication. Heisenberg was able to figure out that the matrix multiplication actually does matter – it does replace the usual multiplication of the \(c\)-number observables in classical physics. Heisenberg mentions Kramers-Ladenburg dispersion theory as a piece of research that "suggested" that it should be done in this way.

But it isn't really too hard to "guess" that the matrix multiplication should be relevant. If one computes the transition from \(\ket i\) to \(\ket f\) through some intermediate states \(\ket m\), one should naturally sum over \(\ket m\), and we therefore deal with the sum of products \(\sum_m U_{fm}V_{mi}\) which is the matrix product. Such a matrix product appears in the product of two evolution operators, for example. But evolution operators are just "some other" functions of positions and momenta etc., so the same product should be relevant for all other functions of positions and momenta, all other observables, too.

At some point, Heisenberg had a well-defined mental (not visualizable) picture: all observables are matrices, their spectrum – as suggested by Bohr's theory etc. – is a claim about the matrices, too. In combination with the (Heisenberg) equations of motion, you have everything to define the new physics. Born, Jordan, and Dirac are actually thanked for expanding the insights to a usable calculational scheme and perhaps even for\[

p_r q_s - q_s p_r = \frac{h}{2\pi i} \delta_{rs}

\] which all of us would associate purely with Heisenberg. These commutators may also be used – along with other things – to prove that things like energy and angular momentum are conserved.

All these laws are extensively formally similar to classical physics, Heisenberg says, and all the difference in the formulation of the laws is concentrated in the nonzero commutator above.

This nonzero commutator has far-reaching consequences, however. The predictions of quantum mechanics are often very different from the classical ones. Discrete atomic spectra and transition probabilities are suddenly predicted and they agree with the experiments. It works well but there is no way to visualize, no counterpart of the Wilson photographs.

Here, on the fifth page, Heisenberg gets to Schrödinger. He shared his 1933 Nobel prize with Dirac and they gave lectures shortly after Heisenberg. Wave mechanics was found and shown equivalent to quantum mechanics – by which Heisenberg means "matrix mechanics" – and Dirac and Jordan are praised for the transformation theory. Schrödinger's picture, a refinement of de Broglie's wave paradigm, allowed people to calculate complicated atoms etc.

However, Heisenberg quickly gets to the defects of the straightforward visualizable interpretation. Schrödinger's "waves" live in a higher-, \(3N\)-dimensional space, and they have a statistical interpretation, so they can't quite be the same thing as the classical waves that de Broglie was envisioning.

Heisenberg spends the sixth page by explaining the Pauli exclusion principle and how it may be derived from antisymmetric wave functions – and from anticommuting creation/annihilation operators. The main point of this discussion is that if Schrödinger's picture is viewed as a visualization, it cannot be the only similarly allowed visualization of the physical system. The anticommuting fields provide us with a different collection of "visualizable" eigenstates etc. Dirac's and Jordan's transformation theory is essential and it is wrong to be attached to a particular basis, Heisenberg says in different words.

On the rest of the seventh page, Heisenberg tells us that classical physics has described the objective evolution of some degrees of freedom in the spacetime. And the way how we acquired the knowledge about them was totally inconsequential. Things are very different in quantum mechanics.
...The very fact that the formalism of quantum mechanics cannot be interpreted as visual description of a phenomenon occurring in space and time shows that quantum mechanics is in no way concerned with the objective determination of space-time phenomena. On the contrary, the formalism of quantum mechanics should be used in such a way that the probability for the outcome of a further experiment may be concluded from the determination of an experimental situation in an atomic system, providing that the system is subject to no perturbations other than those necessitated by performing the two experiments. The fact that the only definite known result to be ascertained after the fullest possible experimental investigation of the system is the probability for a certain outcome of a second experiment shows, however, that each observation must entail a discontinuous change in the formalism describing the atomic process and therefore also a discontinuous change in the physical phenomenon itself. Whereas in the classical theory the kind of observation has no bearing on the event, in the quantum theory the disturbance associated with each observation of the atomic phenomenon has a decisive role. Since, furthermore, the result of an observation as a rule leads only to assertions about the probability of certain results of subsequent observations, the fundamentally unverifiable part of each perturbation must, as shown by Bohr, be decisive for the non-contradictory operation of quantum mechanics. This difference between classical and atomic physics is understandable, of course, since for heavy bodies such as the planets moving around the sun the pressure of the sunlight which is reflected at their surface and which is necessary for them to be observed is negligible; for the smallest building units of matter, however, owing to their low mass, every observation has a decisive effect on their physical behaviour. ...
All these basic philosophical points have been said totally clearly in 1933 – and much earlier than that. Quantum mechanics doesn't and can't describe any objective state of affairs. It predicts future measurements from past measurements. Each measurement inevitably influences the measured object and creates some new uncertainty about all the other, non-commuting observables. And this uncertainty is totally needed for the internal consistency of the whole theory. He elaborates upon that point and gets to his inequality\[

\Delta p \cdot \Delta q \geq \frac{h}{4\pi}

\] Now, unlike the commutator, this inequality should be attributed purely to Heisenberg. Whenever similar classical observables are described by the quantum formalism, similar inequalities simply have to hold. They say that any observable – anything that is in principle measurable i.e. anything that has a scientific meaning in principle – inevitably involves some uncertainty that can't be small if a complementary variable was measured.

A straightforward 4-minute laser experiment which – if properly interpreted – is demonstrating the uncertainty principle. Well, it's a bit demagogic because the patterns may also be explained by completely classical Maxwell's equations. But if you believe that the light may be divided to photons...

You see that from the mid 1920s, Heisenberg's thinking was the quantum thinking. It was his default state of affairs. All the people dissatisfied with quantum mechanics and proposing the alternatives choose the classical thinking as their default one.

But people who have learned to think in the newer, more correct, quantum way would have very different expectations about the "realist interpretations" of quantum mechanics. Take Bohmian mechanics. It has some (classical) guiding wave \(\psi(x,y,z,t)\) and some particles' positions \(\vec x_i(t)\). But if these degrees of freedom were transferred to someone like Heisenberg who thinks quantum mechanically, he would still say that \(\psi(x,y,z,t)\) as well as \(\vec x_i(t)\) have to be promoted to operators or matrices, many of their commutators are nonzero, and these nonzero commutators imply that all these observables can't have well-defined values at the same moment! This is the natural and correct way of thinking. We would get just another quantum mechanical theory, one with a very contrived collection of degrees of freedom and very unnatural Heisenberg equations of motion. And one that disagrees with the empirical data. To assume that all of these observables have objectively well-defined values, even though \(\hbar\) appears all over the place, is the incorrect assumption. It's exactly as incorrect as the assumption that relativistic phenomena are explained by the superluminal transfer of the information. No, relativity says exactly the opposite: superluminal motion is forbidden. Whenever \(v/c\) fails to be negligible, the limitation on speed is important. Similarly, quantum mechanics bans the visualizability. Whenever \(\hbar\) fails to be negligible, all descriptions in terms of pictures are fundamentally wrong.

Heisenberg discusses Bohr's comments to the uncertainty principle which are just half-clear, I would say. He also emphasizes that the measurement itself has to be visualizable. It's the "phenomena" that lead to the quantum predictions that are not visualizable. The visualizability is always just approximate. It's OK if \(\hbar\) is negligible relatively to the objects' properties with the same units. But that is simply not a problem. The whole process of making quantum mechanical predictions requires us to accept and understand that the microscopic phenomena are not visualizable, but their verification and measurements has to be done by some apparatuses that must be visualizable at the same level of accuracy that we demand from such measurements. So these two aspects, visualizable and unvisualizable ones, inevitably co-exist. These formulations are more careful than Landau's, for example, because he uses the adjective "visualizable" and not "classical" for the apparatus side of his cut. This side including the apparatus is "as visualizable as it was in classical physics" but that doesn't mean that there is some incompleteness – hole – in quantum mechanics that would require us to add the whole theory of classical physics. It just means that the very act of measurement has to be as visualizable as it has always been, so certain crucial aspects of classical physics are a good approximation to quantum mechanics (which is still the only exactly true theory we may talk about).

The corpuscular and wave concepts are equally acceptable starting points for visualization; he said it above (search for Pauli).

On the tenth page, Heisenberg reminds us that the laws of quantum mechanics are statistical. Does it mean that there is some chance that the conservation laws are violated? Not at all, Heisenberg replies. They work as accurately as ever. However, it's still true that if you determine things like exact positions or exact momenta, you don't determine the exact energy, and vice versa. These observables don't commute with each other. But if you're sure that the energy at the beginning is something, the energy at the end has to be exactly the same value. The problem is that you can never exactly extract the value of the energy from the measurements of positions and momenta etc. (which you might consider necessary because the energy depends on both positions and momenta) – because those can't be done exactly at the same moment. But there are other ways to observe the energy...

The same page also worships Bohr as the source of the clearest explanations of the foundations of quantum mechanics – Heisenberg particularly means Bohr's comments about the complementarity principle. I would say that Bohr's complementarity is morally correct and Heisenberg and others had to appreciate it as the very general extension of the uncertainty principle etc. On the other hand, I would still view Bohr's complementarity as a not quite well-defined philosophical paradigm which is why the word "clearest" that Heisenberg used for Bohr's comments seems slightly exaggerated to me. It's very general, universally important, and captures the essence of quantum mechanics. But it inevitably remains incomprehensible and unclear to those who don't understand quantum mechanics in any special case.

On eleventh page, he says that the growth of crystals from liquid inevitably depends on chance and it makes no sense to look for "hidden variables" that would decide what shape of a crystal we get. Even with a known initial state of the liquid, one gets nonzero probability amplitudes for very different final shapes of the crystal.

The final page is dedicated to some speculations about the future – relatively to December 1933. It's pretty funny. First, he said that the research had to continue. In particular, the relativistic quantum theory has to be found. Dirac was going to speak momentarily. An amusing speculation that seems wrong today appears in one of the sentences. He suggested that the combination of the principles of quantum mechanics and special relativity will determine the only allowed value of the fine-structure constant \(\alpha\approx 1/137\). Well, that seems incorrect. But at some moment, \(\alpha\) looked almost as universal as \(\hbar\) or \(c\) and one could enjoy similar wishful thinking.

There is a big difference here: \(c\) and \(\hbar\) are dimensionful constants which is why we can set them equal to one in special units, and this is natural for the analysis of the relativistic and quantum phenomena, respectively. The constant \(\alpha\) is dimensionless so it cannot be set equal to one. And the lessons of relativity and quanta have already been "depleted" so there is no good reason to expect that \(\alpha\) becomes uniquely determined when relativity and quanta are combined.

Today, \(\alpha\) is a universal constant that seems "important" because it describes the strength of electromagnetism which is the most important interaction in our everyday lives. But from a deeply theoretical perspective, it is in no way "uniquely" important. It is a constant that is no more important than e.g. the masses (or mass ratios) of the elementary particles in the theories we use to describe particle physics. Just another adjustable parameter. Heisenberg was ready for – and wanted – another revolution around the corner. But the first following similar revolution only occurs if you incorporate gravity and Newton's constant \(G\) – quantum gravity – because gravity does play a more special role than electromagnetism because it's linked to the dynamics of spacetime which is more unique and "omnipresent" than electromagnetic fields. (There may be – and there are – numerous different spin-one fields, think about the gauge group of the Standard Model, but there can only be one spin-two tensor field, the metric tensor, at low energies.)

Heisenberg thought that the analysis of the wave fields wasn't quite exhausted – after all, one needs quantum field theory and it was only "getting born" in the early 1930s and it seems that the very term "quantum field theory" wasn't used in 1933 yet. (But I would place the true beginning of quantum field theory to 1926 when Pascual Jordan understood that all particles are quanta of quantum fields.)

And Heisenberg notices that the heavy particles – he means the proton etc. – don't seem to obey the rules of the Dirac equation well. The magnetic moment has a wrong value, if you need a particular example of the problem. This hadronic confusion already existed in the 1930s and grew up to the 1960s (the very birth of string theory partly occurred thanks to this mythology about Bootstrap etc., and Heisenberg himself was very important in keeping it mythological up to the 1960s) – before QCD eliminated the mysterious fog in the early 1970s. Let me copy and paste a few final sentences:
...But however the development proceeds in detail, the path so far traced by the quantum theory indicates that an understanding of those still unclarified features of atomic physics can only be acquired by foregoing visualization and objectification to an extent greater than that customary hitherto. We have probably no reason to regret this, because the thought of the great epistemological difficulties with which the visual atom concept of earlier physics had to contend gives us the hope that the abstracter atomic physics developing at present will one day fit more harmoniously into the great edifice of Science.
You may see that Heisenberg expected the trend of "deobjectification" and "devisualization" to continue and he viewed it as good news. Why? Simply because the abstracter description of the atoms that emerged from quantum mechanics made more sense – was more internally consistent and compatible with the observations – than the previous, visualizable, classical models.

It's a great recommendation for others to think equally. A theory that is specific, effective, formally analogous to some very simple and successful older theories, but able to describe the data more well and consistently is more desirable than a theory that obeys some philosophical dogmas (of visualizability) but otherwise is very ineffective, contrived, and/or disagrees with the empirical data!


  1. Perhaps you or your readers will find this interesting. It's a (slightly) relevant excerpt from 'A Beautiful Mind,' Sylvia Nasar's biography of John Nash:

    'Nash left the Institute for Advanced Study on a fractious note. In early July he apparently had a serious argument with Oppenheimer about quantum theory—serious enough, at any rate, to warrant a lengthy letter of apology from Nash to Oppenheimer written around July 10, 1957: "First, please let me apologize for my manner of speaking when we discussed quantum theory recently. This manner is unjustifiably aggressive." After calling his own behavior unjustified, Nash nonetheless immediately justified it by calling "most physicists (also some mathematicians who have studied Quantum Theory) quite too dogmatic in their attitudes," complaining of their tendency to treat "anyone with any sort of questioning attitude or a belief in 'hidden parameters' as stupid or at best a quite ignorant person."

    'Nash's letter to Oppenheimer shows that before leaving New York, Nash had begun to think seriously of attempting to address Einstein’s famous critique of Heisenberg's uncertainty principle: "Now I am making a concentrated study of Heisenberg's original 1925 paper. This strikes me as a beautiful work and I am amazed at the great difference between expositions of 'matrix mechanics,' a difference, which from my viewpoint, seems definitely in favor of the original."

    ' "I embarked on [a project] to revise quantum theory," Nash said in his 1996 Madrid lecture. "It was not a priori absurd for a non-physicist. Einstein had criticized the indeterminacy of the quantum mechanics of Heisenberg." He apparently had devoted what little time he spent at the Institute for Advanced Study that year talking with physicists and mathematicians about quantum theory. Whose brains he was picking is not clear: Freeman Dyson, Hans Lewy, and Abraham Pais were in residence at least one of the terms. Nash's letter of apology to Oppenheimer provides the only record of what he was thinking at the time. Nash made his own agenda quite clear. "To me one of the best things about the Heisenberg paper is its restriction to the observable quantities," he wrote, adding that "I want to find a different and more satisfying under-picture of a non-observable reality." It was this attempt that Nash would blame, decades later in a lecture to psychiatrists, for triggering his mental illness—calling his attempt to resolve the contradictions in quantum theory, on which he embarked in the summer of 1957, "possibly overreaching and psychologically destabilizing." '

  2. The message is that if you don't want to get a seriously mentally ill unhinged loon, don't dare to disagree with a letter that a physicist born on December 5th writes about quantum mechanics.

  3. Yep, "a seriously mentally ill unhinged loon" with a well deserved Nobel Prize in Economy.


    More seriously Luboš, congrats and many thanks for one other master piece more of commentary on quantum foundations, epistemology and history of physics.

  4. Thanks, Eclektikus!

    It was surely a deserved prize but one in economics, not economy, and it wasn't a Nobel prize, just a Nobel memorial prize. ;-)

  5. Touché, but recognize that's not bad for a person with such cognigtivas dissonances :)

  6. Hi Lubos, On the non-visualizability of quantum mechanics, back before string-theory physicists were thinking about point particles, but now they are thinking about extended objects called strings (and branes of various dimensions). So I guess my question is, what is the corresponding "uncertainty" for the position of a string relative to its velocity (momentum)? Does it refer to its center of mass? Or to the position of any "point" on the string? Or both? Or what? Is the idea of a string just as misleading as the idea of a particle in some respects?

    Also, is it still true, as I believe I once heard Witten say, that there is as yet no quantum field theory for strings, only a quantum mechanics?

  7. Nash’s problem was simply a very distorted view of himself and his abilities. I’m sure that all astute TRF readers have known individuals who have deluded themselves in to believing that they were much more able than they really were.
    In severe cases these delusions inevitably result in mental and physical illness. The world is full of such people, who come, eventually, yo a bad end.

  8. Dear Luke, first of all, all these questions are perfectly understood by the undergrad who succesfully completes a basic string course.

    Now, a string may be "visualized" as having a particular shape in space. But this is analogous to "visualizing" an electron as a point. In reality, we're interested in the quantum theory of electrons - or strings.

    In the quantum theory, x and p are complementary for the electron. Similarly, the position x(sigma) at each point parameterized by sigma along the string is noncommuting with p(sigma), the density of momentum per unit length of the string. Both x and p are still vectors (many components) in the spacetime, I have suppressed the index labeling the direction.

    In this description, a string is equivalent to lots (imagine infinitely many) of particles - beads on a chain - connected by tiny links or springs. We are interested in the quantum theory, so they are lots of quantum particles connected with lots of springs. We also want to allow the springs to rearrange, so strings are allowed to interact (split and join).

    When the full Hilbert space of these strings is derived, and the effective Lagrangians etc., one finds out that this "first quantized" picture of string theory consisting of strings which are really chains of many particles (beads on a chain) is totally equivalent to a string field theory, which is a quantum field theory with infinitely many fields at each point - corresponding to various excited mass eigenstates of a string.

    At the end, there is only one theory with numerous equivalent descriptions. In practice, string theorists actually often use the "first-quantized" description which is analogous to lots of non-relativistic quantum particles connected by tiny springs. String field theory, the other description, is also possible for most questions, but it has some issues, and all beliefs that string field theory would lead to a deeper (nonperturbative) understanding of string theory - better than the beads on the chain - were disproved. String field theory seems to be just another way to derive the perturbative (power law) expansions for the string amplitudes.

    Lots of evidence exists that there is also a nonperturbatively complete theory whose perturbative approximations are given by the strings above, and lots of things about this string/M-theory is calculable exactly outside the perturbative regime.

  9. Dear Gene, I wasn't 100% sure whether I was joking, but as your comment hints, I probably wasn't.

    It is indeed perfectly possible that his disease exploded because of that, and because he simply ran into a wall that internally convinced him that he wasn't smart enough for those things, although he wanted to believe otherwise.

    A week ago, I watched a movie about Nash (Beautiful Mind?) - mostly, I probably didn't finish watching it. I had very mixed feelings. Of course, on one hand, I had lots of sympathy for him. On the other hand, his priorities were nothing like mine. His applied mathematics was sort of "extremely practically" oriented, something I didn't share at all, and that's why he also looked painfully obnoxious when he were trying to convert his cleverness to picking the chicks and things like that.

    One can be very clever about these applied math (game theory...) questions yet extremely superficial. It's a significantly different kind of intelligence. Some people don't realize their limitations. For example, I realize more than enough that I am completely mediocre person - or worse - when it comes to game theory, the concentration on such things, looking for random patterns, playing chess well etc. Maybe my lousiness is partly because those things look immensely boring to me.

    But maybe Nash couldn't appreciate that he was comparably lousy when it came to very abstract things that are needed in modern physics. And that may be a problem.

    I had an exchange yesterday with a scholar in Prague who was telling me that all the other contests at Kaggle are really the same as the Higgs contest, who cares, calculating the mud in Turkish restaurants is the same as particle physics. My adrenaline went up, of course. The mindless algorithms that are often applied to these contests by average participants may be similar but the actual wisdom behind these things is totally incomparable. Turkish restaurants are stinky piles of chaos without any principles and important findings. Particle physics is the tip of science based on the firmest principles that the mankind knows which provide it with the most robust organization and demand the most disciplined yet creative thinking from the physicists who want to do it right and get somewhere.

  10. I've been to Turkey twice and accordingly have eaten in many Turkish restaurants, so I must say a word in defense of them; they are not very muddy. Nor are they very stinky, despite your scandalous statements to the contrary. But you will see there, somewhat paradoxically, the occasional Muslim woman trying to shove a Burger King whopper into her mouth under her Niqāb while texting furiously on the latest iPhone.

  11. LOL, I didn't mean the stink literally. I meant that it's a non-robust piece of mathematics. What? The other Kaggle contest


    I chose as my example. I didn't spend much time with it, but I am in the middle of the leaderboard, i.e. 1000th place LOL, and I am afraid that spending tons of time is the recipe to get higher. It doesn't motivate me too much. One is predicting the revenue of the restaurants from the breast size of the waitress and 36 other numerical pieces of data, and some categorical data. Now, there's always some correlation but there's no good reason to think that the numbers given imply the revenue in any reliable, causal, or controllable way. No scientific laws are being found in this. It is a typical contest - and most contests are like that - where one may get better score than others but the precise reasons why it's better cannot be quite isolated, and even if they can, these reasons won't be useful elsewhere.

  12. I didn't know he has done any geometry at all. Do you have some references?

  13. Right. I realize that I sound like Sheldon Cooper when his sister insults him by calling him a rocket scientist. ;-) But I just can't help myself.

    It's really like the difference between Howard the engineer and Sheldon the physicist. Applied mathematics is used in numerous disciplines of engineering, economics, and elsewhere, but the actual background and levels of abstractions one has to have to start to solve such things is often just high school mathematics and sometimes undergraduate mathematics.

    But the pyramid of abstraction one needs to master to get to cutting-edge physics is something totally different than some "totally random example of applied mathematics in a random human endeavor".

  14. Yeah, I see. Fundamental physics is supremely beautiful. And I'd devote every second of my life to studying its deepest abstractions (though I know I might not even have the cognitive ability to do so) if my assumption that I've got only one life did not compel me to look upon a life of such study as distasteful - like freely choosing to write the biography of the man who has legally been tasked with executing you in a few hours. I can so easily understand how you find supreme beauty in M-theory. But I simply cannot understand how you can find the motivation to do it when you know that you are going to die. I apologize for this somewhat juvenile, angst-revealing comment.

  15. Nash did more than you think.

    and http://www.ams.org/notices/199810/milnor.pdf


    John Milnor is a well known Princeton topologist who knows Nash well, and Richard Hamilton was instrumental in using Ricci flow techniques used by Grigori Perelman to prove the Poincare Conjecture
    These are hardly applied maths.

  16. Sure, http://www.ams.org/notices/199810/milnor.pdf . You can find also his publications there.

    You may also want to see here : http://www-history.mcs.st-and.ac.uk/Biographies/Nash.html

    It is interesting that he couldn't get into top 5 of Putnam exam, while he was an excellent problem solver.

  17. Another excellent post on Heisenberg, Lubos! I have some questions (unrelated to Heisenberg) but about
    "There may be – and there are – numerous different spin-one fields, think about the gauge group of the Standard Model, but there can only be one spin-two tensor field, the metric tensor, at low energies."

    (1) If under SUSY we find vector particles in TEV range, do we have to modify the current gauge theories substantially or under the effective QFT, current theories may be OK.
    (2) Because of metric tensor connection, additional spin 2 particles may raise more complicated issues. Is that so?
    You may have discussed these issues while discussing SUSY which I missed. In that case please give references. Thanks.

  18. I am unclear why study of the deepest and ,pat epegant insights ever seen would be deterred by mortality?

  19. kashyap vasavadaApr 29, 2015, 4:16:00 AM

    In (2) I mean at very high energies like multi Tev. I suppose, under present understanding spin 2 particle must have zero mass. Right?

  20. Can we say that a point light source (turned off) together with a two slit interferometer and say a photographic plate detector exclude certain photon modes? Light does not go to certain parts of the photographic plate so can we say that the source (turned off), the interferometer, and the detector together modify the electromagnetic vacuum so that when the point light source is turned on photons don't arrive at some regions because those modes of light can not be produced by the light source? Does this idea violate standard quantum physics.

    Thanks for your informative post, posts.

  21. You have glossed over or omitted the Achilles heel of the Copenhagen interpretation: the measurement problem and the Heisenberg cut. What exactly counts as a measurement or an observation? Where does the Heisenberg cut lie?

  22. Maybe he saw that Discovery channel documentary about *the real* life of chimpanzees that was somehow shown even in the US?

    Basically, they eat, masturbate and copulate. That's all they do.

  23. Quantum mechanics doesn't have any Achilles heels. The importance of these concepts isn't an Achilles heel of a theory; it is the most important discovery of the 20th century science.

    The observation - something that abruptly changes the wave function - is anything in which an observer learns something. Whether he's learning something is a subjective matter and this dependence on the subject cannot be eliminated. It's the whole point.

    One can show that there are physical restrictions on how smart, perceptive, equipped etc. the observer has to be to actually measure something. These conditions may be studied "externally", with the observer treated as any other physical object.

    However, when these conditions are obeyed and the observer is capable or collecting and manipulating data, the very realization is his subjective matter that doesn't admit any universal objective definition.

    The Heisenberg cut lies at *any place* that makes the "quantum side" of the cut sufficiently large - at least large enough to preserve the coherence of all quantum process where the coherence isn't lost. However, the Heisenberg cut may be placed anywhere between this minimal line and the place where "almost everything" is treated as the coherent microscopic quantum object.

    As far as the coherent phenomena with any potential for interference are properly described by the microscopic rules of quantum mechanics, the precise location of the Heisenberg cut is a physically meaningless question. It is easy to see that its location has no observable consequences because the information on the "classical" side of the cut has to behave and behaves as classical information, anyway, and quantum mechanics agrees and has to agree in the basic character of this information in the classical limit - which has to apply in the overlapping region.

  24. I agree that for all practical purposes, the exact location of the Heisenberg cut doesn't matter. But in theory, there's still an inversely exponential dependence of quantities on the location of the Heisenberg cut. And the very fact that a Heisenberg cut has to even exist is deeply troubling by itself, don't you think?

    Anyway, if you push the Heisenberg cut way past the scale of the Earth to cosmological spaces, what implications would this have? Basically, the whole of humanity and human history would become like Wigner's friend.

    I'm not sure why you think "quantum mechanics" and the "Copenhagen interpretation" are synonymous.

    One can show that there are physical restrictions on how smart,
    perceptive, equipped etc. the observer has to be to actually measure
    something. These conditions may be studied "externally", with the
    observer treated as any other physical object.

    Could you please spell out these physical restrictions? If you're correct, you'd be making a huge advance on the measurement problem just by spelling them out.

  25. Thanks but apologies, I don't understand your question. When a light source is turned off, there are no photons coming from it and nothing to discuss, right? What the 5 lines can be about then?

  26. Dear Kashyap, thanks.

    1) It is totally plausible that the LHC will find new gauge fields and spin-1 bosons. The most widely expected is just a mundane new broken U(1) group. Its gauge boson would look like the Z-boson, a massive neutral spin-1 particle, and such a new hypothetical particle is usually called a Z' boson (Z prime). Various string models predict many of them. In principle, more complicated gauge groups could be found, too. If those exist, one goes away from the minimal, Standard-Model-like spectrum, and this also means that one has to sacrifice e.g. the simplest accident of gauge coupling unification etc. but those are possible.

    2) Spin-2 particles aren't quite forbidden. They just must be "less elementary". Physics admits a whole infinite tower of massive spin-2 particles (in the spectrum of a string) whose co-existence is essential for their consistency. One may also have Kaluza-Klein modes of the graviton - graviton moving in extra dimensions of any shape (even discretized, the so-called deconstructed ones) behaves as a massive spin-2 particle, too. And of course, one may have spin-2 particles that are clearly composite, like various nuclei (and their so far unobserved heavier counterparts).

    The discovery of a new particle would be great. A discovery of the new apparently elementary massive spin-2 particle would indeed be an even greater shocker, conceptually. It would mean the existence of "some" string-like inner structure of particles, or some extra dimensions, or something that hasn't been thought about yet.

  27. Thanks. I would prefer individual links to some geometry papers that are said to be valuable...

  28. Dear Gordon, someone else posted exactly the same links as you did. I don't understand how the thing appreciated by the Abel Prize differs from the things he was doing in the economics/game-theory concept.

    On the other hand, I view Richard Hamilton as mainly a Perelman-like pure mathematician and geometer.

  29. Why do you find it more sensible to discuss "human death" in relation with M-theory and not in relation with anything else, like playing sports, studying chimps' DNA, racing, drinking wine, or anything else?

    Perhaps, generally, the attachment to the deepest laws of physics makes one feel independent of mundane things in the world including death.

  30. No, there is nothing troubling about those exponentially small effects in quantum mechanics.

    If one wants to predict and verify these predictions including these tiny exponentially small interference effects, he needs an accurate calculation, he needs to place a bigger part of the systems on the microscopic side of the Heisenberg cut, and he needs to use very accurate (and therefore very large) apparatuses.

    If those things are done right, all the arbitrarily small but finite interference effects may be observed and quantum mechanics succeeds perfectly. If they can't be done, only approximate verification may take place, and quantum mechanics predicts it correctly as well - with a greater tolerance about issues like the location of the Heisenberg cut.

    Anyway, if you push the Heisenberg cut way past the scale of the Earth to cosmological scales, what implications would this have? Basically, the whole of humanity and human history would become like Wigner's friend.

    I *am* thinking about the whole Universe as being a Wigner's friend, on the microscopic - exactly quantum mechanically described - side of the Heisenberg cut. What implications does this reasoning have? For almost all macroscopic questions (not just cosmological ones), it has the same implications as classical physics used to have.

    Anyway, if you push the Heisenberg cut way past the scale of the Earth to cosmological scales, what implications would this have? Basically, the whole of humanity and human history would become like Wigner's friend.

    "Copenhagen interpretation" is synonymous to "quantum mechanics and its foundational parts that are controversial among those who don't want to learn and understand quantum mechanics".

    It's because quantum mechanics is a new theory of Nature with new foundations - basic axioms and ways to connect the formalism to observations - and those foundations were laid by a group of physicists who considered Niels Bohr - working at University of Copenhagen - to be their intellectual leader.

    There is no other quantum mechanics than quantum mechanics with the "Copenhagen interpretation" or anything that is scientifically equivalent to it. Except for a few rewordings of quantum mechanics such as Consistent Histories and Quantum Bayesianism, things called "different interpretations" are actually different *theories*, not just interpretations of the same theory, and none of these theories is viable. To say the least, none of them has been brought to the same "usable status" that could agree with all the known observations in the same sense as quantum mechanics (i.e. as "Copenhagen interpretation"). I am talking about specific theories and not about some hypothetical flying castles and quantum theory (=Copenhagen interpretation) is the only theory worth mentioning when it comes to the explanation of this class of phenomena - more or less all phenomena in modern physics.

    Anyway, if you push the Heisenberg cut way past the scale of the Earth to cosmological scales, what implications would this have? Basically, the whole of humanity and human history would become like Wigner's friend.

    No, there is no measurement problem, and I won't spell anything more accurately than I did because it has nothing whatever to do with fundamental physics. These questions belong to neuroscience which is just an "emergent science" that studies some very complex objects but its findings may ultimately be explained by the basic laws of physics, anyway.

    But there is nothing truly fundamental about a human brain and its mechanisms of memory and calculation. They're highly emergent, non-fundamental phenomena and questions, and if you want to claim that fundamental physics first needs to understand neuroscience, then you are completely deluded and you are reverting the whole explanatory hierarchy of sciences upside down.

  31. Let me get this straight. You think quantum mechanics is a fundamental property of nature, and quantum mechanics is fundamentally only concerned with experiences measured by observers and nothing else, and "one can show" what are the precise properties needed for something to count as an observer or a measurement, but yet, it's not worth it to spell out what these precise properties are because they're not fundamental.

    Anyway, by suddenly switching from observers in general to neuroscience, it appears you implicitly identify observers with brains even though there's no a priori reason for such an identification. So, if I have to guess, you think brains have the "precise properties" needed to become observers while "non-brains" don't. Otherwise, why bring up neuroscience when I didn't?

    If you think the whole universe is like Wigner's friend, then an orthodox Copenhagenist like you would have to posit an observer outside the universe. The other alternative is MWI, but you clearly hate that.

    At least now, I understand your insult "anti-quantum zealot". By that, you really mean "anti-Copenhagen zealot". Well, there's no shame in being an "anti-Copenhagen zealot".

  32. It's not important whether I "think" that. What's more important is that it is an important and irrevocable result of the scientific research that has been known since the mid 1920s and Heisenberg has received e.g. this 1932 Nobel prize discussed in this very blog post. Read his Nobel lecture, everything is as clear as sky. Quantum mechanics - the right theory of Nature - inevitably describes not some objective world but instead, it organizes the information that can be collected by an observer.

    Whether one uses the words observations, measurement, perceptions, "qualia" (I had to search for this weird word) may lead to different laymen's emotions but it doesn't change anything about the physical essence. And the fact that every correct usage of quantum mechanics is organizing phenomena from a viewpoint that knows something about them - from an observer's vantage point - is absolutely critical and unquestionable, and it's a big part for what Heisenberg got his prize, one of the most well-deserved prizes in the history of the mankind.

  33. If the observer is really so critical and fundamental, then why do you so consistently evade questions about the nature of an observer?

  34. The observer is an entity that does the observations.

    The observations are so fundamental *exactly* because they cannot be decomposed to anything more fundamental.

  35. You're going round in circles. A measurement is an experience by an observer, and an observer is an entity that makes observations, an observation is an experience.

  36. One can't go "anywhere" along a straight path because the observations are the end of the explanatory story, fundamental building blocks that quantum mechanics needs to operate, so doing anything else than "going in circles" means to be wrong.

    You're like a person who hates the existence of zero as a real number and who insists that the number has to be composed to positive numbers or something like that. It can't. It's as simple as 1 or simpler than that. Who can't get it is an imbecile. And so are the people who can't understand that observations are needed for quantum mechanics to operate, and their general existence can't be decomposed to anything simpler.

    At any rate, this exhange has been absolutely exchausting. Repetitive morons like you who have excessive self-confidence on top of that are insufferable. I've banned you and I will probably be banning commenters after the 1st comment that suggests at least 70% probability that they're similar to you.

  37. I was saying the opposite. I didn't read papers, they are on subjects like algebraic manifolds which I don't have a clue about. But Gromov and John Milnor, who are more than first rate mathematicians, say that he had done extraordinary job and what he had done in pure mathematics. Gromov says that Nash and Smale were the ones who influenced him most.

    If you say that it is irrelevant fot string theory so not important , I don't have anything against to it, but what have done is rated as first class mathematics by first first class mathematicians.

    If I can find links to his papers (legal), I will write here.

    This is what Gromov has said (Also quoted in my first post):
    What he has done in geometry is, from my point of
    view, incomparably greater than what he has done
    in economics, by many orders of magnitude. It was
    an incredible change in attitude of how you think
    about manifolds. You can take them in your bare
    hands, and what you do may be much more powerful
    than what you can do by traditional means.

  38. Hi John, Gromov is a great deep mathematician but I won't uncritically accept the second-hand rumors of the kind you want me to accept.

  39. Lubos,

    I never cease to admire the patience with which you endlessly repeat basically the same and irreducible truth. Your time is not wasted, because every response makes the absurdity of all those "philosophical" objections stand out even more. I am not a physicist, but I do have a math degree and I learned some QM some longish time ago (while helping my brother with his school project). Perhaps when one gets to study these things early in his life, the conclusion appears natural, your outlook being still unpolluted with all that nonsense that you are bound to expose yourself to as you go on. I recall how having absorbed the essence of QM as a late teenager I just said to myself "OK, so this is how it is, this is how the world works" and immediately realized that asking questions about the nature of things that by definition were not part of the game made no sense. Later on I got a bit confused while (somewhat involuntarily) reading some of the popular "mystifications" of QM. If so many certified experts claim that there are all those weird problems, then perhaps there is something to it, right? Your blog has restored my sense of sanity and understanding. Thanks.

  40. Thanks for your pleasing words and understanding, KN.

    Your point about the "young age" could perhaps be converted to some policy.

    It actually seems plausible to me that there is a certain core of the quantum thinking - freed from all the difficult maths etc. - that could be explained to schoolkids.

    Perhaps just to show them some of the basic experiments showing QM - double slit, EPR/Bell's, whatever, some of the quantum games - to make them realize that the naive picture, that something is objectively "out there" before the measurement, doesn't really work, yet all the measurable repeatable numbers from experiments may be explained and calculated.

    Without that, it does look like attempts to teach a new language to an adult. Most people just won't find it as natural as the mother tongue - and they won't believe that it can be equally natural. I am still puzzled whether the French really do speak French at home, or they're just pretending this silly language in public and switch to normal Czech at home. ;-)

  41. In cavity quantum electrodynamics if the metal cavity is very small then if an excited atom in a Rydberg state is in the tiny cavity the atom can not emit a photon, don't we say that the cavity has modified the electromagnetic vacuum in the cavity. I thought something similar might be going on with the turned off light source, double slits, and the photographic plate?

    Thanks for your reply.

  42. Yes, Andy, all metallic and other solid materials modify the boundary conditions for the electromagnetic field. For example, the electric potential A_0 is equal to a constant at the surface of a conductor.

    Because the electromagnetic field - both classically and quantum mechanically - wants to avoid "big changes" from one point to a nearby point, such boundary conditions influence the electromagnetic field at different, perhaps remote, places, too.

    So whatever you place in space modifies the "wave functional" for the electromagnetic fields' ground state, the vacuum state.

    However, if you want to determine the interference pattern, you have to study the (at least) one-photon states, not the zero-photon vacuum states.

    Some of the impact of the barriers etc. on the photons is already included on the impact of these barriers on the vacuum state, but most of the details require a more general calculation.

  43. ‘I quickly ask: Why? Why should I try to sort 10 different possible futures of chess if a computer program I can quickly write could clearly do it much more efficiently? It's like lifting hundreds of kilos in the fitness every day (which some people also find great, but that's another story LOL).’
    I occasionally weightlift to make myself feel good and to give myself an evolutionary advantage at spreading my genes. But if you find weightlifting and even chess mind-boggling as serious pursuits, then take a look, for a laugh, at this MIT review of a philosophy book called the ‘The Geometry of Desert’ by the Yale professor Shelly Kagan. Surely this book is a perfect example of so-called physics envy—i.e., trying to turn morality, justice and desert into something as precisely explainable and understandable as geometry, Kagan having even gone so far as to build elaborate pseudo-mathematical graphs on desert and justice: http://web.mit.edu/bskow/www/research/kagan.pdf.

  44. "You don't seem to be balanced and impartial in your argumentation."...interesting comment--I would have used the identical words to describe your comments about Nash. You seem to base them on the movie or on Sylvia Nasar's book or both. As you know, Nasar is a rather good writer, but is not trained in maths...plus she makes sometimes ill considered value judgements...consider her essay "Manifold Destiny" and its comments about Yao and his students.
    Maybe read John Milnor's short biog of Nash for the AMA...Milnor is about as pure a mathematician as it gets, and has been a superstar for ages, has worked with Nash, and was even set up with Nash's sister.
    The Riemann embedding theorem with Moser is hardly applied math. And just WHAT IS WRONG with applied math? Newton, von Neumann, Gauss, etc were to varying degrees applied mathematicians, as was Stan Ulam. Most dabbled in both.
    Your argument seems to be the "argument from personal incredulity".

  45. Dear Gordon, I am not building anything on the book - I haven't read it - and not even the movie - I haven't completed watching it, as I wrote above.

    Concerning your question, let me remind you that the discussion leading - among other things - to this paranoic reaction of yours was started by a comment about Nash's attempts to criticize the foundations of quantum mechanics which, as the commenter mentioned, may have been the very spark that led to Nash's serious psychological problems. I am not an expert in his life but I find this story plausible.

    If you ask what's wrong with applied mathematics, nothing is "wrong" about it. The only relevant thing in this thread that is "wrong" with applied mathematics is that the people doing applied mathematics - like Nash - don't have the necessary level of abstractions to understand theories at an ever deeper level of abstraction, as those needed in the search for new laws of physics.

    So one may be a Nobel memorial prize winner or a guru in these things but it's still overwhelmingly likely that if he will try to do such things and argue with people who have been established as being great physicists, like Oppenheimer, he (Nash) is probably going to be wrong, most likely embarrassingly wrong.

    This is really the only kind of a discussion that is marginally related to this thread's topic. Your attempts to ignite some flame war concerning applied mathematics is not on-topic here.

    Newton, Gauss, and von Neumann may or may not be called applied mathematicians. It is a matter of terminology that may be skewed and twisted in various ways, feel free to do so, I am not obsessed with spinning terminology and in the terminology I would use, I wouldn't call Newton an applied mathematician and it would be ambiguous for the two other geniuses.

    But there's been a much more clear meaning of the term "applied mathematician" that may be understood from the context of this discussion. By an applied mathematician, I clearly meant someone who is applying mathematical methods to situations working according to the rules of the game that are known in a priori, and whose basic framework - when the difficult mathematical results are removed - is understandable to the layman.

    So an applied mathematician is someone who doesn't necessarily understand the search for the new laws of physics, and some of the newer concepts, principles, and frameworks that became the new rules in physics.

    So an applied mathematician is someone who is expected to be wrong when arguing with top physicists such as Oppenheimer, and Nash did agree with the expectation. So please calm down, I didn't want to say anything else than these self-evident things.

  46. kashyap vasavadaApr 29, 2015, 5:33:00 PM

    Thanks Lubos!

  47. Dear Mike, I am also sometimes weightlifting - going to lift my dumbells 300 times, hopefully, again in minutes. But whether it makes me feel good is questionable. It's good to make the blood circulate through some muscles, and to see that the body isn't quite lazy and the muscles get firmer for a while LOL. But there are lots of papers saying that exercise is really as harmful as being lazy.


    There's been some negative reaction to that but I don't want to go into that. I don't really care about these constant health reports at all. It seems obvious to me that certain things may be harmful but most others are virtually uncorrelated with health and longevity etc.

    The paper you linked to contains too much formalism for apparently too simple and vague ideas, at least it's my impression.

  48. Lubos, when and if time permits, please write one opinionated post about the health in relation to food (including, of course, alcohol) and exercise, so that we can have a nice discussion.

    It may be entertaining, if not educational.

  49. LOL, Tony, it could be fun but I don't know how I would start. Perhaps: Last week, I made a big experiment and replaced drinking beer by drinkiing wine for the whole week. It was expected to be healthier but I felt lousier and tired by Friday. ;-)

    There are so many things... and I believe that if there is any correlation between some normal food and health, it is highly personal and depends on whom you look at. None of the usual things that are being eaten can be "really devastating" because it would have already be imprinted in the life expectancy of nations etc.

  50. Excellent topic Lubos which leads me to 2 comments .


    1) First is that I always find it strange to see how clear, articulate and understandable were cutting edge papers 100 + years ago.

    I still have a copy of the seminal Planck's paper in Annalen der Physik from 1901 and consider it really impresssive.

    (Almost) everybody can read it and understand it. The same is true for Heisenberg, Bohr and many others.

    I believe that this must also say something about science and scientists 100 years ago as compared to today especially when I compare it to some blogs written by scientists supposed to understand what they are doing. But I can't put a finger on what it says.



    You wrote : "You see that from the mid 1920s, Heisenberg's thinking was the quantum thinking. It was his default state of affairs. All the people dissatisfied with quantum mechanics and proposing the alternatives choose the classical thinking as their default one."
    This is excellent and true.
    Herr "Professor Doktor Heisenberg" says so himself (a bit better :)) in the audio from 1968.
    Did you listen to it ? I definitely recommend this audio to everybody reading this post.
    He is demonstrating this with an anecdote.
    In 1922 Sommerfeld brought the very young Werner to Göttingen to listen to Bohr speaking about his planetary model.
    At the end Bohr said "There is much that is still not understood but I am totally convinced that farther observations in the future will confirm this model."
    On the Q&A section, Heisenberg made an intervention basically saying that he didn't believe that at all.
    After the talk, Bohr sought out Heisenberg whom he didn't know and invited him on a Spaziergang to discuss why he didn't believe that.
    Heisenberg has discribed himself as a physical "Dilettant" (interestingly Einstein described himself sometimes as Dilettant too) because he didn't know much about classical physics.
    So he says that he was Lucky that when he was very Young, a new physics appeared where extensive knowledge of classical physics was not really necessary so that he could focus only on the new physics.
    And Bohr told him that he now understood why Heisenberg didn't believe the planetary model while he, Bohr, had not (yet ?) the courage to free himself from the huge weight of "Newtonian physics" that he learned and was perfectly mastering..

  51. Thank you for your remarks, Tom!

    1) You may be right that the scientists were very clearly thinking 100 years ago. Alternatively, it was easier to make big discoveries because low-hanging fruits were waiting to be picked.

    2) Yes, I did listen to the audio. But only the English-spoken one. The story is cute. Maybe, indeed, some "ignorance" or "lack of experience" with classical physics could have helped Heisenberg to find the right one.

  52. Thanks for your time! I start my day here hopping to learn more.

  53. I thought that Classical Mechanics (specifically the Lagrangian and Hamiltonian mechanics formulations) were essential to approach to Quantum Physics. It seems to me that Bohr's words (and also Heisenberg's words) about knowledge/ignorance of CM was rather a metaphorical instance (and an hyperbole when Heisemberg said "extensive knowledge of classical physics was not really necessary") to emphasize the separation of the two formulations... though I guess that having studied classical mechanics before the existence of quantum mechanics indeed must make a difference.

  54. In their original papers Heisenberg, Jordan, Born and Dirac do show that the 'functional form' (for the lack of better term) of Hamiltonian formulation of classical mechanics is preserved in QM. They spend quite some time defining derivatives and rational functions of p and q which now become matrices.

    Heisenberg, however, seems to be the first who didn't care too much about the visualization of p, aka mv, and q in the classical sense.

  55. The funny thing is, every one uses same equations :-) . And the ones who use different equations are completely wrong.

  56. Dear Electikus, quantum mechanical theories of everyday systems do have a classical limit, and may be obtained from the "same" classical formulae for the Hamiltonian and Lagrangian by adding the hats.

    But in general, it is not even true that a quantum theory has to have *any* classical limit. The (2,0) superconformal theory in d=6 doesn't really have one.

    I think that Heisenberg's statement that "extensive knowledge of classical physics wasn't necessary" was meant very seriously and was very carefully formulated.

    I don't know why you think that "classical physics is essential". What does it even mean? In everyday situations, they coincide, anyway, and the classical description may be easier to imagine. But there's surely lots of analyses in classical physics that are too complex -and often wrong because they go beyond the range of validity of classical physics, anyway - like analyses of atoms, electromagnetic fields at some temperature, and so on, and so on. And why do you think that any of the statements was a "metaphor"? All of them were absolutely serious and important, I think.

  57. Yes, of course Luboš, I understand your arguments, I rather refer to the need, from an educational point of view if you want, to study Classical Mechanics before start studying Quantum Mechanics. I honestly can not think of a curriculum in which the concepts (I mean to many classical concepts: Kinematics, energy conservation, dynamics, rigid-body dynamics... and its different mathematical formulism all the way until Hamiltonian mechanics) are explored in the reverse order. Of course I understand the conceptual breakthrough and the critical difference between both visions of nature (I am an old and attentive reader of this blog ;-) ) , but, do you think that someone could understand Quantum Mechanics without a solid foundation of much of Classical Mechanics (if only to dismiss it soberly)? Or put it another way, would you use Quantum Mechanics to teach these concepts and from there go to the limit of classical mechanics?

  58. Yes, Eclectikus, as I have already written, I do have big doubts about the value of the current approach in which too much classical physics is pumped into the people before they learn anything about quantum mechanics. In fact,I have wrtitten - and I still think so - that it may be a good idea to lead children at the basic school to quantum mechanics, in some edible way.

    And again, yes, I think that Heisenberg and Bohr were completely serious when they said that Heisenberg didn't have extensive knowledge of classical physics when he started to work on the problem.

  59. Well, I guess it's a matter of degree of difficulty, it seems more feasible to explain simple concepts from a classical point of view (more comfortable because we can see them), and when they dominate these concepts and also when reach a good mathematical grounds open the doors of the quantum world. At least when speaking of undergraduate level, classical mechanics, and its methods, are useful for too many things, it should not be eliminated although it must be remembered that it is not how nature works and that quantum mechanics is the correct theory to a more fundamental level.

  60. Lubosh, you wrote: "there is no good reason to expect that α becomes uniquely determined when relativity and quanta are combined." But it is determined with h_bar and c (and e^2) uniquely. Next, this dimensionless constant never comes alone, but in combination of other constants and dynamical variables, also in dimensionless functions. Sometimes they together are very big (as for IR contributions), sometimes they are small (the dimensionless combination gets small due to high energy). So "the strength of electromagnetism" is a rather variable thing in QM where the probability (not energy) is of the primary interest.

  61. No Lubos in the post below is right.
    Just listen to the 1968 audio.
    Heisenberg is clearly saying that he was very Young (20 years) and that his knowledge of classical phyisics was lacking.
    Then he says explicitly that it was not very bothersome and he was LUCKY because this knowledge was not really necessary for the new physics. He even designs himself as a "Dilettant".
    He sounds to mean that pretty seriously and not just some joke.

  62. Still, is difficult to me imagine Heisenberg with just a trivial knowledge of Classical Physics, unless you talk that "not much knowledge" for a genius as him is equivalent to a pretty deep understanding for a normal person (and I could say the same of a "Dilettant" Einstein).

  63. Dear Eclectikus, many important truths are hard to imagine for many people.

    When Heisenberg or Bohr talk about Heisenberg's relative ignorance of classical physics, they almost certainly compare him with "other physicists" who have similar jobs and roles in similar scholarly environments.

    But in this comparison, Heisenberg didn't have extensive knowledge of classical physics, and indeed, it could have been rather close to that of an average alumnus of an average school. See e.g.


    He was doing very well at the high school but collided with big hurdles while trying to enter a university, being focused on mathematics, and having views that some math professors viewed as "unorthodox" and not their cup of tea. Interviews didn't go well.

    Sommerfeld (who did work on Bohr's atom...) told Heisenberg - Maybe you know nothing, maybe something, we shall see. This was actually the most positive rating he got about physics and that's why he could start to skyrocket.

    Heisenberg's first research was already on atomic theory, and what he tried to improve was to add relativity. In all senses, he focused almost exclusively on the cutting-edge physics and ignored some old questions.

  64. Thank you so much, very interesting, I think I've convinced, I didn't know that story of Heisenberg and Sommerfeld but it is definitive in favour of your arguments, in this case.

    Maybe I had a simplistic view, and I've extrapolated cases like Feynman (an undeniable instance of applied and theoretical physicist, who felt comfortable with the experimentalism), Gell-Mann (a first order theoretical physicist but maintains a cross knowledge of other sciences and humanities), or Penrose (pure living encyclopedia) to name a few.

    Yourself, Luboš, and your blog mixing cutting-edge Theoretical Physics (String Theory), worldly Classical physics (Climate Change) and political analysis, could be a counterexample to your own arguments (and the Heisenberg's case or even Einstein's case).

    And that is why I always have had the impression that becoming a top physicist on the frontiers of Science, you must have gone through all the previous steps (including of course Classical Mechanics) being also in the top. And indeed this is not true.

  65. Maxwell Clark, ImpMay 1, 2015, 10:34:00 AM

    “The constant α is
    dimensionless so it cannot be set equal to one. And the lessons of relativity
    and quanta have already been "depleted" so there is no good reason to
    expect that α becomes uniquely
    determined when relativity and quanta are combined.”

    Yet may be uniquely determined when a third fundamental is
    discovered and added. The point I’m making is so often misused it’s easy to
    forget there are contexts of legitimate usage, which the position you develop
    is one.

    This is because, while you may well be, and, are correct in
    your insights, that things like masses, relatives masses, certain ratios, α,
    have no fundamental significance precise to the value they are, there is
    absolutely no scientific fact, theory, implication, inference (even by
    induction) on this matter at all. None at all.

    For that reason, it’s worth keeping the other view of this
    in the picture, for now. That the same list of constants can be found on the
    list of what none of our theories have yet been able to explain.

    Which blah blah blah eventually arrives an argued conclusion
    that what we take away from the lessons of relativity you mention, really comes
    tol what we believe is the most true, and most reliable compass of future
    ongoing discovery.

    Your belief is no less legitimate, but my belief would draw
    on the history of how discoverers that went on to get it right, have dealt
    awkward choices like this. The ones that got it, always put their faith in the
    universal principles. Like the conservations laws.

    There are other contexts of the same choice, such as what do
    we do when our best theories run into a serious anomaly. Throw the theory out,
    or put our faith in the theory, and try to derive what it would take for the anomaly
    to be explained assuming theory was correct. E.g. Neptune.

  66. Dear Eclectikus, thanks for your newly found synergy concerning Heisenberg but I am afraid that I disagree with your new claims about the other physicists again (or too).

    I wouldn't say that Feynman was an applied physicist in any sense. He had a heuristic approach and a respect for real-world activities and so on but he was never good or disciplined in them. If he did experiments, they were experiments with ants and meditation or things like that. ;-)

    It seems totally fair to me to say that Feynman was as "purely pure" and "purely theoretical" physicist as Heisenberg.

    Arnold Sommerfeld had to go through the institutions in which the skills in experimental physics were required but as an adult, professionally, he was also a purely theoretical physicist.

    And Roger Penrose may be a living encyclopedia but when it comes to the topic we discussed in relation with Heisenberg, his ignorance about the advanced state-of-the-art physics is at least as intense as Heisenberg's. He really ignores at least the recent 35 years - most of his career - of cosmology and particle physics. That's an even bigger separation from the "current research" than what Heisenberg did.

    If Penrose did find something that really kills inflation or string theory etc., he would be as remarkable a winning maverick as Heisenberg. You know very well that I would bet 100:1 that unlike Heisenberg, Penrose won't find such a thing that would support his disdain for state-of-the-art cosmology and particle physics.

    So when you talk about "extrapolation", it seems to suggest that you consider Heisenberg an exception but I am not getting why. Heisenberg is not an exception in this sense.A majority of similarly great physicists ignores huge parts of the existing knowledge in related disciplines, and disrespects much of them, too.

    While I still think that physicists have vastly more complete "universalistic" knowledge than the average people - or average educated people - this absorption of everything that other people consider to be a part of the human wisdom just isn't a recipe to do great new physics. To do great new physics always means to build on others - and kill and dismantle their ideas at the same moment. These two parts are inseparable. Nature defines Her own rules what it means to find the right balance between these two things.

    Just to be sure, I have always sucked and probably still suck as an experimental physicist, too. I could have gotten *A*'s but there were A's with the help of my lab partner and with some protection, too. I never had the patience for the formalities needed to follow all the standardized protocols how to measure, write experimental reports, and so on, and I an not good in the essence, either.

    There were rare physicists like Fermi who were both great theorists and experimenters. But the body of knowledge and expertise in physics has become so wide that the limited "specialization" of being purely an experimenter or purely a theorist seems inevitable for most.

  67. Well, Feynman was not an experimentalist, but his life is rich in examples when he leaves the sophisticated theoretical physics, and went down to the world of applied physics and engineering (the case of the O-ring in the challenger crash was paradigmatic, wasn't it?). And also The Feynman Lectures are a perfect example of the coexistence (in college's curricula) of Classical and Quantum Physics, and his mastery of both worlds.

    Penrose is 84 years old, I think your bet is surely a win-win, but still he is an example of post-quantum physicist that has never forgotten classical physics (but he fully understand quantum mechanics).

    And sure, you are not an experimentalist, yet I have seen you answering hundreds of questions that could be framed in classical mechanics (or classical electrodynamics), so don't seem you has forgotten Classical physics neither. ;-)

  68. Good points, Eclectikus. The O-ring is a very practical or experimental problem. I am not sure whether the brightness that he exposed in that case could be classified as talent for experimental physics. It's general cleverness applied to a highly random "everyday" practical problem.

    His lectures do combine classical and quantum physics in a way that may be close to what I think is right. It was a course where the classical physics couldn't be painted as the "final point" so if someone wants to end with it, he was made sure that he was missing something, or he was in conflict with some physicists. ;-)

    Of course I've done lots of "classical physics". And I just improved my top score in the stupid Turkish restaurants to 1.75 million. A lousy ranking in the middle of the table still, but a purely my algorithm. ;-)

    What I want to emphasize is the man's ability to realize the limitations of his view that may result from a rather repetitive routine. This is really a very important lesson in all of science - and not just science. For that reason, courses that are "too polished" may ultimately be counterproductive.

  69. I have some suggestions.

    I think I agree with most of what you have said. There is no need to teach lagrangian or hamiltonian before teaching quantum mechanics. You don't even have to teach them at the same time. It may be even better to teach them after teaching quantum mechanics. That should be a comprehensive classical field theory course.

    Also, I believe a first course in quantum mechanics should only include heisenberg picture and discrete systems. Anything with wave-like properties should be avoided. Fundamental principles of quantum mechanics doesn't depend on space. But it depends on time of course. Also, words like wave-function should be avoided. Pre-probability is suggested before.

    Also, before everything, there should be a seminar/short-course on scientific process. It should be stressed that science concerns interaction of an observer with nature and a theory can in principle require an observer. Later it can be questioned whether theory requires an observer or not. Observer centered viewpoint may be useful even when there is objective reality, for example in classical statistical physics. If you don't talk anything about before you have started to observe a macroscopic object, you will avoid many mistakes related with second law of thermodynamics.

    Also existence of arrow of time, before any theory mentioned, should be stressed.

  70. Even avoiding the Schrödinger picture, anyone facing to quantum mechanics, need a considerable doses of mathematics and statistics, and preferably a good knowledge of Statistical Mechanics and other classical branchs. I do not quite see how skipping classical mechanics without leaving a hole in the curriculum of students. I guess a teaching method as the one you and Luboš have raised, would be good for high achievers, but do not see it feasible for the average student.

  71. I was considering an optimized curriculum for a future high energy theoretical physicist.

    If you want you can only consider a spin 1/2 system. *Almost* everything special to quantum mechanics can be taught considering that system I believe.

    You see, the problem with understanding quantum mechanics is never with some technical calculation. There are extremely smart physicists who say extremely stupid things about quantum mechanics. I guess Lubos' purpose was to prevent those anomalies.

  72. I understand. I was being more generic... because ultimately, there's Physics beyond (or behind) Theoretical Physics ;-)

  73. There's a recent paper in Science that connects Heisenberg uncertainty with nonlocality by Oppenheim et. al..did you see it?