Oh man. Shoulda went to the beach today. Dude, really? Totally lame. But wait, doesn't light really have mass? It should. It's got momentum so it's gotta have mass.
It has momentum so it must have mass. Whoa, hey! Everyone just calm the heck down. You see, the worst part of all this wasn't that my joke bombed, it was that I actually managed to confuse people by telling it. My students had read that light has momentum and they were right, light really does have momentum.
But then I come to class and I'm all like, hey, guess what, light has no mass. Now my students are thinking to themselves, dude, but P equals MV. The natural question is: Can the principle of conservation of the momentum be extended to electromagnetic radiations also?
From experience you know that the answer is positive, provided you define the momentum of light as. However you are not allowed to make such extensions since in Physics you must stick to the experimental evidences. There is no evidence that light has also mass. Of course they have mass. When saying "photons have no mass" in LHC rap , they were referring to the rest mass, it just didn't rhyme.
This is a fundamental question requiring fundamental thinking. I shall keep away from theories and concentrate on simple facts. From the day we knew of the Brownian motion and realizing that particles of matter are on a continuous motion and not at rest, we should have realized that motion and not rest is the true influential variable of nature.
Velocity should therefore be adopted as the prime variable we use to study nature. But velocity has the units of space and time locked in an inseparable format, we should then conclude that space-time is a the variable that need to be considered in our scientific endeavor.
But velocity of particles have to involve mass too. This then says that the most fundamental variable of nature is momentum with the units of mass, space and time locked together.
As particles possess electrical charges too, we should also add electrical charge unit to get to the fundamental variable of nature. When we look round we see that E. M radiation has all the above attributes. It has mechanical attributes in the form of energy and momentum flowing along the direction of propagation.
Radiation also have electrical and magnetic attributes in its electric and magnetic fields that are normal to each other and normal to the direction of propagation. These attributes are all verifiable experimentally in the lab by simply directing a beam of radiation onto neutral and charged objects to see them move according to the laws of mechanics and electrodynamics.
That radiation is the fundamental ingredient of nature is supported by astronomical observations- which showed that radiation is all that is there at the start of the life of our universe. It is also supported by experiments in the lab wherein pure radiation gamma rays can produce matter, and pure matter anti matter included can produce pure radiation.
The process is fully reversible and indefinitely. We can thus say that radiation could be considered as evaporated matter and matter as condensed radiation. If radiation condenses by going round at the same speed in closed loops, we get trapped radiaton, or rest energy or rest mass as a result. The circulation of the momentum produces the intrinsic spin, and that of the electric field radial direction creates the electric charge Gauss theorem.
The magnetic field vector is normal to the other two- producing the magnetic dipole moment along the spin direction. This completes all the required matter attributes- emerging as a result of radiation condensing into matter- thus supporting the radiation origin of matter.
Hence, momentum linear or angular is a defining property of our universe, be it in the form of energy or matter. As to why light bends round massive objects, we note that gravity also emerges when radiation condenses into matter.
The key idea here is conservation of momentum. This is a fundamental property of our space and an experimental fact. Even elementary particles and radiation can't afford violating this principle. But if momentum is conserved, the forces between any two isolated particles locked in an orbit must be of the inverse square type as given in Bertrand theorem.
Actually the theorem allows a spring type force Hook's spring force too, but this can be shown to be a limiting case of the inverse square force. Thus Newton's law of gravity and Coulomb's law of static interactions emerge as radiation condenses into matter. Now, the formula for the bending of a projectile in the vicinity of a massive object in the Newton's theory the inverse square force theory have only the speed of the projectile in it, and not its mass. The mass simply cancel's out.
According to this fact, Newton proceeded to calculate the deflection of light caused by the sun for example. As it happened, Einstein calculated the same angle and found it to be double that of Newton. Gluons and the hypothetical gravitons are also massless, and therefore travel at speed c in all frames.
How can an object have momentum without mass? It can do this if it is a wave. A wave transports momentum via its waving motion and not by physically transporting an object with mass.
An object with high momentum such as a truck can greatly influence the object it collides with such as a barrel. If a giant water wave collides with a barrel, it can also influence the barrel to move. The water wave therefore carries momentum even though it has no mass. The water itself has mass, but the wave has no mass. A water wave is not a packet of water traveling along. In fact, the water that the wave is traveling through stays more or less in one place.
Rather, the wave is a rippling domino-effect of motion.
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