He tugged the thick velvet curtain back in place and decided to wash and change before dinner. Already he had made some progress with Debye’s suggestion about finding a wave equation; the difficulty, however, lay in the fact that neither Schrödinger nor anyone else in the world knew what those waves really were. It was like following the tracks of an unknown beast.
If electrons are waves, then these waves must fold themselves around atoms. Yet Schrödinger had tried this calculation, and found the waves were apt to become caustics, like the deformed images produced when light reflects from the curved edge of a coffee cup onto the fluid’s dark surface. He chose a clean shirt and began to put it on, checking his appearance in the long mirror beside the dressing table.
A new vision of nature was emerging, which in the last year or two had come to be called quantum mechanics. Schrödinger had seen a popular book about relativity at the railway station; how long would it be before he would see one on quantum mechanics? And would his own name appear in it? Already there were many contenders. Bohr and others had tried to develop a theory of ‘probability waves’, but found it wanting. Whatever De Broglie waves are, they are certainly not waves of probability. And now Bohr’s young disciple Heisenberg had developed some obscure mathematical game – ‘matrix mechanics’ – with which he thought he could win the prize.
Such were the idle thoughts of our hero as he prepared himself for dinner. We called him young and promising; however, the reader has now had ample time, and has been presented with considerable evidence, to conclude that Schrödinger, quite to the contrary, saw himself in imminent danger of being eclipsed and forgotten. Soon he would be forty; and a physicist who has not found fame by that age might as well abandon hope. It was against such a background that he had recently decided to compose his own philosophical testament; a manuscript he had then filed away in case his reputation should ever rise high enough for it to become publishable. The questions he asked in it were simple. ‘Do I exist? Does the world truly exist? Will I survive bodily death?’ For his answers, Schrödinger had turned to the Eastern philosophy he knew from Schopenhauer: to Brahman, the being of pure thought which is everything, and Maya, the illusory world we must pass beyond.
We think we are surrounded by objects made of particles of matter; yet these are Maya. Everything, Schrödinger felt sure, consists of waves, and all that seems solid amounts to little more than evanescent bubbles, dancing like white shreds of foam on ocean crests.
It was with these thoughts that Schrödinger readied himself for dinner. Straightening his tie one last time before the mirror, he went out along the corridor, then downstairs to the dining room.
Note
* English translation by Celia Carter. Cromwell Press, British Democratic Republic, 1954
GHOSTS
John Ringer steered his car off the deserted main road, past a huge sign showing Annie Atom; the jovial, kilted mascot of Craigcarron visitor centre. The nuclear power station gleamed brightly in winter sunshine as Ringer approached. Far out to sea – beyond the smooth, enormous geometry of the plant – soaring gulls were sunlit specks like stars in daylight. It would be a pleasure working here, thought Ringer.
He came to another sign. Annie Atom directed tourists to the right; Ringer took the alternative route marked Authorized Vehicles Only. Soon he reached a barrier where two armed guards scrutinized his face when he wound down his window.
‘I’m here to see Don Chambers,’ he confirmed for them as they compared his nervous expression with the picture on their clipboard, then they waved him through after radioing to check. The barrier swung up; he drove inside, following a sign that veered him away from the vast reactor hall towards the simpler prefab units of the research centre. Soon he was sitting inside a bland, white-painted waiting room of a kind found in any industrial estate, holding a cup of tea provided by the receptionist. Don Chambers was still in a meeting.
Ringer was to give a talk next day to Don’s small research group; this was the excuse for his visit. But Don had hinted to him on the phone that there was another topic he wanted to discuss. Ringer guessed he was looking for a new job, now that the nuclear plant was due to close.
Don had been his student some years before; the most important lesson he’d learned during his postgraduate studies, he once told Ringer, was that academic life was not for him. Instead he’d chosen this lonely place, with only seals and engineers for company, a receptionist the wrong side of fifty, and a hefty salary by way of compensation. It would be something of a climbdown coming back to work in academia, assuming Ringer could even swing it.
While he waited, Ringer perused the magazines and journals on the coffee table but saw nothing of interest. As the minutes dragged, he wished he’d brought the book that lay in his suitcase in the boot of his car.
It was the cycloids talk that had prompted him to buy it: E. T. A. Hoffmann’s The Life and Opinions of Tomcat Murr. According to the lecturer, this was the inspiration for Schumann’s piano suite Kreisleriana. And from what Ringer had read so far, it was very odd indeed.
Johannes Kreisler, a musician, is writing his auto-biography. But his pet cat Murr mixes up all the pages and writes his own life story on the reverse sheets. So the novel consists of two parallel narratives, Kreisler’s and Murr’s, intercutting randomly. It was one of Franz Kafka’s favourite novels; and Ringer could see why Schumann too was so impressed, given that the composer’s own divided self ultimately landed him in a lunatic asylum.
If Ringer had come across it years ago in the library, his first phone call to Helen could have gone differently.
‘I’ve been thinking about your thesis,’ he might have said. ‘Tell me, have you ever heard of Schrödinger’s cat?’
He hears her laughing. ‘Of course,’ she says. ‘Everybody knows the cat in the box is neither dead or alive until the moment you open the lid and look inside.’
‘Yes,’ he tells her, ‘that’s what everybody knows. But the point Schrödinger was making was a lot more subtle than something Berkeley had already said a long time previously. Have you read Hoffmann’s Tomcat Murr?’
‘Certainly,’ she says.
‘Then you know the book describes two parallel stories: two conflicting realities. And that’s what happened when Schrödinger found the wave equation.’
Why did he need to rerun the past? If their first conversation had been any different, would the rest of their story be altered in any way? The people who know all about the uncertainty principle and Schrödinger’s cat from countless popular books and TV programmes also know about something called the butterfly effect, which says that a gnat’s fart in Angola can alter the history of the world. What they don’t always appreciate is that the theory of dynamical systems – which perhaps includes world history – also allows for things called attractors: destinations you will inevitably reach, as long as you come anywhere within range.
He and Helen were circling such an attractor when they sat together in the Dolphin Cafe. They were still circling it when they walked to the park; when she came to his flat, and they made love on the floor. Perhaps her eventual disappearance from his life was another, greater attractor.
All this, though, was simply a way of passing the long minutes until Don Chambers came out of his meeting. Ringer saw the prim receptionist look up at him from time to time over her half-moon spectacles, as if making sure he hadn’t died yet. He decided that by way of preparation for the other talk he was due to give – for Mr McCrone’s parishioners in Ardnahanish – it might be worth pursuing the alternative history that could have begun with a conversation about Murr and Kreisler.
So now, once more, we are in the quaintly tatty Dolphin Cafe, where Helen’s eyes tease Ringer’s thoughts as he lectures her.
‘Back in 1925, people wanted to know if everything is made of particles, or else waves,’ he says. ‘In the spring of that year, Heisenberg came up with matrix mechanics: a theory of particles making random quantum jumps. Fame beckoned
. Then a few months later, this unknown outsider Schrödinger says it’s all waves, and he’s found the equation showing how they change smoothly and predictably over time. Two completely different interpretations of nature: two parallel stories.’
‘Which one’s right?’ she says.
‘Both.’
Helen laughs. ‘In that case you’re either a romantic like Hoffmann, or else a postmodernist.’
Ringer shakes his head. ‘I’m no postmodernist. The issue is how you interpret nature, and those two men – Heisenberg and Schrödinger – offered contradictory interpretations. It turns out they’re mathematically equivalent – Dirac soon proved this. Both theories make the same experimental predictions, and which you use is like choosing between long division and a pocket calculator. But people don’t just want to calculate; they want to understand how the world really works.’
Helen looks down at her hands on the table top. Her fingertips are almost touching his. This is a moment he enjoys replaying. ‘If you’re not a postmodernist,’ she says, ‘I suppose you must be a romantic.’
Perhaps she was right. Watching the receptionist typing at her computer, Ringer imagined telling the parishioners of Ardnahanish how Niels Bohr summoned Schrödinger and Heisenberg to Copenhagen in 1926 so they could sort out their differences. Eventually Bohr proposed a compromise that E. T. A. Hoffmann might have felt perfectly comfortable with.
Schrödinger’s wave functions change predictably just as long as they remain unobserved; but as soon as a measurement is made, the waves mysteriously ‘collapse’ in one of Heisenberg’s quantum jumps. Thus an electron is everywhere and nowhere, until it interacts, leaving its footprint on the universe. This is known as the Copenhagen Interpretation; and once Bohr got used to the idea that two conflicting stories can both be true, he decided the world is made not of waves or particles, but of things that can be either according to taste.
Schrödinger never accepted Bohr’s compromise; he ridiculed it by means of his famous imaginary cat, trapped in a box alongside a vial of poison gas that will be released if struck by an electron. Since the electron is everywhere and nowhere, the cat is both dead and alive, until the box is opened.
Where did Schrödinger get the idea for his schizophrenic cat? Perhaps he was a fan of Tomcat Murr, thought Ringer; then he heard footsteps approaching, looked round and saw Don Chambers striding in his direction with outstretched hand.
Ringer put down his teacup and got up to greet him. ‘You’re looking well,’ he told Don; and it was true. Don had always been the outdoor type; and here in northern Scotland the abundance of fresh air and lack of human contact had rendered his features more chiselled than ever. The suit and tie were mere concessions to the meeting he’d just attended; muddy Gore-tex was his natural attire.
Don’s handshake was like accidentally slipping one’s fingers inside a piece of industrial machinery. ‘How’s life?’ he asked chummily. Fine, Ringer told him. As they asked about each other’s wives and kids, Ringer saw no indication of a man whose career was in peril. Then, with the introductory pleasantries disposed of, Don suggested they go to his office and talk. Ringer followed him there.
‘Take a seat,’ Don offered, closing the door in a way that suddenly and inexplicably made Ringer feel like a junior employee being treated nicely as a prelude to the sack. If Don wasn’t in trouble, perhaps Ringer was. Don sat himself at the other side of a desk whose neatness showed he really had left academic life far behind. Then he got straight to the point. ‘I’d better fill you in on a few changes happening around here. I think you know about the decommissioning of the plant, and the sell-off. The good news is that the research facility is staying operational.’
‘I’m glad you won’t be out of a job.’
Don smiled at Ringer’s comment, making him understand how naive it was. If only you knew, was the look on his young, weathered face.
Don said, ‘I can’t tell you too much at this stage about the buy-out.’
‘Of course.’
‘But I wanted to let you know that representatives from the Rosier Corporation will be attending your talk. So I thought it’d be a good idea to run through a few of your findings beforehand.’
Don had a copy of Ringer’s paper on his desk. He began flicking through it. ‘There’s an element here of, let’s say, speculation.’
‘Yes, an element.’
‘To begin with, there’s your claim that gravitational effects might influence wave-function collapse.’
‘Penrose says similar things,’ Ringer replied, realizing this appeal to authority was an indication of the way Don’s unexpectedly business-like manner had rendered him immediately defensive.
‘You go further,’ said Don. ‘You imagine a wave function unable to collapse. That’s a bizarre claim. Are you honestly telling me you could open a box and find Schrödinger’s cat alive and dead at the same time?’
‘I don’t know the extent to which decoherence would be disrupted,’ said Ringer. ‘But if the gravitational field were strong enough, and if the cat could stand the tidal forces, then I think the answer might be yes.’
Don gave a matey chuckle whose undercurrent was one of unmistakable derision. ‘Fortunately our visitors aren’t philosophers,’ he said, leafing through Ringer’s paper like an end-of-year examiner intent on failing a troublesome candidate. ‘So I don’t expect we’ll find ourselves getting into any discussion of quantum metaphysics when you deliver your talk. It’s real-life science we do here at Craigcarron, not armchair theorizing.’ Now he’d found the part he was looking for. ‘Let’s talk numbers,’ he said, inspecting the page on his desk whose offending words he now pinned with an accusatory forefinger. ‘Here, for instance, at the end of section five. Non-collapsible wave functions could exhibit themselves at energies as low as 500EeV.’
‘According to my estimates,’ said Ringer, ‘it’s quite possible.’
Don shifted in his chair. ‘Under the new research plans, we need to allow for energies of 1000EeV.’
Ringer couldn’t help laughing. ‘How in God’s name do you intend to do that? I thought you were meant to be doing “real-life science”, Don. Is this corporation of yours going to build a particle accelerator stretching from here to the moon?’
Now Don wasn’t smiling. ‘I can’t discuss technical details. The array will peak at 1000EeV. So maybe we’d better think about how you reached your estimate.’
Ringer realized his mouth had fallen open. He closed it, but the gesture only added to the sense of unreality. ‘You’re telling me this little research station of yours, in a corner of Scotland that nobody’s ever heard of, will have the most powerful particle accelerator in the world?’
Don shook his head. ‘It’s not an accelerator; and by no means will it be the biggest. It’ll be part of a network.’
A network? What was he talking about?
Don pensively rubbed his hands, making a dry and unappealing sound. His blue eyes shone. ‘I only wish I could tell you all I know,’ he said, with a shaft of candour that briefly resurrected something of the younger man Ringer had known. ‘Boy, you’d love this stuff.’
‘What stuff? Why can’t you tell me?’
Don looked down again at the paper on his desk. ‘We’re talking highest-level classification here. The commercial, military, political aspects are all enormous.’ When he paused, it was for effect. Ringer was meant to be impressed that his former student had done so well for himself. Then Don sat back in his chair. ‘It’s all about harnessing vacuum energy.’
This wasn’t the first time Ringer had heard of such a thing. But on previous occasions, the suggestions had come in hand-scrawled letters from cranks. ‘You can’t tap the energy of empty space,’ he reminded Don.
‘It uses leaves of nickel-tantalum alloy. The surfaces have to be perfectly reflecting, with a geometry accurate to one part in fifty million.’
‘Ah, so it’s all done with mirrors,’ said Ringer. ‘Well, I hope they do a be
tter job on this than they did with Hubble.’
Don didn’t appreciate the sarcasm. ‘Vacuum energy is the biggest technological advance since the electric motor or the steam engine. A group in Texas managed a gain of 50GeV.’
‘Let’s see,’ said Ringer, ‘with an output like that you’d only need a few million such devices to power a light bulb.’
‘Please,’ said Don, ‘don’t be frivolous. I had to go through all kinds of hoops to get clearance to discuss this with you. I’ve had to sign God knows how many pieces of paper, telling me what I can and can’t share with you about the project. Last week I was sitting round a desk with the EU technology commissioner, a government minister and the head of one of the biggest communications companies in the United States. They’re all taking vacuum energy very seriously indeed; but if you aren’t prepared to, then you can go back out to your car right now and drive home, and we’ll never say another word about it.’
His eyes now were like ice. He had the passionate, vacant look of a true believer; an ideologue.
‘Tell me more,’ Ringer said softly.
Then Don explained how the idea went back to the 1940s, and the discovery that empty space is in effect teeming with elementary particles, virtual, fleeting and evanescent. Thousands of shiny nickel-tantalum leaves in an American laboratory had apparently plundered a tiny portion of energy from these particles before they could disappear. Though the effect was minuscule, its potential impact was so enormous that the experiment was immediately cloaked in secrecy. A paper was published, stating that no energy release had been measured. This was merely to prevent rival nations from attempting to repeat what now was being covertly scaled up.
‘How much will it all cost?’ Ringer asked.
‘So far, something like thirty million dollars has been committed to our part of it.’
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