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.
Suppose that you have the "entangled" (non-independent) state:
(Sensor-LEFT * Atom-LEFT) + (Sensor-RIGHT * Atom-RIGHT)
considering now only the sensor and the atom.
This state looks nicely diagonalized—separated into two distinct blobs. But by linearity, we can take apart a quantum amplitude distribution any way we like, and get the same laws of physics back out. So in a different basis, we might end up writing (Sensor-LEFT * Atom-LEFT) as:
(0.5(Sensor-LEFT + Sensor-RIGHT) + 0.5(Sensor-LEFT - Sensor-RIGHT)) * (0.5(Atom-RIGHT + Atom-LEFT) - 0.5(Atom-RIGHT - Atom-LEFT))
(Don't laugh. There are legitimate reasons for physicists to reformulate their quantum representations in weird ways.)
The result works out the same, of course. But if you view the entangled state in a basis made up of linearly independent components like (Sensor-LEFT - Sensor-RIGHT) and (Atom-RIGHT - Atom-LEFT), you see a differently shaped amplitude distribution, and it may not look like the blobs are separated.
Oh noes! The decoherence has disappeared!
...or that's the source of a huge academic literature asking, "Doesn't the decoherence interpretation require us to choose a preferred basis?"
To which the short answer is: Choosing a basis is an isomorphism; it doesn't change any experimental predictions. Decoherence is an experimentally visible phenomenon or we would not have to protect quantum computers from it. You can't protect a quantum computer by "choosing the right basis" instead of using environmental shielding. Likewise, looking at splitting humans from another angle won't make their decoherence go away.
But this is an issue that you're bound to encounter if you pursue quantum mechanics, especially if you talk to anyone from the Old School, and so it may be worth expanding on this reply.
After all, if the short answer is as obvious as I've made it sound, then why, oh why, would anyone ever think you could eliminate an experimentally visible phenomenon like decoherence, by isomorphically reformulating the mathematical representation of quantum physics?
That's a bit difficult to describe in one mere blog post. It has to do with history. You know the warning I gave about dragging history into explanations of QM... so consider yourself warned: Quantum mechanics is simpler than the arguments we have about quantum mechanics. But here, then, is the history:
Once upon a time,
Long ago and far away, back when the theory of quantum mechanics was first being developed,
No one had ever thought of decoherence. The question of why a human researcher only saw one thing at a time, was a Great Mystery with no obvious answer.
You had to interpret quantum mechanics to get an answer back out of it. Like reading meanings into an oracle. And there were different, competing interpretations. In one popular interpretation, when you "measured" a system, the Quantum Spaghetti Monster would eat all but one blob of amplitude, at some unspecified time that was exactly right to give you whatever experimental result you actually saw.
Needless to say, this "interpretation" wasn't in the quantum equations. You had to add in the extra postulate of a Quantum Spaghetti Monster on top, additionally to the differential equations you had fixed experimentally for describing how an amplitude distribution evolved.
Along came Hugh Everett and said, "Hey, maybe the formalism just describes the way the universe is, without any need to 'interpret' it."
But people were so used to adding extra postulates to interpret quantum mechanics, and so unused to the idea of amplitude distributions as real, that they couldn't see this new "interpretation" as anything except an additional Decoherence Postulate which said:
"When clouds of amplitude become separated enough, the Quantum Spaghetti Monster steps in and creates a new world corresponding to each cloud of amplitude."
So then they asked:
"Exactly how separated do two clouds of amplitude have to be, quantitatively speaking, in order to invoke the instantaneous action of the Quantum Spaghetti Monster? And in which basis does the Quantum Spaghetti Monster measure separation?"
But, in the modern view of quantum mechanics—which is accepted by everyone except for a handful of old fogeys who may or may not still constitute a numerical majority—well, as David Wallace puts it:
"If I were to pick one theme as central to the tangled development of the Everett interpretation of quantum mechanics, it would probably be: the formalism is to be left alone."
Decoherence is not an extra phenomenon. Decoherence is not something that has to be proposed additionally. There is no Decoherence Postulate on top of standard QM. It is implicit in the standard rules. Decoherence is just what happens by default, given the standard quantum equations, unless the Quantum Spaghetti Monster intervenes.
Some still claim that the quantum equations are unreal—a mere model that just happens to give amazingly good experimental predictions. But then decoherence is what happens to the particles in the "unreal model", if you apply the rules universally and uniformly. It is denying decoherence that requires you to postulate an extra law of physics, or an act of the Quantum Spaghetti Monster.
(Needless to say, no one has ever observed a quantum system behaving coherently, when the untouched equations say it should be decoherent; nor observed a quantum system behaving decoherently, when the untouched equations say it should be coherent.)
If you're talking about anything that isn't in the equations, you must not be talking about "decoherence". The standard equations of QM, uninterpreted, do not talk about a Quantum Spaghetti Monster creating new worlds. So if you ask when the Quantum Spaghetti Monster creates a new world, and you can't answer the question just by looking at the equations, then you must not be talking about "decoherence". QED.
Which basis you use in your calculations makes no difference to standard QM. "Decoherence" is a phenomenon implicit in standard QM. Which basis you use makes no difference to "decoherence". QED.
Changing your view of the configuration space can change your view of the blobs of amplitude, but ultimately the same physical events happen for the same causal reasons. Momentum basis, position basis, position basis with a different relativistic space of simultaneity—it doesn't matter to QM, ergo it doesn't matter to decoherence.
If this were not so, you could do an experiment to find out which basis was the right one! Decoherence is an experimentally visible phenomenon—that's why we have to protect quantum computers from it.
Ah, but then where is the decoherence in
(0.5(Sensor-LEFT + Sensor-RIGHT) + 0.5(Sensor-LEFT - Sensor-RIGHT)) * (0.5(Atom-RIGHT + Atom-LEFT) - 0.5(Atom-RIGHT - Atom-LEFT)) + (0.5(Sensor-LEFT + Sensor-RIGHT) - 0.5(Sensor-LEFT - Sensor-RIGHT)) * (0.5(Atom-RIGHT + Atom-LEFT) + 0.5(Atom-RIGHT - Atom-LEFT))
The decoherence is still there. We've just made it harder for a human to see, in the new representation.
The main interesting fact I would point to, about this amazing new representation, is that we can no longer calculate its evolution with local causality. For a technical definition of what I mean by "causality" or "local", see Judea Pearl's Causality. Roughly, to compute the evolution of an amplitude cloud in a locally causal basis, each point in configuration space only has to look at its infinitesimal neighborhood to determine its instantaneous change. As I understand quantum physics—I pray to some physicist to correct me if I'm wrong—the position basis is local in this sense.
(Note: It's okay to pray to physicists, because physicists actually exist and can answer prayers.)
However, once you start breaking down the amplitude distribution into components like (Sensor-RIGHT—Sensor-LEFT), then the flow of amplitude, and the flow of causality, is no longer local within the new configuration space. You can still calculate it, but you have to use nonlocal calculations.
In essence, you've obscured the chessboard by subtracting the queen's position from the king's position. All the information is still there, but it's harder to see.
When it comes to talking about whether "decoherence" has occurred in the quantum state of a human brain, what should intuitively matter is questions like, "Does the event of a neuron firing in Human-LEFT have a noticeable influence on whether a corresponding neuron fires in Human-RIGHT?" You can choose a basis that will mix up the amplitude for Human-LEFT and Human-RIGHT, in your calculations. You cannot, however, choose a basis that makes a human neuron fire when it would not otherwise have fired; any more than you can choose a basis that will protect a quantum computer without the trouble of shielding, or choose a basis that will make apples fall upward instead of down, etcetera.
The formalism is to be left alone! If you're talking about anything that isn't in the equations, you're not talking about decoherence! Decoherence is part of the invariant essence that doesn't change no matter how you spin your basis—just like the physical reality of apples and quantum computers and brains.
There may be a kind of Mind Projection Fallacy at work here. A tendency to see the basis itself as real—something that a Quantum Spaghetti Monster might come in and act upon—because you spend so much time calculating with it.
In a strange way, I think, this sort of jump is actively encouraged by the Old School idea that the amplitude distributions aren't real. If you were told the amplitude distributions were physically real, you would (hopefully) get in the habit of looking past mere representations, to see through to some invariant essence inside—a reality that doesn't change no matter how you choose to represent it.
But people are told the amplitude distribution is not real. The calculation itself is all there is, and has no virtue save its mysteriously excellent experimental predictions. And so there is no point in trying to see through the calculations to something within.
Then why not interpret all this talk of "decoherence" in terms of an arbitrarily chosen basis? Isn't that all there is to interpret—the calculation that you did in some representation or another? Why not complain, if—having thus interpreted decoherence—the separatedness of amplitude blobs seems to change, when you change the basis? Why try to see through to the neurons, or the flows of causality, when you've been told that the calculations are all?
Another possible problem is that the calculations are crisp, but the essences inside them are not. Write out an integral, and the symbols are digitally distinct. But an entire apple, or an entire brain, is larger than anything you can handle formally.
Yet the form of that crisp integral will change when you change your basis; and that sloppy real essence will remain invariant. Reformulating your equations won't remove a dagger, or silence a firing neuron, or shield a quantum computer from decoherence.
The phenomenon of decoherence within brains and sensors, may not be any more crisply defined than the brains and sensors themselves. Brains, as high-level phenomena, don't always make a clear appearance in fundamental equations. Apples aren't crisp, you might say.
For historical reasons, some Old School physicists are accustomed to QM being "interpreted" using extra postulates that involve crisp actions by the Quantum Spaghetti Monster—eating blobs of amplitude at a particular instant, or creating worlds as a particular instant. Since the equations aren't supposed to be real, the sloppy borders of real things are not looked for, and the crisp calculations are primary. This makes it hard to see through to a real (but uncrisp) phenomenon among real (but uncrisp) brains and apples, invariant under changes of crisp (but arbitrary) representation.
Likewise, any change of representation that makes apples harder to see, or brains harder to see, will make decoherence within brains harder to see. But it won't change the apple, the brain, or the decoherence.
As always, any philosophical problems that result from "brain" or "person" or "consciousness" not being crisply defined, are not the responsibility of physicists or of any fundamental physical theory. Nor are they limited to decoherent quantum physics particularly, appearing likewise in splitting brains constructed under classical physics, etcetera.
Coming tomorrow (hopefully): The Born Probabilities, aka, that mysterious thing we do with the squared modulus to get our experimental predictions.
Part of The Quantum Physics Sequence
Next post: "The Born Probabilities"
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