## Modeling Traffic Flow

Traffic flow is not that different from the flow of anything else. Imagine heat flow along an iron rod or water flowing down a pipe. If you observe the traffic (on a highway) from a far enough distance, the mass of cars would...

## Combining Relativity and Quantum Mechanics – A first step

Quantum Mechanics starting point – The Schrodinger Equation (1)   All laws of physics are required to be Lorentz Invariant . The above equation is not. To try and make it Lorentz invariant, we start with looking...

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## Complex Transformations – The Complex Logarithmic Function

The real logarithmic function has two interesting properties: The Flattening property:  – a product is flattened into a sum The Linearizing property: –> Linearized an exponential (growth) function These...

## Watching a Television broadcast from Earth while moving Relativistically

Imagine you are in a spaceship moving away from the earth at a velocity v. Imagine that a TV broadcast is sent to your spaceship from Earth. How would you see the broadcast? The Approach to the solution We imagine that observers...

## N Points on a unit sphere

Problem Statement Consider n points lying on the Unit Sphere (the image shows a unit circle instead of a sphere). Show that the sum of the squares of the lengths of all segments determined by the n points is less than...

## Mathematics as a hobby (math as a hobby) ? Yes – Really!

Even if you do not consider math to be a hobby, this article may provide an understanding of why a lot of people do. Not being a math-aficionado, my wife thought it a bit strange that I enjoyed solving math problems for fun (I...

## The concept of a ‘function’ – explained through a problem

Imagine a long distance runner who runs 10 miles in 50 minutes (averages 1 mile every 5 minutes).  Is it true that he has to have one stretch of 2 miles which is completed in EXACTLY 10 minutes? Intuitively, there should...

## Solar sails – How do they work?

Light has no mass – yet it can push solar sails. How? It is true that photons do not have “rest” mass. They do have energy  – and hence an associated mass given by m = E/c2. Light has momentum given by p...