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Spooky Action at a Distance: The No-Communication Theorem

10 Eliezer_Yudkowsky 05 May 2008 02:43AM

Previously in seriesBell's Theorem: No EPR "Reality"

When you have a pair of entangled particles, such as oppositely polarized photons, one particle seems to somehow "know" the result of distant measurements on the other particle.  If you measure photon A to be polarized at 0°, photon B somehow immediately knows that it should have the opposite polarization of 90°.

Einstein famously called this "spukhafte Fernwirkung" or "spooky action at a distance".  Einstein didn't know about decoherence, so it seemed spooky to him.

Though, to be fair, Einstein knew perfectly well that the universe couldn't really be "spooky".  It was a then-popular interpretation of QM that Einstein was calling "spooky", not the universe itself.

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Bell's Theorem: No EPR "Reality"

16 Eliezer_Yudkowsky 04 May 2008 04:44AM

Previously in seriesEntangled Photons

(Note:  So that this post can be read by people who haven't followed the whole series, I shall temporarily adopt some more standard and less accurate terms; for example, talking about "many worlds" instead of "decoherent blobs of amplitude".)

The legendary Bayesian, E. T. Jaynes, began his life as a physicist.  In some of his writings, you can find Jaynes railing against the idea that, because we have not yet found any way to predict quantum outcomes, they must be "truly random" or "inherently random".

Sure, today you don't know how to predict quantum measurements.  But how do you know, asks Jaynes, that you won't find a way to predict the process tomorrow?  How can any mere experiments tell us that we'll never be able to predict something—that it is "inherently unknowable" or "truly random"?

As far I can tell, Jaynes never heard about decoherence aka Many-Worlds, which is a great pity.  If you belonged to a species with a brain like a flat sheet of paper that sometimes split down its thickness, you could reasonably conclude that you'd never be able to "predict" whether you'd "end up" in the left half or the right half.  Yet is this really ignorance?  It is a deterministic fact that different versions of you will experience different outcomes.

But even if you don't know about Many-Worlds, there's still an excellent reply for "Why do you think you'll never be able to predict what you'll see when you measure a quantum event?"  This reply is known as Bell's Theorem.

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Entangled Photons

8 Eliezer_Yudkowsky 03 May 2008 07:20AM

Previously in seriesDecoherence as Projection

Today we shall analyze the phenomenon of "entangled particles".  We're going to make heavy use of polarized photons here, so you'd better have read yesterday's post.

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Decoherence as Projection

15 Eliezer_Yudkowsky 02 May 2008 06:32AM

Previously in seriesThe Born Probabilities

Heisensplit In "The So-Called Heisenberg Uncertainty Principle" we got a look at how decoherence can affect the apparent surface properties of objects:  By measuring whether a particle is to the left or right of a dividing line, you can decohere the part of the amplitude distribution on the left with the part on the right.  Separating the amplitude distribution into two parts affects its future evolution (within each component) because the two components can no longer interfere with each other.

Yet there are more subtle ways to take apart amplitude distributions than by splitting the position basis down the middle.  And by exploring this, we rise further up the rabbit hole.

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The Born Probabilities

16 Eliezer_Yudkowsky 01 May 2008 05:50AM

Previously in seriesDecoherence is Pointless
Followup toWhere Experience Confuses Physicists

One serious mystery of decoherence is where the Born probabilities come from, or even what they are probabilities of.  What does the integral over the squared modulus of the amplitude density have to do with anything?

This was discussed by analogy in "Where Experience Confuses Physicists", and I won't repeat arguments already covered there.  I will, however, try to convey exactly what the puzzle is, in the real framework of quantum mechanics.

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Decoherent Essences

16 Eliezer_Yudkowsky 30 April 2008 06:32AM

Followup toDecoherence is Pointless

In "Decoherence is Pointless", we talked about quantum states such as

(Human-BLANK) * ((Sensor-LEFT * Atom-LEFT) + (Sensor-RIGHT * Atom-RIGHT))

which describes the evolution of a quantum system just after a sensor has measured an atom, and right before a human has looked at the sensor—or before the human has interacted gravitationally with the sensor, for that matter.  (It doesn't take much interaction to decohere objects the size of a human.)

But this is only one way of looking at the amplitude distribution—a way that makes it easy to see objects like humans, sensors, and atoms.  There are other ways of looking at this amplitude distribution—different choices of basis—that will make the decoherence less obvious.

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Decoherence is Pointless

10 Eliezer_Yudkowsky 29 April 2008 06:38AM

Previously in seriesOn Being Decoherent

Yesterday's post argued that continuity of decoherence is no bar to accepting it as an explanation for our experienced universe, insofar as it is a physicist's responsibility to explain it.  This is a good thing, because the equations say decoherence is continuous, and the equations get the final word.

Now let us consider the continuity of decoherence in greater detail...

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The Conscious Sorites Paradox

9 Eliezer_Yudkowsky 28 April 2008 02:58AM

Followup toOn Being Decoherent

Decoherence is implicit in quantum physics, not an extra postulate on top of it, and quantum physics is continuous.  Thus, "decoherence" is not an all-or-nothing phenomenon—there's no sharp cutoff point.  Given two blobs, there's a quantitative amount of amplitude that can flow into identical configurations between them.  This quantum interference diminishes down to an exponentially tiny infinitesimal as the two blobs separate in configuration space.

Asking exactly when decoherence takes place, in this continuous process, is like asking when, if you keep removing grains of sand from a pile, it stops being a "heap".

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On Being Decoherent

14 Eliezer_Yudkowsky 27 April 2008 04:59AM

Previously in seriesThe 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.

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Where Experience Confuses Physicists

17 Eliezer_Yudkowsky 26 April 2008 05:05AM

Continuation ofWhere Physics Meets Experience

When we last met our heroes, the Ebborians, they were discussing the known phenomenon in which the entire planet of Ebbore and all its people splits down its fourth-dimensional thickness into two sheets, just like an individual Ebborian brain-sheet splitting along its third dimension.

And Po'mi has just asked:

"Why should the subjective probability of finding ourselves in a side of the split world, be exactly proportional to the square of the thickness of that side?"

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