God does not play banjo with the universe

For Katja

‘Last stop’, called out the conductor.

In the dusk of a Copenhagen winter afternoon, a yellow tram rumbled to a halt with a screech, and the doors opened. Two men got out. Both were wearing hats. One was holding a furled umbrella. The other had a small moustache, and was carrying a copy of Frankfurter Zeitung under his arm.

The first man looked around him in confusion.

‘This does not look like the place,’ said Bohr.

‘It’s your city,’ said Einstein. ‘And your institute. You should know.’

‘It looks like somewhere else,’ said Bohr. ‘If it is somewhere else, I cannot know it.’

‘Well, perhaps we should try to establish it empirically?’ suggested Einstein. ‘What does that sign say?’

‘It says Svanemøllen. The, ah, Swan Mill.’

‘So, is that your Physics Institute?’ asked Einstein, pointing with his newspaper at a small, half-timbered building that looked a bit like a farmhouse. A small dog was lifting its leg at it.

‘Not normally.’

‘Then, my dear Bohr, I think we can conclude that we are in the wrong place.’

‘Not necessarily,’ said Bohr. ‘This might be the right place, but look different.’

‘Perhaps you should find a person with local knowledge?’

‘I have local knowledge if we are in the right place. If we are not in the right place, I do not have local knowledge.’

‘Bohr, ask someone!’ said Einstein.

Bohr walked up to the front of the stationary tram and conferred with the driver through the open door. He returned to Einstein.

‘This is not the stop for the Institute,’ he said. ‘We should have got off at the, ah, Triangle.’

‘Then perhaps we should get back on the tram and go back the way we came? I presume the vehicle follows the same route on the return journey?’

Bohr looked concerned. ‘That I had not thought of,’ he said. He turned and walked back to the tram driver.

Gott im Himmel,’ muttered Einstein.

Bohr returned. ‘The tram follows the same route on the return journey,’ he said. ‘At least, according to the information I have available.’

‘Then, Bohr, I think we should get back into the tram and go back the way we came.’

‘Yes. Yes. I think that would be the best course of action.’

The two men got back into the tram and sat down on the brown leather seats. It was cold with the tram doors open. Einstein drew his coat around his legs.

‘It’s getting late,’ he said. ‘Do you think he will wait?’

‘I cannot know that,’ said Bohr.

In a small, dusty lecture hall at the Physics Institute, Heisenberg was sitting with his notes. The day was growing dark. He glanced at his watch for the fiftieth time, picked up a glass of water and took a gulp to quell his nerves. The decanter was almost empty. Absurd to wait so long for the great man. He could always see him tomorrow. The train from Germany must have been delayed. It often happened. These were unruly times, there was a lack of good order. What was the quote from Hamlet? Something about time being out of joint.

The restlessness inhabited his whole body and made him tap his fingers and sigh. He felt like a gladiator who had prepared for months for a fight to the death, but whose opponent had unaccountably failed to appear. Not that Einstein was a fearsome warrior, exactly – he was far too polite for that, although his characteristic remark of ‘I fear, my dear boy, that there is a fundamental error’ was nonetheless a blow that could kill. But in any case, if he arrived now, his first thought would no doubt be for dinner, not physics. The death blow would not fall before tomorrow.

‘A walk. I should go for a walk,’ said Heisenberg aloud. He picked up his briefcase and began stuffing his notes into them.

Wearing his long woollen overcoat, Heisenberg walked down the stairs of the institute, nodded to some colleagues who were ascending, and exited by the back door. From here, a gate led onto a vast public park, the name of which he found quite unpronounceable. Such a peculiar language, Danish. Bohr had told him that the park used to be a grazing area for the army’s horses, which was why it was so large and open. Heisenberg often walked here when he needed to order his thoughts. He did not usually come here so late, however. He had to stand still on the path for a few moments until his eyes grew accustomed to the gloom. Then he set off in his usual direction.

The winter was clinging on, and there were still patches of snow here and there.

In his mind, he went through the presentation again. What were the parts he should emphasise? Where were the weak spots that Einstein’s razor intellect would inevitably find? Bohr seemed to have confidence in him. But Bohr was a man who would carefully consider even a perpetual motion machine before patiently taking the trouble to explain to its inventor why it would not work. He had seen him do it. Einstein was not a patient man. And the results that Heisenberg had arrived at were alarming, to say the least. So alarming, in fact, that there surely had to be a basic error hidden there somewhere. Some piece of utter idiocy. But where?

He had been walking for fifteen minutes before he realised that he had no idea where he was. The park looked completely unfamiliar in the dark. Where was the lake that he usually passed by? He should have reached it by now. Irritated, he sat down upon a bench and placed his briefcase on his lap.

‘Either there is something wrong with my results, or there is something wrong with the universe!’ he said to the world in general.

‘That’s often how it is,’ said the world in general. Startled, Heisenberg looked up and saw a figure sitting at the other end of the bench.

Sie sprechen Deutsch?’ asked Heisenberg.

Leider nicht,’ replied the figure.

Heisenberg felt confused.

‘But you replied to me in German.’

‘And you told me there was something wrong with the universe. Draw your own conclusions.’

‘But the implications are absurd!’ said Einstein.

The tram, now full of passengers, was once again juddering its way towards the city centre. It was rush hour and the two men were squeezed into their seat by the shoppers and commuters standing in the aisle. Each time they rounded a corner, a women carrying a small dog in one hand leaned in across them and smiled apologetically, as though offering the beast for their inspection. Or perhaps the other way round. The dog looked at the two men, its tongue halfway out of its mouth. Einstein felt that one of them ought to stand up and offer the woman a seat, although that would have been a risky manoeuvre in the crush. Bohr seemed oblivious to everyone around him.

‘Whatever the implications are, my dear Einstein, we must accept them if they are logical and match the given observations,’ he was saying. ‘And by the same token, if there is an error, then we must reject the theory.’

‘But it must still make sense, Bohr. There must be causal relations. Things do not happen by chance. And they certainly don’t go round in circles and start again, to cover the energy deficit. That is cheating. God does not play snakes and ladders with the universe.’

‘We cannot let our conclusions be limited by our imagination,’ said Bohr.

‘Bohr, you’re a mystic!’

Bohr was untroubled by being called the worst thing one physicist could call another.

There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy. People say that a lot here.’

‘I’m sure people say a lot of things here. The whole place seems to be imbued with some kind of hocus-pocus. You, Heisenberg, Schrödinger, you’ve all been infected.’

The tram shuddered to a halt. Einstein looked out of the greasy window and gave a sigh of exasperation. He pointed at the stately building outside.

Bohr leaned across Einstein and squinted through the window. ‘Oh dear,’ he said.

They had arrived back at the central station – from whence they had started out several hours earlier.

Heisenberg peered at the figure sitting at the other end of the park bench. It was hard to make out in the gloom. He – Heisenberg presumed it was a he – appeared to be looking at a map. In the dark.

‘Are you lost?’ asked Heisenberg.

‘Not exactly lost,’ replied the figure.

He could see now that the stranger was very small. His feet stuck out in front of him on the bench. Heisenberg was intrigued. A dwarf, perhaps? He realised that he was staring and quickly turned his head away.

‘What about you? Are you lost?’ asked the stranger.

‘In more ways than one,’ said Heisenberg. ‘I am a scientist. But I have arrived at some rather strange results. I’m not sure where they may lead.’

‘The way I see it,’ said the stranger, turning the map around, ‘is that you can either know where you are, or where you’re going. But not both at the same time.’

Heisenberg looked at him in astonishment.

‘How did you know that? That’s what I was going to say to Einstein.’

‘It’s a simple matter of logic, isn’t it? Especially in the dark.’

‘Yes, I suppose it is. But that’s what worries me. That, and the implications for time.’

‘Time? I shouldn’t worry about that, my dear fellow. Sometimes a stitch in time saves nine, you know.’

Einstein was in rather less amiable humour as they boarded the tram for the third time that day. It even appeared to be the same vehicle, with the same driver. They sat down in the same seats as before.

‘Bohr, do try to keep your wits about you this time.’

‘Yes, of course. I’m most terribly sorry. It’s just that these questions are rather fascinating, don’t you think?’

‘Where did you say we should get off?’

‘At Trianglen. The, ah, Triangle.’

‘Then I will watch out for that. But surely Heisenberg will have gone home by now?’

‘I cannot know,’ said Bohr.

Einstein sighed. ‘You are making a point, I suppose?’

‘A point?’

‘Bohr, epistemological questions are neither here nor there. We are physicists. We deal with what can be seen and measured.’

‘But your Theory of Relativity was hardly that, now, was it?’

‘No, but it could be established experimentally. And indeed, it has been.’

‘Well, exactly. So a theory that fits the known facts must be accepted as correct, until we can come up with a better one.’

‘Even it is complete madness?’

‘Even if it sounds like complete madness.’

‘Nonsense. God does not play hide and seek with the universe,’ said Einstein.

‘What? I don’t quite follow you there.’

Einstein looked perturbed.

‘I don’t know why I said that. That’s not what I meant to say. What I meant to say was that there must be some kind of order in things. As in mathematics.’

‘We’re starting again,’ said Bohr.

The tram driver turned on the cabin lights. Outside, in the city night, it had begun to rain.

‘It is raining. I must go,’ said the stranger. He folded his map and stood up. He was indeed very small, no taller than a child.

Heisenberg peered at him. He still could not make the figure out clearly in the darkness.

‘Who are you?’ he asked abruptly.

‘Me? Oh, I’m nothing special.’

The stranger began to walk away, then stopped and turned around.

‘You’re a scientist, you said. You know how Newton once said God was like a watchmaker?’

‘Yes … but, I mean, it’s just an analogy. There doesn’t have to be an actual deity …’

‘Ah well. You see, watchmakers don’t just build devices to tell the time, do they? Sometimes they build a little extra function into them. For amusement or enlightenment. They’re called complications. Sometimes they’re even necessary for the device to function at all.’

‘Yes, but …’

‘That’s what this city is, you see. It’s a complication. The Copenhagen complication. I’m sorry about that.’

And with that, he turned and walked away into the darkness.

The tram was filling up with passengers again as it made its way back out of the city centre.

‘So if I understand what you’re saying, then time can repeat?’

‘Well, not quite repeat,’ said Bohr. ‘More oscillate.’

‘I’m not sure I understand the distinction,’ said Einstein.

‘There are eddies, vortices, in the river of time. At its edges, so to speak.’

‘So there are areas where time repeats without end? Ceaselessly?’

‘Yes. Or it circles around itself. But this is a necessary consequence of the forward motion. In fact, it is a precondition for it.’

‘So you are saying that these repetitions are what calls the universe into existence?’

‘Well, in theory, yes. They are necessary in order for the universe to exist. In a given state, there can be an oscillation in which there is no diminution of energy. The energy loss at one, ah, end of the system is compensated by the energy gain at the, ah, other.’

‘And where does this energy come from?’

‘From itself. From the other end of time, so to speak.’

‘Bohr, you are talking complete nonsense. God does not play banjo with the universe.’

‘I’m sorry, what?’


‘You said something odd.’

Einstein looked pensive.

‘Yes, I did, didn’t I? I’m sorry, I don’t seem to be quite myself today.’

‘Last stop!’ called the conductor. The tram screeched to a halt, and the doors opened.

Bohr and Einstein stepped out. It had stopped raining. The sky even looked a bit brighter. A dog was raising its leg against a small, half-timbered building. Bohr looked around him in confusion.

‘This does not look like the place,’ he said.