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.

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?

(This no­tion of see­ing through—look­ing for an essence, and not be­ing dis­tracted by sur­faces—is one that pops up again and again, and again and again and again, in the Way of Ra­tion­al­ity.)

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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