Playing with relativity and indeterminism.
This story is one of a number to challenge assumptions about ourselves and reality. Each is inspired by a real-world scientific or spiritual genius (Einstein, LaoTzu, Ramana Maharshi…), and is presented as a visit to a game world in which that thinker’s message is re-imagined in unconventional form.
Welcome to 5chrödinger’s World and 3instein’s World. They are binary, each orbiting the same vacant point in the space between them, the center of their joint masses. They rest on discoveries that emerged from 1905 to 1925. Each predicts behavior in its realm with great accuracy, and the science from these worlds underpins many of the technological advances of the past hundred years.
Isn’t it odd, then, that we haven’t agreed how to incorporate their implications into a single picture of reality, haven’t updated popular understanding with their revelations? Each of these twirling worlds shows that our “common sense,” classical understanding of the universe is, at best, approximate, reliable only within the narrow ranges of size and speed our senses evolved to handle. In other words, they show that our story of the world is an old-fashioned and parochial one.
The worlds are inspired by Erwin Schrödinger and Albert Einstein, respectively. You are familiar with Einstein — the brain with the white, unkempt hair, mustache, and pipe. He helped usher in the quantum revolution and blew humanity’s mind with his (special, then general) theories of relativity. You may not recognize Schrödinger, except as a guy who owns a strange cat. He was a central character in early quantum mechanics, and he illustrated a famous paradox. His thought experiment shows a bizarre implication of how things work at the sub-atomic level.
You jump in and look into the face of an annoyed woman. She’s holding up a white lab coat with stains all over it. “You’re wearing my lab coat. This one is yours. You really should be more careful.”
“Sorry. Must have picked up yours by mistake.” You look at the name tag: Marie Curie.
“Yes, a mistake. Today we visit the cutting edge of science.”
“Marie, this might be a good time to tell you I failed most of my science subjects and stopped taking them as soon as I could.”
“That’s okay. There’s no way you would understand this anyway. None of us do. It is cutting edge, but it has been cutting edge for over a hundred years. Actually, it’s two cutting edges, but like a broken pair of scissors, the edges don’t meet. A brilliant scientist said about some of this material that if you think you understand it, then you don’t.”
“Is there someplace, like a café or a gift shop, where I can hang out until the tour finishes? There’s no way I’ll understand this.”
“That’s what I just said, and it’s not the point. This tour only exists for you. Its success has nothing to do with you understanding the science. Success will be you recognizing how little you know about reality.”
“Oh! Okay. If my teachers and the people I’ve asked out on dates are right, then I can deliver well on that front.”
“First, let’s peek into each of the worlds.” Marie puts on her coat and snaps her fingers. Now you’re standing on an oscillating wave that reminds you of Lao2’s surfing world. Except, the waves here are not in water. They’re in, well… nothing. The waves are all there is.
Marie says, “We are in 5chrödinger’s World. For a moment, we are two non-existent, impossible things that scientists used to believe they were.”
“Rational human beings?”
“Ha! Good one. No. Different science — physics. We are observers who do not alter the systems they observe.”
“That was my next guess.”
Marie doesn’t believe you. She continues:
5chrödinger’s World unfolds at sub-microscopic scale. It reveals features of reality that don’t fit with our accepted wisdom at the human scale. Here, our apparently objective, clockwork reality gives way to a blurred superposition of possibilities, in which either chance or remote instantaneous forces play a central role, in which particles pop into and out of existence. Put bluntly, in 5chrödinger’s World, at the most fundamental level, there is no objective reality “out there” with concrete properties independent of our observation. Hold your questions for just a bit.
You had formulated none, except for perhaps, “Say what?”
She snaps her fingers again, and you’re floating in space, with a perspective taking in about fifty rotating galaxies that resemble pinwheels.
“This is 3instein’s World. It’s basically a supersized telescope plus some clocks and measuring rods. We’re looking at the Local Group, a galaxy cluster that contains the Milky Way, our home. Let’s assume we’re as far from the nearest edge of the group as its edges are from each other. Then the light we’re seeing has been traveling for between ten and twenty million years.”
“Hmmm. Doesn’t look stale.”
Marie’s stare conveys just how unimpressed she is. Still, she tells you more about 3instein’s World.
3instein’s World operates at great speeds and across staggering distances. Here as in 5chrödinger’s World, humanity’s most basic assumptions, which rest on evolved cognitive shortcuts, fail. Space and time cease to be distinct dimensions. In different frames of reference (your velocity relative to the object you are observing), space and time are “traded off” with one another. They behave as a composite “space-time.” This space-time isn’t an unchanging container through which matter moves. It warps in response to mass, and gravity is space-time’s curvature near massive bodies. Like time and space, mass and energy lose their distinctness. One readily converts to the other — they’re the “E” and the “m” in Einstein’s famous E=mc2.
Marie snaps you back to the lab. “Questions so far?”
You’ve not wasted the past few minutes. You’re ready. “Why don’t the scissors work? Why don’t the cutting edges meet? Why are they two worlds instead of one?”
Marie nods, maybe not impressed, but less disappointed than before.
These two worlds are not at war, but they can’t communicate. They are like a squabbling couple who want to work things out but can’t find the right vocabulary to reach an understanding. Some of the explanations that make 5chrödinger’s World comprehensible are inconsistent with the ones that fit 3instein’s, and vice versa. They’ve coexisted for most of a century, but we cannot resolve them into a consistent whole.
Albert Einstein was part of the revolution that spawned 5chrödinger’s World. But Einstein held resolutely to two beliefs under threat. The first, which you might call empirical determinism, holds that every effect has a cause that is, at least in theory, discoverable. The second, which you might call localism, holds that a cause cannot deliver its effect faster than the speed of light.
“Like the light that took ten million years to travel from one edge of the Local Group to the other?”
Yet experiments suggest at least one of these sacred beliefs is false in 5chrödinger’s World.
At sub-microscopic levels, there is not a matched local cause for each effect we observe. We face a degree of unknowability with respect to how these tiny systems flow from a state in one instant, to another state in the next.
Consider radioactivity. The timing of a particle’s emission from a radioactive material like uranium, for instance (that emission is what radioactive decay is), is unpredictable. Statistically, over a long enough period, we can establish that the rate of that decay (say in particles per year) has a high chance of falling within a narrow range. However, we cannot accurately forecast when the uranium will emit its next particle. This may sound equivalent to problems we have with predicting the behavior of individual gas molecules or the weather, but it goes beyond the unpredictability of chaotic systems. There is a fundamental indeterminacy that has nothing to do with the inexactness of our measurement or our imperfect knowledge of initial conditions.
In fact, when it comes down to it, in 5chrödinger’s World, prevailing orthodoxy tells us a particle has no concrete characteristics until we measure it. In the absence of our observation/measurement, the particle exists in a “blended” condition in which all its potential states cohere in a dance of possibility. The particle doesn’t fall from this blended state into a concrete one until we force it to by observing it. It is as if the particle keeps its options open until we make it “choose.”
She’s right. You understand none of this. Well, almost none. “A dance of possibility until our observation makes it ‘choose.’ Right?”
“Well done. Remember that wave we were standing on in 5chrödinger’s World? Made of nothing, propagating through nothing, just an oscillation of probability?”
You muster a half-convincing nod.
“Well, I’m speaking loosely here, but that’s what the world — your world — is like when no one is watching. When someone is watching, it is solid, specific, determined. Unobserved, it is best imagined just like our little cheating glimpse revealed.
“We don’t notice this at the scale of people and cars and buildings, but these days, we can see this weirdness thanks to instruments that detect particles smaller than atoms.”
“We can declare the tour a success. I’m now virtually certain I understand nothing about reality.”
“But wait, there’s more! Want to see a cat that is neither alive nor dead?”
“Is it like the Cleveland Browns?”
Hah! Take that! “A reference beyond your understanding? How does it feel to lack context? Never mind.”
Marie leads you to a table with a box on it.
Schrödinger developed a paradoxical thought experiment to extend this sub-atomic “blendedness” to the human scale. This box contains a radioactive source (uranium), a radiation detector (Geiger counter), a syringe with a lethal poison, and lastly, an uneasy cat. It’s all arranged so that if the uranium emits an alpha particle (a type of radioactive decay), the Geiger counter detects it and triggers a (quick and painless) lethal injection to the cat.
You step back, putting more distance between yourself and the box. Marie continues.
If we absorb the truths of 5chrödinger’s World, then we must admit, until we find a better way to understand and say it, that the cat in the box is neither alive nor dead until we open the box to observe its status. Until then, like the particle the uranium may or may not emit to trigger the injection, the cat exists in a blended, unresolved mix of potential states. In the cat’s case, those are potential “live” and “dead” states.
You will be happy to hear no such physical experiment has been conducted and the universe doesn’t seem set up in a way that so much rides on the chance emission of a single particle.
Marie clicks her fingers again, taking you to a barn, which sits incongruously on a runway. “In case you think 3instein’s World is gentler with your common assumptions than 5chrödinger’s, here’s one final experiment before we end the tour.”
Fighting the fear she’ll ask you to milk a space cow, you agree.
Marie gets things going. “We’re back in 3instein’s World, where two observers traveling at great speed relative to one another see things differently. They will disagree — in perfectly predictable ways — over the length and mass of an object as well as the duration and simultaneity of events. We’ll cheat again and allow you to be both observers.”
“All I need to do is watch?”
“Yes, watch from two different perspectives and record the readings from the measuring devices.”
“Cool. I think I might master this science stuff after all.”
You stand outside the barn. Marie prepares you. “A log will soon fly through this barn. You’re temporarily blessed with superhuman reflexes. You will push the button in front of you at the right moment for the barn’s instantaneous front and back doors to close while the log is inside, then instantaneously open again for the log to continue its travels.”
Moving inside, next to the cow, Marie shows you a machine that will record and display the length and speed of the passing log. It will also detect whether any time gap exists in the closing of the two doors. “First, please measure the length of the barn, front to back.”
“Fifteen feet,” you say, handing the tape measure back to her.
“Keep it. You’ll need it in a moment. Take your two pointer fingers and place them on your temples.”
You do, and a second copy of yourself appears at your side. You both turn to Marie, each as confused as the other.
“Don’t ask. Okay, you…” she points at the “you” on the left, “…come with me.”
You walk with her down the runway to a log with a console on it to record and show the length of the barn, the speed at which you approach it, and whether there is a time difference in the front and back doors’ action.
“You will ride this and note the measurements on the screen. First, please measure the log’s length.”
You’re a little bit nervous, so as she straps you in and prepares to launch the log on its flight, you report and ask, “The log is twelve feet long. Isn’t it all going to happen too quickly? The barn is only about five hundred yards away. At flight speed, I’ll get there in no time.”
“You’ll fly through the barn about a minute after taking off.”
“So I’ll do a detour to build speed?”
“That’s right. A detour equivalent to over three hundred trips around the Earth.”
As your mental arithmetic stumbles over too many zeroes, she presses the launch button.
Two minutes later, the experiment is over, and your two versions reunite, standing in the barn. One has crazy-blast hair, clenched jaw muscles, and a frozen, frightened stare. Still, they (you) are ready to report the findings to Marie.
Marie asks, “Please give me all the readings you took while sitting on the flying log.”
“Log length, twelve feet. Barn length, ten feet. Wait, wasn’t it fifteen when I measured it earlier? Speed of log relative to barn, what? It says half a billion miles an hour.”
“Sounds about right. That’s a smidgen under three-quarters the speed of light. And the door timing?”
Your face ashen at the thought of your speed, “There was no time at which both doors were closed, since the log was too long to fit inside. The front one closed once the log passed inside, but the back one could only close once the whole log had completed its passage through.”
“Thank you. Now, what’s your reading from standing in the barn?”
“Log length, eight feet. Hey, wait a minute! From the log, it was twelve feet.”
“Barn length, fifteen feet. Speed, half a billion miles per hour.”
“And the doors?”
“When I pushed the button, both closed for an instant while the log was inside, with seven feet to spare!”
“With a relative speed between the two observers of three-quarters the speed of light, the log’s length was different. So was the barn’s length. And two events — the closing of the front door and the closing of the back door, were simultaneous for the barn-placed observer but not so for the log-placed observer. If we had the instruments to check, we would also find different measurements for the elapsed time of flight through the barn and for the combined mass of log and rider.”
“Which set of measurements was correct?”
“Both! Each from the perspective of its observer.”
As you scratch your head, Marie continues:
Each of these worlds shows us that the process of measurement is inseparable from the system being measured. At human scales of speed and size, we can continue to assume and act as if there is an external world of durable “stuff” in a stable time and space container, ready, formed, and waiting for us to interact with it. But as we investigate and intervene closer to the foundations of existence, we should recognize the deep ramifications of the truth that we — the observers and measurers — are part of the system we are measuring. We imagine ourselves to be outside it, but our own empiricism proves us wrong. It does so in ways suggesting empiricism may now touch its own limits. The observer is and must be a participant.
You step out, onto the observation deck at the center of mass for the two worlds. From here, you gaze upon your own world and think, “My ‘common sense’ story is blatantly inconsistent with the theories that have driven much of modern scientific and technological progress. The two most important scientific stories are even inconsistent with each other. 5chrödinger’s World and 3instein’s World await marriage, almost one hundred years after their betrothal. Both are strangers to me, but I think I know enough to guess that getting to the altar will require imagination.”
You note in your logbook:
I feel lost, but I think that means I’ve got the picture. In these worlds, my head spins. I can’t come to grips with the reality our experiments reveal, that our technology is based on. It’s not just the technical detail that’s beyond my reach. I lack the concepts and words to express what these experiments show to be true.
Perhaps that’s the point of these worlds. They make me face the fact that my story is out of date and that the reality science consistently predicts is beyond not just my but “our” explanation. They shock me into humility.
You are ready, so you say, “Let’s play.”
Two helpful, patient, and non-technical sources are:
· Gribbin’s In Search of Schrödinger’s Cat;
· Capra’s The Tao of Physics.