Timeless Physics

Pre­vi­ously in se­ries: Rel­a­tive Con­figu­ra­tion Space

Warn­ing: The cen­tral idea in to­day’s post is taken se­ri­ously by se­ri­ous physi­cists; but it is not ex­per­i­men­tally proven and is not taught as stan­dard physics.

To­day’s post draws heav­ily on the work of the physi­cist Ju­lian Bar­bour, and con­tains di­a­grams stolen and/​or mod­ified from his book “The End of Time”. How­ever, some of the ar­gu­ments here are of my own de­vis­ing, and Bar­bour might(?) not agree with them.

I shall be­gin by ask­ing a in­cred­ibly deep ques­tion:

What time is it?

If you have the ex­cel­lent habit of giv­ing ob­vi­ous an­swers to ob­vi­ous ques­tions, you will an­swer, “It is now 7:30pm [or what­ever].”

How do you know?

“I know be­cause I looked at the clock on my com­puter mon­i­tor.”

Well, sup­pose I hacked into your com­puter and changed the clock. Would it then be a differ­ent time?

“No,” you re­ply.

How do you know?

“Be­cause I once used the ‘Set Date and Time’ fa­cil­ity on my com­puter to try and make it be the 22nd cen­tury, but it didn’t work.”

Ah. And how do you know that it didn’t work?

“Be­cause,” you say, “I looked out­side, and the build­ings were still made of brick and wood and steel, rather than hav­ing been re­placed by the gleam­ing crys­tal of di­a­mon­doid nan­otech­nolog­i­cal con­struc­tions; and gasoline was still only $4/​gal­lon.”

You have… in­ter­est­ing… ex­pec­ta­tions for the 22nd cen­tury; but let’s not go into that. Sup­pose I re­placed the build­ings out­side your home with con­fec­tions of crys­tal, and raised the price of gas; then would it be 100 years later?

“No,” you say, “I could look up at the night sky, and see the planets in roughly the same po­si­tion as yes­ter­day’s night; with a pow­er­ful telescope I could mea­sure the po­si­tions of the stars as they very slowly drift, rel­a­tive to the Sun, and ob­serve the ro­ta­tion of dis­tant galax­ies. In these ways I would know ex­actly how much time had passed, no mat­ter what you did here on Earth.”

Ah. And sup­pose I snapped my fingers and caused all the stars and galax­ies to move into the ap­pro­pri­ate po­si­tions for 2108?

“You’d be ar­rested for vi­o­lat­ing the laws of physics.”

But sup­pose I did it any­way.

“Then, still, 100 years would not have passed.”

How would you know they had not passed?

“Be­cause I would re­mem­ber that, one night be­fore, it had still been 2008. Though, re­al­is­ti­cally speak­ing, I would think it more likely that it was my mem­ory at fault, not the galax­ies.”

Now sup­pose I snapped my fingers, and caused all the atoms in the uni­verse to move into po­si­tions that would be ap­pro­pri­ate for (one prob­a­ble quan­tum branch) of 2108. Even the atoms in your brain.

Think care­fully be­fore you say, “It would still re­ally be 2008.” For does this be­lief of yours, have any ob­serv­able con­se­quences left? Or is it an epiphe­nomenon of your model of physics? Where is stored the fact that it is ‘still 2008’? Can I snap my fingers one last time, and al­ter this last vari­able, and cause it to re­ally be 2108?

Is it pos­si­ble that Cthulhu could snap Its ten­ta­cles, and cause time for the whole uni­verse to be sus­pended for ex­actly 10 mil­lion years, and then re­sume? How would any­one ever de­tect what had just hap­pened?

A global sus­pen­sion of time may seem imag­in­able, in the same way that it seems imag­in­able that you could “move all the mat­ter in the whole uni­verse ten me­ters to the left”. To vi­su­al­ize the uni­verse mov­ing ten me­ters to the left, you imag­ine a lit­tle swirling ball of galax­ies, and then it jerks left­ward. Similarly, to imag­ine time stop­ping, you vi­su­al­ize a swirling ball of galax­ies, and then it stops swirling, and hangs mo­tion­less for a while, and then starts up again.

But the sen­sa­tion of pass­ing time, in your vi­su­al­iza­tion, is pro­vided by your own mind’s eye out­side the sys­tem. You go on think­ing, your brain’s neu­rons firing, while, in your imag­i­na­tion, the swirling ball of galax­ies stays mo­tion­less.

When you imag­ine the uni­verse mov­ing ten me­ters to the left, you are imag­in­ing mo­tion rel­a­tive to your mind’s eye out­side the uni­verse. In the same way, when you imag­ine time stop­ping, you are imag­in­ing a mo­tion­less uni­verse, frozen rel­a­tive to a still-mov­ing clock hid­den out­side: your own mind, count­ing the sec­onds of the freeze.

But what would it mean for 10 mil­lion “years” to pass, if mo­tion ev­ery­where had been sus­pended?

Does it make sense to say that the global rate of mo­tion could slow down, or speed up, over the whole uni­verse at once—so that all the par­ti­cles ar­rive at the same fi­nal con­figu­ra­tion, in twice as much time, or half as much time? You couldn’t mea­sure it with any clock, be­cause the tick­ing of the clock would slow down too.

Do not say, “I could not de­tect it; there­fore, who knows, it might hap­pen ev­ery day.”

Say rather, “I could not de­tect it, nor could any­one de­tect it even in prin­ci­ple, nor would any phys­i­cal re­la­tion be af­fected ex­cept this one thing called ‘the global rate of mo­tion’. There­fore, I won­der what the phrase ‘global rate of mo­tion’ re­ally means.”

All of that was a line of ar­gu­ment of Ju­lian Bar­bour’s, more or less, Let us pause here, and con­sider a sec­ond line of ar­gu­ment, this one my own. That is, I don’t think it was in Bar­bour’s The End of Time. (If I re­call cor­rectly, I rea­soned thus even be­fore I read Bar­bour, while I was com­ing up with my un­pub­lished gen­eral de­ci­sion the­ory of New­comblike prob­lems. Of course that does not mean the ar­gu­ment is novel; I have no idea whether it is novel. But if my ar­gu­ment is wrong, I do not want it blamed on an in­no­cent by­stan­der.) So:

“The fu­ture changes as we stand here, else we are the game pieces of the gods, not their heirs, as we have been promised.”
—Raistlin Majere

A fine sen­ti­ment; but what does it mean to change the fu­ture?

Sup­pose I have a lamp, with an old-style com­pact fluores­cent bulb that takes a few sec­onds to warm up. At 7:00am, the lamp is off. At 7:01am, I flip the switch; the lamp flick­ers for a few mo­ments, then be­gins to warm up. At 7:02am, the lamp is fully bright. Between 7:00am and 7:02am, the lamp changed from OFF to ON. This, cer­tainly, is a change; but it is a change over time.

Change im­plies differ­ence; differ­ence im­plies com­par­i­son. Here, the two val­ues be­ing com­pared are (1) the state of “the lamp at 7:00am”, which is OFF, and (2) the state of “the lamp at 7:02am”, which is ON. So we say “the lamp” has changed from one time to an­other. At 7:00am, you wan­der by, and see the lamp is OFF; at 7:02am, you wan­der by, and see the lamp is ON.

But have you ever seen the fu­ture change from one time to an­other? Have you wan­dered by a lamp at ex­actly 7:02am, and seen that it is OFF; then, a bit later, looked in again on the “the lamp at ex­actly 7:02am”, and dis­cov­ered that it is now ON?

Nat­u­rally, we of­ten feel like we are “chang­ing the fu­ture”. Log­ging on to your on­line bank ac­count, you dis­cover that your credit card bill comes due to­mor­row, and, for some rea­son, has not been paid au­to­mat­i­cally. Imag­in­ing the fu­ture-by-de­fault—ex­trap­o­lat­ing out the world as it would be with­out any fur­ther ac­tions—you see that the bill not be­ing paid, and in­ter­est charges ac­cru­ing on your credit card. So you pay the bill on­line. And now, imag­in­ing to­mor­row, it seems to you that the in­ter­est charges will not oc­cur. So at 1:00pm, you imag­ined a fu­ture in which your credit card ac­crued in­ter­est charges, and at 1:02pm, you imag­ined a fu­ture in which it did not. And so your imag­i­na­tion of the fu­ture changed, from one time to an­other.

As I re­marked pre­vi­ously: The way a be­lief feels from in­side, is that you seem to be look­ing straight at re­al­ity. When it ac­tu­ally seems that you’re look­ing at a be­lief, as such, you are re­ally ex­pe­rienc­ing a be­lief about your be­liefs.

When your ex­trap­o­la­tion of the fu­ture changes, from one time to an­other, it feels like the fu­ture it­self is chang­ing. Yet you have never seen the fu­ture change. When you ac­tu­ally get to the fu­ture, you only ever see one out­come.

How could a sin­gle mo­ment of time, change from one time to an­other?

I am not go­ing to go into “free will” in to­day’s blog post. Ex­cept to re­mark that if you have been read­ing Over­com­ing Bias all this time, and you are cur­rently ag­o­niz­ing about whether or not you re­ally have free will, in­stead of try­ing to un­der­stand where your own mind has be­come con­fused and gen­er­ated an im­pos­si­ble ques­tion, you should prob­a­bly go back and read it all again. For any­one who is just now join­ing us… per­haps I shall dis­cuss the is­sue to­mor­row.

Just re­mem­ber Egan’s Law: It all adds up to nor­mal­ity. Ap­ples didn’t stop fal­ling when Ein­stein dis­proved New­ton’s the­ory of grav­ity, and any­one who jumped off a cliff would still go splat. Per­haps Time turns out to work differ­ently than you thought; but to­mor­row still lies ahead of you, and your choices, and their con­se­quences. I wouldn’t ad­vise re­work­ing your moral philos­o­phy based on con­fus­ing ar­gu­ments and strange-seem­ing physics, un­til the physics stops ap­pear­ing strange and the ar­gu­ments no longer seem con­fus­ing.

Now to physics we turn; and here I re­sume draw­ing my ideas from Ju­lian Bar­bour.

For the benefit of any­one who hasn’t fol­lowed the se­ries on quan­tum me­chan­ics, a very very quick sum­mary:

  • In clas­si­cal physics—the mis­taken physics that was de­vel­oped first his­tor­i­cally, and matches hu­man in­tu­itions all too well—a par­ti­cle is like a lit­tle billiard ball. A par­ti­cle is in a sin­gle place in 3D space, and we can de­scribe its po­si­tion with three real num­bers. In quan­tum physics, we need an am­pli­tude dis­tri­bu­tion over all pos­si­ble po­si­tions for the par­ti­cle—a com­plex num­ber for the par­ti­cle be­ing here, a com­plex num­ber for the par­ti­cle be­ing there, and so on through all the po­si­tions in space; a con­tin­u­ous dis­tri­bu­tion. (Con­figu­ra­tions and Am­pli­tude.)

  • In clas­si­cal physics, we can con­sider each par­ti­cle in­de­pen­dently. This par­ti­cle is here, that par­ti­cle is there. In quan­tum physics this is not pos­si­ble; we can only as­sign am­pli­tudes to con­figu­ra­tions that de­scribe the si­mul­ta­neous po­si­tions of many par­ti­cles. In fact, the only math­e­mat­i­cal en­tities that ac­tu­ally have am­pli­tudes are joint con­figu­ra­tions of all the par­ti­cles in the en­tire uni­verse. (Joint Con­figu­ra­tions.)

Jbarbourconfigurationcube_3

Above is a di­a­gram that shows what a con­figu­ra­tion space might look like for three par­ti­cles, A, B, and C. ABC form a tri­an­gle in two-di­men­sional space. Every in­di­vi­d­ual point in the con­figu­ra­tion space cor­re­sponds to a si­mul­ta­neous po­si­tion of all the par­ti­cles—above we see points that cor­re­spond to par­tic­u­lar tri­an­gles i.e. joint po­si­tions of A, B, and C. (Clas­si­cal Con­figu­ra­tion Spaces; The Quan­tum Arena.)

The state of a quan­tum sys­tem is not a sin­gle point in this space; it is a dis­tri­bu­tion over this space. You could imag­ine it as a cloud, or a blob, or a col­ored mist within the space.

Jbarbourrelative

Here we see a rel­a­tive con­figu­ra­tion space, in which each axis is the dis­tance be­tween a pair of par­ti­cles. This has some ad­van­tages I’m not go­ing to re­ca­pitu­late (it was cov­ered in a pre­vi­ous post), so if you’re drop­ping into the mid­dle of the se­ries, just pre­tend it’s a reg­u­lar con­figu­ra­tion space.

Jbarbourtriangleland1

We’ve just chopped up the pyra­mi­dal space you saw be­fore, into a se­ries of slices. In this con­figu­ra­tion space, the slices near the bot­tom show all the par­ti­cles close to­gether (tiny tri­an­gles). As we rise up, the par­ti­cles get fur­ther apart (larger tri­an­gles).

At the very bot­tom of the con­figu­ra­tion space is a con­figu­ra­tion where all the par­ti­cles oc­cupy the same po­si­tion.

(But re­mem­ber, it’s non­sense to talk about an in­di­vi­d­ual par­ti­cle be­ing any­where in a con­figu­ra­tion space—each point in the con­figu­ra­tion space cor­re­sponds to a po­si­tion of all the par­ti­cles. Con­figu­ra­tion space is not the 3D space you know. It’s not that there are a bunch of par­ti­cles rest­ing in the same place at the bot­tom. The sin­gle bot­tom point cor­re­sponds to all the par­ti­cles be­ing in the same place in 3D space.)

Jbarbourtrianglecloud_2

Here we take a closer look at one of the slices of con­figu­ra­tion space, and see a cloud of blue and red mist cov­er­ing some of it. (Why am I only show­ing the cloud cov­er­ing a sixth (ex­actly a sixth) of the tri­an­gle? This has to do with a sym­me­try in the space—ex­changes of iden­ti­cal par­ti­cles—which is not im­por­tant to the pre­sent dis­cus­sion.)

But there is your glimpse of some quan­tum mist—in two col­ors, be­cause am­pli­tudes are com­plex num­bers with a real and imag­i­nary part. An am­pli­tude dis­tri­bu­tion or “wave­func­tion” as­signs a com­plex num­ber to ev­ery point in the con­tin­u­ous con­figu­ra­tion space—a com­plex num­ber to ev­ery pos­si­ble con­figu­ra­tion of all the par­ti­cles.

Yes­ter­day, I finished by ask­ing how the state of a quan­tum sys­tem might evolve over time.

You might be tempted to vi­su­al­ize the mist churn­ing and chang­ing col­ors, as quan­tum am­pli­tude flows within the con­figu­ra­tion space.

And this is in­deed the way that you would vi­su­al­ize stan­dard physics.

Be­hold the stan­dard Schröd­inger Equa­tion:

Schrodinger

Here ψ(r, t) is the am­pli­tude dis­tri­bu­tion over con­figu­ra­tion space (r) and time (t). The left-hand side of the Schröd­inger Equa­tion is the change over time of the wave­func­tion ψ, and the right-hand-side shows how to calcu­late this change as the sum of two terms: The gra­di­ent of the wave­func­tion over con­figu­ra­tion space (at that time), and the po­ten­tial en­ergy of each con­figu­ra­tion.

Which is to say, the deriva­tive in time of the wave­func­tion—the in­stan­ta­neous rate of change—can be in terms of the wave­func­tion’s deriva­tive in space, plus a term for the po­ten­tial en­ergy.

If you tried to vi­su­al­ize Schröd­inger’s Equa­tion—doesn’t look too hard, right?—you’d see a blob of churn­ing, com­plex mist in con­figu­ra­tion space, with lit­tle blobs rac­ing around and split­ting into smaller blobs as waves prop­a­gated.

If you tried to calcu­late the quan­tum state of a sin­gle hy­dro­gen atom over time, apart from the rest of the uni­verse—which you can only re­ally do if the hy­dro­gen atom isn’t en­tan­gled with any­thing—the atom’s quan­tum state would evolve over time; the mist would churn.

But sup­pose you think about the whole uni­verse at once, in­clud­ing your­self, of course. Be­cause—even in the stan­dard model of quan­tum physics!—that is ex­actly the arena in which quan­tum physics takes place: A wave­func­tion over all the par­ti­cles, ev­ery­where.

If you can sen­si­bly talk about the quan­tum state of some par­tic­u­lar hy­dro­gen atom, it’s only be­cause the wave­func­tion hap­pens to neatly fac­tor into (hy­dro­gen atom) * (rest of world).

Even if the hy­dro­gen atom is be­hav­ing in a very reg­u­lar way, the joint wave­func­tion for (hy­dro­gen atom * rest of world) may not be so reg­u­lar. Stars move into new po­si­tions, peo­ple are born and peo­ple die, digi­tal watches tick, and the cos­mos ex­pands: The uni­verse is non-re­cur­rent.

Think of how the uni­ver­sal wave­func­tion ψ(r, t) might be­have when r is the po­si­tion of all the par­ti­cles in the uni­verse.

Let’s call 9:00am the time t=0, mea­sured in sec­onds.

At ψ(r, t=0), then, you are won­der­ing what time it is: The par­ti­cles mak­ing up the neu­rons in your brain, are in po­si­tions ryou that cor­re­spond to neu­rons firing in the thought-pat­tern “What time is it?” And the Earth, and the Sun, and the rest of the uni­verse, have their own par­ti­cles in the ap­pro­pri­ate rrest-of-uni­verse. Where the com­plete r roughly fac­tor­izes as the product (ryou * rrest-of-uni­verse).

Over the next sec­ond, the joint wave­func­tion of the en­tire uni­verse evolves into ψ(r, t=1). All the stars in the sky have moved a lit­tle bit on­ward, in what­ever di­rec­tion they’re head­ing; the Sun has burned up a lit­tle more of its hy­dro­gen; on Earth, an av­er­age of 1.8 peo­ple have died; and you’ve just glanced down at your watch.

At ψ(r, t=2), the stars have moved a lit­tle on­ward, the galax­ies have ro­tated, the cos­mos has ex­panded a lit­tle more (and its ex­pan­sion has ac­cel­er­ated a lit­tle more), your watch has evolved into the state of show­ing 9:00:02 AM on its screen, and your own mind has evolved into the state of think­ing the thought, “Huh, I guess it’s nine o’ clock.”

Ready for the next big sim­plifi­ca­tion in physics?

Here it is:

We don’t need the t.

It’s re­dun­dant.

The r never re­peats it­self. The uni­verse is ex­pand­ing, and in ev­ery in­stant, it gets a lit­tle big­ger. We don’t need a sep­a­rate t to keep things straight. When you’re look­ing at the whole uni­verse, a unique func­tion ψ of (r, t) is pretty much a unique func­tion of r.

And the only way we know in the first place “what time it is”, is by look­ing at clocks. And whether the clock is a wrist­watch, or the ex­pan­sion of the uni­verse, or your own mem­o­ries, that clock is en­coded in the po­si­tion of par­ti­cles—in the r. We have never seen a t vari­able apart from the r.

Jbarbourrelative We can re­cast the quan­tum wave equa­tions, spec­i­fy­ing the time evolu­tion of ψ(r, t), as spec­i­fy­ing re­la­tions within a wave­func­tion ψ(r).

Oc­cam’s Ra­zor: Our equa­tions don’t need a t in them, so we can ban­ish the t and make our on­tol­ogy that much sim­pler.

An un­chang­ing quan­tum mist hangs over the con­figu­ra­tion space, not churn­ing, not flow­ing.

But the mist has in­ter­nal struc­ture, in­ter­nal re­la­tions; and these con­tain time im­plic­itly.

The dy­nam­ics of physics—fal­ling ap­ples and ro­tat­ing galax­ies—is now em­bod­ied within the un­chang­ing mist in the un­chang­ing con­figu­ra­tion space.

This land­scape is not frozen like a cry­on­ics pa­tient sus­pended in liquid ni­tro­gen. It is not mo­tion­less as an iso­lated sys­tem while the rest of the uni­verse goes on with­out it.

The land­scape is time­less; time ex­ists only within it. To talk about time, you have to talk about re­la­tions in­side the con­figu­ra­tion space.

Ask­ing “What hap­pened be­fore the Big Bang?” is re­vealed as a wrong ques­tion. There is no “be­fore”; a “be­fore” would be out­side the con­figu­ra­tion space. There was never a pre-ex­ist­ing empti­ness into which our uni­verse ex­ploded. There is just this time­less math­e­mat­i­cal ob­ject, time ex­ist­ing within it; and the ob­ject has a nat­u­ral bound­ary at the Big Bang. You can­not ask “When did this math­e­mat­i­cal ob­ject come into ex­is­tence?” be­cause there is no t out­side it.

So that is Ju­lian Bar­bour’s pro­posal for the next great sim­plifi­ca­tion pro­ject in physics.

(And yes, you can not only fit Gen­eral Rel­a­tivity into this paradigm, it ac­tu­ally comes out look­ing even more el­e­gant than be­fore. For which point I re­fer you to Ju­lian Bar­bour’s pa­pers.)

To­mor­row, I’ll go into some of my own thoughts and re­ac­tions to this pro­posal.

But one point seems worth not­ing im­me­di­ately: I have spo­ken be­fore on the ap­par­ently perfect uni­ver­sal­ity of phys­i­cal laws, that ap­ply ev­ery­where and ev­ery­when. We have just raised this perfec­tion to an even higher pitch: ev­ery­thing that ex­ists is ei­ther perfectly global or perfectly lo­cal. There are points in con­figu­ra­tion space that af­fect only their im­me­di­ate neigh­bors in space and time; gov­erned by uni­ver­sal laws of physics. Perfectly lo­cal, perfectly global. If the mean­ing and sheer beauty of this state­ment is not im­me­di­ately ob­vi­ous, I’ll go into it to­mor­row.

And a fi­nal in­tu­ition-pump, in case you haven’t yet got­ten time­less­ness on a gut level...

Manybranches4

Think of this as a di­a­gram of the many wor­lds of quan­tum physics. The branch points could be, say, your ob­ser­va­tion of a par­ti­cle that seems to go ei­ther “left” or “right”.

Look­ing back from the van­tage point of the gold head, you only re­mem­ber hav­ing been the two green heads.

So you seem to re­mem­ber Time pro­ceed­ing along a sin­gle line. You re­mem­ber that the par­ti­cle first went left, and then went right. You ask, “Which way will the par­ti­cle go this time?”

You only re­mem­ber one of the two out­comes that oc­curred on each oc­ca­sion. So you ask, “When I make my next ob­ser­va­tion, which of the two pos­si­ble wor­lds will I end up in?”

Re­mem­ber­ing only a sin­gle line as your past, you try to ex­tend that line into the fu­ture -

But both branches, both fu­ture ver­sions of you, just ex­ist. There is no fact of the mat­ter as to “which branch you go down”. Differ­ent ver­sions of you ex­pe­rience both branches.

So that is many-wor­lds.

And to in­cor­po­rate Bar­bour, we sim­ply say that all of these heads, all these Nows, just ex­ist. They do not ap­pear and then van­ish; they just are. From a global per­spec­tive, there is no an­swer to the ques­tion, “What time is it?” There are just differ­ent ex­pe­riences at differ­ent Nows.

From any given van­tage point, you look back, and re­mem­ber other times—so that the ques­tion, “Why is it this time right now, rather than some other time?” seems to make sense. But there is no an­swer.

When I came to this un­der­stand­ing, I for­got the mean­ing that Time had once held for me.

Time has dis­solved for me, has been re­duced to some­thing sim­pler that is not it­self time­ful.

I can no longer con­ceive that there might re­ally be a uni­ver­sal time, which is some­how “mov­ing” from the past to the fu­ture. This now seems like non­sense.

Some­thing like Bar­bour’s time­less physics has to be true, or I’m in trou­ble: I have for­got­ten how to imag­ine a uni­verse that has “real gen­uine time” in it.

Part of The Quan­tum Physics Sequence

Next post: “Time­less Beauty

Pre­vi­ous post: “Rel­a­tive Con­figu­ra­tion Space