## 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.

## How to add speeds; Galileo and Einstein won’t agree.

How to calculate the speed of anything, when their speed becomes closer to the speed-of-light.

— In order to correct the comment I have made earlier  ” unless something is completely mass-less in its rest-frame ” I also add the following. This is a fact which I have realized lately — or rather trapped myself to commit an inconsistent remark, by following the same comment in making other remarks elsewhere.

But it’s better late than never to realize; when something is mass-less, it will never have a rest-frame, because by Einstein’s transformation rules, known as Theory of Relativity, to be consistent, a mass-less particle will always move at the speed of light c, no matter which frame we are looking at it from. This then leads to the velocity addition formula of Einstein.

Now we will discuss in a slightly more detail the two kind of velocity addition formula, one prior to Einstein and one that came from Einstein’s work.

Prior to Einstein.
According to Newton and Galileo ( Galileo Project ), known by a name Galilean Relativity, the following follows; if C moves at speed

## Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity by Steven Weinberg .. review

A highly sofisticated and an elegant text book on general Relativity and its application. I would say a super book. I have read this book and solved for now a few daunting problems in Physics by applications of the content in this book. My research is available on my website but for context I recommend this book for serious practising physicists.

## What is Theory of Relativity !!

Just from a simpler form of Gravity I have proved in an article written couple days ago thats to be completed with these derivations but the ideas have been described: that gravitational time dilation can be derived from old classical theory without using any Einsteinian concept [such as changing mass with speed of frame of reference or universal speed limit]

## Gravity warps space-time.

Since flat space-time can be thought of in Newtonian mechanics as an absence of force or potential of gravity, the presence of such forces is ipso-facto a curvature of space and time, therefore space-time. Thats just another two lines to prove what I claimed, ideally and intuitively.

” eg when earth occupies the space-time around it, its effect, interaction or force is larger at a distance which is closer to the surface and smaller at a distance which is farther away, the force decreases radially-linearly, not linearly as such. So there are equipotential surfaces of gravity which are merely concentric spherical enclosures, one at each value of r=distance. This is tricky because its a potential energy where the reference can be chosen arbitrarily in a given situation. In other words, potential energy being negative, its the absolute or modulus of the energy we are talking about. In essence this is to say, the force without the direction specified.

Its interesting to note, thats so because force is a vector and associated with direction and energy being an integral of force, energy has to go on decreasing if energy continues to produce a force. This is again similar to a situation where like a bank account, the more time you spend in a pub the more you have to spend. “

## Gravity warps space-time !!

Since flat space-time can be thought of in Newtonian mechanics as an absence of force or potential of gravity, the presence of such forces is ipso-facto a curvature of space and time, therefore space-time. Thats just another two lines to prove what I claimed, ideally and intuitively.