Nodding her head as she mentioned bobbing, she saw the students unconsciously nod in time.
‘In the mid-points between the maximum bobbing, we have places where a wave crest from one gap always meets the bottom of a wave from the other gap, cancelling out. So some of our imaginary fishing-floats remain calm, not bobbing at all.’
Again the nods: they were with her.
‘If this were light waves, and the gaps were narrow slits at right angles to the board’ – she gestured, moving her hand in towards the board, then out – ‘then instead of bobbing floats, we’d have lines of light interspersed with shadow, agreed?’
Nods, still.
‘That is an experimental fact, observed of course by Young in the nineteenth century, and thousands of times since. So the puzzle is, if light is a stream of particles as demonstrated by Einstein among others, then each individual photon can surely go through only one slit. So how does it know about the other slit? In particular, how does it know never to go where the two imaginary wavefronts cancel out?’
Fewer nods, but they were still with her, because this was in the realm of what they knew but did not understand.
Them and everybody else.
Gavriela pushed that thought behind her, and focused on the faces, so young-looking.
‘Now Professor Bohr says that reality behaves like either waves or particles, according to which kind of observation we choose to make. In this, he’s factually correct, but only because he’s using the words behaves like in a very technical sense. In everyday terms, you do get wave and particle behaviour together, and I’m going to show you how.’
She turned to the board and drew an X at random.
‘If we shine light through slits onto a piece of card or a blank wall, we get a series of vertical bright lines. But replace the card or wall with an array of photomultipliers, and we detect exactly where each photon lands.’ She drew another X. ‘And that seems pretty particle-like to me.’
Moving apparently at random from right to left across the board, she drew some four dozen Xs in total. A pattern was emerging, and so was comprehension on the students’ faces.
‘As we keep track of the points’ – she drew two more – ‘we see that they gradually build up the vertical lines of light that we expect. Wave behaviour grows from the particle behaviour, while the particles followed wavelike constraints.’
It was time to explore the Schrödinger equation, which would lead to discussing the difference between electromagnetic waves and the ψ waves that the equation dealt with: a varying quantity specified by two numbers, like longitude and latitude combining to give a map location, from which a probability could be worked out. But before that, she needed to ensure her audience was with her psychologically.
‘I hope I’ve thrown some light on the subject’ – she waited for the smiles and groans – ‘and leave you to consider later how new patterns arise from increasing observations, and how, for the Sherlock Holmes devotees among you, it’s the places where the light may not shine that define the pattern, making it depart most strongly from classical reality, so that … that …’
She shivered, hearing nine discordant notes, but only in memory, not in the moment; and knew that her words meant more than intended.
‘… the darkness defines the light.’
After a moment, she was able to continue, but not without awareness of a strange, unfocused image lurking at the back of her mind.
Dmitri travelled in civilian clothes, not uniform, but his papers identified him as a member of the SS. His biography was well established in the Berlin archives, planted there by a V-man who was in fact a double agent: embedded in the Reich’s intelligence hierarchy but run from Moscow. Dmitri’s orders were to rendezvous with a contact in Kreisau, then decide on his own initiative whether to attempt an infiltration of the group in question.
The preliminary intelligence was that local high-ranking officers intended to attempt assassinating Hitler. Dmitri’s cynicism noted that such sentiment was rising now that the Wehrmacht no longer seemed unstoppable: not just their faltering against Moscow, but their destroying less than fifty Allied ships in the North Atlantic during the previous three months, in contrast to the six and a quarter million tonnes of shipping sunk in the prior year.
He knew those figures were accurate. He had purloined them himself via an asset among Admiral Canaris’s staff, and passed them on via courier to Moscow.
The German theatre of operations was where he belonged. His linguistic expertise and cultural knowledge meant that he should never have been sent to Japan; except that it had been a fortuitous posting, far from internal politics: his former superior, Colonel Yavorski, was no more. That had been the gossip from the case officer running the Frankfurt network and engaged in courier work on the side, hence his meeting with Dmitri.
The compartment door rattled open.
‘Ihre Papiere, bitte.’
Dmitri had no qualms as he handed over his ID for inspection. He could fit in here. If Germany won the war, he intended to become part of the establishment; meanwhile, he would continue to perform for his Soviet masters. While the more he quelled his desire for murder and the taste of human meat, the less hold his other master seemed to have on him. Or perhaps it did not care to direct him any more.
Perhaps, by his nature, he furthered its purpose no matter which side he took in humanity’s ephemeral, parochial affairs.
They worked in caverns below ground, a legion of the lost, each of them in the process of being broken down by workload and cold and starvation, each man a unit to be replaced: corpses were one of the waste products of Peenemünde; and Erik Wolf was just one more temporary component among the damned.
He did not believe in the concept of life force, of an élan vital; but there was a shining thought that kept him from death for now, and it was the conviction that Ilse had got away, using the loft that ran through to the house next door, before the Gestapo had come pouring in. There were no illusions: for him, it was only the work-gang and suffering, with death at the end.
But it lasted longer than he had expected, moving from digging and rail-laying to work that demanded more nimble fingers: fastening components inside metal casings of what looked like huge finned torpedoes, designed for flight. The insides had the clunky functionality of refrigerators or cars, robust and inelegant.
‘What is Vergeltungswaffen?’ muttered one of the other prisoners, a Russian.
They could get away with mumbled conversation from time to time, provided they remained bent over their work and did not stop assembling the hardware.
‘You understand “revenge”?’ said Dmitri.
‘Sure. Mest. I understand.’
‘Weapon of revenge, then.’
The Russian, his face lined and collapsed like everyone else’s, became even more grim.
‘Aeroplane bomb without pilot,’ he said.
‘Yes.’
The missiles were to be called reprisal-weapons, propaganda for the people at home who were suffering now as Allied bombers encroached on the Reich’s airspace, the name a joke to any non-Nazi. But the weapons themselves were deadly, urban populations their target.
Overhead on the catwalk, the guards were talking among themselves, paying no attention to their charges below. Escape was impossible for the prisoners, and overseers would check the assembly work before the final part of the casing was fastened in place, so why should they bother spending every second watching sub-humans at work?
Erik was dehydrated but not fully, and he could feel it in his bladder now.