Even Leon Cooper caught as saying completely wrong things about quantum mechanics
In the world of genuine physics, nothing has changed about the quantum foundations of the discipline since the mid 1920s or the late 1920s. In the media world, we are told about a revolution at least once a week. Less than a week ago, the fad would be all about the many interacting worlds. All of it has been forgotten by now. The new fad is about a mysterious electron's wave function shockingly divided and stunningly trapped in helium bubbles.
All of these wonderful echoes in the media echo chamber boil down to the Brown University press release announcing a paper in a journal
Can the wave function of an electron be divided and trapped? (also at Phys.org)by Prof Humprey Maris, a senior experimenter, and collaborators.
Study of Exotic Ions in Superfluid Helium and the Possible Fission of the Electron Wave Function
Now, let me make it clear that I do believe that he is a good experimenter and these are actually good and interesting experiments performed with interesting and probably expensive cryogenics devices. But the shortage of a good theoretical background and a scientifically solid interpretation of their observations is striking and it guarantees that the press release, and especially its echoes in the media, is completely detached from the scientific substance.
What is going on? The first paragraph of the press release says
Electrons are elementary particles — indivisible, unbreakable. But new research suggests the electron's quantum state — the electron wave function — can be separated into many parts. That has some strange implications for the theory of quantum mechanics.Sorry but the insight that the electron wave function can be separated into many parts has been a defining characteristic of any wave function since the 1920s. The most famous example of the quantum behavior of the wave functions, the double slit experiment, divides the wave function of the particle to the part going through the left slit and the part going through the right slit.
So if someone finally realizes – 90 years later – that the wave function may be separated to several parts, it has no implications for quantum mechanics, let alone "strange ones". By definition (or by the superposition principle, a universal postulate of quantum mechanics), the wave function may be divided to two parts in any way you like. The Hilbert space of the allowed wave functions is a linear vector space.
Needless to say, this rudimentary misunderstanding of the complete basics of quantum mechanics is copied in virtually all articles about the "discovery". For example, the title in VICE.com asks
A team of physicists based at Brown University has succeeded in shattering a quantum wave function. That near-mythical representation of indeterminate reality, in which an unmeasured particle is able to occupy many states simultaneously, can be dissected into many parts. This dissection, which is described this week in the Journal of Low Temperature Physics, has the potential to turn how we view the quantum world on its head.Cool. So a basic, most universal concept in modern physics is "near-mythical". And the dissection, which is its most trivial feature, will surely "turn our view on its head". Most other articles in the media are very similar. For example, the title in the Guardian Liberty Voice pleases us with a rhetorical question:
The original press release is better, of course. For example, this paragraph of quotes of the lead author is pretty much fine:
“We are trapping the chance of finding the electron, not pieces of the electron,” Maris said. “It’s a little like a lottery. When lottery tickets are sold, everyone who buys a ticket gets a piece of paper. So all these people are holding a chance and you can consider that the chances are spread all over the place. But there is only one prize — one electron — and where that prize will go is determined later.”He is aware of the fact that the wave function isn't an objective classical wave; it is a quantification of the chances or potential for some objects to be somewhere or to have some properties.
However, the wording still makes the events sound much more mysterious than they are. Why? Because the linguistically contrived proposition
We are trapping the chance of finding the electron...is actually equivalent to and may be totally precisely reformulated as the more mundane and less mysterious proposition
With some probability, we are trapping the electron...These sentences are equivalent. The extra "flavor" that makes the first sentence sound special is that the "chance" is treated as if it were an object. So even though the author apparently realizes that the wave function isn't a "real object" that is being divided to parts, he still formulates the sentences in a contrived way that does suggest that they are material objects that are being divided to pieces.
The following paragraph is worse:
If Maris’s interpretation of his experimental findings is correct, it raises profound questions about the measurement process in quantum mechanics. In the traditional formulation of quantum mechanics, when a particle is measured — meaning it is found to be in one particular location — the wave function is said to collapse.Maris' interpretation is partly correct but it's loaded, misleading, and tendentious, and if it raises some questions, it's still true that it doesn't raise any new questions that weren't raised in the 1920s (and every decade after that). More importantly, all these questions have been answered in the 1920s, too. For example, when the authors ask what happens with the first bubble when the electron is observed in the second bubble, the answer obviously is that the first bubble will be known not to exist. The existence of the whole bubble depends on the electron – they behave as one particle that can't be separated – so there can't be anything left from the bubble if the electron is known not to be there.
If you admit that the division of a wave function to pieces is nothing new, perhaps something new is hiding in the "trapping" part i.e. in the following paragraph of the press release:
“The experiments we have performed indicate that the mere interaction of an electron with some larger physical system, such as a bath of liquid helium, does not constitute a measurement,” Maris said. “The question then is: What does?”However, this is in no way new, either. The macroscopic size of an object doesn't imply "measurement" i.e. the disappearance of the characteristic quantum behavior of the system. As my undergraduate instructor of electromagnetism, physicist of low temperatures and later the dean of my Alma Mater, Prof Sedlák would say:
I love physics of low temperatures because quantum phenomena may manifest themselves at a macroscopic scale.If you cool things down, the rate of decoherence decreases and the rate of some messy effects may strictly drop to zero. That's why we experience things like superfluidity and superconductivity at low temperatures. If you talk about the "macroscopic wave function" of the Cooper pairs in superconductors, it's a bit misleading to call it a "wave function". When many Cooper pairs are found in the same state, their shared wave function actually becomes a classical field and its interpretation is no longer intrinsically probabilistic. Because we measure the numerous Cooper pairs collectively, the number of such pairs with a certain property is macroscopic as well and the relative statistical error margin drops to zero – so this number may be predicted as well as measured. This classical field follows (almost) the same laws as the single Cooper pair's wave function did but its interpretation is different: we deal with an approximately deterministic classical field.
But otherwise it's clear what Mr Sedlák's point was. It's been known for quite some time that the low temperatures are slowing down the "messy" processes such as decoherence. That's why most proposed types of quantum computers depend on very low temperatures. The low temperature slows down decoherence – or discourages any "self-measurement", if you wish, and quantum mechanics is enough to calculate how much. Decoherence only applies to some degrees of freedom if these degrees' of freedom interactions with the environment are sufficiently strong or fast, and if the environment is sufficiently large.
Let's be a little bit more specific and talk about these helium bubbles that the folks played with in this experiment. When a free electron penetrates to liquid helium, it repels the helium atoms in its vicinity and the radius of the round bubble produced in this way is approximately 1.8 nanometers.
Naively (and I will explain what is naive about it later), all such "bubbles with a single electron" should be exactly the same. But over the years, low temperature physicists have detected 14 different kinds of bubbles. Maris et al. claim to have rediscovered all these 14 types plus 4 new major discrete types, i.e. 18 major types of bubbles in total. They have also identified some "minor types" that – they believe – form a continuum.
When those 14 types were known, people would say that they were manifestations of helium ions or other impurities. It's unlikely that there are "that many types" of impurities over there. Leon Cooper, yes, the same one that gave the name to "his" pairs above, a Nobel prize winner who also collaborated, says something else:
The idea that part of the wave function is reflected at a barrier is standard quantum mechanics, Cooper said. “I don’t think anyone would argue with that,” he said. “The non-standard part is that the piece of the wave function that goes through can have a physical effect by influencing the size of the bubble. That is what is radically new here.”The claim that the "part of the wave function" influences the size of the bubble isn't just radically new. It's bullšit because it violates the superposition principle. If you divide a wave function to two "macroscopically separated" parts, each of them follows the same laws – and induces the same radii around bubbles – as the parts would do separately, regardless of the ratio of the wave functions. The ratio only determines the odds that one thing will take place or another.
What's actually happening is that these are simply different "shapes" of bubbles. The "overall content" of these objects is the same but their "state of motion or vibration" is different.
If you imagine that the bubbles are always round, the electron inside the bubble may still be found in various energy eigenstates, the ground state and the excited ones. In reality, you have to solve a more complicated Hamiltonian involving the position of the electron as well as the shape of the bubble. And the spectrum of this more complicated Hamiltonian will have at least those 18 discrete eigenstates and perhaps some continuous part of the spectrum, too. (The continuous spectrum may be described by the word "fission" they used, but with incorrect details, and this "fission" may be analogous to the way how membranes split in M-theory produce a continuous spectrum in the BFSS matrix model.) The relevant operator isn't really the "simple" Hamiltonian but the Hamiltonian in an external field that contains a term proportional to the "mobility" of the ions given by the shape of the bubble which is what is being measured to distinguish those objects.
At any rate, there is an operator of "mobility" (and the Hamiltonian, too) acting on the Hilbert space of "helium plus an electron" and it has a certain spectrum – which is calculable in principle and which is measured. This template of the explanation of a "certain number of possibilities" has always been the same in quantum mechanics, for 90 years. It's remarkable that Cooper and others aren't able to get these basic things right and they are ready to say something as profoundly wrong as the claim that "the relative distribution of the wave function into two pieces determines the size of the bubbles". I think that Cooper and others fail to understand that "mobility" is also an operator (with a spectrum), much like every observable in Nature!
If you look at their candidate explanations from the abstract of the paper
We discuss three possible explanations for the exotic ions, namely impurities, negative helium ions, and fission of the electron wave function. Each of these explanations has difficulties but as far as we can see, of the three, fission is the only plausible explanation of the results which have been obtained.you will notice that the correct answer isn't even considered by them.
It's pretty self-evident that they are thinking classically about this intrinsically quantum system, too. In classical physics, imagine the classical harmonic oscillator as a model for the bubble with an electron, there exists only one stationary configuration, namely the ground state \(x=p=0\). All other configurations are oscillating i.e. nontrivially evolving in time. In quantum mechanics, think about the quantum harmonic oscillator (or an atom or a particle in a well or a vibrating string) as a model of the actual bubble with the electron, \(x=p=0\) is prohibited by the uncertainty principle but it doesn't mean that there are no stationary configurations. On the contrary, there are infinitely many stationary states: all energy eigenstates are stationary configurations. Cooper's implicit assumption that "the state of the electron in the bubble is unique" unmasks his classical thinking because only in classical physics, one has reasons to assume that the stationary states are unique.
I am pretty sure that most top particle physicists would be able to give the right template of the explanation of such observations but the condensed matter physicists have grown genuinely inadequate for these problems and the mess in the literature about these issues seems to affect the real researchers – including the Nobel prize winners – and not just the popular writers.
Just to be sure, all the 18+ types of the bubbles contain the same stuff and the multiplicity arises from different eigenstate of a relevant Hamiltonian-like operator – it's always like that in quantum mechanics. Just like a fundamental string in string theory has different vibration modes that manifest themselves as different elementary particle species, the electron-induced bubble in the liquid helium also has different vibration modes which manifest themselves as objects with different values of mobility. The existence of many possibilities in intrinsically quantum mechanical systems always has the same explanation – a spectrum of the relevant operator.