It’s entirely my own fault. After the first announcement back in September I volunteered on Twitter, then on BBC television to eat my boxer shorts on live TV if this result is proven to be right. Now, many people mistakenly believe that this second repeated experiment is the confirmation needed for me to fetch the ketchup.

Let me begin by making two statements that I hope are very clear and that I can refer back to if necessary:

1. The result from Opera is still only a measurement, not a discovery
2. I would absolutely love it if it were true and particles could indeed travel faster than light. It’s heaven for physicists because it means the whole of modern physics is back up for grabs again. We would need something to replace Einstein’s theories of relativity or at least a way of fixing them.

OK, so, briefly, what is all the fuss about? Well, neutrinos are tiny elementary particles that are almost weightless and which pretty much ignore the presence of all other matter. We all have millions of neutrinos streaming through our bodies that arrive from space, mainly from the Sun. And they do this even at night because those neutrinos can pass right through the whole of the earth (when the sun is on the other side) before coming up through the ground, up our feet and leaving to continue through space. Now, neutrinos are so light that they are able to travel almost at the speed of light. We know there are three types of neutrinos (electron neutrinos, muon neutrinos and tau neutrinos). I won’t go into the technical details. Basically, the most common, the electron neutrinos are produced in what is known as beta decay inside the nuclei of atoms.

The Opera experiment involved timing a beam of mostly muon neutrinos between their point of origin at CERN in Geneva and the arrival point at a the Grand Sasso Lab in Italy (which has special detectors than can capture these elusive particles. The travel distance is 730 kilometers and the neutrinos appear to be able to cover this at a speed faster than light. Basically, they arrive 20 billionths of second sooner than light would were it travelling in a vacuum.  Of course, even though these neutrinos are travelling underground, it’s as though they are moving through empty space since they don’t interact or bump into anything.

Maximum speed limit

There is nothing that annoys people more about Einstein’s theory of relativity than its claim that nothing can travel faster than light. Why can we not conceive of anything moving at a speed of over a billion kilometres per hour? Granted, this is a stupendously high speed to which nothing that we know of (apart from subatomic particles) can get close, but special relativity seems to be saying that the laws of nature forbid anything from going faster.

This is hard to stomach if you haven’t followed the logical steps and the careful experimental tests of Einstein’s relativity. I do not plan to go through the details but will instead try and give a flavour of why physicists are so confident that there is a universal speed limit. You see in a sense it is not light that is so special that it holds the speed record, but rather that way space and time themselves are intertwined in our universe implies that there is a maximum speed limit beyond which those laws of physics break down. In our universe this speed happens to be 299,792,458 metres per second, or 186,282 miles per second. Light, because it has no mass, is able to travel at this speed. In fact, in the vacuum of empty space, light is unable to speed up or slow down but is constrained to always move at this speed.

There are a number of ways to explain why the speed of light is the upper speed possible in our universe. One method is by using algebra. (Oh great, you’re thinking, that will really convince me; a load of equations full of Greek symbols is just what is needed to put my mind at rest.) I will not go into all the gory details. Suffice it to say that, in special relativity, speeds get added up in a very strange way.

It also turns out that the faster an object moves the heavier it becomes, and the harder it gets to make it go even faster. The closer it gets to the speed of light, the larger its momentum becomes, but this is by virtue of its increasing mass, not its velocity. Consider what happens to an object’s mass when it moves very fast. The single most important consequence of the equations of special relativity is how mass and energy are related. Einstein showed that mass can be converted into energy and vice versa. The two are related through the equation E=mc², which tells us how much energy is locked up in any given mass. The c stands for the speed of light, and thus the quantity c² (the speed of light times itself) is a very large number indeed and explains how we can get so much energy out of a small amount of mass. This equation suggests that that we can think of mass as frozen energy.

Since a moving object also has energy due its motion (called its kinetic energy), its total energy will be the sum of the energy frozen as mass when it is not moving plus its kinetic energy. The faster it moves the more energy it has. This means that the real mass of an object will be due to its frozen energy plus the energy due to its motion. Most of the time the frozen energy of an object (its mass) is so much more than the energy of its motion that we can ignore the latter and take the mass to be constant. But as the speed approaches that of light the kinetic energy becomes so great it can exceed the frozen energy. Thus the mass of a fast moving object is much greater than its mass when stationary.

You can now see the problem of trying to attain light speed. Imagine an accelerating train engine pulling a single carriage. What if, for every ten kilometres per hour faster that it goes, another carriage is added. It would therefore have to work harder just to maintain its speed. The faster it goes the more carriages it has to pull, and the more power it needs. In the same way, the faster a body moves the heavier it will seem, and the harder it will be to make it go any faster. To accelerate it up to the speed of light would require an infinite amount of energy, which is impossible.

Finally, the real real real clincher is this: If anything can travel faster than light in our frame of reference, then we will always be able to find another frame of reference (i.e. another perspective from someone moving relative to us) in which it will appear to be moving backwards in time. Remember of course that if Einstein is right then all frames of reference are equally valid (all motion is relative). In this new frame, causality is  violated – that is, causes have to come before their effects, otherwise we are left with a paradox. For instance, if A were to shoot B with a faster than light bullet, then it will appear to some observers as though the bullet is moving backwards from B to A’s gun. That is B is shot before A pulls the trigger, so he could decide not to after B is shot!!

See how crazy violation of causality is, and just how much this neutrino experiment needs to explain away???

Could Einstein have been wrong?

Ultimately, the speed of light being the maximum speed limit is written into the fabric of reality itself. But what if we’re wrong? Is there a way of understanding this result? The simple answer is that we cannot with our current theories and understanding. We would need to overhaul the whole of modern physics, and we would need to find a way of explaining away the thousands of other experiments that over the past century have all confirmed that nothing can go faster than light. We may have to bring back the aether, or modify Einstein’s equations. We would have to explain why no other neutrino experiment showed such a result, and why none of the trillions of neutrinos coming from supernovae manage to exceed light speed.

So, yes of course Einstein could be wrong. The whole point of a scientific theory is that it is there to be shot down – to be shown to be false by new experimental evidence or to be replaced with a better, more accurate or more profound theory that explains more about the universe. But… extraordinary claims require extraordinary evidence, and Einstein’s ideas have been checked too carefully for too long for one experiment to come along and destroy all that. But of course that is all it would take if this experiment is proved correct.

Nobel prize winner, Sheldon Glashow, together with Andrew Cohen have predicted that such faster-than-light neutrinos would have to be radiating electrons and their antiparticles, positrons, all along their route from CERN to Grand Sasso via a process called vacuum Cerenkov radiation and hence lose energy. This is not seen. It’s a bit like an aircraft that manages to break the sound barrier silently and without a sonic boom. It just isn’t possible folks.

So, what would it take for it to be possible. I reckon there are two possibilities (there are other more exotic ones that are rather too speculative):

a)     Einstein was wrong and there is an aether: technically, what is known as Lorentz invariance is violated here and there is a preferred frame of reference.

b)    Einstein was wrong and Lorentz invariance has to be modified: technically, there may be nonlinear correction terms in the mass-energy relation.

I am not prepared yet to buy into these, or notions of tachyons (hypothetical faster than light particles), or wormholes as shortcuts through space-time or replacing the electroweak theory, etc. All this technical hot air basically means I prefer to appeal for now to Occam’s razor and go for the simplest explanation: there is still an error in the experiment.

So what could be wrong with the experiment?

I should say that this experiment is a highly complex one and has been carried out with the utmost care and attention to detail. I am a theoretical physicist not an experimentalist so I certainly refuse to insult my colleagues at CERN and Grand Sasso by trying to point out where they may have gone wrong. They know where uncertainties still lie. So far, they have ruled out one potential source of systematic error.

Not all the scientists involved in the experiment wanted to sign the paper because they were themselves yet to be convinced. After this second check, four of the physicists who had not signed the paper in September now agreed to sign it, but four more who had signed the first one now asked for their names to be removed from the new one.

Having said this, here are a few potential problems:

1. The neutrinos are produced via a complex process: protons from the SPS at CERN are fired in pulses at a carbon target, producing new particles: pions and kaons, which decay to produce muons and neutrinos. The muons are stopped in detectors while the neutrinos continue on to Italy. The start of their journey time is itself not recorded directly but is started from the timing of the proton beam and so the long process has to be subtracted away from total time to leave just neutrino’s travel time.

2. At both ends there are complicated electronics that may contain tiny systematic timing errors.

3. The timing has to be done via GPS satellite. We know that GPS systems only work if we carefully take into account Einstein’s theory of relativity. It seems strange to me that Einstein’s equations (both special and general relativity) need to be taken into account to measure something that is proving them wrong. It just doesn’t make sense. In any case, the experimenters haven’t ruled out an error in the GPS relativistic timing.

What next?

The experiment needs to be re-run independently by other particle physics laboratories, and plans are currently underway for this to take place in Japan and the US, but it will take some months at least.

I am happy to eat my boxers on live TV. It would be a small price to pay for the thrill of so much new physics. But let’s not be too hasty just yet, eh?

In October of this year I start presenting a new science programme on BBC Radio 4. It will be on every Tuesday at 0900 – a fantastic slot just after the Today Programme. In fact, the hope is that this will become a long-running fixture on R4 with around 30 or so episodes a year, so that the Tuesday 9am slot becomes associated with it. Just think what else is on at that time throughout the week: on Monday it’s Start the Week, Wednesday it’s Midweek, Thursday is In Our Time and Friday it’s Desert Island Discs. Tuesday is the only day without a recognised fixture.

The new controller of Radio 4, Gwyneth Williams, has been absolutely key in getting this programme commissioned – well, she’s the boss, right? Anyway, what is so fantastic is that Gwyn is very keen to get more science on Radio 4 and for science to continue its rapid move into mainstream culture – for instance, The Infinite Monkey Cage, presented by Robin Ince and Brian Cox, recently won a Sony Award.

So, what will the programme be about and why do I need your help?

The first thing to say is that this will not be like In Our Time with Melvyn Bragg, nor will it be like Material World, the excellent science magazine programme presented by Quentin Cooper. We have already recorded two pilots for the new series, differing in format, so that the powers that be in the BBC can decide on the style, format and flavour of the programme. At the moment, a very rough way of explaining what it is about is that it is like Desert Island Discs, without the discs. Each week, I will be talking to a different prominent figure from the world of science (by which I mean ‘science’ in its broadest sense: natural science, maths, engineering, technology, medicine and social science). There wil be Nobel Prize winners, shakers and movers, advisers to governments, writers or just fascinating people who have made a contribution to our understanding of the Universe. So, whereas Kirsty Young might ask her guests on DID something like ‘tell me why you never got on with your father’, I might ask ‘tell me where you were when you first had that Eureka moment that led to your scientific breakthrough’, or some such thing.

So, here’s the thing: we still don’t have a title for the programme!

We have come up with ideas like ‘Latitude‘, ‘The Life Scientific’, ‘This Scientific Life‘, ‘Science Talk‘. I even suggested ‘Curious Minds‘ but it was pointed out to me that that is the strapline for the whole of Radio 4: “Radio for Curious Minds”. Although it would be kinda nice to have the programme title reflect so perfectly the ethos of the network.
So, ideas please: either below in comments or tweet them to me (@jimalkhalili) with the hashtag #radio4sciencetitle

I thank you.

P.S. Apparently I am not allowed to offer a prize if a title is used but I will certainly publicise who came up with it if you are happy for me to do so.

Oh, for heaven’s sake, here is a brief update on ‘wot I have been up to recently’.

Relaxing with my sketchpad while filming in Egypt

On Excess baggage this morning I talked about my journey and adventures around the Middle East making my not so recent Science and Islam series for BBC4, and which I found so valuable as part of my research for my very recent book, Pathfinders: The Golden Age of Arabic Science (‘plug’). I regretnownot telling my amusingly appropriate excess baggage anecdote. So here it is instead. After we finished filming in Iran, my film crew and I (OK, just me, my director, Tim, and cameraman, Andy) had paid the few hundred dollars for our excess baggage, consisting of box upon box of film kit, and were boarding at the gate for the flight out of Tehran, when we were stopped and informed that we had underpaid; we had thought it suspiciously cheap at the check-in desk. Now, we were told we could not board until we had settled up the extra twelve hundred dollars! Unfortunately, we were unable to pay by card and, between us, could only cobble together about seven hundred dollars.

So, here is where each of us reverted to type and tried a different approach. I whipped out my wallet, winked at the Iranian Airways agent at the gate and asked in my most reasonable ‘let’s sort this out quickly young man’ voice how much he would accept as a bribe to let us through. Tim, the director, tried appealing to his better nature by wringing his hands together, pleading and beseeching in his best ‘think about the children’ whiny voice; a voice, I might add, that he had been deploying with considerable success throughout our travels on airport security guards to ensure our film rushes avoided going through the security machines (not that they’d have been damaged, I am sure). Neither of our two approaches proved in the least bit effective on the chap at the departure gate now though. So, it fell to Andy the cameraman to offer a pragmatic solution. ‘Look’, he reasoned, ‘this is how much cash we have. Surely you can calculate what excess weight would have incurred exactly this amount. All you have to do is cross out the true weight and replace it with this reduced one and we can then pay you the correct amount’. Incredibly, this was deemed to be an excellent compromise and once a pocket calculator had been located and deployed, we were let through. Cameramen are so wise.

What have I been up to recently? Well, I am mostly through filming my new two-part series for BBC4 called “Everything and Nothing” (a sort of poor man’s version of Brian Cox’s forthcoming Wonders of the Universe). I am making it with the brilliant young director, Nic Stacey, who made my Secret Life of Chaos doc that came out earlier this year and which won an international science film prize in Athens a few months ago. Our new series is about cosmology, Einstein’s theories of relativity and quantum physics – everything from the Michelson and Morley experiment on the ether to the meaning of dark energy. So, while Brian gets to travel the world on a big budget production, I at least get the chance to explain the Lamb shift. How cool is that! I mean, for fuck’s sake, I describe quantum electrodynamics on TV, the sort of stuff I wouldn’t even cover in an undergraduate physics degree. Thank you BBC4. I am also hoping to be able to at last explain the meaning of the Dirac equation beyond just its aesthetic mathematical beauty.

As soon as I finish filming on E&N, I pretty much jump straight into my next TV project, another BBC4 series (this time, a three-parter) called The Story of Electricity, which I am really looking forward to. That will happen throughout Feb-May and has to be fitted around my university duties, mainly teaching my final year course on complex variable theory. I am also pretty excited about being one of the judges on the 2011 Art Fund Prize, the UK’s biggest arts award (£100,000 to the best museum or art gallery). I am the token scientist on a judging panel chaired by Michael Portillo and I follow in the footsteps of Marcus du Sautoy and Steve Jones.

Interviewing Dr Rowan Williams at the University of Surrey in March

Looking back over 2010 though I think I can feel pretty pleased. After an incredibly difficult 2009 for personal reasons, I don’t think I could have crammed much more into this year: Desert Island Discs, a Bafta nomination for my Chemistry series, the five part C4 series, Genius of Britain, getting to introduce Stephen Hawking at the Royal Albert Hall, interviewing David Attenborough and the Archbishop of Canterbury (not at the same time), filmed cameo appearances (for 2011 transmission) on Horizon with Ben Miller and in the finals of Masterchef, and last but by no means least, the publication of my new book, Pathfinders.

With Sir David Attenborough in October at Surrey University.

Three years in the writing, I have to say I am immensely proud of it. It has received some very nice reviews, particularly from academic historians, which is very gratifying considering I have tried to aim it at as broad a readership as possible by make it entertaining as well as both historically and scientifically accurate. It is already being translated into eight languages and the US edition comes out in March, then the paperback in the UK later in 2011.

With Julie at the Great Wall of China while on a recent visit to Beijing.

As the year draws to a close, I am looking forward now to a couple of weeks off with the faaaamly (Eastenders voice please). I’ll be making my traditional coffee fudge again (having almost perfected it last Christmas after 24 years of failed attempts), playing my guitar, eating, watching lots of telly, eating, drinking, eating, thinking about an outline for my new book (still a secret for now), eating, possibly visiting friends in Macclesfield, drinking and eating with them, then back down to Portsmouth for a New Year’s Eve murder mystery party, no doubt with more eating and drinking.

I had been sent a transcript of Stephen’s lecture in advance, along with some briefing notes on the usual welcoming remarks and who I should thank at the finish, and a list of questions he had chosen from amongst the many sent in by readers of the Times Eureka magazine who were supporting the event, along with his answers. I just needed to think about some witty ad-lib remarks to make me sound cool. I felt as though I needed to seize the moment and break into song or do a bit of a stand-up routine.

Anyway, I was very excited. Now, I should say that I wasn’t in the best shape on Wednesday. I had just flown back in from Qatar that morning, having managed less than two hours sleep on a turbulent overnight flight, then I had to give a schools lecture at University College London just a couple of hours before the Hawking event. This was a talk I had agreed to do a while back and didn’t want to pull out of it once the Albert Hall gig came up. I was out of there at 7 p.m. and we (my wife Julie was with me) had a car waiting outside to whisk us off to Kensington. The thousands of people converging on the venue swelled the traffic considerably and it took rather longer than anticipated to get there. When we finally arrived we went in through the Stage Door at the back and met up with the other guests and VIPs in the Green Room.

I had been at other events with Stephen on several occasions in the past (the first time at a Buckingham Palace reception celebrating British science and, more recently, at the launch event of our Channel 4 series which we had co-presented, along with the likes of Richard Dawkins and  Robert Winston) but I had never had the opportunity to talk to him. So this time I was determined to go over and chat to him; after all, we were about to be sharing the stage. I pushed my way through the crowded room to where he was sitting in the corner, being fussed over by his nurse. She told me to come round the other side of his chair so he could see me a little better. I immediately started to gabble on  about how nice it was to finally get the chance to talk to him and how I hadn’t been able to do so at the our channel 4 series launch. Stephen smiled and and his features twitched as I spoke. I didn’t want to put him in the position of having to compose yes/no answers through his computer synthesised voice. When I finally came up for air his nurse said: “you do know how Stephen communicates, don’t you? He raises his eyebrows for ‘yes’ and twitches his mouth for ‘no’. There was a mixture of ‘yes’s and ‘no’s in there while you were talking.” Ah, now she tells me. Oh well, I apologised to him, but I am sure he is used to it. Anyway, guess what my parting comment was as I left him to do my sound check: I said: “Break a leg, Stephen!” “Oh, don’t tempt fate”, said his nurse, possibly not understanding the terminology used by us thespians, “I might accidently push him off stage and that might really happen!” I didn’t hang around for Stephen’s reaction.

As the time to take the stage approached I ran through in my head what extra things I might say to supplement the brief script I had been given. I had heard that Cliff Richard had been performing at the Albert Hall all of the previous week. Good, that would give me something amusing to mention. I already had something to say that I hoped would elevate my presence on stage from mere compere to warm-up act! I had been in email correspondence with Hawking through his PA and had asked him about his lecture and whether he was planning on talking about his pronouncements about the non-existence of God, which had hit the headlines a few weeks earlier. He asked if I would maybe say a few words making his position clear on the issue, so that he would be free to focus on the subject of his lecture: his life, career and the physics he had helped develop. This I was more than happy to do. I agreed to make the following statement: Stephen Hawking never claimed that God doesn’t exist. To him, and this is a view I share, God is the name people give to the reason we are here. For him, that reason is the laws of physics (or the laws of Nature), rather than a supernatural power with whom one can have a personal relationship.

After my introduction, I stepped aside and Stephen began his lecture. What followed was a remarkable eighty minutes or so – not so much because of what he said, but because a five thousand-strong lay audience sat mesmerised by a lecture about imaginary time, space-time singularities and multidimensional unified theories. They couldn’t have followed most of it, but that’s the Hawking effect for you. For the same reason millions buy his books, this audience was happy just being in the presence of this remarkable man. In any case, the lecture was in fact hugely insightful, touching and fascinating.

After he finished I had to go back on stage to read out the few submitted questions. However, I was aware that he would need a minute or two to bring up his answers on his computer. His nurse, who came up on stage with me, said she would give me a signal when he was ready and would I fill in the time by saying something. OK.. good.. I said I would tell a joke. Then, at the last minute, I decided instead to tell my ‘Hawking story’. Here’s how it goes: many years ago, I attended a lecture at Cambridge given jointly by Stephen and his long-time collaborator, the mathematical physicist Roger Penrose. It was the fifth and last in a series of talks they had given alternately throughout the week. I had decided to attend only this the final lecture. At the end, the chairman asked if there were any questions from the large public audience. I was sitting near the back but my arm shot up faster than anyone else’s and I was immediately spotted and invited to stand up and ask Stephen Hawking my question. I don’t remember exactly what it was – something about the entropy of a black hole I think. Anyway, I wasn’t particularly interested in the answer as it was more about wanting to sound clever and to say that I had asked Stephen Hawking a question! Anyway, as soon as I had asked it I realised that, as the first questioner and not having attended any of the previous talks, I wasn’t sure what the convention was: do I remain standing while Stephen composed his answer or do I sit back down? I chose to just stand there, feeling and looking awkward. After what seemed like an eternity, Hawking computer voice burst into life: “Yes”, he said. “I covered that in lecture 2″. I wanted the ground to swallow me up.

Anyway, I told this story at the Albert Hall and the crowd seemed to enjoy it, as I hope Stephen did.

I got the nod from his nurse, asked the questions, Stephen answered them. The crowd cheered again and everyone left happy. I am expecting to be invited back soon to do a gig there, maybe a Royal Variety Act, conduct on the Last Night of the Proms or share the stage with Robbie. Or maybe Sir Cliff will invite me to do a duet….

Yet at the same time, my own career is going rather well thank you very much. I am writing this blog while travelling down from Leeds to London Kings Cross, returning from the Ilkley literature Festival where I gave a talk on my new book, Pathfinders. I had a sell-out audience of about a hundred and fifty people, in a charming venue called The Playhouse, who were on the whole very appreciative (I did have to crank up the charisma dial to its syrupy max to placate a young Muslim woman over my comments that the veil and hijab were in my view relatively recent cultural rather than religious requirements in the Muslim world).

Apart from this far from onerous[1] speaking engagement, my wife Julie and I spent the weekend walking the Moors, eating excellent food (we strongly recommend, if you’re ever in Ilkley, the Wheatley Arms’ Sunday roast) and attending the odd event elsewhere at the Festival. Aleksei Sayle was in excellent form on Sunday evening, and since he was staying in the same hotel as us, we considered hanging around in the bar after his talk to meet him when he got back. Our paths had crossed just once before when, earlier this year we had both been invited to say a few words at the launch of Simon Singh’s libel reform campaign where there had been a mixture of scientists and comedians in attendance, with the likes of me, Richard Wiseman and A.C. Grayling sharing the floor with Aleksei, Dara O’Briain, Dave Gorman and Robin Ince. Anyway, I didn’t end up meeting him again in Ilkley as our hike across the Moors that morning meant we were pretty much done in and so we went up to bed after the one drink.

So yes, my career is in pretty good shape at the moment, with a new book out, half-way through filming a two-part series on modern physics (working title: “Everything and Nothing”) for BBC4, another three-parter commissioned (The Story of Electricity) also for BBC4, due to start production in a couple of months, a radio series for the World Service on nuclear power for early next year, and a whole range of interesting public events, as well as my teaching duties (two undergraduate courses) and research programmes in nuclear theory and quantum biology, on the whole I’d say that my cup runneth over.

Within the space of one week I’ll be sharing the stage with two of the most famous names in science: Stephen Hawking and David Attenborough. Next week, on the evening of the 20th October, I am introducing Stephen at the Royal Albert Hall, where he will be giving a rare lecture on his new book, The Grand Design. There will be a sell-out crowd of five and a half thousand people who have paid handsome prices for tickets (although they do get a copy of his book on arrival). Although my role is mainly to welcome everyone and introduce Stephen, he has asked me to lay to rest the recent furore in the media over his ‘we have no need for God’ comments. I am more than happy to do this as I am familiar with his views and quite understand that he would rather concentrate in his lecture on his thoughts about the nature of the Universe and how close he believes we are to a ‘theory of everything’.

Then, on the following Wednesday evening, I am interviewing the great Sir David Attenborough at the University of Surrey in front of a live audience of around 600 staff, students and members of the pubic. This is part of a regular series of such events called “Jim meets…” during which I chat to major figures in public life about their careers and lives. With Lord Robert Winston and the Archbishop of Canterbury safely ‘met’, I am hugely excited about chatting to David, who is a big hero of mine. Next year, I have Brian Cox and Dara O’Briain lined up.

The only complaint I have, if indeed I am in any position to gripe, is that my schedule in the run-up to Christmas is rather hectic. In the space of six weeks or so I have lined up trips to Qatar, Dresden, Hong Kong, Beijing and New York. Fitting these in during term time has been tough as I do not want to be rearranging too many of my lectures or leave my PhD students stranded for more than week or two at a time. Luckily, neglecting the family is not such a problem any more. Julie is able to travel with me when possible now, David is already settled into university life at Southampton, and Kate, having started her A-levels, seems to have matured into an independent young lady (who has in any case long since got used to my not being around for chunks of time).

I guess what most excites me at the moment is my book coming out last week. Positive reviews in the Times, Telegraph and Observer and Scotsman have appeared and I hope more will follow. The subject of my book, medieval Arabic science, has been a passion for past few years and I am immensely proud of the final product. It’s not up there yet in any best-sellers list but, hey, early days, and one can dream, surely? Actually, all the signs are good: it is already being translated into eight languages – deals that were secured before I had even finished writing. And if the audience at Ilkley is anything to go by, I’d like to think people will find it as fascinating a subject as I do.

Coming up though is next Wednesday. Let’s hope the announcement of the spending cuts doesn’t put too big a dampener on the Royal Albert Hall event with Hawking that evening – interesting times indeed.

By 1927, quantum mechanics was developing along two separate lines. On the one hand, Erwin Schrödinger had come up with a wave theory to describe quantum entities like electrons, describing them not as tiny particles but as waves of pure energy. At the same time, Werner Heisenberg was working with abstract mathematics and had developed a theory based on matrices (basically arrays of numbers). But it was Paul Dirac who saw how to combine these two approaches: Schrödinger’s waves and Heisenberg’s mathematical matrices. But his real motives were different.

You see all this was just a couple of decades after Einstein’s work on relativity theory in which he had shown than when a body moves at close to the speed of light, the rules of the game change. And the only way to describe such a fast moving object properly was to unify the three dimensions of space with the one dimension of time into what is called 4-D space-time.

So, we have the Schrödinger and Heisenberg who could to describe how subatomic entities like electrons move and behave and interact, and we have Einstein’s relativity theory to describe what happens when objects move very fast. BUT… what if it is an electron that is moving very fast? Dirac knew he needed to combine quantum mechanics with relativity. What we say is that he was looking for a relativistic quantum theory. In early 1928, Dirac published his relativistically invariant equation for the electron. What he did was unify If we ignore relativity, then quantum mechanics is described by the Schrödinger equation. Here the energy (E) of a free particle (one just plodding along minding its own business and not under the influence of any force) is related to its momentum via the relation: energy equals the square of momentum divided by twice the mass (E=p²/2m). But Dirac wanted to describe what happens if a particle like an electron moved very fast, close to the speed of light. It is here that we have to take Special Relativity into account. According to Einstein, the total energy of the electron is now related to its momentum in a more complicated way, because we also have to consider the energy frozen in the electron as its mass (the famous mc² bit). And the awkwardness is that the total energy is not just the sum of the old expression and this mc², but comes in as the sum of their squares, namely: E² = (mc²)² + (pc)². If you can remember school geometry then this is similar to Pythagoras’ theorem whereby the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. So, why is this so awkward?