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.


Today's 'User Friendly' is spot on, commenting about a trend in our society that 'natural=healthy'. I've written about this before. Whilst I'm keen to avoid E numbers and all sorts of unneccesary things like that, I'm not naïve enough to assume that 'something with a chemical name is bad' or that 'if it didn't grow from the ground it is bad'. I might cite dihydrogen monoxide as a counter-example in the first case, and deadly nightshade in the second.

Well done, UF. 'Go hug a shark' is officially my favourite phrase of the day (though it wasn't used in that form in the strip).

Of course, dihydrogen monoxide does have some problems... it's a chemical found in virtually all tumours for a start.

Reality TV

In the UK, we've had a spate of mind-numbing, lowest common denominator TV - which tends to fill the so-called newspapers with trivia. We have 'Big Brother', 'Love Island' and all sorts of other trash TV. (Fortunately, though I've avoid these - it's become easier to do so as the saturation coverage has become less pervasive) In India, they've aspirational 'reality TV': 'Scholar Hunt' is a show where people show their academic credentials to compete for a University place in the UK. A world apart.

This speaks volumes. In the UK, the 'popular culture' values 'celebrity' whilst disregarding the importance of Physics, Chemistry, Maths etc. Indeed, these subjects are often seen as something which isn't aspirational - In India, it's reversed. Over the long term, India has the right set of priorities.

Where are the scientific role models for children? Where is the modern Johnny Ball on TV? I used to love shows like 'Think of a Number' and 'Think Again'. Johnny Ball was one of the figures who helped to inspire an interest in science for me (along with 'the Charlie Brown book of Questions and Answers'!)

Come back to TV, Johnny!

Scholar Hunt, if done well, could transfer to the UK, perhaps with UK students competing for am expenses paid place at Harvard, Yale or MIT - in parallel with Indian students competing for a place at Warwick, Oxford, Cambridge or Birmingham (my old University, great place). The trick, of course, would be to ensure that the candidates were not seen as 'nerdy' - which would be the big temptation in the UK market - and that's exactly what should be avoided. It's a format which could work - annually, the students could be followed to show how they'd been getting on, and so each year you could look at the new candidates, and have a programme showing 'whatever happened to...'.

The main thing would be to keep it aspirational - to show that knowing things is enjoyable, useful, and is something which doesn't (necessarily) make you uncool. Every time (especially on American shows) I see some knowledgeable teenager, invariably they're presented as a social pariah, a nerd. Not good.

(The Charlie Brown Thing: I got this when I was about five, it must have been around 1978 - every year, a new book came out - I think there were about five of them. By the time I hit ten, these books were falling apart, I loved 'em!)

Update: The BBC has an article on the show, along with an interview with the winner, Arvind Aradhya. Meanwhile, back in the UK, it looks like Science exams are to be made easier again so that more people can get a warm fluffy glow by fooling themselves that they've got a deep understanding. If an examination doesn't adequately test those sitting it, the qualification achieved is devalued. Slashdot has noted the science examination story.

Climate Change - Trickles

The First 'Trickle' of data for the BBC Climate Change modelling project should be uploaded soon. Trickles are feedback to the servers regarding the progress of the model (some data as it goes is better than none until the end). The BBC/boinc Climate Prediction model

Trickles are sent every 1st Dec (model time) and I'm up to the 1st November 1921.

When the data comes in, graphs will start to be produced from the data. My graph should be here.

I would encourage anyone running this model to also attach to something with smaller workunits (so that in the event of problem with the Climate model, the other model can run). In the preferences you can give different priorities to each model - the climate change gets 3 times the priority of seti@home for me (both run using the same piece of software, boinc.