Saturday, November 19, 2011

Is philosophical babbling on par with rigorous quantitative analyses?

Sean Carroll has realized that by allowing Tom Banks to talk about quantum mechanics, he has given too much space on their Cosmic Variance blog to science, relatively to what the website is primarily dedicated to, namely superficial politically correct left-wing babbling.

So he instantly decided to offer his readers a compensation.

A Gentleman named David Wallace wrote an "essay" arguing that the wave function is a real or physical object. As you know very well, I simply can't hide that I can't stand pompous fools of this type: a chemical compound known as adrenaline would make any attempts to hide it futile. He clearly has no idea about these matters but he presents his confused ranting as an important insight and calls himself a "philosopher".

It's a waste of time for you to read his text but here's a sketch: he says that the wave function may be either a real object or a probabilistic object. Then he awkwardly discusses beam splitters to claim that it can't be a probabilistic one because it is able to interfere (wow). Later, he uses Bell's theorem and the Kochen-Specker theorem to argue it can't be probabilistic (even though the theorems imply exactly the opposite). And finally, he also praises the fresh crackpot paper by Pusey et al. which surely excludes the probabilistic interpretation as well (even though it makes no sense).

At the end, he urges everyone to abandon proper probabilistic quantum mechanics because it is "instrumentalist" – philosophers love these labels that are meant to carry emotions – and "instrumentalism" must be surely bad because it makes you think that the purpose of the theory about dinosaurs is to understand fossils and other traces they left (even though this is obviously the purpose of, the justification of, and the only available benchmark to evaluate a particular theory of dinosaurs), that the purpose of astrophysics is to be able to explain the data from telescopes and photographic plates (yes, that's exactly the goal of astrophysics), and the only purpose of the theory of the Higgs boson is to understand the LHC data (indeed, it is).

Those who avoid demagogy also know that the theories also explain other things, some of which we can't measure today, but if we can't access them today, they don't really influence how the theories will look like after they're guessed and refined by the scientific method. Nevertheless, even according to the instrumentalist paradigm, the same theories also explain any other conceivable observations one could make if he could visit other celestial bodies or, less realistically, the past eons on Earth, as well as many other particle interactions in the Universe when we talk about the Higgs. The fact that quantum mechanics is instrumentalist doesn't bring any limitations of the reach of these theories whatsoever. All the conceivable traces of the objects we may (but don't need to) consider real (dinosaurs, stars, Higgs bosons) are available for analysis and correlated with each other in the right way, even if we rigorously stick to the instrumentalist paradigm.

The only thing that instrumentalism doesn't do is to scream: "The most important thing is that it is real! It is real! Look and worship." Indeed, the purpose of science is not to scream, especially not ill-defined and problematic adjectives such as "real". The purpose of science is to explain the observed data in the past, find regularities and relationships between them, and predict the observable data for the future. Except for the observations, all other concepts are theoretical constructs: Higgs fields, angular momentum, and even stars. Calling something "real" may emotionally please you (it may make you think how you could "touch it", befriend it, or interact with it in another way) but science in no way forces you to imagine such things and the purpose of science is in no way to nurture such emotions (or any other emotions). The purpose of science is, once again, to explain and predict the observed and observable data.

Some of the portions of Wallace's text are literally comical in character. For example, as we mentioned, he discusses what the probabilistic waves in quantum mechanics are. At some point, he decides to call them "amplitudes". And he says: but that changes everything! Now we have no reason to link the amplitudes to probabilities! Well, except that the decision to name a thing differently doesn't change a damn thing; the irrational focus on the words instead of their exact meaning will be discussed below.

Needless to say, Wallace's opposition to instrumentalism is rationally unjustifiable and the fact that the amplitudes are not yet probabilities, but have to be summed and squared (I mean their absolute values), doesn't change the fact that the amplitudes are probabilistic objects, not observables, and they're simply much closer to probabilities than e.g. classical electromagnetic waves. If two numbers differ because one of them is the other number squared, they're much closer than Apple laptops are to oranges or than state vectors are to classical fields.

Fine, Wallace's rant is completely nonsensical, no one really cares about deluded philosophers, and you may be shocked that this junk has earned several paragraphs on TRF. But it continues to be interesting. The main reason is that Tom Banks contributed to the discussion by his comment #16 which is more valuable than Wallace's original text plus 20 other average blog entries on the Cosmic Variance combined.

Tom Banks comments on David Wallace

In a completely polite way, Banks explained that the probabilities extracted from quantum mechanics smell as probabilities, may be calculated from distributions like probabilities, and behave as probabilities, so they are probabilities, whether or not some terminological jugglery by a philosopher, defending some irrational ad hoc dogmas, would like to make such a term "blasphemous".

Let me add that we're often generalizing the previous meaning of a word because we need to do so: we often need to update the whole theoretical framework. Tom Banks also sketches some basic ideas of the consistent histories approach by Gell-Mann and Hartle, my favorite axiomatic structure added upon proper quantum mechanics (but changing nothing whatsoever about the ways how we calculate and interpret objects we knew before).

The consistent histories approach may also calculate probabilities of various histories – sequences of events or measurements at different times – as long as the set of mutually exclusive histories satisfies the mathematical condition known as the consistency (a natural generalization of orthogonality for histories). At any rate, many things in quantum mechanics may be assigned probabilities and these probabilities are clearly the same concept as the old one, but now extracted from a more general and more modern theory.

At this point, using my Sheldon-like empathy skills, I can say that Tom's polite answer gets slightly more irritating for the babblers. He essentially says that "elementary reasoning" (a term that Wallace repeatedly used for his flawed, superficial, verbal arguments) can't replace a proper mathematical analysis. Tom starts to explain the striking difference between physicists and philosophers. (It's hard to imagine that these disciplines belonged to "one species" a few thousand years ago. On the other hand, we could say that we're observing a similar ongoing split within the physics departments, too.)

Science in general and physics in particular is based on roughly three pillars, namely experiments of the most general kind; a mathematical formalism; and an interpretational framework connecting the two previous groups with each other and our intuition. These are my words but they're surely close to what Tom wanted to say. The third pillar of physics, the interpretational part, contains all the "stories" and these stories, amazingly enough, may hugely change – and have repeatedly changed – when we switched to a more accurate theory even though the quantitative predictions of the old and new theories were extremely close to each other. The words are still important but to correctly understand things, we simply can't throw away the detailed quantitative content of the theories which remains essential.

Philosophers, on the other hand, just work with words. These words keep them confined in a scheme that may be wrong, for example the scheme of de facto classical physics. They may label it with many words that make it "sound" unavoidable, like "common sense" or "elementary reasoning", but this reasoning is usually wrong (e.g. in this case) and their focus on the words prevents them from seeing and acknowledging the flaws. Tom also mentions an article by Stanley Fish in the New York Times that quoted Francis Bacon who essentially said – and this is my rephrasing of it – that words may be good slaves and messengers but they unfortunately often become bad masters. BTW Tom doesn't know how to find the article; I needed about 10 seconds. ;-)

At the level of the words and common language that is rooted in the logical scheme of classical physics, things like quantum physics will probably always sound unintuitive. That's why we must focus on the precise mathematical description. Tom almost invisibly offered that he could also write something about the Bohm-deBroglie-Vigier theory and the GRW theory which would double the price of the Cosmic Variance blog :-) but at this moment, he's "blogged out". (GRW is the silly theory with random "collapses" that try to make the world non-fuzzy; Vigier was a life-long radical communist and an assistant to his almost equally radical communist David Bohm; Vigier "promoted" the pilot-wave re-interpretation to a whole new "stochastic" alternative to proper quantum mechanics.) Relatively to his life and research, blogging is a waste of time, he implicitly and rightfully suggests, and finally he asks how to overcome some new $$\LaTeX$$ problem introduced at the arxiv.org because, it seems, no sufficiently computer-literate students from the post-socialist Europe are doing these simple tasks for him (and his wife and her fellow secretary) anymore. ;-)

Sean Carroll backs pseudoscience

I of course agree with Tom Banks' words as much as he would disagree with the impolite tone of my summary of the situation. But be sure that things will get much tougher now. The reason is that in the comment #19, Sean Carroll who often presents himself as a scientist, is pretty unambiguously displaying his opposition to quantum physics and his proximity to Wallace's nonsensical pseudoscientific philosophical babbling. Carroll tells us:
Tom’s complaints about “telling stories” and “elementary reasoning” seem to be very much beside the point.
Oh, really? So what's the role that words and stories may play in science and the interpretation of quantum mechanics (relatively to the quantitative formalism) is "beside the point"? Holy cow. This is the main reason why people like Wallace produce so many invalid texts. They don't actually quantitatively check the physical content hiding behind the words they emit: they only check them as words, at the level of linguistics. That's why their words can't have any direct trustworthy implications for physics.
The point is that David gave us a particular piece of elementary reasoning, meant to illustrate why it is useful to think of the wave function as really existing, rather than just a crutch for calculating probabilities.
The only problem is that Wallace's text is, from a scientific viewpoint, totally irrational and it is not only useless but it is plain incorrect to think about the wave function as an observable. Wallace's "reasoning" is just a game with words, emotions, and arbitrary assumptions about what the words should satisfy and whether they're good or bad. However, Carroll makes his opposition to science even more flagrant in the next sentence:
It’s okay to take issue with that bit of reasoning, but not with the very idea of using reasoning to understand your theory.
Holy cow. So it's even "not okay" i.e. "politically incorrect" for Tom to say that reasoning in terms of words can't be used to decide about the validity of scientific theories or the right interpretation of concepts in these theories. That's really too bad.

Tom used the most polite language to express the obvious point that Wallace doesn't have a clue what he's talking about – he uses words but doesn't understand what is really hiding behind them in physics and whether his sequences of these words are right or not; after all, he obviously believes that he can determine the validity of all such propositions about physics by pure thought. That's why there are fundamental errors in Wallace's reasoning. In science, arguments that are identified to contain errors are thrown to the trash bin. As we were assured once again, philosophers never use trash bins. But Sean Carroll who wants to call himself a scientist not only gives excuses for the philosophers' unscientific attitude: he says that the scientific attitude that dismisses babbling – the canonical "shut up and calculate" attitude – is actually "not okay"!

I can't believe my eyes. What a [adjective] [noun]. [No, I meant a tougher one. Add a few degrees.]

Carroll's next sentence says:
Neither David nor anyone else is making appeals to “common sense” or “pure reason,” so that’s a pretty transparent straw man.
Of course that he is. He has used the very term "elementary reasoning" twice in his essay and the whole essay was nothing else than an example of how the common sense of a mediocre man has no chance to understand modern physics.

True facts about Nature were dismissed in Wallace's stream of consciousness because they didn't look intuitive enough for his common sense. There hasn't been a single rational argument in Wallace's text. So how can someone possibly call it a "straw man"? Quantum mechanics radically changes the intuitive framework underlying science (the third pillar of a scientific theory, as described by Tom) and its validity must be evaluated impartially and scientifically. The outcome of this appraisal is that quantum mechanics is right and the intuition of people such as David Wallace is just wrong.

Immediately after Sean Carroll uses the term "straw man" for an objection that is obviously essential, he pulls out a straw man himself. And it's the same one that was previously used by Wallace: the complex amplitudes are not probabilities themselves, they're just amplitudes. Relatively to the big question "real or not", this is a totally irrelevant detail related to the squaring but squaring can't change an observable object to a probabilistic one so the amplitude can't be an observable object. The following sentence says:
David’s point (or my understanding thereof) is that the wave function serves the same role in explaining where the photon hits the plate as dinosaurs serve in explaining where fossils come from — namely, you can’t do without it.
Oh, I see. So if you can't do without two things, then it follows that "they serve the same role". Holy cow. It's better for us not to observe how Sean Carroll uses kitchen knives and toilet paper. The whole discussion is about whether a concept represents an observable real object or a probabilistic construct. Both real objects and probability distributions are important. But that doesn't mean that they "serve the same role", especially not in an article whose very purpose should be to figure out which of the two roles it serves!
It’s a crucial part of our best explanation, and therefore deserves to be called “real” (or “physical,” if you want to be a bit more precise) by any sensible criterion.
That's a very shocking assertion because the state vector is, by any sensible criterion, not real. First of all, it is not real but complex and it is essential that it is complex. Second of all, the state vector isn't an observable. According to modern physics, all observables are associated with linear Hermitian operators acting on the Hilbert space. The state vector itself isn't an operator so it isn't an observable. Using empirical arguments, the wave function isn't an observable simply because its values can't be measured by a single measurement.

And by the way, its phase can't be measured even by an arbitrary number of measurements. At least some part of the information stored in the state vector, namely the overall phase, is completely unphysical because it can't be measured even in the statistical sense, by repeating the same experiment many times. Physicists actually often say that the overall phase is unphysical, using these very words, and similar assertions are often very important. You could successfully claim that even this modest fact kills any conceivable attempt to consider the wave function "real".

But even the wave function modulo its phase isn't really "real". As long as the adjective "real" makes any sense, so that there can be both "real" and "unreal" objects, it must be possible to observe it, at least in principle. But if a single electron's wave function has a shape of an elephant, we will still see just a point on the photographic plate, not an elephant. The elephant isn't "real" in the usual meaning of the word. (The stupid anti-quantum folks often complain: Why don't we see superpositions of macroscopic cats etc.? Well, that's exactly because the wave function isn't a physical or observable wave but a template for a statistical distribution only. So adding two wave packets concentrated in two regions means "or", not "and".)

If we generalize the term "real" so that it may be anything that is useful for anyone to make calculations, then the wave function – but also all non-gauge-invariant observables – will have to be considered "real". The adjective "real" would become completely vacuous.

On the other hand, the adjective "probabilistic" isn't ambiguous at all. The wave function is always a probabilistic object. If you combine a couple of its values, i.e. some of its amplitudes, and if you square the absolute value of the sum, you get the probability or the probability density. Any object whose simple functions quantify the probabilities surely deserves to be called a "probabilistic object". The whole treatment by David Wallace and Sean Carroll is just dishonest. Whenever they see an irrational reason why the wave function should be called "real", they inflate it and remain silent about all reasons why the argument is wrong (or just a demagogic linguistic trick). And whenever they hear a demonstration that it is a probabilistic object, they stifle the debate and tell you that it is not "okay" to say such things.
You can’t make sense of the outcome of an experiment without believing that something really goes down the different paths of the interferometer.
Well, I surely can. If something has happened along the paths, in the physical or operational sense, it had to leave some traces. In other words, whether something has happened or changed on the two paths of the interferometer is a physical question and the physical answer is a clear No.

It's easy to demonstrate that nothing has happened on the possible paths of the interferometers. If something, an interaction of the photon with something else, happened over there, the interference pattern would be destroyed. So Carroll's conclusion is really upside down. According to quantum mechanics, photons are prepared in the initial state, nothing – except for calculations by physicists who sum over all conceivable histories or something equivalent (and the calculation is happening in the brain, not along the paths) – is happening in between, and the only next thing that happens is the detection of the photon on some place chosen from the calculable statistical distribution.

This is the quantum mechanical answer, I would say the only valid answer according to quantum mechanics. In what sense we "can't" describe the situation correctly? Is there a new law in the U.S. that prohibits people to say things that are found offensive by idiots such as Sean Carroll? The appropriate comment is exactly the opposite one: Sean Carroll shouldn't say things that are clearly incorrect.

It may be tempting to imagine that something particular is happening at particular places before the measurement but quantum mechanics speaks a clear language: we aren't allowed to imagine any particular facts or events in between because this would inevitably lead to wrong results. Instead, we have to sum over all histories and trajectories – whether they go through the two paths or through the Andomeda Galaxy – and only associate the total result of this sum with the probabilities of the outcomes of the measurement at the end.
There’s no important difference here in the purposes or methods of scientists and philosophers — we’re all trying to understand nature by fitting sensible models/theories/stories (whatever you want to call them) to the empirical data.
It's surely not the job for philosophy to look for theories that match the empirical data and David Wallace – and Sean Carroll himself – have given us another proof that they have nothing to do with this enterprise at all. More generally, philosophers themselves admit that their dominant school, "rationalists", really disagree with any focus on the empirical evidence which is promoted by the evil "empiricists". But don't get me wrong: empiricists still fail to be scientists and they largely produce gibberish about Nature.
Again, it’s okay not to care, but the empirical data seem to indicate that people do care, since they can’t stop talking about it (including repeatedly insisting that they don’t care).
But these particular empirical data are not relevant for the scientific discipline of quantum physics: they're only relevant for the scientific discipline of psychopathology. Quantum physics collects its empirical data by measurements of much smaller or much cleaner objects than people's dysfunctional brains.
I completely agree that the more interesting part of Tom’s original post was the claim about the inevitability of QM (whether one agrees with that point or not). But if you start discussing that and end by saying that the wave function isn’t real and appreciating this fact answers all the interpretational puzzles of quantum mechanics, you can’t be surprised that the former discussion generates little response.
Well, I am not surprised, either. It's because human stupidity has no borders, nationality, or gender. At any rate, the appearance of the "blasphemous" comment that the wave function is just a probabilistic, not observable, object didn't eliminate any potentially successful readers of the sketched proof of the inevitability of quantum mechanics because the knowledge of the probabilistic character of the wave function was obviously a necessary pre-requisite of the sketched proof, much like it is an essential pre-requisite for all of modern physics.

Too bad that people like Carroll who clearly have nothing to do with the modern physicist's picture of the world are allowed to claim otherwise.

And that's the memo.

(Update: Just to reinforce the end of the first paragraph about Cosmic Variance's being primarily a left-wing propagandistic blog, the first post-quantum blog entry on CV Sean posted after this blog entry was written attacked the U.S. police and glorified the communist homeless criminal "Occupy UC Davis" rabble. Obama and Bloomberg failed to stop and properly spank members of this distasteful criminal movement when it was born so they deserve to see where such anarchy leads when politicians are irresponsible. The rabble may keep on expanding like a tumor and – now loudly – scream how much it hurts when the law is suddenly and unexpectedly enforced now which it clearly has to be. κῦδος to Linda Katehi, Greek-born electrical engineer who leads UC Davis and who first ordered the occupants to remove the tents from the quad, anyway. However, I still won't cry too much when the Davis commies get the scalp of this climate alarmist: just mixed feelings. She organized a Climate Crusaders' Fest a year ago at UC Davis, including Schwarzenegger etc.)

1 comment:

1. "Except for the observations, all other concepts are theoretical constructs: Higgs fields, angular momentum, and even stars." Sure, that sounds good to me. It sounds rather like Copenhagen. So does that mean, there is little point in asking "what is the photon or electron 'really like' as it goes through a beamsplitter or suitable divider of 'wave function'"? Then you could say, the WF isn't literally real, but that doesn't leave a clear alternative. It *is* true that "something" (even if as construct not "real thing") takes both paths of an interferometer so the patterns can form. So, you can say
1. "The particle really goes through one or other leg, but something like pilot wave - itself unobservable and ad hoc - guides it to simulate it interfering with itself."
Or,
2. "that which traverses both paths really is the particle, and somehow it just pops into one little spot when it hits the right (?) kind of target later on", or
3. "we just can't represent it realistically."
I don't think any of those is what physics traditionally considered "satisfactory", but maybe we have to accept that?

In any case, the probabilities in e.g. the density matrix are "put in by hand" and not derived, nor when they should manifest as such. It's really the old problem over again, not IMHO a solution.