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Quantum Mechanic's Problem Of Heisenberg Uncertainty May Have Been Solved Using "Pilot Wave Theory" Fluid Dynamics Rather Than Copenhagen Interpretation Of Quantum Mechanics

By Andrew Urban | September 13, 2014 11:31 AM EDT


Scientists have put forward a new system of fluid dynamics that may replace the orthodoxy of quantum mechanics. Quantum mechanics stems from the breakdown of Newtonian physics at the sub atomic level. Sometimes the smallest parts of matter will behave as waves, and sometimes they behave as particles. It all stems from the Heisenberg uncertainty principal, which states that you can not know both the trajectory and location for a particle at the same time. 

The Copenhagen interpretation of Quantum mechanics would explain this by saying a particle is a wave smeared accross everything that exists, and only collapses into a defined location upon observation. Essentially that there is no trajectory of the particle.

Louis de Broglie has a different interpretation of this phenomena, the Pilot Wave Theory. The theory postulates that quantum particles are borne along on some type of wave. The particles have definite trajectories but due to the pilot wave's effect, they still exhibit wavelike statistics. Imagine a buoy floating on water, it bobbs up and down like a wave, but is solid like an object. This differs from the Copenhagen theory, which, to maintain the metaphor, would be like a wave breaking upon being observed, being hit by a wave feels solid while sticking your hand in feels like a liquid. 

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 very limited situations, behaves according to quantum systems.

The system propounded by Couder and Fort consists of a bath of fluid vibrating at a rate which is just below the threshold at which waves will form on its surface. A drop of the same liquid is released above the bath and when it strikes the surface it will create waves which will radiate outwards. The droplet will then move forward by the waves it has created.

John Bush, a professor of applied mathematics at MIT, believes that pilot-wave theory deserves a second look.

Bush says "This system is undoubtedly quantitatively different from quantum mechanics. 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?"

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, who now works at the Max Planck Institute for Dynamics and Self-Organization, 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. In the fluid system, both the bouncing droplet and its guiding wave are plainly visible. If the droplet passes through a slit in a barrier, like Max Planck's famous experiement, 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 comes from advances in 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 chatoic system is one where the results are greater than the sum of its initial conditions, or rather a system with so many parts that the smallest variable can ripple into having a large effect, 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 quantum-like statistics observed in their experiments.

In a recent 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 primacy awarded to the Copenhagen interpretation. Scientists have found it difficult to accept the notion that a particle can be in two places at once, or nowhere at all.

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.

David Griffiths, a physicist whose "Introduction to Quantum Mechanics" has become the standard entry text 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."

"The work of Yves Couder and the related work of John Bush... provides the possibility of understanding previously incomprehensible quantum phenomena, involving 'wave-particle duality,' in purely classical terms," says Keith Moffatt, a professor emeritus of mathematical physics at Cambridge Univ. "I think the work is brilliant, one of the most exciting developments in fluid mechanics of the current century."


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