Apr 27, 2008
Previously in series: The So-Called Heisenberg Uncertainty Principle
"A human researcher only sees a particle in one place at one time." At least that's what everyone goes around repeating to themselves. Personally, I'd say that when a human researcher looks at a quantum computer, they quite clearly see particles not behaving like they're in one place at a time. In fact, you have never in your life seen a particle "in one place at a time" because they aren't.
Nonetheless, when you construct a big measuring instrument that is sensitive to a particle's location—say, the measuring instrument's behavior depends on whether a particle is to the left or right of some dividing line—then you, the human researcher, see the screen flashing "LEFT", or "RIGHT", but not a mixture like "LIGFT".
The standpoint of the Feynman path integral suggests viewing the evolution of a quantum system as a sum over histories, an integral over ways the system "could" behave—though the quantum evolution of each history still depends on things like the second derivative of that component of the amplitude distribution; it's not a sum over classical histories. And "could" does not mean possibility in the logical sense; all the amplitude flows are real events...
Nonetheless, a human being can try to grasp a quantum system by imagining all the ways that something could happen, and then adding up all the little arrows that flow to identical outcomes. That gets you something of the flavor of the real quantum physics, of amplitude flows between volumes of configuration space.
Now apply this mode of visualization to a sensor measuring an atom—say, a sensor measuring whether an atom is to the left or right of a dividing line.
Which is to say: The sensor and the atom undergo some physical interaction in which the final state of the sensor depends heavily on whether the atom is to the left or right of a dividing line. (I am reusing some previous diagrams, so this is not an exact depiction; but you should be able to use your own imagination at this point.)
You may recognize this as the entangling interaction described in "Decoherence". A quantum system that starts out highly factorizable, looking plaid and rectangular, that is, independent, can evolve into an entangled system as the formerly-independent parts interact among themselves.
So you end up with an amplitude distribution that contains two blobs of amplitude—a blob of amplitude with the atom on the left, and the sensor saying "LEFT"; and a blob of amplitude with the atom on the right, and the sensor saying "RIGHT".
For a sensor to measure an atom is to become entangled with it—for the state of the sensor to depend on the state of the atom—for the two to become correlated. In a classical system, this is true only on a probabilistic level. In quantum physics it is a physically real state of affairs.
To observe a thing is to entangle yourself with it. You may recall my having previously said things that sound a good deal like this, in describing how cognition obeys the laws of thermodynamics, and, much earlier, talking about how rationality is a phenomenon within causality. It is possible to appreciate this in a purely philosophical sense, but quantum physics helps drive the point home.
Let's say you've got an Atom, whose position has amplitude bulges on the left and on the right. We can regard the Atom's distribution as a sum (addition, not multiplication) of the left bulge and the right bulge:
Atom = (Atom-LEFT + Atom-RIGHT)
Also there's a Sensor in a ready-to-sense state, which we'll call BLANK:
Sensor = Sensor-BLANK
By hypothesis, the system starts out in a state of quantum independence—the Sensor hasn't interacted with the Atom yet. So:
System = (Sensor-BLANK) * (Atom-LEFT + Atom-RIGHT)
Sensor-BLANK is an amplitude sub-distribution, or sub-factor, over the joint positions of all the particles in the sensor. Then you multiply this distribution by the distribution (Atom-LEFT + Atom-RIGHT), which is the sub-factor for the Atom's position. Which gets you the joint configuration space over all the particles in the system, the Sensor and the Atom.
Quantum evolution is linear, which means that Evolution(A + B) = Evolution(A) + Evolution(B). We can understand the behavior of this whole distribution by understanding its parts. Not its multiplicative factors, but its additive components. So now we use the distributive rule of arithmetic, which, because we're just adding and multiplying complex numbers, works just as usual:
System = (Sensor-BLANK) * (Atom-LEFT + Atom-RIGHT)
= (Sensor-BLANK * Atom-LEFT) + (Sensor-BLANK * Atom-RIGHT)
Now, the volume of configuration space corresponding to (Sensor-BLANK * Atom-LEFT) evolves into (Sensor-LEFT * Atom-LEFT).
Which is to say: Particle positions for the sensor being in its initialized state and the Atom being on the left, end up sending their amplitude flows to final configurations in which the Sensor is in a LEFT state, and the Atom is still on the left.
So we have the evolution:
(Sensor-BLANK * Atom-LEFT) + (Sensor-BLANK * Atom-RIGHT)
(Sensor-LEFT * Atom-LEFT) + (Sensor-RIGHT * Atom-RIGHT)
By hypothesis, Sensor-LEFT is a different state from Sensor-RIGHT—otherwise it wouldn't be a very sensitive Sensor. So the final state doesn't factorize any further; it's entangled.
But this entanglement is not likely to manifest in difficulties of calculation. Suppose the Sensor has a little LCD screen that's flashing "LEFT" or "RIGHT". This may seem like a relatively small difference to a human, but it involves avogadros of particles—photons, electrons, entire molecules—occupying different positions.
So, since the states Sensor-LEFT and Sensor-RIGHT are widely separated in the configuration space, the volumes (Sensor-LEFT * Atom-LEFT) and (Sensor-RIGHT * Atom-RIGHT) are even more widely separated.
The LEFT blob and the RIGHT blob in the amplitude distribution can be considered separately; they won't interact. There are no plausible Feynman paths that end up with both LEFT and RIGHT sending amplitude to the same joint configuration. There would have to be a Feynman path from LEFT, and a Feynman path from RIGHT, in which all the quadrillions of differentiated particles ended up in the same places. So the amplitude flows from LEFT and RIGHT don't intersect, and don't interfere.
You may recall this principle from "Decoherence", for how a sensitive interaction can decohere two interacting blobs of amplitude, into two noninteracting blobs.
Formerly, the Atom-LEFT and Atom-RIGHT states were close enough in configuration space, that the blobs could interact with each other—there would be Feynman paths where an atom on the left ended up on the right. Or Feynman paths for both an atom on the left, and an atom on the right, to end up in the middle.
Now, however, the two blobs are decohered. For LEFT to interact with RIGHT, it's not enough for just the Atom to end up on the right. The Sensor would have to spontaneously leap into a state where it was flashing "RIGHT" on screen. Likewise with any particles in the environment which previously happened to be hit by photons for the screen flashing "LEFT". Trying to reverse decoherence is like trying to unscramble an egg.
And when a human being looks at the Sensor's little display screen... or even just stands nearby, with quintillions of particles slightly influenced by gravity... then, under exactly the same laws, the system evolves into:
(Human-LEFT * Sensor-LEFT * Atom-LEFT) + (Human-RIGHT * Sensor-RIGHT * Atom-RIGHT)
Thus, any particular version of yourself only sees the sensor registering one result.
That's it—the big secret of quantum mechanics. As physical secrets go, it's actually pretty damn big. Discovering that the Earth was not the center of the universe, doesn't hold a candle to realizing that you're twins.
That you, yourself, are made of particles, is the fourth and final key to recovering the classical hallucination. It's why you only ever see the universe from within one blob of amplitude, and not the vastly entangled whole.
Asking why you can't see Schrodinger's Cat as simultaneously dead and alive, is like an Ebborian asking: "But if my brain really splits down the middle, why do I only ever remember finding myself on either the left or the right? Why don't I find myself on both sides?"
Because you're not outside and above the universe, looking down. You're in the universe.
Your eyes are not an empty window onto the soul, through which the true state of the universe leaks in to your mind. What you see, you see because your brain represents it: because your brain becomes entangled with it: because your eyes and brain are part of a continuous physics with the rest of reality.
You only see nearby objects, not objects light-years away, because photons from those objects can't reach you, therefore you can't see them. By a similar locality principle, you don't interact with distant configurations.
When you open your eyes and see your shoelace is untied, that event happens within your brain. A brain is made up of interacting neurons. If you had two separate groups of neurons that never interacted with each other, but did interact among themselves, they would not be a single computer. If one group of neurons thought "My shoelace is untied", and the other group of neurons thought "My shoelace is tied", it's difficult to see how these two brains could possibly contain the same consciousness.
And if you think all this sounds obvious, note that, historically speaking, it took more than two decades after the invention of quantum mechanics for a physicist to publish that little suggestion. People really aren't used to thinking of themselves as particles.
The Ebborians have it a bit easier, when they split. They can see the other sides of themselves, and talk to them.
But the only way for two widely separated blobs of amplitude to communicate—to have causal dependencies on each other—would be if there were at least some Feynman paths leading to identical configurations from both starting blobs.
Once one entire human brain thinks "Left!", and another entire human brain thinks "Right!", then it's extremely unlikely for all of the particles in those brains, and all of the particles in the sensors, and all of the nearby particles that interacted, to coincidentally end up in approximately the same configuration again.
It's around the same likelihood as your brain spontaneously erasing its memories of seeing the sensor and going back to its exact original state; while nearby, an egg unscrambles itself and a hamburger turns back into a cow.
So the decohered amplitude-blobs don't interact. And we never get to talk to our other selves, nor can they speak to us.
Of course, this doesn't mean that the other amplitude-blobs aren't there any more, any more than we should think that a spaceship suddenly ceases to exist when it travels over the cosmological horizon (relative to us) of an expanding universe.
(Oh, you thought that post on belief in the implied invisible was part of the Zombie sequence? No, that was covert preparation for the coming series on quantum mechanics.
You can go through line by line and substitute the arguments, in fact.
Remember that the next time some commenter snorts and says, "But what do all these posts have to do with your Artificial Intelligence work?")
Disturbed by the prospect of there being more than one version of you? But as Max Tegmark points out, living in a spatially infinite universe already implies that an exact duplicate of you exists somewhere, with probability 1. In all likelihood, that duplicate is no more than 10^(1029) lightyears away. Or 10^(1029) meters away, with numbers of that magnitude it's pretty much the same thing.
(Stop the presses! Shocking news! Scientists have announced that you are actually the duplicate of yourself 10^(1029) lightyears away! What you thought was "you" is really just a duplicate of you.)
You also get the same Big World effect from the inflationary scenario in the Big Bang, which buds off multiple universes. And both spatial infinity and inflation are more or less standard in the current model of physics. So living in a Big World, which contains more than one person who resembles you, is a bullet you've pretty much got to bite—though none of the guns are certain, physics is firing that bullet at you from at least three different directions.
Maybe later I'll do a post about why you shouldn't panic about the Big World. You shouldn't be drawing many epistemic implications from it, let alone moral implications. As Greg Egan put it, "It all adds up to normality." Indeed, I sometimes think of this as Egan's Law.
Part of The Quantum Physics Sequence
Next post: "The Conscious Sorites Paradox"
Previous post: "Where Experience Confuses Physicistss"