In some cases, the dissatisfaction depends on a technical result and there are many of them to be learned. However, I would say that way too often, people are dissatisfied because of reasons that are utterly non-technical and that are universal.
One source of such dissatisfaction has been discussed often: certain results or principles in science are counter-intuitive and many people simply want to prefer their intuition over whatever evidence you may get. They're not ready to give up intuition and accepts the scientific method. Quantum mechanics is the most frequent victim – but not the only victim.
After all, the reason usually is that these people believe that science is just a slave that "fills the details" and isn't allowed to touch some important questions that are decided by "someone more powerful than science" which means either intuition or religion or ideology or philosophy or another package of scientifically unsubstantiated dogmas and prejudices.
But the laymen often get dissatisfied because of slightly different reasons, too. One of them is closely related to the "intuition" that I have already mentioned. People often want some "intuitive understanding" of concepts, equations, laws, and theorems in physics. Sometimes they call it their "physical meaning" but it's really the same thing because if you ask them why some accurate description of a concept isn't a "physical meaning", they end up saying that it isn't intuitive for them.
Sebastian asks a question suggesting that he understands the claim of the virial theorem and its proof (well, one of several proofs that differ by the strategy and the choice of ensemble); he seems to be using this theorem in some programming related to molecular physics. But he's not satisfied:
Right now this is just some math to me (which I totally get) to calculate the temperature of a system of particles in thermal equilibrium. Is there more to it? Am I not getting it? What is the intuition behind this?What to do with this dissatisfaction? How is one supposed to "answer" it? I had a friendly chat with the chap but I am just not getting where the feeling comes from. I am not understanding whether he understands what I was telling him. It just remains a mystery because the dissatisfaction is ultimately powered by some totally irrational drivers.
I told him that "just some math" is a loaded expression because it refers to mathematics in a disrespectful way. Mathematical results and their mathematical proofs are the most solid – and the only truly solid – results and proofs we really have in science. The virial theorem is undoubtedly such a mathematical result. But it's not "just maths" because the objects in the theorem have a physical interpretation.
A new cute Andrew Borisiuk's time-lapse video of my hometown of Pilsen (where a roof of a movie theater in the Plaza Mall collapsed today). YouTube. Vimeo.
Now, the importance of the virial theorem in statistical physics is also self-evident. Statistical physics is about the computation of average values of various quantities in the statistical ensembles – that's really the explanation what the adjective "statistical" means. It means that statistical physics is all about such computations and if some average value may be explicitly determined, of course that this portion of physics or mathematical physics and its practitioners have to be interested in such a conclusion.
The particular quantity appearing in the virial theorem is special because its average value may be simplified to the simple result proportional to the temperature; and because this quantity is often equal to kinetic or potential energy or other natural or simple functions of positions or momenta (e.g. their powers, in a popular example of the theorem). So of course that we're interested in their average values if we're interested in average values at all – if we're interested in statistical physics at all! Moreover, even for quantities that aren't exactly addressed by the virial theorem, they may often be "similar" to those that are addressed by the virial theorem.
We have spent some time with the proof, too. It's rather simple and it may be even simplified or replaced by approximate arguments – this goes up, this goes down – that explain that it passes all the expectations and/or reduces to some "simple common sense" results in special cases. Nice but the dissatisfaction didn't go away.
One may also review the history – how the claim was first known for the harmonic oscillator, kinetic and potential energy, and then it was generalized because with some data about particular examples, it's not hard to guess what the generalization looks like and it's not hard to construct the proof even if you're the first one. Sebastian told me he wasn't really interested in the history i.e. how people got it in the actual history of science.
So what is he interested in and asking about? What is he dissatisfied with? I am absolutely not getting it. And I find it sad that people are dissatisfied in this way because physics and its results – including things like the virial theorem, if we stay in the modest waters of classical physics etc. – are very exciting. Sebastian clearly doesn't see this exciting nature of physics at all. 99.99% of the people don't see it, either. I don't know why. I don't know what's stopping them. But I am annoyed by that and I still refuse to believe that whatever the obstacle is, it cannot be destroyed, nuked, neutralized, liquidated in some way. I surely want to liquidate it because while I like physics, I am annoyed by the sour faces and frustrated whining that any mentioning of physics (especially advanced physics) immediately ignites in a more normal human society (and sometimes even elsewhere)!
Needless to say, the exchange may have stayed friendly, especially in the chat, but it just didn't lead anywhere and couldn't lead anywhere. The obstacle preventing people from understanding the actual key results that form the skeleton of our physics knowledge is a formidable enemy. I don't know how to nuke it and destroy it. I don't even know how to locate it. ;-) Anyone can help me?
Another example is a minor curiosity but the lesson of the following story is also much more general. Terry asked whether the Higgs mechanism addresses the "spin-statistics problem". Cute. Now, there is no spin-statistics problem. There is a spin-statistics relationship or spin-statistics theorem and it's a good thing, an insight (and theorem) about Nature, not a problem, so it shouldn't be "addressed" but learned, exploited, and celebrated. I feel that the wrong idea that some important result in physics is actually a "problem that should be wrestled with" is also a rather general misunderstanding that appears quite often. It must come from somewhere. It must come from some negative emotions that are being conveyed together with the technical material and that make people feel that there is a problem even if the instructor or textbook etc. never says such a thing.
Maybe Terry saw or heard that there was a problem with theories that combine half-integer spins with the Bose-Einstein statistics or vice versa. Indeed, it's a problem for these theories – they're dead – but for us, the death isn't a problem. It's a precious piece of knowledge. Maybe Terry and others think that the ban is a problem because everything should be allowed in physics. Anything goes. Well, that's not how Nature works and thank God for this fact. Every new insight we make proves that "anything goes" is even more wrong than previously thought. There are laws, there are patterns, only some statements are right while others are not.
Or take this bizarre question about the measurement of the cosmological constant. QSA suggests that when people say that they measure the constant, they are actually calculating it, so they're sloppy about semantics and terminology. Holy cow. Why would they say "measure" if they meant "calculate"? They're completely different verbs, aren't they? Now, a measurement of the cosmological constant sometimes needs to do some calculation aside from the "manual work with the measurement apparatus" but that's true for any other measurement of anything, too. The difference between a measurement and a calculation is that we still need some observational apparatus so the determination of the cosmological constant is really not a (mere) calculation.
(No one knows how to uniquely calculate the observed value of the cosmological constant, due to the largeness of the "landscape" and the absence of a known selection mechanism etc. When people learn how to perform this calculation, it will probably mean that the theory of everything has been fully understood. On the contrary, the measurement of the cosmological constant is a standard procedure in cosmology these days; the 2011 Nobel prize in physics was awarded for these achievements.)
This guy sees people who are saying "measure" but he hears "calculate". He convinces himself that they must be saying something else than they are saying. Why? What leads him to incorporate these random distortions and misprints into sentences he hears? What leads him to believe that the mistake is created by those who use the verb (and say that they're sloppy about semantics) – and not by himself, a person who manifestly fabricates what he's actually hearing?
A user named rsg asked about the applications of entangled states. The general theme is much more general here, too. He's asking what the concept is good for. He is apparently assuming that physical concepts are always "objects" that are about as large as a car, that have an application, and that must be justified by an application for them to be allowed to exist at all.
But this is a complete misunderstanding what science tries to do. Science is meant to understand how Nature works. It is not a collection of gadgets we collect to improve our lives. Moreover, different concepts in science may refer to situations and objects that vastly differ in their frequency or omnipresence. In particular, entangled states aren't a device that you use twice a day, like your car. Almost all states in the Hilbert space – all states describing Nature – are entangled (and non-maximally entangled). Sometimes we don't even talk about the situations in this way. We don't say they're entangled states. Most people don't realize that they're observing objects in entangled states. But there are still entangled states everywhere.
So it's really a very bad question to ask for an application of a concept such as an entangled state. It's analogous to asking what prime integers are good for. I don't know. They're numbers that can't be factorized which may be relevant, useful, or harmful in various situations. Of course that one can't pick any single representative example – one that would be as visualizable as the car ride from A to B. But this non-specificity doesn't mean that prime integers or entangled states aren't essential in maths or physics. When we want to understand or predict the behavior of physical systems, we need to think in terms of propositions that do talk about entangled states (and other things). Entangled states manifest themselves by a certain behavior that's pretty clear from their very definition: they lead to correlations in the measurements of various quantities. So they matter. It's nonsensical to ask about a particular application that would be as specific as a car ride. Such a question is really missing the reason why concepts exist in physics. They're not designed for one particular goal such as a car ride. They're invented to organize our knowledge in lots of ways. Also, unlike cars or animals, they don't have a contrived inner structure. On the contrary, they try to be as sharp and simple, to help us to quickly get to the heart of the problems (I don't mean bad problems, I mean any questions we want to understand!).
Needless to say, this discussion has pretty much nothing to do with entangled states. It's much more general. Entangled states were picked as a scapegoat, a particular concept that the user hasn't yet internalized or understood, for that matter. But the same thing occurs to pretty much all concepts or theories in physics that differ from a "car", something that does a specific service to the people.
I have discussed the value of the virial theorem but let me wrap this blog entry with another dissatisfaction about thermodynamics and statistical physics – one that boils down to a general feature or virtue of these disciplines. Douglas complained that no one ever says which microscopic interactions are responsible for the emission of the black body radiation from a heated solid body.
This is potentially a good question from a beginner but once you see that Douglas vehemently refuses to listen to the answer, you will realize that it's not a good question at all. It's another irrational roadblock, an additional brain defect that should be liquidated but I don't know how to do it.
The answer is, of course, that thermodynamics and to a large extent even its more constructive and more microscopic underlying theory, statistical physics, are pretty much defined by their ability – or desire – to predict certain general features of large macroscopic objects (with a temperature) by methods that don't require to study every microscopic detail of how these conclusions arise; methods that are largely independent of the identity of the elementary building blocks and their fundamental interactions. And the wonderful thing is that it is possible!
In fact, all available interactions – dipole interaction between the atoms and the electromagnetic fields, and all others – are employed in a very chaotic way when the black body radiation is being emitted. For a large enough near-black body, it would be a hopeless task to follow every interaction that takes place and study how they "conspire" to produce the Planck curve. But statistical physics is nevertheless able to predict some macroscopic properties of the final result – e.g. the whole Planck's black body curve – without knowing which interactions are actually transferring the energy from the solid body to the electromagnetic field!
(The reason is that after a time that is short enough if the interactions are sufficiently strong, the electromagnetic field – and any other object – reaches the thermal equilibrium with its surroundings and the statistical properties and distributions of photons in thermal equilibrium are completely calculable and only depend on the temperature. We can exactly predict the Planck curve even though we don't know which microscopic processes created which photons.)
Now, this fact is a wonderful news. We're able to learn something pretty much exactly without doing some messy work. It's a gospel. And this is the type of tricks – alternative arguments that work when and because the number of degrees of freedom in thermodynamic systems is large – that both thermodynamics and statistical physics are doing all the time. These disciplines are not about the analysis of one or several elementary particles, about the reduction of everything to particular microscopic processes, about the focus on a particular fundamental force. Instead, they don't care much what the microscopic architecture is but they may still derive certain statements about the statistical properties of a large number of atoms, thermal properties of macroscopic bodies, and so on.
Statistical physics and thermodynamics are self-evidently important and this sort of tricks – the ability to calculate things without analyzing every microscopic detail – surely belongs to their "defining character". So Douglas' dissatisfaction with these disciplines' not being specific about the microscopic interactions that dominate etc. is a dissatisfaction with the basic character of statistical physics and thermodynamics. He is clearly rejecting the whole point of these disciplines of physics because this "independence of certain results on the microscopic details" is indeed what these disciplines are all about.
One can talk for hours but he just won't get it. In some sense, this dissatisfaction is analogous to the criticisms of string theory by the ultrashitty scumbags who don't like the very fact that string theory deals with phenomena that can't be directly tested in our labs. But again, that's the whole point of the discipline that it focuses on the fundamental processes at the fundamental scale that we've known for more than 100 years (thanks, Max Planck) to be dozens of orders of magnitude away from the conditions we may reproduce in the contemporary lab. So their unhappiness is nothing else than their admission that they just don't give a damn about physics at the fundamental scale: they're primitive uncultural bastards and scum although they use all kinds of makeup to sell their shittiness almost as a virtue.
The criticism of statistical physics and thermodynamics is analogous except that the type of knowledge that "is not welcome" is different: the insights that are independent of some mechanical microscopic calculations shouldn't be allowed, Douglas thinks. But they should be allowed and science gets richer whenever it finds a totally new way to look at things. Some people or many people don't share the sentiment behind the previous sentence because they ultimately don't give a damn about the knowledge of Nature, they ultimately don't give a damn about the truth.
It seems that the roadblocks powering all the kinds of dissatisfaction that were described in this blog entry – and others – can't be detonated because the cause of this dissatisfaction probably isn't the presence of something but the absence of something. Unfortunately, this hole can't be detonated away.
And that's the sad memo.