Season's Greetings

A rant, just in time for the 'Festive Season.'

Autumn is often regarded as the most emotive of seasons. The bright glory of lazy summer days or the high activity of holidays in the resplendent sunshine give way to the fading grandeur of woodland in a gaudy yet decaying plumage. It is with a feeling of being reconciled that the year is coming to an end. Yes, Autumn is a season of resigned calm. This is what autumn does to us writers and poets.

Not so, the season of Winter. Winter is an ugly beast that chillingly wants to suck on the marrow of our bones. But there is a most hideous evil at the heart of Winter! I speak openly of none other than the abomination that is called: "Christmas."

Everyone knows that Christmas is bad for you. Normally sensible people who diligently handle their financial affairs suddenly lose all sense of reason and blow every penny. People binge openly. Habitually-temperate individuals are to be seen as drunk as a lecturer with a pay rise, or a poet with any pay at all. Alcohol intake soars, tobacco, otherwise eschewed, is suddenly fashionable, as cigars light up like bonfires, food is gobbled in vast quantities as diets are cast aside, waistlines bulge, five a day comes to mean "meals," rather than "portions of vegetables." Promiscuity is encouraged, with sinister rituals dragged up from antiquity involving sprigs of plants such as mistletoe. Never mind how many children are conceived outside wedlock during this period, the number who start life outside any kind of enduring relationship must be staggering. All the more frightening is proportion where the act of conception has been captured for posterity on a photocopier at office parties.

And then there’s the lies to the children. How many children are dumb enough to believe a fat interloper in a conspicuous costume but with his hooded face covered can enter umpteen different properties all around the globe simultaneously though an antiquated and indeed often non-existent heating system? And then just give things away for nothing in return, no favours of any kind. The fat guy and the sleigh, all the supernatural creatures and the cloven-footed animals with illuminating body parts, it is revealed as the children get older, were invented, and used as a form of behavioural modification blackmail as the year’s end approached. Trust you parents after that? Why should you? They’ll say rubbing belly-buttons makes babies next!

Then there’s the extended family and the problems Christmastime entails. Families are extended for a reason – the reason is they can’t stand being near each other and want to put as much distance between who they share a blood line with. Blood is thicker than water and it usually ends up spilled on the carpet. Families getting together is the biggest cause of family breakdown in the world today. This is not rocket science – they couldn’t break down if they weren’t brought together in a supercritical mass in the first place, could they. It’s a sociological atom bomb waiting to go off.

While all that’s going on, there are questions about the damage inflicted on commerce and industrial activity. Whole industries close down while others, briefly, like fungus, spring up in their place. Just when they are needed most, in what should be their money-making peak of the year, plumbers and electricians disappear. And not only does God not exist, try finding a doctor or dentist at Christmas. Absenteeism is so rife, some companies can’t even tell whether they are actually still operating any longer or have gone into receivership. From the customers’ point of view, as far as public transport is concerned, it may as well have done so. "How was your journey then?" "How do you bloody think it was? No wonder Joseph and Mary had to stay in a stable – we nearly had to break our trip at a bloody Travelodge!"

Almost the ultimate indignity is yet to come. This is referred to as The Christmas Number One. For music-lovers everywhere, this alone is justification to stick a pencil into each ear and swirl it around until you stop moving. (A similar phenomenon with the eye is to be encountered when you are forced by some niece you have discovered makes you watch a DVD of Dude Where’s My Car? or Weekend at Bernie’s II. While on the TV, just to get you in the Christmas mood, there’s Saving Private Ryan followed by Schindler’s List.)

Christmas is as desperate as a famine inside a war inside a plague. Finally there is the social cost. This is best illustrated by the colossal, soul-crushing feeling of desperation when you find that you are actually left out of the festivities, that you have no cringe-inducing parties to attend, no visitors nor people to visit, no presents, no cards and only the wallpaper for company. As if to rub salt in the wound, the televisions companies have started to pick up on this and just as you are sitting through your umpteenth viewing of North By Northwest they spray across the screen a phone number you can call "if you’d like to talk to someone." How would you start such a conversation? "I’m such a Billy-No-Mates, I was going to slash my wrists but I can’t find the kitchen knife so I thought I would call you, you self-pious, do-gooding little bastard."

Christmas begins to blight us now from the beginning of September along with the anniversary of the start of World War II – a re-enactment of the Somme artillery barrage rumbles on from mid October till advent calendars come into use. Then New Year (why does the Year of Our Lord start seven days after the anniversary of His arrival – did someone forget to post the birth announcement? Had they been sniffing too much myrrh to remember till a week later? "Messiah arrived – must make a note." Then it’s back to work, just preceded by carting car-loads of wrapping paper, greetings cards, the odd dodgy present and possibly the odd clingy relative, to the recycling centre, staggering credit car bills or mind-numbing overdrafts until the final embarrassment of St Valentine’s Day. At last, you can remind yourself, Summer is now not far off, once you’ve got past Easter.

Then you’ve got about six months before the whole ghastly spectacle begins all over again. Let nothing you dismay, you merry gentlemen! God rest ye!

The End (-ish)

The Road To Perdition

What might happen if you let students - an intemperate bunch at best by all accounts - to throw a party behind the students union bar. Nostalgia about what might have happened afterwards

"Where does this road go?"

"It doesn’t go anywhere – it’s stationary."

"Stationery!" I said in mock surprise, at an attempt of surreal humour. "You mean it’s made of paper? It’ll collapse into the Bristol Channel!"

"It’s stood here for years," said Tariq. "Solid as a rock." All night he’d adopted this insouciant tone. At first it had seemed hilarious. Then funny. Then slightly amusing. Now, in the grey morning, it was getting just a tad irritating. This may have been in inverse proportion to how sober I was. "What’s to stop a big gust of wind blowing us off this bridge and into the water, dozens of feet –"

" – hundreds of feet – " He corrected.

" – hundreds of feet below?"

"Well, there’s that railing there."

"Then what?"

"Nothing."

"Nothing?"

"Absolutely nothing."

"Would the authorities come and rescue us?" I pressed the point.

"God, no."

"Why not?"

"Well… if they’d seen us here at all, they’d have come and arrested us for trespass."

"But that’s still no reason not to rescue us."

"It is, if you think about it," Tariq reasoned, reasonably. "You see, if they’d not seen us to arrest us, they’d can’t have seen us to rescue us, can they? Besides…"

"Besides – what?"

"Besides, the fall would kill you, and even if it didn’t, you would drown in the current. If the hypothermia didn’t get you first. So it’d hardly be worth their bother."

I digested this. We’d been walking for about half an hour on the path-and-cycle-way that ran alongside the elevated approach to the Severn Bridge. This, Tariq had informed me, was a cantilevered path. I looked up ‘cantilever’ much later, and it said: "A cantilever is a beam anchored at one end and projecting into space." I could aver that this was true. The path was "temporarily closed for safety reasons" with a small barrier but we’d scrambled over that. We were now barely out over the water and hadn’t even reached the huge concrete structure, the size of a large block of flats, into which the suspension cables were anchored. There was absolutely no cover of any kind and we would have been clearly visible for miles to anyone who’d cared to look.

"Well I’d hate to put them out, if they’re so busy not seeing trespassers and all. I mean we’re hardly hidden from view." Even to myself I was beginning to sound a little grumpy.

"No, but we are a long way off. That’s probably why they haven’t seen us." Tariq still seemed as chipper as ever. "That and the fact that no-one in his right mind normally crosses on foot."

"Tariq, exactly why are we crossing the Bristol Channel by suspension bridge on foot at nine o’clock in the morning."

"Ah. You do you remember last night?"

"Which bits?"

"The later bits."

"The bar-staff party."

"And afterwards?"

"Nope." I strained to recall something. Something that might have been important, the sort of thing that explained why I was here now doing this thing. "Not really. Little bits. The bar closed. We tidied up in twenty minutes and that left us forty minutes in which to cram an entire party evening’s drinking, before the Students’ Union building shut and we all got slung out. We started drinking and… I don’t think I remember anything after that."

"The people all lying around on the grass?"

"Not really. Were they drunk?"

"It was hard to tell. They were all unconscious." Tariq seemed remarkably unconcerned about this, much as he was about everything else.

"Don’t you think they might have been drunk before they became unconscious?" I asked.

"Oh, yes. Let’s face it, everyone was drunk. In fact, every thing was drunk by the time we were thrown out."

"Why weren’t we unconscious?"

"Must have been down to our robust constitutions," Tariq grinned. "Anyway, that’s when I suggested that we go down to Keele motorway services and hitch a ride with the first truck-driver who’d give us a lift."

"You did what?" I’m not sure how much I was surprised, feigning outrage, or genuinely outraged. "Why couldn’t I have just been unconscious like everybody else?

"You said you thought it was a good idea."

"I said that? Why didn’t you disagree with me?"

"I thought it was a good idea, too. After all, it had been my idea. So that’s what we did. You insisted on going back to your room first for some reason, then we set off."

"You can’t just hitch-hike away from a hangover."

"Oh no? Look at you now? Up, fresh as a daisy, out in the bracing open air. Imagine all those others – just waking up with their heads throbbing. Have you got a hangover?"

He had a point. But so did I. "No – but I’m nearly getting my tits blown off in this ‘bracing air’!"

"So it wasn’t such a bad idea."

"But… but how? What happened?"

"We got a lift to Aust Services back there and the driver said he was having a stop-over, so we said we’d walk."

"But why are we crossing the River Severn bridge on a pathway closed to the public?" I persisted.

"Because it’s there!"

"But we don’t have to be!"

"And to get to the other side, of course."

"Of course. How silly of me."

"Because, on the other side is where my uncle lives. He owns a pub in Caerleon. The Red Lion. Or the White Lion, I’m not sure which. But I’m sure we’ll find it. And he can give us a lift back to Keele."

I was starting to worry that this was actually making some kind of sense, when it shouldn’t. "Tariq, don’t take this personally, but you’re, sort of, of a dusky Asian hue and you’re from Bolton. How come you’ve got an uncle who owns a pub in south Wales?"

"What’s wrong with that? I’m a good barman back at the Students’ Union, aren’t I? Serving booze to white folks runs in our family."

"I suppose you’ve got a point. How far is it to Caerleon?"

"Oo… only a few minutes’ walk. We’ll soon be there."

"Tariq, we’ve been walking for hours and we’re not even half way across and I can barely see land in either direction."

"It’s just a trick of perspective. The bridge is only a couple of miles long – at most – including the approach sections.

"Then – how far to Caerleon?"

"Not far. Only about 15 miles."

"Only!…"

"There’s two things to keep in mind. Firstly, don’t look down."

I looked down. We appeared to be walking on thin steel plate. Well, it looked like steel plate. Its apparent thinness was revealed because at frequent if irregular intervals there were holes right through the metal, for no readily apparent reason, about the diameter of a ten pence piece, revealing the steel to about the thickness of a ten pence piece. Clearly visible below that, about as far down as a ten storey building, curling, twisting brown waves, like a pit of vipers, wriggled, waiting with waning patience for their prey to fall amongst them.

"What was the second thing?" I croaked.

"We’ll be alright, just so long as we don’t hit a spot of bad weather."



We reached about half-way across the bridge, and became the centre of a sphere of air, sky and water, with just a puny piece of engineering to indicate Man’s existence. At that point, some weather – a spot, bad – blew in from the general direction of America, and it seemed to be in a hurry. The metal at our feet was matched by the metal sky overhead, and the metal water below disappeared from view as we became entombed in a racing ball of cloud. Every step we took seemed to turn us sideways. To have jumped up, losing contact with the armour-like decking, would have been suicidal.

Then the rain came in. To call it rain was a bit of a liberty, insofar as the only resemblance this phenomenon had to rain was that it was wet. Horizontal spears of water daggered into us, making us yelp. But this was just the beginning. We started to realise we might be in serious trouble when it became unwise even to lift one foot off the slicked surface, and we attempted a cross-country skiing movement. Progress went from slow to slower. Then, as the bullet rods and hydro-tracer puckered and cratered my denim jacket, making it dark as though stained with blood, we fell to our knees. As an afterthought, we decided to lie down altogether and time froze – as, indeed, did we – until the venom of the elements subsided once more. Eventually, the wind lessened, we got to our feet and we plodded on in what was to me a bubble of misery.

Long after we were no longer over the waters of the Bristol Channel, the road continued in an elevated arc round to the west parallel to the bum of Wales. Hours seemed to drag past. Eventually road met land, and we were able to get off the motorway and walk on the grass embankment alongside. Caerleon, whatever it was like, still did not hove into view. I was not sure how it would appear but I was imagining something like Valhalla. The morning grew old and tired.

At long last, we crossed under the motorway to get on its northern side and approached a motley collection of buildings. This was Caerleon. This was Caerleon? It was, probably, quite a pleasant village – it even had some Roman remains somewhere, to which some human remains were in danger of being added – mine – but it was hard to appreciate under the circumstances. Its one merit was that it contained a public house where we could find shelter, rest, food and, most importantly, transport to take us back to the home whence we’d so pointlessly come.

It took some time for Tariq to identify the correct pub. It turned out that Caerleon, with a population of just two thousand souls, had twelve of the establishments. The one we wanted was in fact called The Black Bull – Tariq had been close, apart from an appalling lack of awareness of colour and zoology.

The only thing was, we were too early and the place was still shut.

We had nowhere left to go.

All we could do was wait for his relatives to wake, open up, let us in and take us back to the little student residence blocks we called home.

"Drink has driven me to this," I exhaled, and, exhausted, slid to the ground, where fatigue enveloped me like a foggy pall, and I sank from the conscious world.



When I finally saw my room again, many, many hours later, several things argued for my attention. Firstly, not only was the door unlocked, but it was slightly open. Secondly, the light was left on. Thirdly, an empty vodka bottle was embedded, neck first, into the wall plaster. It came back to me. I had taken this bottle back to my room "for later," but having got there, I had drained the last of its contents then flamboyantly thrown it at the wall, as if completing some dramatic toast. To my befuddled amazement, it hadn’t shattered and I hadn’t the heart to attempt to heap further injury upon it.

And that was how, for me, the one and only Keele University Students’ Union bar-staff party ended.

The End

The Twins Paradox

Non-fiction about one aspect of Special Relativity

The other day somebody sent me a recording of the play, Insignificance, by Terry Johnson, made into a radio production. In it, at one point, a character – who happens to resemble Marilyn Monroe – explains – to a character resembling Albert Einstein – parts both of Einstein’s theory of Special Relativity and General Relativity. In particular, she refers to something known as The Twins Paradox and adds that Special Relativity is inadequate to explain how it works, and that the General Theory is required.

I will not digress to comment here on a play where characters resembling Marilyn Monroe and Albert Einstein discuss Relativity (not to mention that characters resembling Joe DiMaggio and Senator MacCarthy show up) nor ponder why the play is called Insignificance. However, I will state here and now quite categorically that you do not need General Relativity to explain The Twins Paradox and that the Special Theory is perfectly adequate. Indeed, using the General Theory would probably mess up your answer while the Special Theory gives you the right answer. What’s more, I’ll show what that answer is and prove it is right!

And no maths.

(Just a tiny bit of arithmetic, and you can even skip that.)

So what’s all the fuss about? Well, it gives an opportunity to look into what Relativity really means and hopefully make it a bit more easy to understand for more people. I’ll show you don’t have to be a maths genius to understand it too.

Why Two Theories?

Just to explain, for the moment, why there are two theories of Relativity – or, more accurately, two parts – Relativity is all about things moving. It concerns the speeds of things. The word "velocity" is sometimes used in place of speed (in physics, "velocity" has a more precise meaning.) But, for simplicity, I have used the word "speed" most of the time to help keep things clear and used the words physicists prefer when it matters. For the moment, what you need to know is that Special Relativity deals with constant speed while General Relativity is about changing speed, going faster or slower. This is not just playing with words – if you were moving at constant speed smoothly enough – on a train or a plane, for example – you might feel as if you were standing still. If you were on a train, plane or anything else that was speeding up or slowing down, you would always know that you were moving. This difference is vitally important. There will be more about this later.

I have used the word "mass," as preferred by physicists, in place of "weight," just to keep the physicists happy. But they mean almost the same thing.

Einstein was probably the most famous physicist – indeed the most famous scientist – of the 20th century. His face is instantly recognisable in any picture even today, and, as most people are aware, his work led to the development of atomic energy and the atomic bomb (though he emphatically did not work on the atomic bomb himself, as he was a pacifist.) His work also explains how stars burn (though I won’t be going into that here.)

Not surprisingly, Einstein won a Nobel prize for physics. More surprisingly (and quite unfairly, in my view) he did not win it for either versions of his theory of Relativity, but for a piece of work that led to an area of physics called Quantum Mechanics, which a lot of people have never even heard of (although I talk about some bits of it in other articles on this website.)

(His work could also have saved someone from committing suicide, but alas this tragedy was not averted – the news of yet another discovery by Einstein that proved the existence of atoms did not reach, as far as we know, the ears of Ludwig Boltzmann, also a brilliant physicist who worked on a theory of atoms. Boltzmann suffered from manic-depression, it is believed, and was sometimes ridiculed by other physicists. With no proof that he was in fact right, he killed himself a year after Einstein’s proof might have lifted his mood and saved him.)

So what is all this theory of Relativity about then? I’ll try to keep this brief, but if you’ve already had an introduction to this subject, concerning the speed of light, you may want to skip this altogether and get straight to The Twins Paradox.

Light Speed

It had been known for some time that light had a finite speed, although a very great one. Sir Isaac Newton did some work on light (also discussed elsewhere on this website) but he did not, as far as I am aware, investigate what the speed of light might be. He may have been hampered by the absence of telescopes and very accurate clocks during his lifetime, though Newton was such a clever-clogs he probably could have got round this, if he’d set his mind to it.

By the nineteenth century, all the necessary equipment was available. It was still no mean feat to measure something so fast. A man named Albert Michelson came up with a clever method which I will sketch out here. Imagine light from a lamp focussed to shine off a flat mirror to another mirror some distance away – a distance we have measured with extreme precision. The light reflects back to the first mirror and then back to the experimenter with his face just above the lamp. You can see that a bright lamp and a telescope would be quite handy for doing all this. Now, if the first mirror is in fact mounted on the edge of a wheel that is made to turn after a flash from the lamp has reflected off it, the returning flash will no longer be visible to the experimenter – the mirror will now be turned to the wrong angle.

To get round this (literally) how about covering the rim of the wheel with a series of mirrors all placed at precise angles, and spinning the wheel? If the wheel is going fast enough, by the time the flash of light gets back from the second mirror in the distance, another mirror on the wheel will have moved into just the right position for reflecting the light back to the experimenter – he will see the reflected lamp again!

All you need to do is have enough mirrors on the wheel, and spin the wheel fast enough to make this work. And if you know how fast the wheel is spinning (and, as I said before, the exact distance to the far mirror) you can get an exact measure for the speed of light, because you know how long it takes the wheel to turn one mirror’s-worth and therefore how long it takes the light to cover the distance. Nice and simple (and I’ve not used any maths to explain this, notice.)

For a moment we need to consider what speed is. Well, obviously, it’s distance covered in a certain amount of time. If only things would stay that simple.

Let’s think about two cars colliding – fun, I know, providing no-one gets hurt, but who said this couldn’t be fun? If a car runs into a brick wall at 60 miles an hour it hits the wall with a speed of – d’ur! – 60 miles an hour. If it runs into a car driving towards it at 59 miles an hour, the speed of the collision is 119 miles an hour. This seems obvious – we just add up the two speeds. (This is about as hard as the maths gets in this writing so I hope you are keeping up.)

However, if the second car was driving away at 59 miles an hour, the collision would be just 1 mile an hour. Simple.

(Only – it isn’t. For reasons I’m not going to go into here, combination of velocities is not determined by addition of velocities, but don’t worry about it – addition is good enough for speeds much slower than the speed of light, and we will not be looking at faster collisions.)

Another, less obvious thing is that there is no such thing as the speed of something on its own. The speed has to be relative to something else. For cars, this is usually the ground. The important thing is that you have to have two things moving relative to one another to have a value for speed. It’s more obvious if you talk about rate of change of distance between two things, if a bit clumsy. You simply cannot have rate of change of distance between something and nothing else. (It’s a bit like the sound of one hand clapping… but we won’t go into that!)

Now back to the speed of light. From what I’ve just said, if we are moving towards or away from a lamp flashing at us, we ought to get different answers for the speed of light. Also, there are other ways in which we should be able to alter the answer, by shifting the whole experiment about. The thing is, when Michelson tried doing tricks like this, he didn’t get any variation in the value for the speed of light. He always got exactly the same answer! This should be impossible. But what turns out to be impossible is to get the speed of light ever to change!

Various means were used to attempt to explain this. One by one, however, they didn’t work.

Speed Invariance, and Special Relativity

Meanwhile, along comes Einstein. He didn’t worry about how or why the speed of light was fixed. He simply accepted that it never changes, and that was that. He never liked the name ‘theory of Relativity’ for his theory – he wanted to call it the ‘theory of invariance.’

The thing is, if light never changes its speed, you’ve got to fiddle around with other mathematics in order to get the sums to add up. In fact, the maths is not difficult, it’s just that what the answers mean sounds a bit weird. But here we go.

Imagine you are sat still in a room, wearing a watch. On the mantle-shelf stands a clock. As your watch ticks, so does the clock. Time seems to go at the same rate everywhere.

Now we will need a bit more arithmetic here. To make things easier, let’s imagine that light-speed is 10 centimetres per second. (It’s a lot faster, but using made-up figures makes it easier to see what’s going on and, apart from the values, doesn’t have any effect on reality.)

Suppose the clock now began to slide smoothly across the mantle-shelf towards you at one centimetre per second (never mind what’s making it move.) A flash of light comes from behind the clock, passes it and on to you. In one second the light would go 10 centimetres. But if you measured how far the light had gone past the clock, using the clock’s time-keeping and measure of distance, it would only have gone 9 centimetres. If you used the moving clock to measure the speed of light, you would get only 9 centimetres per second – which is the wrong answer!

It’s easy to get back to the right answer (though you have to ignore how weird the answer seems to be.) All you have to do is have the moving clock run more slowly. By stretching out a second on the moving clock, light again travels 10 centimetres in one clock-second.

A similar correction works for any other speed.

This is the first bit of Special Relativity – time goes more slowly, relative to someone watching, for moving objects. It has to, in order to get the speed of light to be constant.

However, if you were moving with the object, you’d notice no difference.

How about – instead of using the clock’s timing, we used the thickness of the clock to measure the distance light travels in one second? If the clock was itself 10 centimetres thick and it was moving at 1 centimetre per second, in one second the light would appear to move 9 centimetres past the clock in travelling from the back to the front. Again, the wrong answer. Again, it is easily fixed, mathematically. We just say that the clock gets thinner in its direction of travel when it is moving. Once again, we get that light takes one second to move from the back to the front of the clock because the clock, while moving at one centimetre per second, is only 9 centimetres thick, from our point of view, giving a light-speed of 10 clock-centimetres per second.

Again, a similar correction works for any other speed.

This may sound very peculiar and not at all true, but it is, in fact, exactly how the Universe works, and that is that. The only ‘fiddling’ I’ve done is to make the numbers easier to work with.

This is the second bit of Special Relativity – things get shorter, relative to someone watching, when they are moving, in their direction of travel.

However, if you were moving with the object, you’d notice no difference.

Using our imaginary light-speed of 10 centimetres per second, it’s easy to see that, if the clock itself were sliding towards you at 10 centimetres per second, it would have stopped ticking altogether, and it would have no thickness at all! This still gives the right answers for the speed of light, as measured by the moving clock. It also shows that to travel at or faster than the speed of light is impossible for a physical object – time can’t go backwards and you can’t have negative thickness or length.

A third problem arises. When a thing with a certain mass is moving at a certain velocity, it has momentum which is calculated by multiplying its mass and velocity together. If it collides with something else – which may also have its own momentum, it’s a law of the Universe that the total amount of momentum after the crash must be the same as the total momentum before. It doesn’t matter if the things get smashed up and the parts scatter in all directions – do the arithmetic properly and you will see that no momentum has been gained or lost. This is known as The Law of Conservation of Momentum, and it’s been known about and proved to be absolutely true for ages.

The thing is this. If you stuck clocks on all the moving objects involved in the crash, those clocks start running slow, depending on how fast the things are moving. As velocity is distance covered in a given time, you start getting speeds that are too slow and the momentum doesn’t add up properly any more. The Law of Momentum seems to be broken – which it can’t be – so something again has to altered to allow for this. The only thing is left is the mass, so the Universe needs to increase that to make up for the loss of apparent velocity.

This is the third bit of Special Relativity – things get more mass, relative to someone watching, when they are moving compared with when they are still. (We’ll see where they get the extra mass from in a moment – you don’t get anything for nothing!)

However, if you were moving with the object, you’d notice no difference.

In fact, if you had something moving at very nearly the speed of light, its mass would become very nearly infinite. You would therefore need a very nearly infinite amount of energy to push it that little bit faster – and even then this energy would be turned into mass – the fat thing you were pushing would get fatter rather than faster. It was from this that Einstein realised that energy would turn into mass, and could be turned back again, in certain circumstances, giving us atomic power, the atomic bomb, radioactivity, why the core of the Earth is still hot after so many years of trying to cool down, and how stars burn. But we’re not going to go into that.

So, in a nutshell, in Special Relativity, when things are going at constant speed, things get shorter, more massive and their clocks runs more slowly.

Now, in practice, light goes an awful lot faster than this. But it is absolutely true to say that, every time you move, relative to your surroundings, all the things around you get more massive, shorter, and have time going slower. It’s just that at ordinary everyday speeds, you never notice it and can ignore it. (Global Positioning System satellites works to such high precision, their movement and altitude do have to be taken into account, however.)

But, just for a moment, let’s go back to the clock sliding towards you at constant speed. From its point of view, the clock feels as if it isn’t moving, and that you are. So the clock sees you get heavier, thinner and your watch running more slowly. How can they both be running slow, and which one is right? What time will each show after you’ve been moving for a while? This is where The Twins Paradox comes from.

First of all, let’s look at the clock and the watch both looking as if they are going slow from the point of view of the other, while each ‘feels’ as if it is running normally. This is a bit like watching a ship sail over the horizon (possibly through a telescope, for a clearer view.) From someone watching on land, the ship appears to sink into the sea (and, if we could look very carefully, the mast of the ship would appear to tip away from us.) But, from the point of view of someone on the ship, you and the land would appear sink into the sea (and tip slightly backwards) while the ship stayed afloat and its mast vertical. What we have is two different horizons caused by being in two different positions. In a similar way, we have two different ‘time horizons’ for things moving. Neither clock is ‘right’ while the other is ‘wrong.’ If you brought the two clocks to the same speed – that is, stationary relative to each other – the two clocks would show time going at the same rate, much as bringing the ship back to the same place, at shore, shows neither of them sinking and that vertical things point straight up.

The maths of all this, when things are moving at constant speed, is really quite simple and any teenage maths pupil at school should be able to do it (though I have deliberately left as much maths out as I possibly could.) Things get tricky when you start looking at things speeding up and slowing down, accelerating or decelerating. The maths for this probably needs you to be a graduate maths student. Einstein’s Special Theory of Relativity is so called because it deals with the special case of constant speed. When he wanted to work out what was happening generally, when things are changing speed, he had to resort to much more complicated maths. Surprisingly, some of the maths had been done already by a man called Berhard Riemann, about thirty years earlier, but Einstein was such an appalling student (from the point of view of his lecturers) that he skipped the lectures where he would have learned about it so, sadly in some ways and impressively in others, it took him longer to come up with the General Theory as he had to work out the maths for himself. Notice that, in the General Theory, if you have a velocity change of zero, that is a special case – the same as the Special Theory and why the Special Theory is so called.

However, we want to avoid the maths of the General Theory as much as we can, and this is why The Twins Paradox is interesting. Many people think you can only explain The Twins Paradox with the General Theory. But they are wrong!

But what is The Twins Paradox? Well, I’ve hinted at it already, but here it is in full.

The Twins Paradox

Take a pair of twins – who are, naturally, the same age. To distinguish them, we’ll have fraternal twins, a boy and a girl. The girl becomes an astronaut. She gets on a rocket, cruising steadily at a sizeable fraction of the speed of light (which is not forbidden, but would require a pretty powerful rocket) and she flies to the star nearest to Earth, which is Alpha Centauri, 4 light-years away. (A light-year is the distance light travels in a year. It is not a time, it is a distance.) She turns round and comes back to her stay-at-home brother, still on Earth. OK so far?

Looking over the theory of Relativity as explained above, because she’s been a gal on the move, her clock has been running slower than her brother’s on Earth, so she is now younger than her twin brother!

As odd as this is, things get worse. Also according to what I’ve said earlier, the brother has seen her fly away and come back, so it’s from his point of view that her clock looks slow. But it also depends on whose point of view you are looking from. From her point of view, he has moved away (along with the Earth) then come back, so, as she sees it, his clock has run slow and he’s younger.

They can’t both be right. Are they the same age? No – as we shall see. Which one is younger? Well, it depends – in some way something that has happened to one of them is different from something that has happened to the other. The questions are: what? To which? And with what result?

The usual explanation – and the one referred to in the play Insignificance, is that she has had to undergo an acceleration in order to fly away from Earth. She also had to slow down when she got to Alpha Centauri, turn round and speed up again to fly back. She probably had to put the brakes on as well when she got back to Earth so that she could have a chat with her ageing, Earthbound brother. This involves changes of speed, so we have to use General Relativity with all its horribly difficult maths to explain why – as it turns out – she is younger than her twin.

This is true. The astronaut twin ages less. She is younger. So that’s the answer to that one. But it’s nothing to do with General Relativity.

That’s because we can cut out the bit about speeding up and slowing down. It’s not so important that the two people are twins now – any two people will do – we just want to see which one ages less – who has the slower clock, and why.

Suppose that we use stopwatches to time everything and our lady astronaut sets off in the opposite direction from Earth, away from Alpha Centauri, to start with. She turns round, has a good run-up and gets to her steady cruising speed just as she passes her brother on Earth, and both of them start their watches. Onwards she travels. As she gets level with Alpha Centauri, she stops her watch and applies the brakes; back on Earth he stops his watch at the same time. There is a problem with this – she is 4 light years away so can’t actually see her pass Alpha Centauri for another 4 years (and with a very good telescope.) But he knows, for a given cruising speed, how long it should have taken her, from his point of view, so he trusts nothing has gone wrong and stops his watch by dead reckoning. (This might not sound very convincing, but it is not a fiddle – read on.)

Sister now turns her spaceship round, accelerates to steady cruise speed just as she gets level with Alpha Centauri, and, as she does so, she and her brother both start their stopwatches once more. (To do this, they will have had to plan the mission out very carefully and stick to the plan, but as long as they do so, everything will be fine.)

Now, she gets level with Earth and, as she does so, both brother and sister stop their watches a final time. (She can now get on with braking and coming back to Earth for a soft landing.) The important thing is – both watches have only been timing the part of the journey when the rocket was flying at a steady, unchanging, Special Relativity-friendly speed. So what do the watches show?

They show her watch is slow compared with his! She has aged less! How is this possible, when, from the point of view of each of them, it’s the other that has been moving?! Surely, now that we’ve cut out the speeding up and slowing down bit, they have experienced exactly the same things!

Not so. It’s a bit like a magician’s trick. We’ve been looking at the wrong thing about the experiment.

The thing is – she has flown to Alpha Centauri and back, a distance of four light years as seen by the brother on Earth. Earth and Alpha Centauri have not been moving, as far as the brother is concerned. But she has been moving, and quite quickly too. And from her point of view, Earth has moved away and Alpha Centauri has moved towards her. Or, thinking of it another way, the Earth-Alpha Centauri route are two ends of something moving past her, like light going past our old clock on the mantle-shelf.

Anything that moves, shrinks in length of the direction of travel. Remember?

From her point of view, the journey to Alpha Centauri, and back, has been shorter than it looks to the brother on Earth. Because the journey is shorter, as she sees it, her watch hasn’t had enough time to run for as long as her brother’s, nor has she aged as much. The two siblings have not had the same experience and that’s why they’ve not had the same number of birthdays by the moment she gets back. Speeding up and slowing down have nothing to do with it – at least as far as our stopwatches are concerned, because they weren’t running for that part of the experiment.

So that is the answer and explanation to The Twins Paradox. The travelling twin ages less and is no longer as old as her brother, but you only need Special Relativity to explain it. General Relativity can be kept out of it.

That’s about it, really.

The End

(Much of the information for this article was drawn from lecture notes made available on line by Michael Fowler at http://galileo.phys.virginia.edu/classes/252/ - however, all errors, faults and general confusion are my fault. For much more – puzzling, interesting and accurate information on Relativity and other stuff - see this site.)

Addendum - For all you Doubting Thomases out there
(Gary, this means you!)
Some people have doubted that the difference in ages can be a Special-Relativity-only effect. Here is a worked example using actual maths and figures to demonstrate that the twins will age by different amounts even without considering acceleration and deceleration – that is, constant speed.

The situation.
One twin – the female – is going to fly to Alpha Centauri, a distance of 4 light years, and back, 60% of the speed of light (v = 0.6c) while the male twin stays at home.

During the trip, each will send off a flash of light from a beacon, once a month. In other words, each will have aged one month between emitting each flash.

It is vital to realise that each flash from its sender means that one month has passed for that person. In other words, counting up the flashes sent by either person shows how much they have aged.

As she sets off at 0.6c, she sees flashes arriving from him just once every two months, just as he does from her. This is partly owing to the ever-increasing distance, (an ‘optical’ effect) and time dilation (a relativistic effect.)

Not convinced? And I think I can hear you say - Hang on - after 1 month travelling at .6c, the next flash ought to be after 1 + 0.6 = 1.6 of a month! But you are forgetting that time dilation is slowing her clock. The amount by which it is slowed down is worked out using the following formula: Time observed = Time at rest / square root (1 – v^2 / c^2 ) where v is her speed and c is the speed of light. Her speed is 0.6 so v^2 = .36. So v^2 / c^2 = 0.36. 1 – 0.36 = 0.64. The square root of 0.64 is 0.8. So her time is dilated 1/0.8 which is 1.25. In other words it takes her 1.25 months between signals, owing to time dilation. But in that time, she has travelled 0.6 * 1.25 light-months which is 0.75 light-months. Therefore her next light signal takes 1.25 + 0.75 = 2 months to reach Earth. (And, of course, swapping things around to her point of views, his signals reach her only once every two months as well.)

On the way back, the situation is reversed as far as the change in distance is concerned. Each signal is sent out, as seen by the other, with time dilated to 1.25 months. But in that time, the distance has closed by 0.6 * 1.25 = 0.75 light-months. So the signal arrives at the other end of its journey 1.25 – 0.75 = 0.5 of a month, in other words, two signals a month.

From the Earth, the total journey time (excluding speeding up slowing down and turning around) is 8 light years at 60% the speed of light = 13 years 4 months, or 160 months.

What does she see?
The distance of the trip to Alpha Centauri, where she sees the star rushing towards her, is shrunk by length contraction. The formula for this is the original distance multiplied by the square root of 1-v^2/c^2. This equals 80% of 4 light-years, which is 3.2 light years. (The square root of 1-0.36, which equals square root of .64, which is 0.8.) It therefore takes her 64 months to get there (3.2 light-years/0.6 = 5 years 4 months.) Therefore she sees 32 flashes from her brother.

She turns round and heads back, and immediately sees the frequency of flashes from her brother increase. This is despite time dilation as she is shortening the distance to her brother. She now sees flashes twice a month. It takes her another 64 months to get home, and she sees 128 flashes. By the time she reaches Earth her brother has flashed, and aged, 32 + 128 = 160 months. This is just what we would expect (see above.)

What does he see?
From his point of view, the distance to Alpha Centauri remains 4 light years, so he expects her to take 4 light years / 0.6c = 6 years 8 months = 80 months to get there. But, because Alpha Centauri is 4 light years away, he doesn’t see her turn round for another 4 years = 48 months. (This is a key difference in their experiences – she sees the flashes from her brother change immediately she turns round. He doesn’t see her turn round till 4 years later.) So it is 80 + 48 = 128 months into the mission before he sees her turn round, during which she has flashed 64 times and aged 64 months.

There is now only 160 – 128 = 32 months left before she gets back Earth. Because the distance is closing and despite time dilation, he too sees flashes from her at twice a month, 64 flashes in total.

By the time she arrives back, he has seen 64 + 64 = 128 flashes from his sister who has therefore aged only 128 months to his 160. So his twin sister is now 32 months younger than he.

Note that this difference is regardless of accelerations and is a constant velocity, Special-Relativity-only effect.

Don’t take my word for it, doubt all you want to – but do the maths

(I apologise for breaking my word about there being no maths in this article, but sometimes sums speak louder than words!)

P.S. Notes
Equations of Special Relativity
Length observed = Length at rest * square root (1 – v^2 / c^2 )
Time observed = Time at rest / square root (1 – v^2 / c^2 )
Mass observed = Mass at rest / square root (1 – v^2 / c^2 )

Extra, Extra - Read All About It

Non-fiction article about what it’s like to be in a TV drama – stood at the back

The call came through just before eight o’clock in the evening on my mobile. I had switched it to silent so as not to disturb the others attending the meeting I was in. The buzz of the little phone going off in my pocket almost made me jump. You think I’d be used to it by now. I excused myself and went outside to take the call in the corridor.

"We’ve got a job for you to do."

"When?"

"Tomorrow."

"I had things planned."

"They need you in C.I.D." said my agent.

"What’s the call time?"

"It’s good, twelve noon."

I sighed. "I’ll reschedule what I had planned. I’ll be there."

"Wear the dark suit."

The industrialised hinterland of Merseyside north of Speke Boulevard, not far from the Liverpool John Lennon Airport, is a drab and dreary place that no-one in his right mind would visit on a sight-seeing trip. I turned in to one of the innumerable business parks and pulled up at the barrier.

"BBC," I said.

"Do you know where you are going?"

I knew where I was going. Formerly the offices of a potato crisp factory, this is where the BBC filmed the TV series, Merseybeat, and I where I was going to be an extra.

Not so long ago, filming on location was rare. When it did take place, there would be a fleet of large vans in green BBC livery. That doesn’t happen anymore. Reality in TV has become the order of the day as technology has improved to the point where cameras are small and portable, and much less demanding on studio level lighting. Real locations are used, even for interior scenes, and independent production companies make TV programmes. Hire vans are more common – only a few have legends on them indicating a film crew is about.

Spotting crew is much easier, principally because of their dress-sense. Difficult to describe, but impossible to miss, you head for the bunch of people meandering around that most look like refugees, in very casual clothes. Jeans, sneakers or boots, fleeces and sleeveless puffa jackets are common. On colder days this would be topped off with massive hooded waterproof jackets, and often waterproof leggings as well.

Crew roughly divide into two subtypes – one lot, basically technicians, always wear belts from which dangle every hand tool known to Man, along with bum-bags, reels of gaffer tape, clips and cables, making them look like a DIY-er’s convention, and others such as costume, hair and make-up. The other type are assistant directors and always have walkie-talkies that crackle and squawk from time to time if anything is actually happening. The technical people tend to be male and of any age, the others female, and the A.D.s young but sometimes looking half-way to being burnt out by their work.

One good thing about getting a call-time of noon was that I couldn’t possibly be here all day – unless a night shoot was planned as well, in which case we could be here till ten in the evening. The other good thing was lunch would be included. Today it was steak. But first, there was work to be done. And, first of all, that meant going to wardrobe. Mary, the wardrobe mistress, had a shooting script, a shooting schedule, Polaroids of me from my last appearance, and the tie I had to wear, plus a change of shirt. Other clothes were my own.

Being an extra is in some ways a job like any other, and in others, a job like no other. You find yourself rubbing shoulders with people who you’ve seen loads of times on TV and are famous – that is to say they are recognised by literally millions of viewers. Your face too will appear on a million TV screens – but in the background, and no-one will recognise you. They’ll probably not even notice you. All the viewer perceives is that the action of the drama they are watching occurs in " a busy place," – one with other people moving around, but in no way part of the story, and with no identity.

Nevertheless you are going to be on the Tele, and that puts some people in awe of you and they think you are famous in some way and wonder how you ever got the job. It’s not a secret. You subscribe to an agency and they get you the work. (In a few instances, some extras get work directly, but this is not so common.) To find an agency, you get a weekly newspaper called The Stage, and look in the ads at the back. There – none of that was rocket science, was it? Some agencies charge, and some just take a commission.

The next question might be "Why?" In my case, that’s simple – I needed the money! However, that’s not the only reason. I have done some amateur dramatics and I was always curious as to what it would be like to act on camera compared with acting on stage. Remarkably, very few people doing work as extras are or have ever aspired to be actors. For me, however, this often leads to the question, "What is the difference between acting on stage and acting on camera?" and for me the most obvious, if not entirely serious answer is that on camera you don’t need a prompt! Mess up, and you just do it again. And people don’t throw stuff. Apart from the crew, that is. I find it a lot less nerve-racking.

As for the money – it’s not bad but it’s not brilliant. Worst of all it’s unpredictable. You might get only one day’s work in several weeks, which is definitely not going to keep body and soul together. However, some people work at it to get a multitude of jobs so they keep busy. Nice little earners include being some sort of regular in the Rover’s Return or The Woolpack. Unfortunately, some productions don’t like to have the same anonymous faces over and over.

There are three inventions that make modern movie-making possible. One I’ve mentioned is the Polaroid, one is the walkie-talkie and the last is the mobile phone. Everybody has one. It never ceases to amaze me how rare it is for a take to be ruined by one going off – there’s discipline for you – everyone remembers to switch them off. But, between takes, the extras are whipping them out left, right and centre, phoning friends, colleagues and, of course, agents. One girl I was sat opposite to during a break had two – one for personal calls and one for business – and during the interval she was setting up work for up to six months in advance.

Another way in which the job is unusual is the variety and precocity of the start times. Seven-thirty in the morning is not uncommon and that’s just the extras. The actual actors, or principles, can be in as early as six, for costume and make-up. What a life! And shooting can go on all day, into the evening. A plus point about the early call is you get a full (and I mean full) breakfast thrown in. And, by the way, the stars all eat the same food as everyone else, either in the canteen or, when on location, the catering bus.

Besides the principles, there’s us – the extras. You’re almost never called that. Technically, on the shooting schedule you are referred to as NS – non-speaking, which is fairly self-explanatory – or SA, which rather more grandly stands for "supporting artistes." However, the ubiquitous word used by all the assistant directors is the depersonalising term "background," which is really all you are – just walking scenery.

Being background means you are herded about by A.D.s taking instructions from the first A.D via radio, and sometimes it does feel a bit degrading. But you are still an important part of the creative process (which translates as: you mess up, and everything’s messed up.) To me, the A.D.s seem to be the hardest working people on the set (which is probably why they sometimes look so weary), but that’s probably only true when there are background to deal with. They will give you simple instructions, like "Walk over there," or "Look through this pile of papers." It’s seldom complicated and, in case you were thinking of getting nervous, it’s not worth the bother. I have learned not to question any orders, or ask the A.D. anything unless it is absolutely necessary, such as, "Which side of that light/sound technician/mobile crane should I go?" I never listen to any instructions that are meant for someone else, and I never, ever ask, "How was I?" If there was anything wrong, they’d tell you (and it would probably have been their fault in the first place, unless you are a complete dummy.) It’s a bit like being in the army – you obey orders and you don’t ask questions, and I suspect the A.D.s like it that way.

There are a couple of run-throughs, rather fulsomely called "rehearsals" with everything except the camera running, just to see if it works. Then you’re ready to make picture.

Other things some people like to know include, "Is there really a clapper board? Does the director really shout ‘action’?" Some of the clichés are true. There is a clapper board, but it is now plastic with a whiteboard marker, but it’s used in exactly the same way as they always have been throughout the history of movies. Someone does shout "action," but the process is a tad more complicated. There is a sequence of events which include a call for silence, then "ready," then "turning," then "camera set," (I’ve no idea what that means) and finally, often after a long pause, the A.D. will shout "and action." No-one thinks to tell you these things the first time you are ever on set, but it is vitally important that you do absolutely nothing until that shout of "action."

The long pauses between instructions – not to mention sometimes between takes – can be baffling, but is almost invariably because some technical flaw has been spotted. Quite often, the camera is left running, without compunction, while the problem is fixed. No-one cares about wasting film – in any case it’s not film or video tape, turning on reels, as the shout of "turning" would suggest. This must be just an old convention that’s stuck. Everything is direct to digital, and fed straight into a computer in the editing suite, where the bits are assembled into a show. Nor should "turning" be confused with "turning round," which means we are all going to do exactly the same scene again, only photographed from the opposite direction so that we see the other principle’s face during a conversation. And I do mean, "exactly the same." Never do anything in a take that is so complicated that you can’t remember what it was afterwards, like scratch your head or bite a thumbnail.

Sometimes the pauses and breaks can seem interminable. Often the job is mildly boring, occasionally tedious, and sometimes excruciating. But in movies more than most jobs – labour intensive as it is – time is money, and during every delay, with actors and even seasoned crew looking wearily at the edge of their patience, someone, somewhere is hurrying – probably desperately – to fix something. No – I take that back; I’ve never seen anyone panicking to sort something out – there is just an air of quiet professional efficiency that problems are promptly dealt with.

Then comes the retakes. Even if the first take was perfect, the director will always want a "safety." Typically, however, something will not be quite right. Quite often you were still not 100% sure of what you were going to do, even despite the "rehearsal." The A.D will shout "reset," or "First positions," and you do it all again. The usual number of takes is about four. There is a high level of attention to detail, to getting it just right, but it doesn’t stretch to needless perfectionism.

After that, given the director’s nod, lights and camera, on its little trolley, and anything else that needs to be set are moved around by the ant-like army of technicians, while the actors – their one-trick-pony piece done, look on. Or, if that’s them done for the day, buzz off as speedily as anyone getting out of work early. The shooting schedule, which indicates scene lengths in eighths of a page of script, tells them when they can go home. Incidentally, despite what you may have heard about formats for screenplays, the actual script sheets are simply typed on a word processor, with very little formatting.

And, eventually, as you get to the last eighth on the shooting schedule, your feet are aching from standing around, and you’re beginning to wonder if becoming an extra was such a good idea, the final scene of the day is shot, the work is done, and you all wait for the assistant director to call out the words you are now longing to hear.

"And that’s a wrap."

THE END