Timeless Beauty

Fol­lowup to: Time­less Physics

One of the great sur­prises of hu­man­ity’s early study of physics was that there were uni­ver­sal laws, that the heav­ens were gov­erned by the same or­der as the Earth: Laws that hold in all times, in all places, with­out known ex­cep­tion. Some­times we dis­cover a seem­ing ex­cep­tion to the old law, like Mer­cury’s pre­ces­sion, but soon it turns out to perfectly obey a still deeper law, that once again is uni­ver­sal as far as the eye can see.

Every known law of fun­da­men­tal physics is perfectly global. We know no law of fun­da­men­tal physics that ap­plies on Tues­days but not Wed­nes­days, or that ap­plies in the North­ern hemi­sphere but not the South­ern.

In clas­si­cal physics, the laws are uni­ver­sal; but there are also other en­tities that are nei­ther perfectly global nor perfectly lo­cal. Like the case I dis­cussed yes­ter­day, of an en­tity called “the lamp” where “the lamp” is OFF at 7:00am but ON at 7:02am; the lamp en­tity ex­tends through time, and has differ­ent val­ues at differ­ent times. The lit­tle billiard balls are like that in clas­si­cal physics; a clas­si­cal billiard ball is (alleged to be) a fun­da­men­tally ex­is­tent en­tity, but it has a world-line, not a world-point.

In time­less physics, ev­ery­thing that ex­ists is ei­ther perfectly global or perfectly lo­cal. The laws are perfectly global. The con­figu­ra­tions are perfectly lo­cal—ev­ery pos­si­ble ar­range­ment of par­ti­cles has a sin­gle com­plex am­pli­tude as­signed to it, which never changes from one time to an­other. Each con­figu­ra­tion only af­fects, and is af­fected by, its im­me­di­ate neigh­bors. Each ac­tu­ally ex­is­tent thing is perfectly unique, as a math­e­mat­i­cal en­tity.

New­ton, first to com­bine the Heav­ens and the Earth with a truly uni­ver­sal gen­er­al­iza­tion, saw a clock­work uni­verse of mov­ing billiard balls and their world-lines, gov­erned by perfect ex­cep­tion­less laws. New­ton was the first to look upon a greater beauty than any mere re­li­gion had ever dreamed.

But the beauty of clas­si­cal physics doesn’t be­gin to com­pare to the beauty of time­less quan­tum physics.

Time­ful quan­tum physics is pretty, but it’s not all that much pret­tier than clas­si­cal physics. In time­ful physics the “same con­figu­ra­tion” can still have differ­ent val­ues at differ­ent times, its own lit­tle world-line, like a lamp switch­ing from OFF to ON. There’s that ugly t com­pli­cat­ing the equa­tions.

You can see the beauty of time­less quan­tum physics by notic­ing how much eas­ier it is to mess up the perfec­tion, if you try to tam­per with Pla­to­nia.

Con­sider the col­lapse in­ter­pre­ta­tion of quan­tum me­chan­ics. To peo­ple raised on time­ful quan­tum physics, “the col­lapse of the wave­func­tion” sounds like it might be a plau­si­ble phys­i­cal mechanism.

If you step back and look upon the time­less mist over the en­tire con­figu­ra­tion space, all dy­nam­ics man­i­fest in its perfectly lo­cal re­la­tions, then the “prun­ing” pro­cess of col­lapse sud­denly shows up as a hugely ugly dis­con­ti­nu­ity in the time­less ob­ject. In­stead of a con­tin­u­ous mist, we have some­thing that looks like a maimed tree with branches hacked off and sap-bleed­ing stumps left be­hind. The perfect lo­cal­ity is ru­ined, be­cause whole branches are hacked off in one op­er­a­tion. Like­wise, col­lapse de­stroys the perfect global unifor­mity of the laws that re­late each con­figu­ra­tion to its neigh­bor­hood; some­times we have the usual re­la­tion of am­pli­tude flow, and then some­times we have the col­laps­ing-re­la­tion in­stead.

This is the power of beauty: The more beau­tiful some­thing is, the more ob­vi­ous it be­comes when you mess it up.

I was sur­prised that many of yes­ter­day’s com­menters seemed to think that Bar­bour’s time­less physics was noth­ing new, rel­a­tive to the older idea of a Block Uni­verse. 3+1D Minkowskian space­time has no priv­ileged space of si­mul­tane­ity, which, in its own way, seems to re­quire you to throw out the con­cept of a global now. From Minkowskian 3+1, I had the idea of “time as a sin­gle perfect 4D crys­tal”—I didn’t know the phrase “Block Uni­verse”, but seemed ev­i­dent enough.

Nonethe­less, I did not re­ally get time­less­ness un­til I read Bar­bour. Say­ing that the t co­or­di­nate was just an­other co­or­di­nate, didn’t have nearly the same im­pact on me as toss­ing the t co­or­di­nate out the win­dow.

Spe­cial Rel­a­tivity is widely ac­cepted, but that doesn’t stop peo­ple from talk­ing about “non­lo­cal col­lapse” or “retro­cau­sa­tion”—rel­a­tivis­tic time­ful QM isn’t beau­tiful enough to pro­tect it­self from com­pli­ca­tion.

Shane Legg’s re­ac­tion is the effect I was look­ing for:

“Stop it! If I in­tu­itively took on board your time­less MWI view of the world… well, I’m wor­ried that this might en­dan­ger my illu­sion of con­scious­ness. Think­ing about it is already mak­ing me feel a bit weird.”

I wish I knew whether the unim­pressed com­menters got what Shane Legg did, just from hear­ing about Spe­cial Rel­a­tivity; or if they still haven’t got­ten it yet from read­ing my brief sum­mary of Bar­bour.

But in any case, let me talk in prin­ci­ple about why it helps to toss out the t co­or­di­nate:

To re­duce a thing, you must re­duce it to some­thing that does not it­self have the prop­erty you want to ex­plain.

In old-school Ar­tifi­cial In­tel­li­gence, a re­searcher won­ders where the mean­ing of a word like “ap­ple” comes from. They want to get knowl­edge about “ap­ples” into their be­loved AI sys­tem, so they cre­ate a LISP to­ken named ap­ple. They re­al­ize that if they claim the to­ken is mean­ingful of it­self, they have not re­ally re­duced the na­ture of mean­ing… So they as­sert that “the ap­ple to­ken is not mean­ingful by it­self”, and then go on to say, “The mean­ing of the ap­ple to­ken emerges from its net­work of con­nec­tions to other to­kens.” This is not true re­duc­tion­ism. It is wrap­ping up your con­fu­sion in a gift-box.

To re­duce time, you must re­duce it to some­thing that is not time. It is not enough to take the t co­or­di­nate, and say that it is “just an­other di­men­sion”. So long as the t co­or­di­nate is there, it acts as a men­tal sponge that can soak up all the time-ness that you want to ex­plain. If you toss out the t co­or­di­nate, you are forced to see time as some­thing else, and not just see time as “time”.

To­mor­row (if I can shake to­day’s cold) I’ll talk about one of my points of de­par­ture from Bar­bour: Namely, I have no prob­lem with dis­card­ing time and keep­ing causal­ity. The com­menters who com­plained about Bar­bour grind­ing up the uni­verse into dis­con­nected slices, may be re­as­sured: On this point, I think Bar­bour is try­ing too hard. We can dis­card t, and still keep causal­ity within r.

I dare to dis­agree with Bar­bour, on this point, be­cause it seems plau­si­ble that Bar­bour has not stud­ied Judea Pearl and col­leagues’ for­mu­la­tion of causal­ity

—which like­wise makes no use of a t co­or­di­nate.

Pearl et. al.’s for­mu­la­tion of “causal­ity” would not be any­where near as en­light­en­ing, if they had to put t co­or­di­nates on ev­ery­thing for the math to make sense. Even if the au­thors in­sisted that t was “just an­other prop­erty” or “just an­other num­ber”… well, if you’ve read Pearl, you see my point. It would cor­re­spond to a much weaker un­der­stand­ing.

Part of The Quan­tum Physics Sequence

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