Following

Dear Valeriy

If the longitudinal mass of each photon is E/c2 as you assume, don't you think that if both fly in the same direction, then their longitudinal mass can only be 2E/c2 which would mean that the longitudinal mass of the system will also be 2E/c2?

Actually, the true definition of "mass" in electromagnetism amounts to "omnidirectional inertia" of the transversely oscillating half of a photon's energy, the other half being its longitudinal momentum energy (its impulse energy from the continuous wave concept in some underlying medium).

From this perspective, the deflection angle of light by the Sun as verified by numerous experiments during solar eclipses seems to confirm that the transverse inertia of photons amounts to only half of their longitudinal inertia, clearly relating the concept of mass to the transversely oscillating half of the longitudinally detectable inertia of a photon:

Ref:

Ohanian H C, Ruffini R (1994) Gravitation and Spacetime, Second Edition, W.W. Norton. P. 194.

and

Michaud, A. (2016). On De Broglie’s Double-particle Photon Hypothesis. J Phys Math 7: 153. doi: 10.4172/2090-0902.1000153. P. 14.

https://www.omicsonline.org/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.pdf.

Best Regards, André

No. And the implication in the statement ``The total impulse of such a system is zero, and the total energy is 2E, i.e. mass of this system is 2E/c2. '' is incorrect. The two-photon system isn't a localized object.

Photons are massless particles and the meaning of this statement is the consequence of the fact that E^2-|p|^2c^2 is invariant under Lorentz transformations. For photons this combination vanishes in all inertial frames.

That they have only transverse polarization refers to their spin, that's independent of their mass.

André Michaud

Stam Nicolis

Dear Colleagues,

Let us reason simply with common sense. Mass is the amount of matter in the body. Where does the mass of the electron and positron go in the annihilation reaction? It becomes a mass of photons. It does not matter at all that the speed of the photon is equal to the speed of light (c is the thermal speed of the quanta of the environment of the electromagnetic field). The mass of a photon manifests itself in transverse inertness (the beam is a symbol of straightness) and weight (the sun deflects the beam).

Let's reason by the formula E^2 - p^2 * c^2 = m^2 * c^4, p = v * E /c^2

We tacitly assume that the photon is a point object. But there are no points in nature. The photon has dimensions. Therefore, we must expand this equation along the coordinate axes:

Ez^2 - pz^2 * c^2 = mz^2 * c^4, pz = vz * Ez /c^2

Ex^2 - px^2 * c^2 = mx^2 * c^4, px = vx * Ex /c^2

When vz = c then mz = 0, when px =0 then mx > 0.

Here x is the angular or transverse coordinate.

More details in the book "Electromagnetic Gravity. Part 1" in my profile.

Yours

Valeriy Pakulin