## Spooky Action at a Distance: The No-Communication Theorem

**Previously in series**: Bell'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.

## Bell's Theorem: No EPR "Reality"

**Previously in series**: Entangled 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.

## Entangled Photons

**Previously in series**: Decoherence 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.

## Decoherence as Projection

**Previously in series**: The Born Probabilities

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.

## The Born Probabilities

**Previously in series**: Decoherence is Pointless**Followup to**: Where 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.

## Decoherent Essences

**Followup to**: Decoherence 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.

## Decoherence is Pointless

**Previously in series**: On 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...

## The Conscious Sorites Paradox

**Followup to**: On 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".

## On Being Decoherent

**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.

## Where Experience Confuses Physicists

**Continuation of**: Where 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?"