New Research Suggests The Electron's Quantum State Separated into Parts

Can the wave function of an electron be divided and trapped?

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.

PROVIDENCE, R.I. [Brown University] 28/10/2014

New research by physicists from Brown University puts the profound strangeness of quantum mechanics in a nutshell — or, more accurately, in a helium bubble.

[caption id="attachment_456" align="aligncenter" width="580" class=" "] The electron wave function
A canister of liquid helium inside the blue cylinder allowed researchers to experiment with tiny electron bubbles only 3.6 nanometers in diameter. The work suggests that the wave function of an electron can be split and parts of it trapped in smaller bubbles.[/caption]

Experiments led by Humphrey Maris, professor of physics at Brown, suggest that the quantum state of an electron — the electron’s wave function — can be shattered into pieces and those pieces can be trapped in tiny bubbles of liquid helium. To be clear, the researchers are not saying that the electron can be broken apart. Electrons are elementary particles, indivisible and unbreakable. But what the researchers are saying is in some ways more bizarre.

In quantum mechanics, particles do not have a distinct position in space. Instead, they exist as a wave function, a probability distribution that includes all the possible locations where a particle might be found. Maris and his colleagues are suggesting that parts of that distribution can be separated and cordoned off from each other.

“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.”

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.

“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?”

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?

"It really raises all kinds of interesting questions," Maris said.

The new research is published in the Journal of Low Temperature Physics.

Electron bubbles

Scientists have wondered for years about the strange behavior of electrons in liquid helium cooled to near absolute zero. When an electron enters the liquid, it repels surrounding helium atoms, forming a bubble in the liquid about 3.6 nanometers across. The size of the bubble is determined by the pressure of the electron pushing against the surface tension of the helium. The strangeness, however, arises in experiments dating back to the 1960s looking at how the bubbles move.

In the experiments, a pulse of electrons enters the top of a helium-filled tube, and a detector registers the electric charge delivered when electron bubbles reach the bottom of the tube. Because the bubbles have a well-defined size, they should all experience the same amount of drag as they move, and should therefore arrive at the detector at the same time. But that’s not what happens. Experiments have detected unidentified objects that reach the detector before the normal electron bubbles. Over the years, scientists have cataloged 14 distinct objects of different sizes, all of which seem to move faster than an electron bubble would be expected to move.

“They’ve been a mystery ever since they were first detected,” Maris said. “Nobody has a good explanation.”

Several possibilities have been proposed. The unknown objects could be impurities in the helium—charged particles knocked free from the walls of the container. Another possibility is that the objects could be helium ions — helium atoms that have picked up one or more extra electrons, which produce a negative charge at the detector.

But Maris and his colleagues, including Nobel laureate and Brown physicist Leon Cooper, believe a new set of experiments puts those explanations to rest.

New experiments

The researchers performed a series of electron bubble mobility experiments with much greater sensitivity than previous efforts. They were able to detect all 14 of the objects from previous work, plus four additional objects that appeared frequently over the course of the experiments. But in addition to those 18 objects that showed up frequently, the study revealed countless additional objects that appeared more rarely.

In effect, Maris says, it appears there aren’t just 18 objects, but an effectively infinite number of them, with a “continuous distribution of sizes” up to the size of the normal electron bubble.

“That puts a dagger in the idea that these are impurities or helium ions,” Maris said. “It would be hard to imagine that there would be that many impurities, or that many previously unknown helium ions.”

The only way the researchers can think of to explain the results is through “fission” of the wave function. In certain situations, the researchers surmise, electron wave functions break apart upon entering the liquid, and pieces of the wave function are caught in separate bubbles. Because the bubbles contain less than the full wave function, they’re smaller than normal electron bubbles and therefore move faster.

In their new paper, Maris and his team lay out a mechanism by which fission could happen that is supported by quantum theory and is in good agreement with the experimental results. The mechanism involves a concept in quantum mechanics known as reflection above the barrier.

In the case of electrons and helium, it works like this: When an electron hits the surface of the liquid helium, there’s some chance that it will cross into the liquid, and some chance that it will bounce off and carom away. In quantum mechanics, those possibilities are expressed as part of the wave function crossing the barrier, and part of it being reflected. 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.

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.”

Further, the researchers propose what happens after the wave function enters the liquid. It’s a bit like putting a droplet of oil in a puddle of water. “Sometime your drop of oil forms one bubble,” Maris said, “Sometimes it forms two, sometimes 100.”

There are elements within quantum theory that suggest a tendency for the wave function to break up into specific sizes. By Maris’s calculations, the specific sizes one might expect to see correspond roughly to the 18 frequently occurring electron bubble sizes.

“We think this offers the best explanation for what we see in the experiments,” Maris said. We’ve got this body of data that goes back 40 years. The experiments are not wrong; they’ve been done by multiple people. We have a tradition called Occam’s razor, where we try to come up with the simplest explanation. This, so far as we can tell, is it.”

But it does raise some interesting questions that sit on the border of science and philosophy. For example, it’s necessary to assume that the helium does not make a measurement of the actual position of the electron. If it did, any bubble found not to contain the electron would, in theory, simply disappear. And that, Maris says, points to one of the deepest mysteries of quantum theory.

“No one is sure what actually constitutes a measurement. Perhaps physicists can agree that someone with a Ph.D. wearing a white coat sitting in the lab of a famous university can make measurements. But what about somebody who really isn’t sure what they are doing? Is consciousness required? We don’t really know.”

Authors on the paper in addition to Maris were former Brown postdoctoral researcher Wanchun Wei, graduate student Zhuolin Xie, and George Seidel, professor emeritus of physics.

News Release Source : Can the wave function of an electron be divided and trapped?

Image Credit : Mike Cohea/Brown University

Fluid Mechanics Shows Alternative View of Quantum Mechanics

Fluid mechanics suggests alternative to quantum orthodoxy

The central mystery of quantum mechanics is that small chunks of matter sometimes seem to behave like particles, sometimes like waves. For most of the past century, the prevailing explanation of this conundrum has been what's called the "Copenhagen interpretation" — which holds that, in some sense, a single particle really is a wave, smeared out across the universe, that collapses into a determinate location only when observed.

[caption id="attachment_432" align="aligncenter" width="500"] Fluid Mechanics Shows Alternative View of Quantum Mechanics[/caption]

But some founders of quantum physics — notably Louis de Broglie — championed an alternative interpretation, known as "pilot-wave theory," which posits that quantum particles are borne along on some type of wave. According to pilot-wave theory, the particles have definite trajectories, but because of the pilot wave's influence, they still exhibit wavelike statistics.

John Bush, a professor of applied mathematics at MIT, believes that pilot-wave theory deserves a second look. That's because Yves Couder, Emmanuel Fort, and colleagues at the University of Paris Diderot have recently discovered a macroscopic pilot-wave system whose statistical behavior, in certain circumstances, recalls that of quantum systems.

Couder and Fort's system consists of a bath of fluid vibrating at a rate just below the threshold at which waves would start to form on its surface. A droplet of the same fluid is released above the bath; where it strikes the surface, it causes waves to radiate outward. The droplet then begins moving across the bath, propelled by the very waves it creates.

"This system is undoubtedly quantitatively different from quantum mechanics," Bush says. "It's also qualitatively different: There are some features of quantum mechanics that we can't capture, some features of this system that we know aren't present in quantum mechanics. But are they philosophically distinct?"

Tracking trajectories

Bush believes that the Copenhagen interpretation sidesteps the technical challenge of calculating particles' trajectories by denying that they exist. "The key question is whether a real quantum dynamics, of the general form suggested by de Broglie and the walking drops, might underlie quantum statistics," he says. "While undoubtedly complex, it would replace the philosophical vagaries of quantum mechanics with a concrete dynamical theory."

Last year, Bush and one of his students — Jan Molacek, now at the Max Planck Institute for Dynamics and Self-Organization — did for their system what the quantum pioneers couldn't do for theirs: They derived an equation relating the dynamics of the pilot waves to the particles' trajectories.

In their work, Bush and Molacek had two advantages over the quantum pioneers, Bush says. First, in the fluidic system, both the bouncing droplet and its guiding wave are plainly visible. If the droplet passes through a slit in a barrier — as it does in the re-creation of a canonical quantum experiment — the researchers can accurately determine its location. The only way to perform a measurement on an atomic-scale particle is to strike it with another particle, which changes its velocity.

The second advantage is the relatively recent development of chaos theory. Pioneered by MIT's Edward Lorenz in the 1960s, chaos theory holds that many macroscopic physical systems are so sensitive to initial conditions that, even though they can be described by a deterministic theory, they evolve in unpredictable ways. A weather-system model, for instance, might yield entirely different results if the wind speed at a particular location at a particular time is 10.01 mph or 10.02 mph.

The fluidic pilot-wave system is also chaotic. It's impossible to measure a bouncing droplet's position accurately enough to predict its trajectory very far into the future. But in a recent series of papers, Bush, MIT professor of applied mathematics Ruben Rosales, and graduate students Anand Oza and Dan Harris applied their pilot-wave theory to show how chaotic pilot-wave dynamics leads to the quantumlike statistics observed in their experiments.

What's real?

In a review article appearing in the Annual Review of Fluid Mechanics, Bush explores the connection between Couder's fluidic system and the quantum pilot-wave theories proposed by de Broglie and others.

The Copenhagen interpretation is essentially the assertion that in the quantum realm, there is no description deeper than the statistical one. When a measurement is made on a quantum particle, and the wave form collapses, the determinate state that the particle assumes is totally random. According to the Copenhagen interpretation, the statistics don't just describe the reality; they are the reality.

But despite the ascendancy of the Copenhagen interpretation, the intuition that physical objects, no matter how small, can be in only one location at a time has been difficult for physicists to shake. Albert Einstein, who famously doubted that God plays dice with the universe, worked for a time on what he called a "ghost wave" theory of quantum mechanics, thought to be an elaboration of de Broglie's theory. In his 1976 Nobel Prize lecture, Murray Gell-Mann declared that Niels Bohr, the chief exponent of the Copenhagen interpretation, "brainwashed an entire generation of physicists into believing that the problem had been solved." John Bell, the Irish physicist whose famous theorem is often mistakenly taken to repudiate all "hidden-variable" accounts of quantum mechanics, was, in fact, himself a proponent of pilot-wave theory. "It is a great mystery to me that it was so soundly ignored," he said.

Then there's David Griffiths, a physicist whose "Introduction to Quantum Mechanics" is standard in the field. In that book's afterword, Griffiths says that the Copenhagen interpretation "has stood the test of time and emerged unscathed from every experimental challenge." Nonetheless, he concludes, "It is entirely possible that future generations will look back, from the vantage point of a more sophisticated theory, and wonder how we could have been so gullible."

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News Release Source : Fluid mechanics suggests alternative to quantum orthodoxy