modern phyics

Introduction to special theory of relativity.

Special Theory of Relativity:
Galilean Transformations,. Newtonian Relativity.

This was a lecture delivered to physics-elective class of a 3 year non-physics degree students on 10th April 2017. This is also a good exposition to honors students and anyone at an introductory level of the special theory of relativity, with requisite mathematical background. 

Let us consider an inertial frame of reference S. The space and time coordinates of any event occurring in frame S are given by x, y, z, t.

Now let us consider another frame of reference S’ which is inertial but moves wrt frame S at speed v, along +x direction.

The coordinates of the same event in the S’ frame are given as: x’, y’, z’, t’. The relationship among the coordinates of any event in two different frames of reference both of which are inertial frames, is known as Galilean Coordinate Transformation or Galilean Transformation.

If we assume that time passes by at the same rate in both S and S’ frames, the resulting laws satisfy Newtonian Relativity. We say time is an absolute quantity in an infinitude of equivalent inertial frames of references as the rate of time change is independent of the particular inertial frame of reference we have chosen. Consequently: t = t’.

The above equation is known as velocity addition rule in Newtonian Relativity. This is valid only for classical mechanics in the sense of speed of objects and speed of frame of reference, which are quite insignificant with respect to the speed-of-light value.

Velocity addition is nothing but a relation of velocities of objects in different frames among each other. So its exactly what we call “relative velocities” in elementary mechanics. Relative velocity, velocity addition and velocity transformation are the exact same thing. Read more about these here and here. The second link also expounds on what happens when speeds approach that of light.

Optical Path and Fermat’s Principle.

We can see ourselves in mirror and take our mirror reflected selfie as a consequence of Fermat’s Principle, the topic of discussion of the blog.

In the last few weeks I am trying to understand why light traverses straight lines and why it refracts. The other day I saw a little mug floating inside a bucket full of water. Inside water any object would look shortened, a phenomena known as refraction. That’s because light rays would “bend” inside water (towards a direction where they have to take a shorter path) as their speed must reduce, given to the fact that in the same time in a rarer medium light would have traveled a longer distance in the exact same time, which is no longer possible due to the crowd of molecules and subatomic ghetto that it meets along its way.

Feynman Diagram of Higgs Boson Production.

This is a copy of the diagram from Wikipedia. I produced this using codes developed by me as previously instructed here with other examples. — What to do when its 2 am around here, you are fresh but nowhere to go.

Here is the code:

% Feynman diagram

% Requires PGF >= 2.0

\documentclass{article}

\usepackage[latin1]{inputenc}

\usepackage{tikz}

\usetikzlibrary{trees}

\usetikzlibrary{decorations.pathmorphing}

\usetikzlibrary{decorations.markings}

\usepackage{verbatim}

The basics of Physics — is Gravity amenable to Quantization?

The basics of Physics — is Gravity amenable to Quantization?

This is a very detailed and long article, but written in a very simple language, as it seems to me, describing such concepts as; the basis of expectations of “Quantization of Gravity with other forces” which is colloquially known as Einstein’s dream of GUT — or, Grand Unified Theory, and whether such is possible or not and what we may be missing.

This article also describes briefly Pseudo Forces — check a detailed description here. (web-link)

In detail the basis of Physics Formalism — check a discourse here (web-link) and

What are waves and particle — (a link to an extensive discussion will be provided, upon further review), the discussion is in terms of a Formal POV of Physics — ‘slightly”, but much can be based and expanded on such.

This would be one of the most well written article by me as I would think.

So lets get back to the discussion of our original topic of interest.

The basics of Physics — is Gravity amenable to Quantization?

I like to speak first; about a development of Physics, in this article, that follows a chronological path, rather than, how we look at the cumulative understanding, in modern times, upon which we base our statements and help ourselves be inconsistent, because we forget or rather are oblivious; to the deeper framework, in which things were developed.

— Today I want to focus on Gravity. But before I talk about Gravity; I would like to speak something, on Physics itself.