According to classical electrodynamics theory, an accelerating charged particle emits an electromagnetic radiation. Unruh on the other hand found that an accelerating observer (charge) will find itself immersed in a black body radiation from the vacuum. How the de Broglie wave interacts with the electromagnetic radiation created by the particle? Is there a relation between wavelength and acceleration for an accelerated charged particle? Does the black hole evaporate completely or end in a finite mass (e.g., planck mass)?
I'm not sure the idea of the de Broglie wave interacting with the radiation is a fruitful way to think of things--the de Broglie wave idea is a nice starting point for quantum mechanics, but once you have QM you have an equation for a "wave" that doesn't necessarily "live" in three-dimensional space.
However: The de Broglie wavelength depends on the momentum--and therefore the speed--of the particle. So acceleration doesn't necessarily change the de Broglie wavelength (a particle can move in a circle at constant speed, but since the direction is changing it's accelerating). However, in any case where the acceleration is changing the speed (magnitude of the velocity)--such as when a charged particle loses energy by radiating--the de Broglie wavelength will change. There's a related quantity, the wave vector k (magnitude 2 pi divided by wavelength) which is proportional to the momentum. This does change whenever the velocity changes (so even for uniform circular motion).
Acceleration affects changes in the shape of an accelerating body. De Broglie wavelength is a relative quantity depending on relative velocity. I see something interesting in the issue of the spatial relation between decoherence and de Broglie wavelength.
There is a relation between the wavelength of a particle and the acceleration. I can't tell you anything about what Unruh found, but the solution of the problem of a quantum particle in an accelerating field is given by the Airy equation, see
https://en.wikipedia.org/wiki/Airy_function
For instance, this equation describes the movement of a charged particle in a constant electric field, i.e. a field imposing a constant acceleration of the particle. The wavelength of the particle will not be constant, see the graph, but you'd better read the artile in Wikipedia.
By the way, such experiments were performed, if you are interested I can give you references.
Four dimensional Lorentz invariant expression for acceleration given by Eqn. 25 in following article can give you the relation between acceleration and the de Broglie wavelength as follows.
Progress in Physics, 2015, v.11(1), 43-49.
http://www.ptep-online.com/complete/PiP-2015-01.pdf
Substitute following in eqn. 25.
ds/dt = v = h/(m*L)
v = particle velocity
m = relativistic mass
L = Lambda = de Broglie wavelength.
Nu = de Broglie frequency.
d2s/dt2 = -v[(1/L)(dL/dt) + (1/m)(dm/dt)]
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@Vikram,
You either work with the classical mechanics, or with QM. You can't mix them. Since the question here is about wavelength, you must work with QM, in classical mechanics there is no de Broglie wave-length.
The formulas vlocity = ds/dt, and acceleration = d2s/dt2, are pure classical mechanics, and to use them in QM is WRONG.
I recommend you to look at the formula of derivative of operators in QM. The operator velocity is the time-derivative of the operator position, and acceleration operator is the time-derivative of the operator velocity.
Both velocity and acceleration don't usually have definite values, s.t. one should decide, according with the specific of the problem, whether to calculate the averages.
You'd better withdraw your reply, it is a total confusion.
@Sofia:
It looks like your understanding of physics is limited to what you find in the text books and published research articles. You are not able to go beyond these and have your own ideas or appreciate other people’s advanced research ideas. Your comments tells me that you have not even read my article, or tried to understand the formalism. So I suggest you first read the article and try to understand it. If you cannot understand the formalism, then my article is not meant for you, don’t waste your time on it.
L-1 = gamma*v/(T*c2)
with
L = De Broglie wavelength
gamma = 1/sqrt(1-(v/c)2)
v = particle speed
c = light speed
T = Zitterbewegung period of the particle at rest
(Telectron ~= 8.0933*10-21 sec)
for non relativistic speed
a = dv/dt = -(T*c2/L2) dL/dt
Maybe you folks can answer a related question:
I walk across a carpet and then touch a doorknob. A big fat spark leaps from my hand to the doorknob. The doorknob is now charged. It is also being accelerated at 9.8 m/sec^2 (like everything else on this planet).
1. Does the doorknob radiate as long as it retains the charge? Why or why not?
2. Is this a valid question? (I am often accused of "thinking too much").
I am an engineer, not a physicist.
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