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Parts of wave function trapped in helium bubbles

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

Study of Exotic Ions in Superfluid Helium and the Possible Fission of the Electron Wave Function
by Prof Humprey Maris, a senior experimenter, and collaborators.

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 asks
How Could Quantum Physics Get Stranger? Shattered Wave Functions
On the contrary. The very reason why wave functions were introduced to physics was their ability to get "shattered" and it would be very strange if some wave functions couldn't do such a thing! I got allergic to this kind of unlimited stupidity but sometimes, e.g. now, the stupidity is so original and self-mocking that I simply have to laugh out loud again. The first paragraph says:
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:
Could Quantum Mechanics Change Forever After Shocking Electron Study?
It has the same chance to "change forever" as it had a few days ago or two weeks ago or three weeks ago – or at any time in the previous 90 years when similar claims were made.

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.

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reader QsaTheory said...

This story is very old, I remember reading about it many years ago. The explanation was more toward a condensed matter type, I don't remember this new spin.

reader Luboš Motl said...

Like almost all stories on basic enough low-energy physics, the story is old, but I assure you that the paper on the bubbles and the media echoes accompanying it are quite new.

reader lukelea said...

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.

Regarding the double-slit experiment, I recall some wag in the back of the room pretending to be Feynman (or maybe it was Feynman) asking the instructor what happens when you put three holes in the wall? How about four? How about ten? Twenty? And so on.

reader lukelea said...

The researchers: '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

So who said the truth -- quantum mechanics -- is plausible? Doesn't plausible mean easily believable? The whole point about QM, I thought is that for all those who grew up and live in the classical world -- ie, everybody -- the quantum world is absolutely implausible (or "really crazy" in the words of Neils Bohr). Nobody "understands it" as Feynman said -- and a lot of people have gone crazy trying to.

reader Luboš Motl said...

Dear Luke, three or four or more slits will still produce interfering terms in the wave function and an interference pattern - a more complicated one - that may be easily calculated.

In fact, the first experimentally measured version of this interference was equivalent to the case of "infinitely many slits" - the electron diffraction on gratings (it was Davisson and Germer in 1927, long before the actual experiments with just two slits were made):

reader Uncle Al said...

A good experimentalist gives theorists employment. A good theorist gives theorists employment. Empirical falsification of theory is so Galileo.

reader Juline An said...

before I saw the paycheck which said $4260 , I didn't believe that my mother in law was like they say truly making money in there spare time on their apple laptop. . there friends cousin haz done this for less than twenty three months and by now cleard the morgage on there condo and purchased a gorgeous Honda http://GOOGLE/

reader Gene Day said...

You could also point out the discovery of Bragg diffraction by the father and son team, William Henry Bragg and William Lawrence Bragg in 1912.

reader Luboš Motl said...

Except that this applies to electromagnetic waves - X-rays - which might have been described using classical fields, without any concept of a "wave function".

Of course that at the end, the wave is composed of photons and a photon may have its wave function in the same way as an electron - but the electrons are fermions so one can't squeeze them into the same state to promote "their" wave function to a classical wave.

reader Swine flu said...

"... most top particle physicists would be able to give
the right ... explanation of such observations but the
condensed matter physicists have grown genuinely inadequate for these
Top condensed matter physicists would also be able to give the right explanation, but does 84 year-old Cooper still qualify as a top condensed matter physicist, at least when it comes to quantum condensed matter?

When Cooper was a postdoc, Bardeen invited him to work on superconductivity because he wanted someone with a field theoretical background on the team. This was clearly successful. However, it appears that Cooper drifted into rather different areas by the early 1970's. I don't know anything about his work in neural networks, learning, etc.,
which appears to have been his focus for many decades now. He may have
done great things in those fields, for all I know, but it really isn't obvious that he has done much work on quantum problems in decades.

reader Luboš Motl said...

Good point, Swine flu. You may be right. The lead author

has lots of successful articles. With one exception from 2012, all 100+ citation papers are written in 2002 or earlier which is a hiatus that may have changed his status, too.

But maybe I didn't mean just "top". What if I wrote "those HEP physicists who have the same number of papers and citations in the last 20 years as these people"?

reader Swine flu said...

I am sure many formulations are possible here :).

I actually wrote my post above because I was a bit surprised by your comment - I have somehow had the prejudice that condensed matter physicists are forced to think deeper about quantum mechanics because they perform, and must interpret, many different kinds of experiments besides scattering. Perhaps this is not as relevant as I imagine.

P.S. For those who find history entertaining, here is an interview with Cooper:

reader Luboš Motl said...

I share your expectations. They should have tons of knowledge and applicable common sense in these quantum issues. But this paper with its mystical language and 3 completely, conceptually different ideas about what's going on indicates otherwise.

reader lukelea said...

Right, that was what I was getting at. Or what the anecdote was getting at rather.

reader Gene Day said...

I don’t think that condensed matter physicists think deeper about quantum mechanics but they do spend virtually all of their time completely immersed in a world where classical mechanics is less than useless. With the passage of a few decades the quantum world becomes the real one and the classical world the artificial one.
This is my own, personal experience as a solid-state physicist and I find comfort in knowing that my new world is the real one.

reader Swine flu said...

A lot of traditional solid state physics is based on a single-particle approximation. These "single particles" certainly are quantum, but in most problems one doesn't need to worry about them splitting into several spatially distinct parts.

Perhaps quantum optics guys get to think about quantum mechanics in a deeper way more regularly, but I don't really know enough about that field to be certain.

reader Tony said...

So, if I get this right, renowned physicists are making a huge issue out of discovering that some quantum operator has different eigenstates, which in this case correspond to shape/size of the bubbles? Hard to believe, but then I am only recently starting to follow physics more closely, so I sure lack a full context.

reader Luboš Motl said...

Dear Tony, yes and no. They didn't really discover the existence of such a spectrum - it was known before. Well, 14 states of the bubble. They discovered 4 more plus some unclassifiable ones, and they gave a wrong interpretation to this.

I think that the discovery of the diversity of the bubbles was a pretty big discovery. One may say that it's not new because it's just some discovery of an observable that has a spectrum - but *every* discovery of fundamental or microscopic enough things in physics has this form! ;-)

reader Luboš Motl said...

Dear Gene, the comparison of condensed matter physicists and e.g. particle physicists - who is more quantum - is interesting and hard.

Particle physicists more safely realize that quantum mechanics underlies every nontrivial calculation they ever make. So they don't have a doubt that it's quantum mechanics that is the root of all the laws of Nature and regularities they study.

On the other hand, particle physicists work with rather narrow "geometric setups". While the dynamics is given by quantum mechanics and path integrals, what they typically describe are point-like particles that move like point masses in classical mechanics, or properties of these objects that are measured "globally".

Condensed matter is much more connected with the continuum of matter, with the idea that the quantum processes are happening everywhere and continuously. Like in chemistry, this connects quantum mechanics with the usual everyday life experience more than what the particle physicists encounter. On the other hand, the same connection also has the undesirable effect in the opposite direction - that condensed matter physicists and chemists often end up thinking classically about certain things because they study objects similar to those that would be described by classical language (and classical ape sounds) for millions of years. So chemists are imagining that the wave functions in the atoms are "real clouds" that repel and so on, and it seems that the condensed matter sentiment sometimes isn't that different.

reader NikFromNYC said...

But for chemists the time scale of practical reactions is such that molecular orbital wave functions are fully populated by dynamic electron motion so indeed they are real objects. They show up perfectly well in scanning probe “micrograms.”

Molecular orbitals also break electron wave findings into “bubbles,” I note:

reader Luboš Motl said...

I don't think that a longer-than-atomic time scale is enough for the quantum character of the wave function of orbitals to become irrelevant.

It's still important that these orbitals may form linear superpositions, like in the benzene aromatic ring, and tunnel through classically forbidden regions etc. And of course, the spin j_x,j_y,j_z of an electron is always intrinsically and importantly quantum mechanical, at arbitrarily long scales.

So you can visualize them as if they were "a real object with a shape" but this interpretation is always wrong, even at longer time scales!

reader Lino said...


The authors are quoted as saying something like this:

"That an electron (or other particle) can be in many places at the same time is strange enough, but the notion that those possibilities can be captured and shuttled away adds a whole new twist."

Isn't that what's so stunning about this experiment? IOW, we use the wavefunction to give us probabilities of where to find things like electrons, and yet this "chance" of something being somewhere is itself "somewhere."

If you compare it a double (or treble, or cuartic, etc) slit experiment, we might say that the wavefunction passes through the slits, and then recombines. But it is a little bit odd that these "probabilities" associated with the wavefunction can be sort of 'floating around' in the helium. And how do they recombine? Or do they?

Lastly, "probabilites" cannot exert "pressure;" and it's some sort of pressure that is forming those bubbles. Personally, I think it is heat radiation due to the difference in temperature of the electrons and the helium (but they don't raise this issue in their paper, nor do they give any data. I'm just guessing there's a difference in temperature.)

reader Luboš Motl said...

It's complete nonsense. No similar experiment with helium bubbles or anything else changes the basic facts about quantum mechanics and the wave function - or any interpretational or conceptual feature of the wave function - that have been known since the mid 1920s.

reader Tony said...

Right. I am also trying to understand what is it exactly that these authors want us to wonder about? What kind of mental image are we supposed to form? The way I'm understanding Lubos, in extremely oversimplified way, is that this is not any more strange than electron tunneling: that little probability ended up as the real electron on the other side of the barrier, doing some real things.

reader Tony said...

If something is very probable, it is almost real :) I, for one, am thankful that good questions and great answers, that you can read in this blog, help me deepen (and sometimes reaffirm) my understanding of QM. That classical world is such a pesky fellow: wants to creep into everything.

reader Bill Marsh said...

"I think I can safely say that nobody understands quantum mechanics." Richard Feynman

reader Tony said...

After pondering more and reading their article again, in the analogy with electron tunneling, it goes like this, in my understanding:
You have a probability that electron will reflect from the barrier and a probability that it will pass through it. In analogy they say: we detect the electron reflected from the barrier (a bubble containing the electron), yet we also see a physical effect on the other side of the barrier (a bubble without electron), at the same time. Thus the probability wave behaves like a classical wave field.

reader Luboš Motl said...

Why would one think that he is "seeing a bubble without an electron"? By definition of all the terms etc., a bubble without an electron instantly collapses to zero size.

They are surely not seeing a bubble without a charge that is needed to keep it. If they are seeing some new quasiparticle, which may arise from splitting the original electron to two, they should give it a new name.

The wave function for a single (or few) particles can never behave as a classical field.

reader Tony said...


"And the fact that the wave function can be split into two or more bubbles is strange as well. If a detector finds the electron in one bubble, what happens to the other bubble?"

"Perhaps the small electron bubbles are formed by the portion of the wave function that goes through the surface. The size of the bubble depends on how much wave function goes through, which would explain the continuous distribution of small electron bubble sizes detected in the experiments"

... any bubble found not to contain the electron would, in theory, simply disappear. And that (that it doesn't), Maris says, points to one of the deepest mysteries of quantum theory"

That's them saying, not me.

reader Tony said...

From your post I couldn't understand that they are going that far. But yes, they are very clearly claiming a wave function to be an observable. It doesn't make any sense to me either. Why would a wave function 'decide' to become and observable in this singular case but not in any other phenomena that we are observing for decades?

reader Luboš Motl said...

I know they're saying it, Tony, that's why I wrote this blog post explaining that it's nonsense.

If there's no supporting charge, there can be no bubble. If a bubble gets split into two, it's because there had to be two "seeds", two electrons or other charges.

reader Luboš Motl said...

Exactly, Tony. It would be quite a miracle if a rather mundane low-energy experiment almost identical to many previous ones that were working just fine in QM suddenly discovered that the wave function is something completely different than what the rest of the experiments has always been showing.

reader Lino said...

The wavefunction, however, does give you probabilities via its amplitude. And QM talks about how the wavefunction spreads, and how it collapses.

I spent years trying to figure out what "collapse" meant, only to audit a course in QM, hoping at last to understand this "collapse," and then come to find out that this 'collapse' is axiomatic. You can imagine how disappointed I was.

Indeed, I take a "realist" position towards QM, in the line of Einstein, Schrodinger, de Broglie and Bohm.

Yet, in the meantime, QM, used with its Copenhagen interpretation, works just fine. Amazingly fine.

So anyone who wants to counter the Copenhagen interpretation, better have a pretty good argument.

Nevertheless, I'm struck with the "real" aspect of these "probabilities" floating around in liquid Helium. Yes, the wavefunction is broken up into portions of its energy, and if you sum over the space of the Helium you recover the wavefunction of the electron, but it is strange to have what amounts to portions of the total probability of the electron's wavefunction floating around.

It's almost as if you have an electron surrounded by a photon that never gets emitted. Strange.

reader Luboš Motl said...

Dear Lino, please try to think about it rationally.

You may proudly boast to "take" the realist approach but it's up to Nature to decide whether your "take" is correct - and make no doubt about it, Her answer is a loud No.

The wave function doesn't have a "reality" in the helium, hydrogen, lithium, metals, gases, or anywhere else.

By its basic defining properties and its raison-d-etre, the wave function is always allowed to split to pieces, reinterfere, or avoid later reinterference. There is nothing strange about it. It's exactly why the wave function has ever been introduced.

reader Tony said...

Let me take, just to play a devil advocate, another realist stance. What they are really implying is that a single electron splits into many pieces and each bubble should then realistically contain a fractional charge. Not just 1/3 but a continuum of 0.113, 0.456, etc. of charges. That would be a revolution and the most important scientific discovery of this century. But they don't measure fractional charges in those "exotic ions" (which they think are chunks of one electron) so they come up with the statement that measurement is something that nobody understands anyway.