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.)

You could be Johnny

I've just posted the following to this article about the tendency in the UK to see being bad at Maths (and Science) as a mark of pride.

It really annoys me every time a presenter on the news 'jokes' that they can't do maths or science. Melvyn Bragg on the usually excellent "in our time" is another. If you can't do it, then research your topic - or at least stay quiet!

I grew up with Johnny Ball. I really miss him on TV - he was enthusiastic and willing to find out about things which he didn't know about. Today's "science" shows are more about blowing things up in the microwave, or the caravan (yes, Braniac, that means you).

An honourable exception is discovery's mythbusters (UK site) - they don't always get the scientific terms right (misusing terms like force, pressure etc, the narrator in the UK is especially guilty of this) - but they have the sense of the scientific method, and of exploration.

On UK TV, there is no modern equivalent. We need a modern day Johnny Ball! (Maybe next year it won't be 'You could be Nancy', but 'You could be Johnny' - I can only dream)

I really like the idea. Each week, wannabe Johnny's would present a piece about some aspect of science. It'd need to be fun, accessible, as well as being good science. The panel would consist of, a non-scientist, a scientist (not Adam Hart-Davies!) and the 'Lloyd-Webber figure' - Johnny Ball himself.

Each week, Graham Norton would tell the contenders 'You could be Johnny'.

The theme tune would end with Jack Nicholson bursting through a door saying "Here's Johnny!"

The public would vote (usually on style over substance) and there'd be a 'present-off' between the two who had the lowest public vote, they'd explain some particularly gnarly bit of science or maths. Johnny would save one of them.

I could be a getting a little flippant here, but I'm deadly serious about the issue at hand. Personally, I think some sort of contest might be a lot of fun, as well as helping to increase interest in science and maths. It could work, couldn't it?

The Bicycle

As I was cycling into work this morning my mind started to wander. I looked down at the bike beneath me and had a weird sensation of 'solidness'. It's hard to put this into words, but I'm going to try. There I was, doing about 15miles an hour, balanced on a device which itself was sitting on two patches of rubber a few centimetres across. It felt quite improbable, surely this thing must topple to one side - yet it doesn't. It must be this reasonable expectation which makes it hard to learn to ride a bike in the first place - the brain is convinced it can't work.

Despite going along, thinking about the precariousness of my situation, I didn't begin to wobble. It is always a danger that if you start to think about something which you normally do instinctively, you begin not to be able to do it!

This feeling of 'solidness' might seem an odd thought to have (especially once you know that bikes are more stable when moving due to dynamic effects), but stop to think about a world without bicycles, and then think of someone conceiving of this device: "I know, I'll invent a two wheeled means of personal transportation that people can balance on, propelling themselves by means of a crank mechanism attached to the back wheel" - it's just a phenomenal leap. Admittedly the penny-farthing looks very different to modern bikes, but that's evolution, not revolution. The imaginative leap to conceive that everyday people, without circus training, could balance without any difficulty on a two wheeled vehicle is just astounding - and then to go and make it happen....

Of course, this thought was founded on unsound principles. The bicycle did not emerge fully formed, the penny-farthing wasn't revolution. It was preceded by Baron Karl Drais von Sauerbronn's 'running machine' (essentially a bike without pedals) which people propelled with their feet. People would have found by trial and error that they could balance on the machine (even if the designer intended that their feet would be on the ground) - and then, this leads by an evolutionary process into giving the wheels some motive push with the feet (pedals).

Once you have pedals, you can then gain speed with bigger wheels (gearing) and then you have a penny farthing. With the addition of a chain we allows cogs and smaller wheels (modern bike). In the early days, the recumbent bicycle was another path being explored, but was ruled out of races as the advantage was too great - and so they're rare today (but seem to be getting more available again).

So, there I was, cycling along, relishing in the feeling of stability - and thinking about all the engineering that made it possible.

Then, my wonder at the engineering marvel speeding me along the road was broken by a roadside bunny who hadn't heard me coming and got spooked as I went past.

I liked my commute today.

Papal Infallibility

15 years ago, the church apologised for the trial of Galileo. This in itself should have given the hint that Papal infallibility isn't what it was.

The current Pope has just gone back on that, saying the trial was 'reasonable and just'.

It's a Papal showdown!

Both Popes can't be right (you can't apologise if you've done nothing wrong, and you can't have done something wrong if your action was reasonable and just)... yet, both are infallible.

Does not compute.... warning... error.... *BAA-boooom!*

Roller Coaster Power Cut

A power cut in Arkansas left roller coaster riders dangling upside-down My first reaction is 'how'. My understanding is that roller-coasters are constructed such that once lifted up the climbing hill, the coaster proceeds under gravity. Given that, how could a power cut cause it to stop in the position described?

The big worry for me if there were a power cut whilst I was in a coaster would be the braking system, not gravity ceasing to operate normally!

So, how could this happen?

X Ray sources in Europe

Following the construction of the Diamond synchrotron in Oxfordshire, a high intensity X-ray source, it's been announced that XEFL has received the green light in Hamburg. They're billing it as an 'X-ray laser'. I had my doubts that it was actually a laser, that there really was stimulated emission, the block diagram on the BBC site looked like it was just electrons being 'wiggled', and hence made to radiate, however according to the XFEL site "In February 2000, for the first time worldwide, laser light in the far-ultraviolet range was created using the SASE effect, which is also the basis for the XFEL." SASE is a new one on me, and so I've done a little research. Brookhaven refers to the SASE effect in 2002. This Japanese paper (in English) goes into some more detail .

From what I gather, the electron beam is undulated. There is an interplay between the undulating beam and the light produced by virtue of the undulation. This means that the light produced becomes coherent. The electrons are then stripped from the beamline. The beam produced is spatially coherent, but not temporally coherent. In other words, there is a fixed phase relationship between parts of the beam as one moves across the beam - however knowing the phase now tells you nothing about the phase a short time later.

Tonight's Eclipse

Tonight is a total lunar eclipse. These aren't very rare, and there isn't much science to be done, but they can be beautiful, and tonight's is predicted to be a good one. Tonight's eclipse beginsThe Earth's shadow is already visible across the moon, I took the photo shown here at about 2125GMT.

At totality, between 2244 and 2358 GMT, the only light which reaches the moon will be that which has refracted and bent through the Earth's atmosphere. As the Earth's atmosphere scatters the blue end of the visible spectrum (hence blue sky) what's left is the red end. This means that the moon will have a red hue. The exact colour will depend upon all sorts of factors, pollutants and weather for example.

More poetically, when you look at the moon tonight you will be seeing all the sunsets and all the sunrises simultaneously.

UPDATE: This photo was taken at about 2151GMT.

The Eclipse Continues