Answerer

Hi guys, I know that the principle of uncertainity works for particles with rest mass but what about those massless particle like photons, gravitons and gluons, does the principle apply as well? If yes, what are the wavefunctions for photons and gluons?
Hope that you guys have some answers to my questions.

ohwilleke

I am fairly certain that the priciples of uncertainty and wave/particle duality apply to photons and believe that there are experiments to back that up.

I don't know that there are any cases of gluons being directly observed to be sure -- gluons are inferred from the way particle collisions break up. I also am not certain that gluons are in fact massless -- W particles are not.

Gravitons are merely conjectural particles for which we have no evidence, so there is no way to know about them. My physics isn't good enough to provide a wave function.

Answerer

I had guessed before that the wave function of a massless particle should be very similar to that of a free particle in a free space. However, I don't see how Schrodinger equation works in this case.

Friar Bellows

I think you need to use the relativistic Schrodinger equation in this case. I also have a faint memory that Dirac was the first to come up with it, and so it might also be called the Dirac equation. At least there's a couple of phrases for you to look up on Google.

[ November 02, 2002: Message edited by: Friar Bellows ]</p>

Answerer

Could you offer me some links? I have some difficulty in searching for that Dirac equation in the web.

beausoleil

I don't understand why you think it shouldn't. Uncertainty relations govern momentum/position and energy/time. A photon may be massless but has well defined momentum and energy. Since momentum is related to wavelength, you can see that the more precisely we know the photon's wavelength the less precisely we know its position. In a sense you can think of it this way - you need to measure over a significant distance to determine wavelength.

Frequency and energy are related so there is an uncertainty principle relating frequency and time. In practice, this means that a short pulse laser is limited in how pure a fequency it can have ('transform limited bandwidth') - the photons are definitively within a short interval in time and so have uncertainy in energy (=frequency) - bandwidth and pulse length are inversely related. On the other hand, a continuous wave laser can have a much purer frequency since it has effectively an 'infinitely' long pulse.

Friar Bellows

Actually, I now seem to recall that the Dirac equation is for spin-1/2 particles, and the photon is spin-1. I think you need to turn to Quantum Electrodynamics to get a quantum "understanding" of the photon. Again, Dirac pioneered this field of study.

Also, beausoleil is right as usual. Photons have momentum:

p = E / c

where E is their energy, c is the speed of light.

Feather

If an object can be represented using the Schrodinger equation (which all particles can be), then there are uncertainty relations associated with it. Whether the particle has no rest mass (i.e. is "massless") or not.

Starboy

All particles mass less or not exhibit wave particle duality, which is the foundation of quantum mechanics. Photons have zero rest mass; everyone has seen a rainbow (diffraction as a wave property) and almost everyone has used a CCD camera (photoelectric effect as a particle property). Electrons as well as all other non-zero rest mass particles will diffract just as light does. Everything is a wavicle, that is, both particle and wave. This is only the tip of the ice burg but with this knowledge a great deal can be discovered about quantum effects.

As for the “wavefunction” for any physical system this is obtained by solving the suitable quantum equation for the physical system. To create the quantum equation one usually constructs the classical Hamiltonian and then converts it to a quantum equation by applying the operator transformations for momentum and energy. If you are lucky this will result in a second order linear differential equation with constant coefficients. The standard mathematical techniques can be used to solve this equation. It usually results in a set of Eigenfunctions which are referred to as the Eigenstates. Since the equation is linear any solution can be constructed as a linear superposition of these Eigenstates. Using this and the boundary conditions of the physical system results in what is called the “wavefunction” of the system. You can also take these Eigenstates and using the Schmitd Orthogonalization method create a basis set of Eigenvectors. This is the starting point for the Dirac interpretation of QM. IMO it is impossible to understand QM using common sense. The best you can do is master the machinery of the mathematics and use it to make predictions.

It is pointless to try to use common sense to understand, that which is not common to the senses.

Starboy

galiel

I'm not sure