On one occasion recently (in one of my articles that talks about photoelectric effect) I said “photon rest mass”. This is a serious lapse with the Physics I intended to give. First off this I might have given on more than this occasion I don’t know. But let me correct myself rest-mass and rest-frame for a photon is a spurious concept.

*And we should not talk about non-inertial or inertial frames for the photon so much, although its true for also particles with masses, non-inertial frames are merely a different amount of energy due to the added amount of speed at every instance because of acceleration. *

Since Gravity is a potential energy, its potential (or force) also amount to acceleration and this is the principle of equivalence (PoE).

*A photon always moves at the constant speed in all frames* which is why non-inertial frames only add or subtract a different (or same) amount of energy every other instant.

But the situation for particles with **mass** is still *more complicated* because there is a trade-off between mass and momentum with energy. That does not happen for the photon. Photon is really special. [I just finished writing another article on the special attributes of photon, today, 5th Aug 2014, barely a week before the dob of my kanojyo ]

The other specialties of photon were described in one of the initial articles on this website, perhaps with the title “what is photon” (or was it “whats so special about photon”) .. In Relativistic Q. Mechanics (**high** speed elementary particles *that is*) one should not at all talk about the position of a photon. It was explained in a different perspective based on reasoning from QFT text of Landau. But if you see from my recent article with insights I gained of [same as linked article on top] **invariance mass**, its clear that a very high speed photon is not possible (more than the *speed of light*), which is why there must be more than one photons to receive very high energy or speed, the invariance mass is no longer zero and the speed is an average, the thing is a wave or bunch of photons now and (*its center may not moving at*** speed c?), **its called a **wave-packet**.

Since you **cannot talk** about precise position of a bunch of particles as they are moving wrt each other, the position vs momentum uncertainty starts showing up, like for other particles with masses. (**See,** for single particle of photon has a sharp momentum, hence Uncertainty Principle does not apply there but with many it does). **So very** beautiful.

This is what is special about a Photon and this is why **we can’t talk ***about the rest-mass or rest-frame of a photon. We can’t also talk about a position of a photon if its really high energy; due to Uncertainty Principle*. That means ray optics **is** when the wavelength is large so that the **uncertainty** isn’t going to blurr the ray, in other words small frequency or low energy photons, which means essentially individual photons hitting you in intervals of larger distance.

1. The photon is always moving at **speed c** and its a **zero mass** particle. This is the reason why rest-frame and rest-mass are spurious concepts; only for photon and not for proton eg.

2. Given that its zero mass, the **Pythagorean Triangle** of mass, energy and momentum means; its energy and momentum are **same**. (in a suitable unit). For a single photon, that is for a wave of photon with really low energy; the invariant mass is **zero**. The invariant mass of a high energy photon is **not** zero, since there has to be many more than **1** single photon to comply with the fact that *extreme high energy single photon would not be possible in nature*, it would break Uncertainty Principle and through that the Relativistic Principles.

3. Since Energy = Momentum for a really low energy photon, (again because thats a particle equation of motion, classical intuition worked and you talk about ray of photons etc, the moment it enters higher energy, actual wave-particle duality enters, but because single photon is always zero mass, its a wave-equation of motion, there are no big size photons, its only many photons = wave) and energy occurs only in definite value (**so,** many small size photons possible: they correspond to different frequency *that is*) so is momentum (definite values).

In other words the single photon has always a constant energy, momentum, frequency, wavelength, zero mass = zero invariant mass, and an effective mass because there is energy. Its this zero invariant mass which un-necessitates the concept of rest-mass because there is no rest for photon (constant speed c = NO rest-frame) even for single photons. (**photon essentially means vacuum**, if you want to talk about speed of light in dense media thats still **single photons with speed of light = c** but mean free path is really less hence the average invariant mass is not zero and therefore it behaves like any other particle with mass, and thats because its a wave-packet now).

4. One shall only talk about a **single** photon to **not** get confused and do all calculations, then one will be led to the actual properties of photon (or light) etc, by adding phase and amplitude separately.

5. Photon is a zero mass particle (not a zero rest mass particle) and its deflection in gravitational field, called gravitational lensing is due to two reasons; i. single photon effective mass is due to the definite energy and momentum of the same. ii. multiple photons have non-zero invariant mass, hence they behave like any ordinary particle with mass, bends under gravity therefore, in both cases.

6. talk about inertial or non-inertial frames hardly does complicacy (unless its a particle with mass, hence further degrees of trade-off in phase space) especially if you are dealing in terms of energy and not force etc. Which is why Physics is formulated on higher parameters like energy and action, from where these concepts do not make difference. Energy is already **integrated** and having an acceleration on every instant has already been taken into consideration.

I THINK THATS ENOUGH FOR YOU TO REMEMBER ABOUT PHOTONS FOR NOW. IF I STUMBLE ACROSS ANY MORE CONFUSION WE WILL DISCUSS MORE.

## 2 thoughts on “The photon saga.”