The Weekend Read
Introduction to Relativity
By Pippa Goldschmidt
13th Apr 2018
14 week course. Some experience of maths required.
You’re in the front row of the lecture theatre listening to the lecturer, ‘Alice is travelling on the train, flashing her torch at Bob who is standing on the station platform.’
You haven’t had this lecturer before, he must be new. You shift in your seat and sure enough, he looks at you. There is a minute pause, the merest stutter in his words that is undetectable to anyone else, as you watch him analyse the geometry of your blouse.
You wonder whether Alice regularly rides around on trains flashing her torch at men. You picture her in a plastic mac and high-heeled boots. You wonder what Bob gets out of this arrangement, perhaps he fancies Alice.
‘Alice sees the torchlight expand equally in all directions, hitting the front and back of the train at the same time.’ The other students are writing this down in their notebooks. You doodle a heart on the cover of yours, and consider undoing another button on your blouse.
‘But Bob sees the light strike the back of the train before the front. Can anyone tell me who is right? Alice or Bob?’ Silence. You glance at the other students before putting up your hand, and he nods at you to speak.
‘They’re both right. From Bob’s point of view the back of the train has travelled towards the light and the front has travelled away from it. So he sees the light reach the back of the train before it reaches the front. But Alice is travelling with the train and to her the front and back of the train aren’t moving. So for her, the light strikes the front and back at the same time.’ You pause. ‘They’re both right,’ you repeat.
He nods again before continuing, ‘The speed of light is a constant, and that leads to different versions of reality. All are equally valid.’ You like this. Brusque and efficient. You continue to doodle hearts as he lectures.
You feel a bit sorry for Bob. He never goes anywhere, just stands around on station platforms waiting for Alice to communicate with him. She gets all the fun. You’ve noticed that the other students write down everything the lecturer says, but they can’t answer any of his questions. You don’t need to write anything down. You’ve done all this stuff before. You like the way he looks at you now when he asks a question, as if he expects something from you.
His wedding ring glints in the artificial light of the lecture theatre. You stroke the buttons on your blouse.
Alice is in a lift, plummeting to Earth. The lecturer says she doesn’t feel anything as she falls, not even gravity, but you’re pretty sure she might feel terrified. Bob is probably still waiting for her on a platform somewhere, wondering where she is. Poor, faithful Bob. What an idiot.
There are fewer students now. This always happens at this point in the course. They can’t take it. The extrapolation from the everyday stuff; the clocks, trains and torches, to the imaginary; inertial forces, curved space-time, and the vacuum. You’re used to it. You can cope.
At the end of the lecture, when the other students are shuffling out, the lecturer walks over to you. You cover the front of your notebook so he can’t see the hearts.
‘You never write anything down.’ Again, that brusqueness.
‘I don’t need to,’ and you smile and walk off.
You’re given coursework; ‘Quantify Newton’s error in his derivation of Mercury’s orbit around the Sun, and show how Einstein was able to correct this error in the context of general relativity.’
This is standard textbook stuff. You’re almost disappointed that the lecturer appears to show such little imagination. You hope he’s more imaginative in other aspects of his life. You email the answer to him and you don’t have to wait long for his reply. He wants to see you, in his office. It’s taken a week longer than usual, but that doesn’t matter. There’s still plenty of time.
You’ve been to the office before, when the last lecturer had it. This one’s rearranged the furniture, but the rug’s in the same place. You remember the rug.
‘There is a practical element to the coursework,’ he tells you, ‘You must choose an experiment and I need to approve it.’
You suggest a quick, straightforward experiment, one that you and he can carry out on the floor of the office. He agrees.
Alice is now in a spaceship, travelling around the Universe at almost the speed of light while, as usual, Bob waits for her back at home. You suspect Bob doesn’t look so hot now, with all that waiting around for Alice and worrying about her.
‘Who can explain why Bob ages faster than Alice?’ He’s wearing a nice shirt today, crisp and ironed, presumably by his wife. You imagine running your hands up his arms, along the ridge of his shoulders and down his chest, feeling the heat of his body.
There are only three other students in the lecture hall today. The lecturer waits for you to answer, but you stay silent. You don’t see why you should do all the work.
You suggest to the lecturer that your experiment should be repeated, to make sure you can get the same result as before. He agrees. Afterwards, in the lecture theatre, his shirt looks a little crumpled.
Space-time has been compressed by your experiment. The lecturer is standing in front of the white board, picking his way along an equation, and he’s also lying stretched out on the rug, a sheen of sweat still visible on his stomach.
The experiment starts to be repeated regularly, sometimes twice a day. In his office, he shuts the door behind you and tips your head back to kiss your throat.
The lecturer introduces Carol to Bob and Alice. Carol is more adventurous than either of them. She falls into black holes, where she gets stretched into string by warped space-time, and becomes cut off from the rest of the Universe. As she sends out a last message before she sinks below the event horizon, Bob and Alice see a static vision of her, forever poised above it.
You can also see her. She’s wearing your favourite jeans, the ones the lecturer ripped in his hurry to get them off you. You’re wearing them again today, in spite of the tear in the fabric. You’re hoping he’ll notice them and remember.
The lecturer deviates from the course material and talks about dark matter. You can picture it slipping around the Universe, fastening itself to discrete objects. You already know how quick it is to react to certain forces, such as the proximity of a hand, or the unbuttoning of a blouse.
‘Dark matter fills the Universe,’ he tells you and the other students, ‘It doesn’t interact with light, only with mass.’
You trace a spiral with your finger on the desk; thinking about the slow, sweet curve of bodies as they orbit around each other, before falling inwards. But his wedding ring is gold, and although it’s soft enough to show your teeth marks, it will last until the Earth and Moon finally plunge into the Sun.
His wife is pregnant. He shows you the scan of the baby, its head arched in profile as if already searching the starless space around it for answers. Now, you don’t know what to say. Now, as he pulls you towards him to get at your throat, you wonder what will happen in the future. You’re not used to thinking like this. These courses are completely predictable. That’s the best thing about them.
The next piece of coursework is about mass and its dependence on speed. As objects travel faster, they get heavier. You think that maybe Bob won’t find Alice so attractive now that she’s getting heavier and her ankles are fat. Your calculation shows that he should always prefer Carol, but you get the answer wrong. This is the first time this has happened to you. You question the lecturer about it, but he’s able to show a mistake in your logic.
This week he’s onto entropy, and the growth of disorder and decay as time moves from the past to the future. This contradicts relativity, which doesn’t depend on time. You hoped relativity would win out over entropy, but you know what entropy is now.
Now, after each experiment, he picks the fluff from the rug off his clothes, smoothes his hair, and sniffs himself before he sends you out of his office. He has work to do; other courses to write. You find it difficult to concentrate on your own work. You are not sure what else to do apart from the experiment. You thought that would be enough for this course.
The next deviation occurs. He talks about calculating the orbits of bodies. A two-body problem is analytical. Once the initial conditions are known, the entire future of the orbit is known. But if there are three bodies, the system becomes uncertain. The effect of any perturbation on this system, however tiny, can’t be predicted in advance. It can only be observed.
You check through your notes. You don’t know this material, previous courses haven’t covered it. He shouldn’t be talking about it.
When you are both lying on the rug in his office, you ask him why he is making changes. His shirt and trousers are still open, but his skin reveals nothing.
‘Nothing stays the same,’ he says finally. He stares straight ahead when he speaks, not looking at you. ‘Nothing should stay the same.’
Clocks, trains and torches are always there. Carol, Bob and Alice are always there. You lean over to touch him, but all you can reach are his fingertips.
Entropy means that things change, orbits decay. Planets spiral into stars and are annihilated. As they do so, they send out gravitational waves; beacons of distress emitted across the Universe.
He doesn’t have much time any more, so the experiment is stripped down to the essentials. He doesn’t bother with your throat.
‘Is this happening at the same time?’ you ask, afterwards.
‘The same time as what?’
At the same time for both of us, you think, but there is no point in saying it, not now. You should have said it before, at the beginning, when he did have time.
‘I have to go,’ he says, and he hands you your bra as if he doesn’t want to see your breasts any more. You feel like weeping. You consider refusing to accept it, abandoning it here as definitive evidence. Now that there is a past to this, and maybe not a future, you want someone else to see your bra hanging from his chair, and know what has happened here. You’re not the observer of this experiment any more. Perhaps you never were.
Bob has surprised everyone and bought a motorbike. It’s his turn to accelerate to the speed of light. Alice isn’t allowed to join him. As he roars along the motorway the light he emits settles into a sort of cloud around him, shielding him from everything else in the Universe, even Carole.
When you walk along the corridor to the lecturer’s office, the door is shut. He’s either not there, or he is there. You don’t know which is worse.
The lecturer puts his notes into his briefcase, and leaves without looking at you. The course is over and the only other student is asleep at the far end of the lecture theatre. All you can do is follow the lecturer to his office. He has told you that you must keep a certain distance as you walk behind him, and that nobody must see as you follow him inside. You must not disturb anything, apart from yourself. Those are the rules of this experiment.
You sign up for a different course next term. You hope the next lecturer will be pleased at your understanding of the subject. You hope your coursework will be satisfactory.