The Monty hall problem, Quantum Games

The original problem Three doors, a prize behind only one door (say, a new car). Other two doors are each hiding a goat. Contestant has to pick a door – and hope that she wins the car.  At just this stage, the chance of...

Prove that there are a countable number of intervals (in R) with rational endpoints

Counting Elements versus Counting Intervals  The interval [0,1) for example is uncountable, but we are not counting ELEMENTS of an interval, we are counting INTERVALS. [0,1] is one interval, [0,1/3] is another and so...

Problem books for advanced math ( and physics ) students

How often have you stared at a math (or physics) problem, unsure of where to begin?  Most math books are unusually pedantic and dull – all in an attempt to be more ‘rigorous’. Screw rigor, I say.  Students are...

Is zero point energy exploitable?

The short answer is ‘No’. If you think about what the zero-point energy represents, it is the lowest POSSIBLE energy state of a system. For us to extract any energy out of this system would leave it in an even lower energy...

Teaching Relativity

Galilean Transformation – v’ = v +- V –  cannot be applied to light If (x1 , t1) and (x2,t2) are two events in K, and (x1’,t1’) and (x2’,t2’) are their co-ordinates in K’, then (x2 –x1) / (t2 –...

A Logical Paradox – The British Air Force Bombing Paradox The British Airforce announces that it will bomb the city sometime during this week; but at an unpredictable date. Why is this paradoxical. Suppose, they announce this...

Understanding Quantum Physics–as Intuitively as Possible

Several classical, common sense notions like the momentum of a  particle hold no meaning in the quantum realm. Momentum and velocities are no longer ‘material’ aspects of a microscopic particle; they are rather...

Bohm and DeBroglie’s Pilot Wave

The phenomenon we are trying to explain is the interference pattern seen when you send a stream of particles through a double slit (barrier with 2 slits) apparatus. As long as you do not make any measurement, you ALWAYS get an...