What vibrates in De Broglie waves?

[shripathee]

Hi, I am very new to Quantum Physics.

In every wave, something should oscillate.
In water waves, water molecules oscillate.
In electromagnetic waves, electric and magnetic fields oscillate.
So what oscillates for a de broglie wave?
Take a neutron as an example.

 

[Dale]

The wavefunction:

http://en.wikipedia.org/wiki/Wave_function

 

[shripathee]

Thank you very much.

 

[haael]

So what oscillates for a de broglie wave?

Simple answer: we don't know. We don't even know if a wavefunction actually exists. But we are closer to the answer thanks to gravity waves.

Graviton is a QM particle, it has its de Broglie wave, frequency and momentum. At the same time graviton manifests macroscopically as a gravity wave. The frequency of a wave is equal to de Broglie frequencies of its gravitons.

So, when you ask what is vibrating, my bet is: the space-time.

 

[LouieHussey]

In a de Broglie wave, what is it that is waving?

Shripathee, it is the “quantum potential” (potential energy per unit mass) that is waving in a de Broglie wave. And the gradient of the quantum potential is the “quantum force” that acts together with the field forces on the particle to determine its motion. The complete description of the dynamics of a quantized particle requires that the quantum force be included in the forces acting upon it. See, for example, Feynman’s Lectures on Physics Volume III, Section 21-8 ("The dynamics of superconductivity"), in which Feynman solves the Schrödinger equation for the equations of motion of an electron in a superconducting fluid.

Louis de Broglie wrote a series of papers in his latter years in which he revisited his earlier work and showed that the quantum mechanical equations have a “double solution”, as de Broglie described it--see, for example, "The Reinterpretation of Wave Mechanics", by Louis de Broglie, Foundations of Physics, pg 5, 1970, see also his paper, "Theory of the Double Solution", by Louis de Broglie). On one hand, the square of the amplitude of the wave function represents the probability of finding the particle in a little volume of space (an interpretation first discovered by Born after Schrödinger discovered his famous quantum mechanical equation), but on the other, the wave function also describes a concrete physical potential field (potential energy per unit mass) in space-time. In these papers, de Broglie shows that when the quantum potential acts upon a particle such as an electron, the proper rest mass of the particle and the quantum potential fluctuate together. This fluctuating mass gives rise to a fluctuating force (the quantum force) on the particle according to Newton’s law F = d(Mv)/dt, where the derivative is taken also on the variable M.

It is interesting to note, by the way, that the wavelength of the de Broglie wave of a rest mass particle is analogous to the modulation envelope wavelength of a standing wave set up between two mirrors that are moving together through space. And the particle’s group velocity is analogous to the velocity of the standing wave apparatus--see, for example, "Moving Standing Wave and deBroglie Type Wavelength", by Walter Roy Mellen, American Journal of Physics, Feb 1973, Volume 41, pg 290.

 

[mikelepore]

Perhaps the word "wave" was an unfortunate choice originally. It's not a kind of motion. As Born found, it indicates a probability distribution in space. It's more probable that you would find something in one region, and less probable that you would find it in another region.

 

[LouieHussey]

Mike, it was not the wave function itself, but the square of the amplitude of the wave function that Born interpreted as a probability distribution. Generally speaking, the wave function itself is a fluctuating, complex valued function, but the square of the wave function is positive valued, as is also probability itself (negative probabilities are generally not considered to be physically possible). The whole point of de Broglie's "Reinterpretation of Wave Mechanics" and "Theory of the Double Solution" papers is that two different interpretations of quantum mechanics are simultaneously possible, that in addition to Born's statistical probability distribution interpretation, which you cite, there is some actual fluctuating physical quantity underlying it that gives rise to the quantum potential and the quantum force.