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I have wondered for a long time why the wavefunction associated with a photon is a tangible and measurable change in an electromagnetic field

I have wondered for a long time why the wavefunction associated with a photon is a tangible and measurable change in an electromagnetic field whereas (all?) other particles have a less tangible probability amplitude associated with them.

An example is an electron which exhibits interference and diffraction but for which the wave function appears as just an abstract probability amplitude.

Are there any other particles for which the wavefunction is a sinusoidal change in a field?

If not, can any insight be drawn from this?

If a Higgs Boson is found, would its associated wavefunction be tangible gravity waves?

As the photon mediates the em force, the graviton mediates the force of gravity and the pion the nuclear force (I think this is right but it is from memory), do these particles have tangible waves in their associated fields that produce identical results to a probability amplitude?

Quote from: graham.d on 10/08/2010 12:36:01Are there any other particles for which the wavefunction is a sinusoidal change in a field? But isn't the sinusoid nothing more than a way of describe the components of a generic wave? I'm not able to do the same with a generic field which allow for a wave description?

I didn't grasp the meaning of the 6 spatial dimensions but I took it to be a way of representing the wave function of two quantum-entangled photons occupying the same physical space; splitting the x,y,z components into 2 independent sets of axes maybe a way of doing it. I have not the time to follow up the references.