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On the Size and Constitution of a Photon

Suggested background reading: A Suggested Stable Model for the Electron

According to the Equivalence Principle (and experiment) the trajectories of every entity, with a velocity v orthogonal to an ambient uniform gravitational field, is a single parabolic curve. In particular, one trajectory applies to every photon.

Now the time-honored equation that the mass of a sub-light-speed particle is a function of its speed (m=mo/(1-v2/c2)1/2) can apply to photons if they have “infinitesimal rest masses”. According to this view m could be any finite quantity. We can determine a particular  value for m by noting that, according to Planck, the photon has a momentum of

p=h/l.      (1)

If we also assume that

p=mc,       (2)

then we see that the photon’s mass is small but finite:

m=h/lc.   (3)

Now the photon has zero charge and hence (according to the classical model of a sub-light-speed particle being a spherical shell of mass concentric with a spherical shell of charge) it can be modeled as a shell of gravitational mass. Assuming m is imaginary, the radius of this shell of mass is theoretically(1)

r=2|m|G/3c2=2Gh/3c3l.           (4)

Or, defining the constant c to be

c=2Gh/3c3=1.09419333e-69,           (5)

we find that

r=c/l.                 (6)

A photon of light can evidently be modeled as a miniscule spherical shell of gravitational mass of radius r. In a uniform gravitational field the photon would accelerate opposite to the field vector g (since g, according to gravitomagnetic theory, is also imaginary).

It is worth noting that a free photon is stable while in transit between a source and an absorber. It has previously been concluded that a lone sphere of charge could not persist with a constant radius. For with nothing to hold it together the charge would disperse.

In the case of a sphere of mass, nothing is required to hold the sphere together since like-signed masses attract. The question becomes: “What keeps the shell of mass from collapsing to a point?” Eq. (6) suggests an answer. In order for r to decrease, l would have to increase. There is evidence that this might actually occur as the photon’s path length increases. The phenomenon is of course referred to as “red shift.”