8.7 The Ar­row of Time

This sec­tion has some fur­ther mus­ings on the many worlds in­ter­pre­ta­tion. One ques­tion is why it mat­ters. What is wrong with pos­tu­lat­ing a fairy-tale col­lapse mech­a­nism that makes peo­ple feel unique? The al­ter­nate re­al­i­ties are fun­da­men­tally un­ob­serv­able, so in nor­mal terms they do truly not ex­ist. For all prac­ti­cal pur­poses, the wave func­tion re­ally does col­lapse.

The main rea­son is of course be­cause peo­ple are cu­ri­ous. We would also want to un­der­stand what na­ture is re­ally all about, even if we may not like the an­swer very much.

But there is also a more prac­ti­cal side. An un­der­stand­ing of na­ture can help guess what is likely to hap­pen un­der cir­cum­stances that are not well known. And clearly, there is a dif­fer­ence in think­ing. The Everett model is a uni­verse fol­low­ing the es­tab­lished equa­tions of physics in which ob­servers only ob­serve a very nar­row and evolv­ing part of a much larger re­al­ity. The Copen­hagen model is a sin­gle uni­verse run by gnomes that al­low mi­cro­scopic de­vi­a­tions from a unique re­al­ity fol­low­ing the equa­tions of physics, but kindly elim­i­nate any­thing big­ger.

One ma­jor dif­fer­ence is what is con­sid­ered to be real. In Everett's the­ory, for an ob­server re­al­ity is not the com­plete wave func­tion but a small se­lec­tion of it. That be­comes a philo­soph­i­cal point when con­sid­er­ing vac­uum en­ergy. Ac­cord­ing to quan­tum field the­ory, even empty space still con­tains half a pho­ton of elec­tro­mag­netic en­ergy at each fre­quency, {A.23.4}. That is much like a har­monic os­cil­la­tor still has half a quan­tum of ki­netic and po­ten­tial en­ergy left in its ground state. The elec­tric and mag­netic fields have quan­tum un­cer­tainty. If you mea­sure the elec­tric or mag­netic field in vac­uum, you will get a nonzero value. The same ap­plies to other fields of par­ti­cles. Un­for­tu­nately, if you sum these en­er­gies over all fre­quen­cies, you get in­fin­ity. Even if the fre­quen­cies are as­sumed to be lim­ited to scales about which there is solid knowl­edge, there is still an enor­mous amount of en­ergy here. Its grav­i­ta­tional ef­fect should be gi­gan­tic, it should dwarf any­thing else.

Some­how that does not hap­pen. Now, in Everett’s in­ter­pre­ta­tion a par­ti­cle only be­comes real for a uni­verse when a state is es­tab­lished in which there is no doubt that the par­ti­cle ex­ists. That ob­vi­ously greatly lim­its the vac­uum en­ergy that af­fects that uni­verse. The ex­is­tence of other par­ti­cles might be firmly es­tab­lished in other uni­verses, but these will then af­fect those other uni­verses. In the Copen­hagen in­ter­pre­ta­tion, how­ever, there are no other uni­verses, and there­fore no good rea­son to ex­clude any vac­uum en­ergy from af­fect­ing the grav­ity of the only uni­verse there is.

Then there is the ar­row of time. It is ob­served that time has di­rec­tion­al­ity. So why does time only go one way, from early to late? You might ar­gue that early” and “late are just words. But they are not. They are given mean­ing by the sec­ond law of ther­mo­dy­nam­ics. This law says that a mea­sur­able de­f­i­n­i­tion of dis­or­der in the ob­served uni­verse, called en­tropy, al­ways in­creases with time. The law ap­plies to macro­scopic sys­tems. How­ever, macro­scopic sys­tems con­sist of par­ti­cles that sat­isfy mi­cro­scopic me­chan­ics. And the Schrö­din­ger equa­tion has no par­tic­u­lar pref­er­ence for the time $t$ above the back­ward time $\vphantom{0}\raisebox{1.5pt}{$-$}$$t$. So what hap­pened to the processes that run ac­cord­ing to $\vphantom{0}\raisebox{1.5pt}{$-$}$$t$, back­wards to what we would con­sider for­ward in time? Why do we not ob­serve such processes? And why are we com­posed of mat­ter, not an­ti­mat­ter? And why does na­ture not look the same when viewed in the mir­ror? What is so dif­fer­ent about a mir­ror im­age of the uni­verse that we ob­serve?

The con­ven­tional view pos­tu­lates ad-hoc asym­me­tries that “just hap­pened” to be that way. Why would that hap­pen and why would it be in the same di­rec­tion every­where in an in­fi­nite space-time and an in­fin­ity of pos­si­ble uni­verses therein?

Then the con­ven­tional view adds evo­lu­tion equa­tions that mag­nify that asym­me­try us­ing small per­tur­ba­tion the­ory. That sounds rea­son­able un­til you ex­am­ine those evo­lu­tion equa­tions more closely, chap­ter 11.10. The mech­a­nism that pro­vides the in­creas­ing asym­me­try is, you guessed it, ex­actly that poorly de­fined col­lapse mech­a­nism. Col­lapse is sim­ply stated to ap­ply for times greater than the mea­sure­ment time. Ob­vi­ously that pro­duces asym­me­try in time. But why could the col­lapse not ap­ply for times less than the col­lapse time in­stead?

Now stand back from the de­tails and take a look at the larger philo­soph­i­cal ques­tion. The well es­tab­lished equa­tions of na­ture have no par­tic­u­lar pref­er­ence for ei­ther di­rec­tion of time. True, the di­rec­tion of time is cor­re­lated with mat­ter ver­sus an­ti­mat­ter, and with mir­ror sym­me­try. But that still does not make ei­ther di­rec­tion of time any bet­ter than the other. Ac­cord­ing to the laws of physics that have been solidly es­tab­lished, there does not seem to be any big rea­son for na­ture to pre­fer one di­rec­tion of time above the other.

Ac­cord­ing to Everett's the­ory, there is no rea­son to as­sume that it does. The many-worlds in­ter­pre­ta­tion al­lows the wave func­tion to de­scribe both uni­verses that are ob­served to evolve to­wards one di­rec­tion of time and uni­verses that are ob­served to evolve in the other di­rec­tion.

That is not a triv­ial ob­ser­va­tion. The prob­lem of the ob­served time asym­me­try for a sym­met­ric physics has now been re­moved. It has been re­placed by the ques­tion why for­ward evolv­ing sys­tems ap­pear to cor­re­late with for­ward evolv­ing sys­tems, and back­ward evolv­ing sys­tems with back­ward evolv­ing ones. While that is not a triv­ial ques­tion ei­ther, it is not im­plau­si­ble.

Per­haps, if we spend more time on lis­ten­ing to what na­ture is re­ally telling us, rather than make up sto­ries for what we want to be­lieve, we would now un­der­stand those processes a lot more clearly.