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A Photon has no mass. It can’t rest.

A) A Photon has no mass. B) A implies “It can’t rest”. C) Therefore it doesn’t have rest mass. D) Photon rest mass is zero.

Assertion and reasoning; A is correct. B is correct and follows from A. C is correct, it does follow from B. But D is incorrect it does not follow from A, B, or C. Its erroneous, a sloppy language that has been thought to be correct for ages now.

The trick is to realize there is no property called mass of photon — at-least in the same sense as it is for other particles with mass, therefore no rest mass. To say rest mass is zero is a special value of mass or rest mass. It just doesn’t have rest mass, as it neither has mass, nor rest, which are equivalent formulations, one leads to other. But A, B or C do not lead to D. They are not equivalent way of saying each other. They invalidate each other actually.

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Waves, particles and Einstein !

Waves are something that have no mass and move at the maximum speed, mass m = 0. speed c = 1. So whats their momentum? p = m.v = 0? Right?

No. For pure waves; momentum does not come from mass. It comes only from motion.

(pure wave; they do not have mass)

For matter waves, on the other hand, momentum comes in two ways, mass as well as motion.

(impure, now they have mass)

Albert Einstein recognized this fact and derived his relation; $latex E = \sqrt {(pc)^2+(mc^2)^2}$

This relation is called as Einstein’s relativistic equation, also Einstein’s mass-energy relation. But more appropriately mass-energy-momentum relation.

Let us consider E as the hypotenuse, p and m; as base or perpendicular as is your choice.

triangle_copyThen $latex E = \sqrt {(pc)^2+(mc^2)^2}$ is Pythagoras Theorem; when p is momentum and m is mass.

For pure waves such as photon … the quanta of light, m = 0.

Hence the Pythagorean Triangle is now one, where the mass side is arbitrary small. Thus E = p.

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What happens when cows move rapidly !

Cows not moving and moving fast. How does this difference impact the image in a modern digital camera?

Honestly I haven’t checked it with old day manual camera neither do I remember what impact motion brings into mages taken by such, eg does anyone remember when he/she took a picture of a friend standing in a platform and a train was coming, what happened to the image due to such motion?

Do you see where the fuzziness coming from, in the pictures, where the cows are moving?

Its coming from the relative motion between “objects being imaged” (cows and grass etc) and equipment of imaging (camera). This fuzziness is quite small when they are both still (the object and camera, wrt each other).

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Why is the helicity for a mass-less particle Lorentz invariant?

Result; now that photons are mass-less, their energy, momentum, speed, etc are no more variables, in the sense of arbitrariness. They are constants, taking only a few values, but constant in a given situation. But other particles have these properties; arbitrary. So electrons energy and momentum are not fixed, but arbitrary.

But as long as we are considering only elementary particles (that is, we are in a Quantum Zone) eg, electrons, protons, photons, and not nutmegs, soccer balls and airplanes and satellites there is another quantity that is of important consequence that is constant. Spin; whether a mass-less particle or not, spin has the same magnitude for them. that is spin is same for photon, its always 1. Spin for an electron is always 1/2. Spin for proton is always 1/2. Its for this reason photon is called a Boson**. Any thing with spin, 0, 1, 2, etc will be a Boson. Anything with spin 1/2, 3/2 etc will be called Fermion.

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A particle that defies classical mechanics !

A photon has no mass but energy and it has speed and it has momentum although it does not have mass. Thats impossible in Classical Mechanics. Because Classical Mechanics associates with every mass; momentum and kinetic and potential energy. All those would be zero if mass were to be zero.

Also the speed of the photon is constant while its energy and momentum are changing. This is unimaginable in classical mechanics. In CM first momentum can’t be defined from mass and speed if mass is zero, then while speed is not changing how is momentum changing? So both variables speed and mass fail to define a momentum for the photon, and not just the failure to have a mass. How then momentum is defined for this particle? Its not defined as long as photon is just a particle. Thats impossible.

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