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".
As you might have guessed from reading about decoherence and Heisenberg, this is because we ourselves are governed by the laws of quantum mechanics and subject to decoherence.
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"
Speaking of the Big Bang, after being reminded of a question elsewhere I'm curious as to whether people knowledgeable of it can evaluate my interpretation of it here.
I don't yet see how the possible existence of "duplicates" of me 10^(10^29) (is this different than 10^30?) light years away or "decohered amplitude-blobs of me" has an effect on my subjective conscious experience. Is the known/extrapolatable universe 10^(10^29) years old? That sounds a bit older than popularly presented ages of the universe.
It sounds like you're writing that these "duplicates" have no effect on our subjective conscious experience. And that does seem to me to be the case (I assume "decohered amplitude-blo... (read more)
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 implied by the Standard Model of physics.
How exactly do you get spatial infinity from a big bang in finite time? The stories I hear about the big bang are that the universe was initially very, very small at the beginning of the big bang. If it was small then it was finite. How does an object (such as the universe) grow from finite size to infinite size in finite time?
It's not known whether the Universe is finite or infinite, this article gives more details:
If the Universe is infinite, then it has always been so even from the moment after the Big Bang; an infinite space can still expand.
It hadn't quite sunk in until this article that looked at from a sum-over-histories point of view, only identical configurations interfere; that makes decoherence much easier to understand.
Sebastian, so 10^30 is 10 with 30 zeros after it. 10^10^29 is 10 with zillions of zeros after it. Thanks for making that clear.
Eliezer, I think your usage of "Standard Model" is different from that of physicists.
Quantum suicide is a good way to ensure that your next experience will be the trivial "experience" of being a corpse with no brain activity.
So what you're saying is that God does not play dice, and that frequentism is fundamentally true.
I think this has been the best post so far. I'd like to answer one of my previous questions to make sure I am grokking this; please weigh in if I am off. Here was my question:
Q: Am I correct in assuming that [the amplitude distribution] is independent of (observations, "wave function collapses", or whatever it is when we say that we find a particle at a certain point)?
A: As I suspected, a bit of a Wrong Question. But yes, there is only one amplitude distribution that progresses over time
Q: For example, let's I have a particle that is "probab... (read more)
BTW, are you going to cover why the probability of a configuration is the square of its amplitude? Or if that was somehow already answered by the Ebborians, could I get a translation? :)
"And both spatial infinity and inflation are standard in the current model of physics."
As mentioned by a commenter above, spatial infinity is by no means required or implied by physical observation. Non-compact space-times are allowed by general relativity, but so are compact tori (which is a very real possibility) or a plethora of bizarre geometries which have been ruled out by experimental evidence.
Inflation is an interesting theory which agrees well with the small (relative to other areas of physics) amount of cosmological data which has bee... (read more)
"But you talk about some of your ideas like it's obvious and accepted by anyone who isn't an idiot. This does your readers a disservice.
I realize that this is a blog and not a refereed journal, so I can't expect you to follow all the rules. But I can appeal to your commitment to honesty in asking you to express the uncertainty of your ideas and to defer when necessary to the academic establishment."
Eliezer this is really great advice. Please take it.
Jess Reidel: I enjoy your take on Quantum Mechanics, Eliezer, and I recommend this blog to everyone I know. I agree with you that Copenhagen untenable and the MWI is the current best idea. But you talk about some of your ideas like it's obvious and accepted by anyone who isn't an idiot. This does your readers a disservice.
I realize that this is a blog and not a refereed journal, so I can't expect you to follow all the rules. But I can appeal to your commitment to honesty in asking you to express the uncertainty of your ideas and to defer when necessary to... (read more)
Greg Egan also said:
"Though a handful of self-described Transhumanists are thinking rationally about real prospects for the future, the overwhelming majority might as well belong to a religious cargo cult based on the notion that self-modifying AI will have magical powers."
Maybe it's time to stop holding up Greg Egan like some kind of icon.
"But what do all these posts have to do with your Artificial Intelligence work?"
Some of us are in fact pleased by how closely this does have to do with your AI work.
Maybe it's time to stop holding up Greg Egan like some kind of icon.
Why? Quarantine and Permutation City are still really good books. Egan is a icon of idea-based science fiction, not an icon of futurism.
Maybe you can admire someone who directly thinks you're a crackpot, but I can't.
"Yes, I talk about these ideas as if they are obvious. They are. It's important to remember that while learning quantum mechanics. It's not difficult unless you make it difficult. Just because certain academics are currently doing so, is no reason for me to do the same. I explicitly said at the outset (in "Quantum Explanations") that the views I presented would not be a uniform consensus among physicists, but I was going to leave out the controversies until later, so I could teach the version that I think is simple and sane. Bayesianism befo... (read more)
Hopefully and Jess,
I understand what you're saying, but I truly and honestly believe that quantum physics as it works in the real universe truly is a hell of a lot simpler than the arguments that people have about quantum physics. I think the arguments are overcomplicated and pointless. Every time I even mention their existence, I worry whether I'm unnecessarily confusing the readers.
Let's start with the simple version. It's even the majority version - no, not the unanimous version, but the majority version among theoretical physicists, yes.
I'm not sure... (read more)
"... the overwhelming majority might as well belong to a religious cargo cult based on the notion that self-modifying AI will have magical powers."
"Maybe you can admire someone who directly thinks you're a crackpot, but I can't."
I have a high regard for most extropians (a subset of Transhumans, I think) I know well, but that doesn't make me believe that the Egan line is more than hyperbole at most. I don't take it as a slur against anyone whose name I know. I've certainly seen evidence that the majority wouldn't be able to distinguish... (read more)
Hopefully: If an exact duplicate of you 10^(10^29) light years away was being tortured you would know because torture is the description of a physical state. Another copy of your physical state can't be subject to torture without your also being subject to it. OTOH, I think that you are imagining a physical system that has evolved from a system that was, when described classically just like you. Such a system doesn't transmit any information to you so your consciousness can't be of it being tortured.
When I say "me" here, I mean my consciousness, the one I'm experiencing right here right now in this locality. So I think it's your OTOH statement that would be relevant. I read from your post the reasonable point that it's a presumably impossible paradox that any exact duplicate of me would be tortured while I am not, because then it wouldn't be my exact duplicate. But presumably by the same big universe logic, 10^(10^29) light years away (or closer) something that is otherwise an exact duplicate of me IS being tortured. Sucks to be that guy! :P
I just wanted to say I've benefited greatly from this series, and especially from the last few posts. I'd studied some graduate quantum mechanics, but bailed out before Feynman paths, decoherence, etc; and from what I'd experienced with it, I was beginning to think an intuitive explanation of (one interpretation of) quantum mechanics was nigh-impossible. Thanks for proving me wrong, Eliezer.
The argument (from elegance/Occam's Razor) for the many-worlds interpretation seems impressively strong, too. I'll be interested to read the exchanges when you let the one-world advocates have their say.
Hopefully: What do you mean by saying that your consciousness is "in this locality"? How is consciousness "in a locality" at all? "(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.)" was a joke.
Like another Dave almost three years ago, I think this post was the most effective so far. Not as in 'constructed better', because I suspect that almost everything in previous posts in the QM series and quite a lot in posts elsewhere was building up to this.
I'd been getting used to thinking in terms of sensors being entangled with the particles they sense etc. but references to humans being entangled too seemed to be somewhere between obvious and avoiding the issue: I didn't feel what that meant. In this thread I'd got to the bottom and was wondering why ... (read more)
My twin 10^29^29 ly away... if he picks up an astronomy atlas, will he find the exact same objects listed with the exact same coordinates digit for digit? That implies that space itself repeats, like tiles in a desktop pattern.
Is cyclicity a necessary consequence of filling an infinite space with things that can only have a finite number of configurations? If so, does that mean if I zoom in on a Mandelbrot set far enough I will see an exact replica of the image I started with and if I run a cellular automaton long enough I will get a regular pattern?