Why can't we say that photon has very very small mass?

[Pradyuman]

Any wave mass term decays, similarly if I want to explain redshift by considering massive photon, how much should be the mass? Is it less than today's upper limit.

Solution of wave equation $□ϕ=0$ gives a wave that doesn't disperse over time.

But wave solution of the form $(□+m^2)ϕ=0$ has some dispersion If I consider a wave traveling with speed #v# from A point to B point there will be some dispersion,

Now consider a wave-packet from point A and it is observed that at point B its wavelength has increased due to dispersion,

Now how to calculate the #m# for a wave, and

why can't one apply this to electromagnetic waves

 

[malawi_glenn]

Because then we would not have EM as a gauge theory, the mass term is not gauge invariant.

 

[vanhees71]

That's also not entirely true. For the Abelian gauge symmetry U(1) you can have a "naive mass term" without destroying gauge invariance. It's the so-called Stückelberg realization of the massive spin-1 field. That photons are massless is in this sense an empirical input. According to the particle data booklet the bound is $m_{\gamma}< 10^{-18} \;\text{eV}$.

 

[PeterDonis]

there will be some dispersion

But dispersion doesn't change $m$ so I don't understand what point you are trying to make.

 

[PeterDonis]

its wavelength has increased due to dispersion,

Dispersion doesn't increase the wavelength; it spreads out one wavelength into multiple wavelengths.

 

[vanhees71]

Dispersion changes the "dispersion relation", $\omega=\omega(\vec{k})$. For em. waves in the vacuum you have $\omega=c|\vec{k}|$, where $c$ is the vacuum-speed of light. In which sense do you think that means it "spreads out one wavelength into multiple wavelengths"?

 

[Demystifier]

That's also not entirely true. For the Abelian gauge symmetry U(1) you can have a "naive mass term" without destroying gauge invariance. It's the so-called Stückelberg realization of the massive spin-1 field. That photons are massless is in this sense an empirical input. According to the particle data booklet the bound is $m_{\gamma}< 10^{-18} \;\text{eV}$.

Stuckelberg is perhaps one of the most undervalued theoretical physicists.

 

[Pradyuman]

Dispersion doesn't increase the wavelength; it spreads out one wavelength into multiple wavelengths.

A wavepacket is composed of many waves and I imagine the light travel as a quanta which is equivalent to wavepacket, and since it spreads over all wavelengths, the net result must be spread of crust and trough of the wavepacket which in essence is like increasing wavelength

 

[Sagittarius A-Star]

Any wave mass term decays, similarly if I want to explain redshift by considering massive photon, how much should be the mass?

If you mean the redshift of distant celestial bodies, this can be explained with the Doppler effect and massless photons. This is verified i.e. by the observed duration of explosions of differently distant supernovae.

Source:
https://astro.ucla.edu/~wright/tiredlit.htm

 

[Vanadium 50]

The thread title reminds me of the old joke "How many legs does a dog have if you call a tail a leg? Four - calling a tail a leg doesn't make it so." We can say anything we want about a photon's mass.

However...

1. Adding a mass to the photon improves no experimental measurement.
2. Adding a mass to the photon solves no theoretical problem, and in fact causes some.
3. The limits are very, very tight: ~27 otfrts of magnitude smaller than a hydrogen atom.

 

[vanhees71]

Stuckelberg is perhaps one of the most undervalued theoretical physicists.

That's true, and also in general for the Swiss contribution to what I'd call the 2nd development step of QFT (the first was Born and Jordan, Heisenberg and Pauli 1926-1930ies), i.e., the development of renormalization theory, and that was not only the Nobel by Schwinger, Feynman, and Tomonaga (with a very important clarifying contribution by Dyson) but also again Pauli, Villars, Weisskopf, and Stückelberg. The latter was also one of the pioneers of the renormalization-group idea (Stückelberg & Petermann). All this finally culminated in the general renormalization theory by BPHZ. The 3rd step was then the discovery of non-Abelian gauge theories and their renormalizability (most prominently 't Hooft, Veltman, but also Ward et al), which paved the way for the Standard Model as its most successful application.

 

[malawi_glenn]

We need an insight on the history of relativistic qft

 

[PeterDonis]

since it spreads over all wavelengths, the net result must be spread of crust and trough of the wavepacket

Why?

 

[vanhees71]

We need an insight on the history of relativistic qft

Before we have that, I recommend to read the historical intro in Weinberg, Quantum Theory of Fields, vol. 1.

For the early history (QED from 1925 to Feynman, Schwinger, Tomonaga, and Dyson):

S. S. Schweber, QED and the men who made it

About the "modern period" (non-Abelian gauge theories and their renormalizability):

F. Close, The Infinity Puzzle