Physics

Quantum Cryptography (a background)

In this article I hope to illustrate some of the ideas behind the strange topic of Quantum Cryptography, though I won't be discussing cryptography itself, that comes later - just the necessary physics. First we must consider the nature of light (this can be generalised to any particle once we get all quantum mechanical, but let's stick with light for now).

Classically, light can be thought of as a wave. It's a transverse wave meaning that the 'oscillations' of the thing doing the waving are at right angles to the direction that the wave is travelling in. Another example of transverse waves are waves on the surface of water.

Picture showing waves horizontally and vertically polarised

These oscillations defined a 'plane' in which the waves are oscillating, and this plane can be oriented at any angle. Waves on the surface of water are vertically polarised. Though the plane of polarisation can be any angle, it is convenient to pick two planes which are at 90 degrees to each other. We can express any polarisation by talking about how much of each is present. Hence, we can talk of 'vertical' and 'horizontal' polarization. Here is an applet which demonstrates this.

You can see polaroid filters in action if you have a pair of polaroid glasses (often sold as 'anti-glare'). Find a light shining on a surface such as a desk. You don't want to be 'square on' to the surface, the light should be bouncing at an angle, 45 degrees is a good start. For the most obvious effect, don't use a mirror.

Look at the surface through your polaroid glasses, then rotate them 90 degrees, and keep looking. You should see the glare change in brightness. You will find that polaroid glasses are best at reducing glare from horizontal reflections when held normally. (See: Brewsters' Angle)

If you use your glasses for driving, you may find that you have trouble with the LCD screens on petrol pumps, this is because the LCD screen relies on polarising light!

If you take a polarised filter, this will ensure that all the light which passes through has the same polarisation. Classically, if a particular wave comes in with an amplitude of A, and a plane of polarisation at angle θ to the plane of polarisation, the amount of light which emerges has amplitude Acosθ.

Picture showing the effect of multiple polarising filters

Suppose that we have two polaroid filters. Unpolarised light hits the first and emerges polarised. It emerges with amplitude, A (on average). This light hits the second filter. The two filters have an angle θ between their planes of polarisation - the amount of light which emerges is Acosθ. So, if the filters are aligned, the second filter has no effect. If it is turned 90 degrees, no light emerges (note, if it is turned 180 degrees, it has no effect - the sign of the amplitude doesn't matter, it's not 'negative light'!)

(Note that for real filters, there is a little scattering, so 90 degrees doesn't give total black, and zero degrees does give some reduction in intensity)

Imagine we have two filters, aligned at 90 degrees. No light emerges. This is because the cosine of 90 degrees is zero.

Now, insert a filter at 45 degrees between the two. What happens? More 'stuff' can only make the amount of light getting through smaller, right? The cunning reader will have assumed that I wouldn't ask the question if the answer were obvious. Some light emerges. In this circumstance, two filters allows through less light than three.

This counterintuitive result is easily explained. Imagine the second filter is at an angle of θ compared to the first.  The third is at 90 degrees. In other words, the angle from the second is (90-θ). From the first filter, we have light with amplitude Acosθ. This is then reduced by the third filter by cos(90-θ). The overall light intensity is now Acosθ.cos(90-θ) or Asinθcosθ, this reduces to A(sin2θ)/2. In other words, we get most light out when sin2θ=1, or when 2θ=90°, or when θ=45° 

The newly inserted second filter is changing the polarisation of the light.

Take your time on polarisation, it's important that you understand the above if you're to comprehend subsequent articles. We'll put this aside for a while, though - the next step is to talk about photons.

Large Hadron Collider

The LHC at Cern will be switched on today, though there won't be collisions for a little while. The LHC will collide Hadrons (obviously) at high speeds. Hadrons are particles which contain quarks. Everyday examples are Protons and Neutrons. The LHC can only accelerate charged particles and so it'll collide protons. The high energy collisions will produce new and interesting particles - and the hope if to find the predicted Higgs Boson. Though if it's not found, that'll also be interesting....

There has been idle chat that it could create miniature black holes that'll destroy the Earth. This will not happen. It probably won't create black holes. But if it does create black holes they'll be moving so fast that they'll leave the Earth. Even if they don't they'll evaporate due to Hawking radiation as they're so small... and in the unlikely event that it does create a black hole that hangs around to destroy the planet - there'll be nobody to contradict me.

Seriously: cosmic rays have collided with the Earth with huge energies since time immemorial - a particle accelerator experiment in the upper atmosphere. We're still here.

As Wil Wheaton said on Twitter: "Stupid people at table next to me are convinced LHC will destroy the world tomorrow. Resisting urge to tell them how stupid they are. "

(P.S. I'm not saying this to boast, only to show that I know what I am talking about: I post as someone with a damned good Physics degree. Irrelevantly, I've visited LEP, the Large Electron Positron Collider and LHC's predecessor. Tragically, I took time out of my first USA trip to go to Fermilab. I've been to RAL in the UK many times.)

How to Destroy the Earth

An amusing little documentary about 'How to Destroy the Earth' - and it's all factually correct (if silly).

One thing, with an anti-mountain, crashing it into the Earth from space isn't going to be a major factor - just being on Earth will do it. Admittedly though, the anti-mountain would have to be manufactured away from the Earth so it didn't annihilate as it was built, so....

Einstein

I bought some chalk today, and after some experimenting I decided to have a go at an exercise in one of the art books which I bought. That is to take a photograph and attempt to copy it upside down. This is the result, which frankly I am both amazed and thrilled at.

Albert Einstein

It is a sketch in Chalk, fixed with spray as it's in my moleskine book. I am absolutely astounded with this - I drew it! I tried to draw the wife a few days ago, and the results were less than convincing, don't go hunting on the site, the pictures are not even worthy of that. The book I got is wonderful, I'm a convert, the simple act of turning a photo upside down works!

The thinking is that if you draw a face, your brain gets in the way, it interprets what it sees, 'nose', 'ear' and so on - and one draws the symbols, not the patterns of light and dark. This exercise is a first step to disconnecting the symbolic part of the brain and demonstrating to the student that it's the powers of observation which are the biggest impediment to progress.

It makes a sort of sense, though it does not stop it being magic.

The Calendar

At the moment I am reading The Calendar by David Ewing Duncan. This is a nice little book which covers the history of the calendar. Its brief takes us from carving notches on bones to count the days between full moons to trying to establish a true length for the year (and prevent the calendar drifting compared to the seasons).

The book encompasses science (astronomical measures), maths (being able to specify fractions of a day), religion (the date of easter) and history. It seamlessly takes us on a chronological journey through the ages.

I like cross-curricular books, my favourite books tend to be those which span subjects, as there is something familiar to take us on into the unknown. Also one can spot how one discipline feeds off another, other books of this ilk include Dava Sobel's "Longitude" and William Poundstone's "The Prisoner's Dilemma".

The closest I can find for Amazon.com users is a similar book by the same author. "Longitude" and "The Prisoner's Dilemma" are available in the US.