The cracked mirror

“I know who I WAS when I got up this morning, but I think I must have been changed several times since then.”
— Alice Through the Looking-Glass

Magritte - La Reproduction Interdite
Magritte – La Reproduction Interdite

Professor Lee Tsung gripped the edge of the sink and stared into the eyes of her reflection. In the Physics department’s toilets, all was silent, except for the dripping of a single tap, and her terse breathing. Finally, the door swung open and someone else entered, breaking the spell. The intruder was momentarily baffled by the end of a phrase that Lee whispered to herself on her way out. Something about her eyes being switched.

“I’m a mess,” she confessed later to Yang Chen, her friend and colleague in the particle physics department. Both women had been offered jobs at the American Institute of Particle Physics at the same time, and had become close friends and collaborators in their work on extensions to the Standard Model. Lee Tsung’s ambition and penetrating vision had overflowed into her personal life. It infiltrated her mannerisms, giving her nervous ticks, fiery and unstable relationships and a series of dramatic break-downs and comebacks that littered her increasingly illustrious career. Chen was the antidote to Lee’s anxious and hyperactive working style; calm, meditative and thorough, her students’ biggest complaint was that she was boring. But united by a common goal, the two scientists had worked perfectly together to uncover some of the deepest secrets of nature, pioneering the field of research on neutrino oscillations and being heavily involved with experimentalists and theoreticians in the recently successful hunt for the Higgs Boson.

“I have to quit physics. I can’t look at another textbook. I don’t dare.”

Chen was visibly shocked. In all of the ups and downs she had experienced with Tsung, the idea of quitting physics altogether had never arisen.

“What’s going on? What happened?”

Lee fixed her friend with a two-colour gaze. Her eyes, normally hidden in brooding black shadows beneath her eyebrows, now reflected the dim light of the university cafe. One eye was green and the other brown.

“You’ll think I’m crazy.”

“I already do. You’ve got nothing to lose.”

Lee studied her friend a moment longer, then sighed in resignation.

“Well if I don’t tell you, I suppose I’ll go mad anyway. But before I tell you, you have to promise me something. Promise me that you won’t tell me, not even drop a hint, which way the bias went in the Wu experiment.”

“What, you mean the parity violation experiment?”

“Don’t even talk about it! It is too dangerous. You might let something slip. I don’t want to know anything about their result.”

“But you already know the result — you lectured on particle theory back when you were an associate professor.”

“Shush already! Just listen. Last night I was working late at the cyclotron. Nothing to do with the machine itself, I was just hanging out in the lab trying to finish these damn calculations — that blasted theoretical paper on symmetry breaking. Anyway, I could barely keep my eyes open. You know how the craziest ideas always come just when you are dozing off to sleep? Well, I had one of those, and it was, –” Lee broke off to give a short laugh, “– well, it was as crazy as they come. I was thinking, isn’t it weird that the string theorists tell us every particle has a heavier super-partner, so that their calculations balance out. Well, why don’t we do the same thing for parity?”

“You lost me already.”

“You know, what if there is another universe that exists, identical to ours in every way — except that it is flipped. Into its mirror image.”

“Like in Alice through the looking-glass?”

“Exactly. In theory, there is nothing against having matter that is ordinary in every respect, except with left and right handedness reversed. The only question would be, if such a mirror-image universe existed, where is it? So I did some back-of-the-envelope calculations and found out that the coupling between mirror-matter and ordinary matter would be extremely weak. The two worlds could co-exist side by side, and we wouldn’t even know!”

Chen stirred her coffee, looking almost bored, but she didn’t drink it for a full minute. In any case, it didn’t need stirring — there was no sugar in it. Lee could almost see her friend’s mind working. At last she said:

“That’s pretty unlikely. We have some really sensitive instruments downstairs, and some really high energies. Are you telling me even they wouldn’t be able to pick something up?”

Lee’s eyes glittered with excitement.

“Exactly! That’s what I thought. It turns out that, with just a small modification of the collider experiment — the one we’re running right this minute — we could instantiate a reaction between our universe and the mirror universe. We could even exchange a substantial amount of matter between the two worlds!”

Chen’s looked up sharply.

“Lee,” she said, “Please tell me you didn’t already do it.”

Lee shrugged guiltily.

“It only cost them a few hours of data. Nobody will care – they’ll assume the diversion of the beam was due to a mistake by one of the grad students. But it worked Chen! I opened up the mirror world.”

“That’s great! You’ll be famous!”

But Lee stared down at her fingers, the nails chewed raw, and said nothing.

“That’s a Nobel prize right there! Why are you freaking out?”

“Just wait. We’re about to get to the really weird part,” said Lee.

“At first I thought the experiment wasn’t working. I had expected to see a definite interaction region, generating all kinds of particles. But I guess I hadn’t really worked out the details of what to expect. Nothing seemed to be happening to the beam. I was puzzled for a few seconds. But then there was a weird change in the light of the whole building – it seemed to get slightly brighter. And everything doubled — even the humming of the machine seemed to get twice as loud. And the numbers coming up were really bizarre. I started seeing not just the normal data stream, but additional characters superimposed on top. I don’t know that much about the displays we have, but I’m pretty sure they can’t make figures like that.”

“What do you mean?”

“They were backwards. You know, like when you try to read a book in the mirror. When I looked at the clock on the wall, it had six hands, and the two second-hands were ticking in opposite directions. The three wrong hands seemed to flicker in and out of existence, along with the extra light and sound that was coming through. ”

“Wait a second,” said Chen breathlessly, “you’re saying the interaction region encompassed the whole building?”

“Yes. Well, at least the lab and most of the surrounding infrastructure. I don’t know if it extended outside. Nobody would have noticed, I think. It was 3am.”

Chen exhaled and leaned back in her chair.

“Wow. Okay, that does sound pretty nuts. In fact, it sounds just like a crazy dream. Have you seen a therapist?”

“It felt pretty real to me. And it gets crazier. I got this overwhelming sense of dread. Fear, like you can’t imagine. I couldn’t figure out where it was coming from, and then I realised that my PC screen had gone dark, and I could see my own reflection in it.”

She swallowed.

“Not just everything in the room, but me too — I was also doubled up. There were two versions of me coexisting at once. One of them was facing me, but the other, sitting in the same place — I could only see the back of her head. I don’t know why I felt so afraid. But I did.”

“But if the two worlds were really superimposed on each other like you said, and the interaction region was so large, than the coupling must have still been very weak. Probably mostly electromagnetic. So it would have ended the party pretty fast, right? And with a very low rate of matter exchange.”

“Yes, that’s what I expected too. But it didn’t happen. The double-images persisted for at least a minute. It seemed like forever, just me sitting there staring at the back of my own head bizarrely superimposed on my face. I kept wondering, if I were in the other world, would I also just be sitting here? But it was the strangest thing … it was quiet enough that I could hear us both breathing. Her and me — or me and me, I suppose. But I could also hear buttons being pressed at the console, very slowly and softly. I recognised the `click’ they made. It was unmistakable. I swear she had an arm up somewhere where I couldn’t see in the reflection, controlling the beam.”

“Wait. What does that mean? What are you saying?”

Lee leaned forward, almost hesitating to speak. When she did, it was in a low voice, uncharacteristic of her.

“Don’t play dumb Chen. I’m saying, maybe that interaction was exactly as strong as I expected. But maybe all the matter exchange was happening at a single location. It’s against protocol, but I know that in principle we can localise the beam almost anywhere within the facility … including the console where I was sitting.”

“You think your mirror-self was focusing the interaction on herself? On you? Swapping your matter with hers between the two universes?”

“Well, I don’t know really – I sort of blacked out. I woke up after 5am, slumped at the desk by the beam controls, drooling like a baby. First thing I did was look at the clock. The second hand was moving clockwise, like always. I checked every document I could find, it was all written left to right. I still have the birthmark on my left hand, not the right. You can verify that.”

Lee held up her hand. Chen said:

“So, everything’s fine then! You’re not in the mirror world. You’re in the real world. I’m the real me, you’re the real you. And you’ll be famous for discovering mirror matter!”

Lee shook her head.

“There’s more. I was looking at myself in the mirror just before I called you today. Staring at my eyes. Of course, as you might guess, the left one was still brown and the right one was still green, as it always was. But a thought occurred to me. These eyes being examined — they themselves are the examiners. The world looks the right way around, alright, but what if I’m seeing it through mirrored eyes? Sure, when you look in the mirror everything looks flipped left and right from your perspective. But what if your perspective also gets flipped?”

“You mean, if a mirror image reads a book, does it look backwards to her?”

“Exactly. You look at your reflection and you see its left and right hands are switched. But if you point to the hand that you think is your right hand, the image points to its left hand. The image perceives it’s left hand as its right hand. It looks at you, and from its perspective, you are the one who has got it wrong. The mirror image can’t tell that it is a mirror image.”

Chen was silent.

“Imagine that, next time you wake up, you have a fifty-fifty chance of waking up as your own mirror image, in the mirror universe. Could you leave any kind of trace or signal for yourself that you could use to tell if it happened or not? You can try to use books, clocks, birthmarks or even tattoo yourself with big signs saying `left hand’ and `right hand’ — but it won’t do any good, because the switch is always compensated by your own switch in perspective. You lose your reference point.”

“Come on. There has to be some way to tell. Gyroscopes? Spinning stars? Light polarisation?”

Lee shook her head.

“Not quite. We know that classical physics is parity invariant. Newton’s equations, even electromagnetism, all invariant under flipping left and right. Think more fundamental. More modern.”

Chen sucked on the end of her spoon, frowning at the ceiling of the cafe. She still hadn’t touched her coffee. Then she gasped:

“Beta decay! Weak interactions violate parity! You could just dig up the paper by Wu and check whether the direction of emission was — mmf!”

Lee lunged over the table, upsetting a glass of water, to block Chen’s mouth forcibly with her hand.

“Sorry!” Chen whispered breathlessly. Lee glared at her.

“I told you! I don’t want to know which way those experiments came out.”

There was a pause as a waiter came to mop up the spill, glancing nervously at the two women before moving on.

“But why not?” said Chen when he was gone.

“It will resolve your question once and for all. In fact, –” she rummaged around in her bag, “I have my lecture notes here that I prepared for the particle physics course. It’s on page 68 … or maybe 69. One of those.”

She carefully placed the paper on the table, her lips pursed to prove to Lee that she wasn’t going to accidentally mention the answer. Lee took the paper and placed her coffee cup solidly on top.

“You have to understand,” said Lee, “what it would mean if I was right. If I find out that the direction of parity violation in this universe is different to what it is in my memory, that means that I live in the wrong world. Could I live with that knowledge?”

Chen shrugged.

“Why not? You said everything is the same between the worlds, right? Who cares if your left hand turned into your right?”

“Yes. That’s the point. Doesn’t it all seem rather convenient? That the mirror world should exactly match our universe, in all details, apart from things like the direction of beta decay. Don’t forget, we are talking about physics here. Simply reversing the handedness of matter doesn’t say anything about what kind of world is constructed out of it. In all probability, I should have coupled through to just empty space — after all, most of the universe is empty space. Why should the orbits of the two Earth’s match up so precisely, and their rotations, right down to the location of my laboratory? Think about it Chen. What kind of powerful force could arrange everything just so that, if one person should find a way to open up a gateway between the worlds, it would be possible to switch her with her mirror copy, and she wouldn’t notice a thing?”

“I don’t know, Lee!” said Chen, now visibly exasperated.

Lee slumped in her chair.

“I don’t know either,” she said at last.

“That’s the thing that bothers me. Maybe there really is a perfectly good reason why there should be another copy of Earth in the mirror universe, and another copy of me. But why would the people on the other side try to hide it? It is like they were waiting for it. Like they didn’t want me to know the difference. So that I wouldn’t try to go back after the switch was made. But if that’s true, then who — or what — took my place?”

Chen held her friend’s hand tight.

“Okay. I believe you. But please listen to me. It might seem like a fifty-fifty chance whether you are in the real world or the mirror world. But that’s not how probability works. Taking into account human psychology, you have to admit, it’s far more likely that you are suffering from delusions. I beg you, read the results of the Wu experiment. Set your mind at rest. The odds aren’t even — they’re a billion to one against. Do it right now, and end this.”

Lee looked at the document in front of her. She sighed. What was worse, knowing or not knowing? She leafed over to page 68.


Chen waited eagerly.

“Just preliminaries.”

“Must be the next page!”

Chen nearly tore the page while turning it, and pointed to the relevant paragraph.

“Look. That’s where I describe the set-up.”

Lee was looking curiously at her friend.

“What? Don’t you want to know?”

“I don’t know. Why are you so eager to show me? Is this part of the plan?”

Chen was caught off guard.

“What plan? Come on, Lee. I just want you to stop acting crazy so we can go back to how things were before.”

Lee held Chen’s eyes a moment longer, then finally looked down at the page.

“Okay. From what I remember, the electrons were biased parallel to the direction of current through the coil.”

She skimmed through the paragraph with her fingertip and then froze. For a moment, she seemed unable to lift her head, and when she did, her eyes held a peculiar expression.

“Chen…” she said, and her voice barely came out, “this says the bias was against the current.”

A strange blank stare had come over Chen’s face.

“Who … what are you?” said Lee. Her voice rose and her eyes flickered over the people around her in the cafe:

“Why did you do this? What world is this?”

She stood up and her chair scraped backwards and almost toppled. At the sound, Chen’s peculiar paralysis seemed to break. She held up both her hands.

“Woah woah woah. Calm down.”

“What! Explain to me what the hell is going on!”

“Listen to me,” said Chen urgently, “what charge convention were you using?”

Lee stared, speechless. Chen blustered on:

“I know you like to be unconventional. I remember you often saying that sometimes you define current as being in the direction of positive charge, just to keep your students on their toes. If so, then your memory of the result would be that the electrons were emitted parallel to positive current — which means against the actual flow of electrons. Just like it says in my notes.”

Lee stood still for a full ten seconds, and the entire cafe had gone quiet, waiting for a scene to break out. But after what seemed like an eternity, she fell back into her seat and buried her face in her arms.

“I can’t remember.”

And all the while, as Chen tried to console her, as Lee slowly came to terms with the fact that with the one escaped memory of that lecture she had given, ten years ago, where she may or may not have used an unconventional definition of electric current, another memory kept returning to her. It was a memory, not form ten years ago, but in fact from that very same day, after she had woken up — from what might have been a dream — and staggered down to the bathroom to stare at herself so long in the mirror. The memory of what might have been an involuntary twitch of the eye of her reflection. Nothing to notice at the time, but on reflection, now that she thought about it, it seemed almost, unmistakably: a suppressed wink.


2 thoughts on “The cracked mirror

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s