The first part said some basic things about Bell's theorem and except that the importance of that paper of Bell's was overstated by an order of magnitude (and except for the popular derogatory "weird" adjective used against quantum mechanics), the content was marginally OK. That can't be said about the second part. I was seeing red for an hour after I read that thing. This text is just terrible and serves as a testimony of the catastrophic degradation of the intelligence of science journalists and some loud people calling themselves scientists, too.
First of all, the title is obviously wrong. In 2015, no genuine physicists are debating whether "quantum math is as real as atoms". All genuine physicists know what quantum mechanics actually says about this question. What it says can't be exactly reproduced by the human language or the language of philosophers, other laymen, or stupid people in general who like to debate meaningless questions with ill-defined words rooted in tons of invalid prejudices such as "is it real?". Only armchair physicists, third-class physicists, and "philosophers" may consider these foundational debates about quantum mechanics to be a part of the actual research in 2015. Physicists know that all these questions have been settled since the middle or late 1920s.
Siegfried begins with Ernst Mach's opinion that "atoms may be useful for visualization or calculation but I don't believe that they are real". Not only because Ernst Mach was born in the Czech lands, I feel the urge to defend him. It is not quite clear whether he really disbelieved the derivations – such as those in statistical physics or the Brownian motion (he was already rather sick at that time) – based on the notion of the atom.
As far as I can say, his point could have been completely correct, namely that the derivations based on the atomic theory were useful and often insightful methods telling us something about our actual observations. But at that time, atoms weren't really directly observed which is why it was legitimate to consider them virtual, auxiliary theoretical constructs.
My broader point was that Ernst Mach was an important representative of positivism in philosophy and while no philosophy may be treated as a permanently solid basis for science, positivism was positively correlated with the way of thinking that was needed for quantum mechanics (and in fact, even relativity) to emerge and replace Newtonian physics.
Positivism states that all of our trustworthy knowledge about Nature comes exclusively from sensory experience – from observations, if we use a little bit more physical jargon. In the context of physical theories, it means that a physical theory a priori declares "all objects in the world around us" and words describing them as meaningless. Every physical theory has the right to do so. Every physical theory may work with its own fundamental and auxiliary concepts to describe our experience. The experience is the only "provably real" thing. But the point is that every question about Nature that can't be reduced to our experiences is considered physically meaningless or unphysical.
(The Vienna Circle elaborated upon these important positivist observations and probably was the culmination of philosophers' understanding of the essence of modern science. When other philosophers such as Thomas Kuhn or Karl Popper began to be popular, the degeneration and putrification of philosophy of science was already underway. To return to Mach and his positivist predecessors, they generally erred by forecasting that "something would remain unobservable forever". For example, the founder of positivism Auguste Comte would predict that the chemical composition of stars would remain a mystery forever – just years before spectroscopy answered all those questions. But this error must be seen as a side effect of their important and right understanding that certain questions and claims are physically meaningless.)
A reason why I consider Ernst Mach (and perhaps a few others before him) rather smart was that he was apparently able to switch to the new way of thinking that is so important in quantum mechanics – and, to a lesser extent, in relativity – decades before quantum mechanics actually emerged in physics. It's remarkable because almost all of today's philosophers of science are unable to think properly even 90 years after quantum mechanics was discovered.
With a grain of salt, we could argue that about 100 years ago, the philosophers were actually useful for the progress in physics. That's also why most of the greatest theoretical physicists of that time considered themselves part-time philosophers. After the Second World War, the philosophers had largely lost it. The greatest physicists of the post-war generation, the likes of Feynman and Schwinger, to mention two, were no longer admiring philosophy in the usual sense. They diverged. The propagation of the anti-quantum delusions by the contemporary philosophers may be viewed as a revenge against physics – revenge for the fact that science had to completely escape away from philosophy and the best physicists no longer have any intellectual respect towards the contemporary philosophers.
Let me return to Ernst Mach.
If you think about his philosophy, it makes quite some sense and in variations, it may be said to capture the spirit of relativity as well as quantum mechanics. Mach's positivist spirit allows us to say that the "(objective) simultaneity of events" in special relativity may be said to be meaningless because it cannot be operationally decided – it cannot be converted to an experiment producing some perceptions. If we try to prepare the experiment, we may find out that the results depend on the observer and his inertial frame. The simultaneity may very well be relative – and in relativity, it certainly is. There doesn't exist any "objective" or "absolute" way to experimentally decide whether two events occurred simultaneously, and that's why it's right to say that the question whether two events are (objectively) simultaneous doesn't belong to physics. This is really the key to special relativity.
In the same sense, the precise information about the "point in the phase space" (which is just a slightly more mathematical synonym for the "objective state of the world") may be said to be physically meaningless because the position and the momentum can't be simultaneously measured, thanks to the uncertainty principle. Even by incomplete arguments, it may be seen that the observation necessarily modifies the system, and we need two observations that "interfere" with one another, so they can't be done simultaneously. The fact that these pieces of "classical information" – which were meaningful to ask about in classical physics – are no longer meaningful is of course the key (or at least a key) to the new quantum mechanical thinking and the founding fathers of quantum mechanics actually praised positivist philosophers for that helpful attitude.
Ernst Mach also promoted his version of "extreme general relativity", Mach's principle. It inspired Einstein when he was searching for the right new relativistic theory of gravity. According to Mach's principle, there can't be a difference between non-rotating and rotating (or accelerating and non-accelerating...) frames in the otherwise empty Universe, so whether a bucket is rotating in an empty Universe must be determined by its location and orientation relatively to other objects – stars that may exist.
Now, this was another possible excellent step to remove the shackles and possible wrong (because experimentally unsubstantiated) assumptions. I would say that Mach's principle, despite its role of having stimulated Einstein, is wrong in general relativity. Experiments in rotating and non-rotating buckets certainly differ and this difference may exist even without stars. But we may present the reason why Mach's conclusion was wrong in a pleasant way, too. Mach's conclusion (that the bucket's rotation only makes sense when there are stars) was wrong because he incorrectly assumed that the Universe without the stars is "empty" (carrying no information that could distinguish the rotation). But the Universe without the stars is still filled with the metric tensor field and that carries some information.
So we may say that the positivist philosophy was positively useful in 2 of the 3 revolutions, and it only seemingly worked in the third in which it was finally rejected. That's a pretty good, positive overall score for positivism, isn't it?
By the way, I mentioned both positivists and Popper. It may be useful to mention that the similarity between their principles is misleading. Both Popper and positivists say something like "if [something] can't be operationally measured, it's physically meaningless". But Popper was never a member of the Vienna Circle – he was named the "official opposition" – and it's important what is "[something]" in the previous sentence. Popper says (or at least his followers say) that a [theory] that doesn't connect to bread and butter is unscientific. But in some sense, positivists are saying the opposite thing because their "[something]" is often the "things that the critics of a theory demand to be observed". Positivists say that it is perfectly OK for a theory to say that many (a priori all) such things are unobservable! The winner of this disagreement is the theory, positivists say, and not those who demand some feature to be observable! The difference may be subtle but from some viewpoint, Popper tried to reverse all the rules of the game and these seemingly subtle changes are the reason why Popper was so much further away from the actual research scientists.
Reality of atoms vs wave functions
Now, Siegfried asks: Are wave functions as real as atoms? Well, that's a good or bad question, depending on what you mean by "something is real" and other things. There is a sense in which the answer to the question is obvious: The degree of reality of both atoms and wave functions is the same because atoms are nothing else than particular wave functions of the elementary particles. If wave functions are "not real", then of course we may say that "atoms are not real, either" because they're almost the same things!
People got used to saying that "atoms are real". But if we are careful about the meaning of this sentence in physics, it is only correct in the Machian sense. It means that the derivations working with the concept of an atom yield predictions for our perceptions that actually agree with the perceptions we have. There is no scientific justification for a much stronger interpretation of the sentence "atoms are real". If by "real", you mean an objective reality as imagined by classical physics, of course that atoms are not real. They may only be described by (complex) wave functions with a probabilistic interpretation.
Ontic vs epistemic
An armchair physicist and anti-quantum zealot Matthew Leifer is mentioned at the beginning of a would-be important discussion whether the wave function is "ontic" or "epistemic". The words are derived from Greek roots – because the philosophers incorrectly assume that they may hide their stupidity in front of everyone by using words that sound Greek to others – but they may be translated in a simple way. The wave function is "ontic" if it "objectively exists" (the root means "to be") while the wave function is "epistemic" if it describes what we "know" (the root "episteme" means "knowledge" or "understanding").
OK, so the would-be deep question is whether the wave function tells us something about "what exists" or "what we know". At this level, you see that it's a classic example of a meaningless philosophical question using ill-defined words. The right answer is to ignore the details of the question, to point out that it is sloppily formulated, and to explain that the correct theory – quantum mechanics – predicts the probability of perceptions from some knowledge about the initial state – obtained from other perceptions – using mathematical procedures that may be written in terms of mathematics. Is it "ontic" or "epistemic"? You may pick. But to demand anything else beyond the explanation how quantum mechanics works to predict observations is scientifically meaningless according to the positivist principles.
Well, if I had to pick, I would pick "epistemic". The wave function describes the state of knowledge. It's important that there is fundamentally no "objective reality" in quantum mechanics because quantum mechanics isn't equivalent to any classical theory. The previous sentence isn't any "interpretation" or controversial assumption. It is a basic fact about the status of quantum mechanics. Nothing about quantum mechanics makes sense if you are uncertain about the fact that it is a different kind of a theory than any classical theory.
So we may have picked "epistemic" because "ontic" was totally wrong. "Ontic" claimed that the wave function describes just another classical (probably deterministic) theory – that the wave function is a kind of a classical wave – which is surely not the case. Fine. The problem is that this way of choosing "epistemic" is negative. We refuse the first one so we may be forced to pick the second one. But the second option, "epistemic", is also wrong if you study what these philosophers actually imagine under "epistemic" in detail.
If you try hard to learn how they imagine "ontic" and "epistemic" wave function and translate these vague feelings of these would-be thinkers into some more accurate language of physics, you will easily find out that
by "ontic", they mean that the world is described by classical physics with some phase space coordinates and momenta \(x_i(t)\) and \(p_i(t)\), perhaps infinitely many, so something "objectively exists" and may be assumed to be exactly determinedI have read a dozen of papers by "this kind of writers" and everything I have seen is consistent with the claim that they assume that the world either works as a mechanical clockwork that is conceptually a classical theory with determined coordinates and momenta (that's the "ontic" option); or as a description of classical statistical physics with an evolving probability distribution (that's the "epistemic" option).
by "epistemic", they mean that the wave function is in some way related to the probabilistic distributions \(\rho(x_i(t),p_i(t))\) in classical statistical physics.
However, Nature around us doesn't work in either way. Just like the electron in Nature is neither a classical particle nor a classical wave, the wave function is neither "ontic" nor "epistemic". The world is simply described neither by classical physics evolving a point in the phase space; nor by classical statistical physics.
Let me mention that these two options would describe the same class of possible Universes, anyway. The description in terms of a single well-defined trajectory or history \(x_i(t)\) is a special example of classical statistical physics whose probabilistic distribution \(\rho\) is a \(\delta\)-function. On the other hand, the statistical description involving \(\rho(x_i)\) is relevant in a world with \(x_i(t)\) when we simply don't have the full information about the system, and we mostly don't have it.
So this whole "choice" is spurious. You didn't get any choice about the "type of the Universe" at all. You were only offered two formalisms to describe the same kind of a Universe, a classical Universe. It's similar to being offered two political parties with different names and colors. But both parties promote the climate hysteria, bailouts, advantages for a specific "class", and similar toxic junk. Clearly, you are not getting much freedom to choose. The right option isn't there among the two at all. Similarly, the correct character of quantum mechanics is neither "ontic" nor "epistemic" in the sense understood by the "philosophers". Quantum mechanics is a conceptually new type of a theory that has never been seen in the classical world.
The wave function is "epistemic" in the sense that it forces us to talk about our knowledge and not about an objective reality – and to formulate our predictions in terms of probabilities. But it is "ontic" in the sense that unlike a smeared \(\rho(x_i,p_i)\) in classical statistical physics, it contains the maximum knowledge that anyone can ever have! The description in terms of a \(\ket\psi\) is "complete". That's simply how it works. There are no hidden variables. If you know as much as you can know about a physical system, then you describe it by a pure state. The mixed state means that you add some extra ignorance that could in principle be eliminated. But the pure state still means that most questions about the properties of your system remain "uncertain" – the answers are inevitably probabilistic. This is not some bug that may be removed. The very claim that this uncertainty can't be removed (e.g. by better or more extensive measurements of the initial state) is the content of the uncertainty principle!
So the wave function represents the maximum knowledge about the physical system but the maximum knowledge still forces us to admit that most questions have uncertain answers and we still need to talk about probabilities!
That's how it works and all of these basic things have been perfectly understood for 90 years. One can't say whether the wave function is "ontic" or "epistemic" because none of the options we are being offered is really right. Everyone who tries to say that something remains open about these basic matters – beyond the clear answers I have presented above so that intelligent schoolkids must be capable of understanding the point – misunderstands modern physics at a fundamental level and should shut up (and perhaps also calculate, a skill that these people are unlikely to possess).
Not surprisingly, Tom Siegfried also relies on some popular and really atrocious sociological argument, literally "consensus science":
Bohr’s attitude was incorporated into the view of quantum physics known as the Copenhagen interpretation, once the predominant approach but now widely challenged.The reason why quantum mechanics (and yes, "Copenhagen interpretation" is being used just as an insulting synonym for quantum mechanics: there exists no "other" quantum mechanics than one described by the Copenhagen school) is being "widely challenged" these days is that the postmodern system has failed to eliminate incompetent pseudointellectuals and populist demagogues from the wider physical environment – science journals and even universities (especially their philosophy departments but not only philosophy departments). This fact changes nothing whatsoever about the point that physics has perfectly understood the status of the wave function for 90 years (without a few months: I guess that I will celebrate the 90th anniversary of the Heisenberg et al. results this year).
Of course that if someone will pay attention to what rather generic stupid – albeit sufficiently loud – people say about modern science, modern science will look like completely incoherent chaos to him. And even if there will be apparent consensus about something, the answers included in the consensus will probably be wrong.
Wojciech Zurek, the guy who coined the word "decoherence" and much of the modern description of this effect (that he sold under different brands but it's always the same thing) is the only living guy in Siegfried's article who is saying things that are mostly right. Everything else is a gallery of nuts. Sorry, in this case, I must include Mark Strednicki straight to this category, too.
Normally, I would be explaining how crazy the Pusey-Barrett-Rudolph paper (mentioned by Siegfried) was. It's a typical paper that is incapable of understanding that quantum mechanics is neither "ontic" nor "epistemic" in the sense above, another paper among (now) thousands of worthless texts by mediocre thinkers that are trying to force Nature to recant and accept classical physics once again.
And I won't dare to swim in the cesspool which would be needed for a really comprehensive reaction to the preposterous concept of the Boltzmann Brain – the idea that the Boltzmann Brains may be real. The mental midgets who promote this junk are not only failing to realize the important lessons of positivism – that questions that can't be reduced to operational tests are meaningless – but they are also hysterically demanding totally unjustified assumptions such as that "everyone is equally likely to be anyone", including "anyone" which are random pieces of matter at any time of the history of any Universe. This is clearly completely wrong – probabilities are almost never uniform – and the assumption is, in fact, mathematically inconsistent. I won't swim in this cesspool created by "scientists" such as Sean Carroll because I would have to wash myself for a week.
Much of this blog post was saying nice things about positivists and Mach. So let me end on the same semi-optimistic note. Siegfried's last paragraph says
“As the intellect … grows in discipline,” Mach predicted, “physical science will give up its mosaic play with stones and will seek out the boundaries and forms of the bed in which the living stream of phenomena flows.”Times were promising 100 years ago. The intellect was growing and people were abandoning naive classical "stones". Quite symmetrically, we may say:
“As the intellect … decreases in discipline,” Motl observed, “physical science is returning to its mosaic play with stones and will cease to understand the boundaries and forms of the bed in which the living stream of phenomena flows.”As you can see, because people still live 99 years after Mach's death, his prophesy that could be used in both ways wasn't too optimistic, after all. With Siegfrieds and Carrolls behind the steering wheel, the mankind is happily flowing towards complete idiocracy.
And that's the memo.