Mach’s Principle: Anti-Epiphenomenal Physics

Pre­vi­ously in se­ries: Many Wor­lds, One Best Guess
Fol­lowup to: The Gen­er­al­ized Anti-Zom­bie Principle

Warn­ing: Mach’s Prin­ci­ple is not ex­per­i­men­tally proven, though it is widely con­sid­ered to be cred­ible.

Cen­turies ago, when Gal­ileo was pro­mot­ing the Coper­ni­can model in which the Earth spun on its axis and trav­eled around the Sun, there was great op­po­si­tion from those who trusted their com­mon sense:

“How could the Earth be mov­ing? I don’t feel it mov­ing! The ground be­neath my feet seems perfectly steady!”

And lo, Gal­ileo said: If you were on a ship sailing across a perfectly level sea, and you were in a room in the in­te­rior of the ship, you wouldn’t know how fast the ship was mov­ing. If you threw a ball in the air, you would still be able to catch it, be­cause the ball would have ini­tially been mov­ing at the same speed as you and the room and the ship. So you can never tell how fast you are mov­ing.

This would turn out to be the be­gin­ning of one of the most im­por­tant ideas in the his­tory of physics. Maybe even the most im­por­tant idea in all of physics. And I’m not talk­ing about Spe­cial Rel­a­tivity.

Sup­pose the en­tire uni­verse was mov­ing. Say, the uni­verse was mov­ing left along the x axis at 10 kilo­me­ters per hour.

If you tried to vi­su­al­ize what I just said, it seems like you can imag­ine it. If the uni­verse is stand­ing still, then you imag­ine a lit­tle swirly cloud of galax­ies stand­ing still. If the whole uni­verse is mov­ing left, then you imag­ine the lit­tle swirly cloud mov­ing left across your field of vi­sion un­til it passes out of sight.

But then, some peo­ple think they can imag­ine philo­soph­i­cal zom­bies: en­tities who are iden­ti­cal to hu­mans down to the molec­u­lar level, but not con­scious. So you can’t always trust your imag­i­na­tion.

For­get, for a mo­ment, any­thing you know about rel­a­tivity. Pre­tend you live in a New­to­nian uni­verse.

In a New­to­nian uni­verse, 3+1 space­time can be bro­ken down into 3 space di­men­sions and 1 time di­men­sion, and you can write them out as 4 real num­bers, (x, y, z, t). De­cid­ing how to write the num­bers in­volves seem­ingly ar­bi­trary choices, like which di­rec­tion to call ‘x’, and which per­pen­dicu­lar di­rec­tion to then call ‘y’, and where in space and time to put your ori­gin (0, 0, 0, 0), and whether to use me­ters or miles to mea­sure dis­tance. But once you make these ar­bi­trary choices, you can, in a New­to­nian uni­verse, use the same sys­tem of co­or­di­nates to de­scribe the whole uni­verse.

Sup­pose that you pick an ar­bi­trary but uniform (x, y, z, t) co­or­di­nate sys­tem. Sup­pose that you use these co­or­di­nates to de­scribe ev­ery phys­i­cal ex­per­i­ment you’ve ever done—heck, ev­ery ob­ser­va­tion you’ve ever made.

Next, sup­pose that you were, in your co­or­di­nate sys­tem, to shift the ori­gin 10 me­ters to the left along the x axis. Then if you origi­nally thought that Grandma’s House was 400 me­ters to the right of the ori­gin, you would now think that Grandma’s House is 410 me­ters to the right of the ori­gin. Thus ev­ery point (x, y, z, t) would be re­la­beled as (x’ = x + 10, y’ = y, z’ = z, t’ = t).

You can ex­press the idea that “physics does not have an ab­solute ori­gin”, by say­ing that the ob­served laws of physics, as you gen­er­al­ize them, should be ex­actly the same af­ter you perform this co­or­di­nate trans­form. The his­tory may not be writ­ten out in ex­actly the same way, but the laws will be writ­ten out the same way. Let’s say that in the old co­or­di­nate sys­tem, Your House is at (100, 10, −20, 7:00am) and you walk to Grandma’s House at (400, 10, −20, 7:05am). Then you trav­eled from Your House to Grandma’s House at one me­ter per sec­ond. In the new co­or­di­nate sys­tem, we would write the his­tory as (110, 10, 20, 7:00am) and (410, 10, −20, 7:05am) but your ap­par­ent speed would come out the same, and hence so would your ac­cel­er­a­tion. The laws gov­ern­ing how fast things moved when you pushed on them—how fast you ac­cel­er­ated for­ward when your legs pushed on the ground—would be the same.

Now if you were given to jump­ing to con­clu­sions, and more­over, given to jump­ing to con­clu­sions that were ex­actly right, you might say:

“Since there’s no way of figur­ing out where the ori­gin is by look­ing at the laws of physics, the ori­gin must not re­ally ex­ist! There is no (0, 0, 0, 0) point float­ing out in space some­where!”

Which is to say: There is just no fact of the mat­ter as to where the ori­gin “re­ally” is. When we ar­gue about our choice of rep­re­sen­ta­tion, this fact about the map does not ac­tu­ally cor­re­spond to any fact about the ter­ri­tory.

Now this state­ment, if you in­ter­pret it in the nat­u­ral way, is not nec­es­sar­ily true. We can read­ily imag­ine al­ter­na­tive laws of physics, which, writ­ten out in their most nat­u­ral form, would not be in­sen­si­tive to shift­ing the “ori­gin”. The Aris­totelian uni­verse had a crys­tal sphere of stars ro­tat­ing around the Earth. But so far as any­one has been able to tell, in our real uni­verse, the laws of physics do not have any nat­u­ral “ori­gin” writ­ten into them. When you write out your ob­ser­va­tions in the sim­plest way, the co­or­di­nate trans­form x’ = x + 10 does not change any of the laws; you write the same laws over x’ as over x.

As Feyn­man said:

Philoso­phers, in­ci­den­tally, say a great deal about what is ab­solutely nec­es­sary for sci­ence, and it is always, so far as one can see, rather naive, and prob­a­bly wrong. For ex­am­ple, some philoso­pher or other said it is fun­da­men­tal to the sci­en­tific effort that if an ex­per­i­ment is performed in, say, Stock­holm, and then the same ex­per­i­ment is done in, say, Quito, the same re­sults must oc­cur. That is quite false. It is not nec­es­sary that sci­ence do that; it may be a fact of ex­pe­rience, but it is not nec­es­sary...

What is the fun­da­men­tal hy­poth­e­sis of sci­ence, the fun­da­men­tal philos­o­phy? We stated it in the first chap­ter: the sole test of the val­idity of any idea is ex­per­i­ment...

If we are told that the same ex­per­i­ment will always pro­duce the same re­sult, that is all very well, but if when we try it, it does not, then it does not. We just have to take what we see, and then for­mu­late all the rest of our ideas in terms of our ac­tual ex­pe­rience.

And so if you re­gard the uni­verse it­self as a sort of Gal­ileo’s Ship, it would seem that the no­tion of the en­tire uni­verse mov­ing at a par­tic­u­lar rate—say, all the ob­jects in the uni­verse, in­clud­ing your­self, mov­ing left along the x axis at 10 me­ters per sec­ond—must also be silly. What is it that moves?

If you be­lieve that ev­ery­thing in a New­to­nian uni­verse is mov­ing left along the x axis at an av­er­age of 10 me­ters per sec­ond, then that just says that when you write down your ob­ser­va­tions, you write down an x co­or­di­nate that is 10 me­ters per sec­ond to the left, of what you would have writ­ten down, if you be­lieved the uni­verse was stand­ing still. If the uni­verse is stand­ing still, you would write that Grandma’s House was ob­served at (400, 10, −20, 7:00am) and then ob­served again, a minute later, at (400, 10, −20, 7:01am). If you be­lieve that the whole uni­verse is mov­ing to the left at 10 me­ters per sec­ond, you would write that Grandma’s House was ob­served at (400, 10, −20, 7:00am) and then ob­served again at (-200, 10, −20, 7:01am). Which is just the same as be­liev­ing that the ori­gin of the uni­verse is mov­ing right at 10 me­ters per sec­ond.

But the uni­verse has no ori­gin! So this no­tion of the whole uni­verse mov­ing at a par­tic­u­lar speed, must be non­sense.

Yet if it makes no sense to talk about speed in an ab­solute, global sense, then what is speed?

It is sim­ply the move­ment of one thing rel­a­tive to a differ­ent thing! This is what our laws of physics talk about… right? The law of grav­ity, for ex­am­ple, talks about how planets pull on each other, and change their ve­loc­ity rel­a­tive to each other. Our physics do not talk about a crys­tal sphere of stars spin­ning around the ob­jec­tive cen­ter of the uni­verse.

And now—it seems—we un­der­stand how we have been mis­led, by try­ing to vi­su­al­ize “the whole uni­verse mov­ing left”, and imag­in­ing a lit­tle blurry blob of galax­ies scur­ry­ing from the right to the left of our vi­sual field. When we imag­ine this sort of thing, it is (prob­a­bly) ar­tic­u­lated in our vi­sual cor­tex; when we vi­su­al­ize a lit­tle blob scur­ry­ing to the left, then there is (prob­a­bly) an ac­ti­va­tion pat­tern that pro­ceeds across the columns of our vi­sual cor­tex. The seem­ing ab­solute back­ground, the ori­gin rel­a­tive to which the uni­verse was mov­ing, was in the un­der­ly­ing neu­rol­ogy we used to vi­su­al­ize it!

But there is no ori­gin! So the whole thing was just a case of the Mind Pro­jec­tion Fal­lacyagain.

Ah, but now New­ton comes along, and he sees the flaw in the whole ar­gu­ment.

From Gal­ileo’s Ship we pass to New­ton’s Bucket. This is a bucket of wa­ter, hung by a cord. If you twist up the cord tightly, and then re­lease the bucket, the bucket will spin. The wa­ter in the bucket, as the bucket wall be­gins to ac­cel­er­ate it, will as­sume a con­cave shape. Water will climb up the walls of the bucket, from cen­tripetal force.

If you sup­posed that the whole uni­verse was ro­tat­ing rel­a­tive to the ori­gin, the parts would ex­pe­rience a cen­trifu­gal force, and fly apart. (No this is not why the uni­verse is ex­pand­ing, thank you for ask­ing.)

New­ton used his Bucket to ar­gue in fa­vor of an ab­solute space—an ab­solute back­ground for his physics. There was a testable differ­ence be­tween the whole uni­verse ro­tat­ing, and the whole uni­verse not ro­tat­ing. By look­ing at the parts of the uni­verse, you could de­ter­mine their ro­ta­tional ve­loc­ity—not rel­a­tive to each other, but rel­a­tive to ab­solute space.

This ab­solute space was a tan­gible thing, to New­ton: it was aether, pos­si­bly in­volved in the trans­mis­sion of grav­ity. New­ton didn’t be­lieve in ac­tion-at-a-dis­tance, and so he used his Bucket to ar­gue for the ex­is­tence of an ab­solute space, that would be an aether, that could per­haps trans­mit grav­ity.

Then the ori­gin-free view of the uni­verse took an­other hit. Maxwell’s Equa­tions showed that, in­deed, there seemed to be an ab­solute speed of light—a stan­dard rate at which the elec­tric and mag­netic fields would os­cillate and trans­mit a wave. In which case, you could de­ter­mine how fast you were go­ing, by see­ing in which di­rec­tions light seemed to be mov­ing quicker and slower.

Along came a stub­born fel­low named Ernst Mach, who re­ally didn’t like ab­solute space. Fol­low­ing some ear­lier ideas of Leib­niz, Mach tried to get rid of New­ton’s Bucket by as­sert­ing that in­er­tia was about your rel­a­tive mo­tion. Mach’s Prin­ci­ple as­serted that the re­sis­tance-to-chang­ing-speed that de­ter­mined how fast you ac­cel­er­ated un­der a force, was a re­sis­tance to chang­ing your rel­a­tive speed, com­pared to other ob­jects. So that if the whole uni­verse was ro­tat­ing, no one would no­tice any­thing, be­cause the in­er­tial frame would also be ro­tat­ing.

Or to put Mach’s Prin­ci­ple more pre­cisely, even if you imag­ined the whole uni­verse was ro­tat­ing, the rel­a­tive mo­tions of all the ob­jects in the uni­verse would be just the same as be­fore, and their in­er­tia—their re­sis­tance to changes of rel­a­tive mo­tion—would be just the same as be­fore.

At the time, there did not seem to be any good rea­son to sup­pose this. It seemed like a mere at­tempt to im­pose philo­soph­i­cal el­e­gance on a uni­verse that had no par­tic­u­lar rea­son to com­ply.

The story con­tinues. A cou­ple of guys named Michel­son and Mor­ley built an in­ge­nious ap­para­tus that would, via in­terfer­ence pat­terns in light, de­tect the ab­solute mo­tion of Earth—as it spun on its axis, and or­bited the Sun, which or­bited the Milky Way, which hur­tled to­ward An­dromeda. Or, if you preferred, the Michel­son-Mor­ley ap­para­tus would de­tect Earth’s mo­tion rel­a­tive to the lu­minifer­ous aether, the medium through which light waves prop­a­gated. Just like Maxwell’s Equa­tions seemed to say you could do, and just like New­ton had always thought you could do.

The Michel­son-Mor­ley ap­para­tus said the ab­solute mo­tion was zero.

This caused a cer­tain amount of con­ster­na­tion.

En­ter Albert Ein­stein.

The first thing Ein­stein did was re­pair the prob­lem posed by Maxwell’s Equa­tions, which seemed to talk about an ab­solute speed of light. If you used a differ­ent, non-Gal­ilean set of co­or­di­nate trans­forms—the Lorentz trans­for­ma­tions—you could show that the speed of light would always look the same, in ev­ery di­rec­tion, no mat­ter how fast you were mov­ing.

I’m not go­ing to talk much about Spe­cial Rel­a­tivity, be­cause that in­tro­duc­tion has already been writ­ten many times. If you don’t get all in­dig­nant about “space” and “time” not turn­ing out to work the way you thought they did, the math should be straight­for­ward.

Albeit for the benefit of those who may need to re­sist post­mod­ernism, I will note that the word “rel­a­tivity” is a mis­nomer. What “rel­a­tivity” re­ally does, is es­tab­lish new in­var­i­ant el­e­ments of re­al­ity. The quan­tity √(t2 - x2 - y2 - z2) is the same in ev­ery frame of refer­ence. The x and y and z, and even t, seem to change with your point of view. But not √(t2 - x2 - y2 - z2). Rel­a­tivity does not make re­al­ity in­her­ently sub­jec­tive; it just makes it ob­jec­tive in a differ­ent way.

Spe­cial Rel­a­tivity was a rel­a­tively easy job. Had Ein­stein never been born, Lorentz, Poin­caré, and Minkowski would have taken care of it. Ein­stein got the No­bel Prize for his work on the pho­to­elec­tric effect, not for Spe­cial Rel­a­tivity.

Gen­eral Rel­a­tivity was the im­pres­sive part.

Ein­stein—ex­plic­itly in­spired by Mach—and even though there was no ex­per­i­men­tal ev­i­dence for Mach’s Prin­ci­ple—re­for­mu­lated grav­i­ta­tional ac­cel­er­a­tions as a cur­va­ture of space­time.

If you try to draw a straight line on curved pa­per, the cur­va­ture of the pa­per may twist your line, so that even as you pro­ceed in a lo­cally straight di­rec­tion, it seems (stand­ing back from an imag­i­nary global view­point) that you have moved in a curve. Like walk­ing “for­ward” for thou­sands of miles, and find­ing that you have cir­cled the Earth.

In curved space­time, ob­jects un­der the “in­fluence” of grav­ity, always seem to them­selves—lo­cally—to be pro­ceed­ing along a strictly in­er­tial path­way.

This meant you could never tell the differ­ence be­tween firing your rocket to ac­cel­er­ate through flat space­time, and firing your rocket to stay in the same place in curved space­time. You could ac­cel­er­ate the imag­i­nary ‘ori­gin’ of the uni­verse, while chang­ing a cor­re­spond­ing de­gree of free­dom in the cur­va­ture of space­time, and keep ex­actly the same laws of physics.

Ein­stein’s the­ory fur­ther had the prop­erty that mov­ing mat­ter would gen­er­ate grav­i­ta­tional waves, prop­a­gat­ing cur­va­tures. Ein­stein sus­pected that if the whole uni­verse was ro­tat­ing around you while you stood still, you would feel a cen­trifu­gal force from the in­com­ing grav­i­ta­tional waves, cor­re­spond­ing ex­actly to the cen­tripetal force of spin­ning your arms while the uni­verse stood still around you. So you could con­struct the laws of physics in an ac­cel­er­at­ing or even ro­tat­ing frame of refer­ence, and end up ob­serv­ing the same laws—again free­ing us of the specter of ab­solute space.

(I do not think this has been ver­ified ex­actly, in terms of how much mat­ter is out there, what kind of grav­i­ta­tional wave it would gen­er­ate by ro­tat­ing around us, et cetera. Ein­stein did ver­ify that a shell of mat­ter, spin­ning around a cen­tral point, ought to gen­er­ate a grav­i­ta­tional equiv­a­lent of the Co­ri­o­lis force that would e.g. cause a pen­du­lum to pre­cess. Re­mem­ber that, by the ba­sic prin­ci­ple of grav­ity as curved space­time, this is in­dis­t­in­guish­able in prin­ci­ple from a ro­tat­ing in­er­tial refer­ence frame.)

We come now to the most im­por­tant idea in all of physics. (Not count­ing the con­cept of “de­scribe the uni­verse us­ing math”, which I con­sider as the idea of physics, not an idea in physics.)

The idea is that you can start from “It shouldn’t ought to be pos­si­ble for X and Y to have differ­ent val­ues from each other”, or “It shouldn’t ought to be pos­si­ble to dis­t­in­guish differ­ent val­ues of Z”, and gen­er­ate new physics that make this fun­da­men­tally im­pos­si­ble be­cause X and Y are now the same thing, or be­cause Z no longer ex­ists. And the new physics will of­ten be ex­per­i­men­tally ver­ifi­able.

We can in­ter­pret many of the most im­por­tant rev­olu­tions in physics in these terms:

  • Gal­ileo /​ “The Earth is not the cen­ter of the uni­verse”: You shouldn’t ought to be able to tell “where” the uni­verse is—shift­ing all the ob­jects a few feet to the left should have no effect.

  • Spe­cial Rel­a­tivity: You shouldn’t ought to be able to tell how fast you, or the uni­verse, are mov­ing.

  • Gen­eral Rel­a­tivity: You shouldn’t ought to be able to tell how fast you, or the uni­verse, are ac­cel­er­at­ing.

  • Quan­tum me­chan­ics: You shouldn’t ought to be able to tell two iden­ti­cal par­ti­cles apart.

When­ever you find that two things seem to always be ex­actly equal—like in­er­tial mass and grav­i­ta­tional charge, or two elec­trons—it is a hint that the un­der­ly­ing physics are such as to make this a nec­es­sary iden­tity, rather than a con­tin­gent equal­ity. It is a hint that, when you see through to the un­der­ly­ing el­e­ments of re­al­ity, in­er­tial mass and grav­i­ta­tional charge will be the same thing, not merely equal. That you will no longer be able to imag­ine them be­ing differ­ent, if your imag­i­na­tion is over the el­e­ments of re­al­ity in the new the­ory.

Like­wise with the way that quan­tum physics treats the similar­ity of two par­ti­cles of the same species. It is not that “pho­ton A at 1, and pho­ton B at 2” hap­pens to look just like “pho­ton A at 2, and pho­ton B at 1″ but that they are the same el­e­ment of re­al­ity.

When you see a seem­ingly con­tin­gent equal­ity—two things that just hap­pen to be equal, all the time, ev­ery time—it may be time to re­for­mu­late your physics so that there is one thing in­stead of two. The dis­tinc­tion you imag­ine is epiphe­nom­e­nal; it has no ex­per­i­men­tal con­se­quences. In the right physics, with the right el­e­ments of re­al­ity, you would no longer be able to imag­ine it.

The amaz­ing thing is that this is a sci­en­tifi­cally pro­duc­tive rule—find­ing a new rep­re­sen­ta­tion that gets rid of epiphe­nom­e­nal dis­tinc­tions, of­ten means a sub­stan­tially differ­ent the­ory of physics with ex­per­i­men­tal con­se­quences!

(Sure, what I just said is log­i­cally im­pos­si­ble, but it works.)

Part of The Quan­tum Physics Sequence

Next post: “Rel­a­tive Con­figu­ra­tion Space

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