Julian Barbour's The End Of Time - in klasikal fysiks:

( 1 ) Triangl Land.

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( Kapital-i, in 'I, myself', now spels Il as in isle or aisle.
Leter y spels sym for seem or seam and partys for parties.
Leter w spels swn for soon. )

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Al the world's a kinema.

Supos the audiens of a piktur hous ar imortal souls and that the hapenings on skryn relat to this world of ours. A holografik movy wud be even mor lIk thry-dimensional reality. The audiens of souls bekom so absorb'd in the goings-on, on skryn, that they forget themselvs and identifI with the aktors, som mor than others, and perhaps uon in partikular, hw bekoms uon's ( mortal ) self. Konsiusnes has shifted from tImlesnes to tIm.

Our holografic lIvs, in the kinema, ar aparently kinematik or moving in tIm. But God, the greit movy maker, nos beter. A movy ryl is mayd up of a lot of statik imajes. The projektor runs them tu fast for us to sy the jumps betwyn them, giving an impresion of flowing motion. God's kutings flor is strwn with rejekted imajes, imensly mor than left out by any human direktor, bekaus the divin direktor works on a grand skail.

This stupendus totality of imajinary realitys, from wich a miniskul number ar selekted to bekom our konsius reality, is kal'd Platonia by Julian Barbour.
This is after Plato's belyf in an underlIing reality of perfekt forms, to wich our world only aproximats. We ar liken'd to kaiv-dwelers, round a fIr, hw sy only shadows of a ryl world out-sId.

Platonia is a tImles jumbl of praktikly infinit posibilitys. The imajes most lIkly to kom together in an apyrans of tIm's motion ar the kinematik slIds best match'd to ych other.
If yu kut a movy ryl into its individual slIds, yu kud put them bak together in sequens by komparing thos wich wer best match'd to run kontinuusly. In platonia, tho, ther is an embarasment of chois from every konsyvabl posibility of imaj, tho the vast majority ar so il-match'd that they ar ysily dismis'd from any probabl historikal sequens.

The explanatory sukses of quantum theory has mayd fysisists tak seriusly the notion that ther is a graded potential for al lojikal posibilitys of existens to bekom reality. Barbour maks the point that thes posibilitys kud inklud unimajinabl heven, purgatory and hel. ( He has a pantheistik belyf in platonia, rather than in a personal god. )

Julian Barbour's 'The End Of Time' ( 1999 ) is about how such a tImles natur of reality mIt work. It is about fysiks not the metafysiks of God and imortal souls. Tho not Barbour's viw, it is perhaps worth mentioning that karma, for exampl, is a sort of probability theory of re-inkarnation, wer-by the moral konditions of souls best-matches them to a suksesion of mortal bodys.

TIm and motion

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I atempt to explain Barbour's bwk to myself, but dont pretend to fuly understand it, and apologis to ryders for erors or infelisitys. Barbour givs us pasenjers a privilej'd tur of the enjin rwm to the ship of fysiks. This reviw is ment to be no mor than a gId to a gId.

Julian Barbour is a fysisist, hw forswk main-strym university lIf, to konsentrat on the myning of tIm. He desided, as a yung man, that tIm kud be redus'd to terms of 'movment'. This was the motiv for, to quot the sub-tItl of his bwk: 'The next revolution in our understanding of the universe.'

This is rather as if a klok was konsider'd not as teling 'the tIm' but as its 'movment', wich is the naim for the mekaniks of a klok. Mekanikal toy trains wer deskrib'd as ( runing on ) 'klok-work'.

The hevenly bodys regulat living bodys, so that they hav ther own 'biolojikal kloks'. Human beings even regulat themselvs with an abstrakt konsept of tIm. Wer dos this notion kom from? And from wat dos tIm ultimatly deriv?

Astronomers yus'd the erth's rotation for ther klok. About the turn of the twentieth sentury, they found erth's rotation rait was not quIt regular enuf, bekaus of the mwn's gravitational efekts. The erth may be put out of synk by the mwn. But it is posibl to tak the sun and its planets, as a houl, as a mor regular klok-work, bekaus they ar isolated from any such intrusiv influenses.

( This chanj to a nwer hevenly tIm-pys may be kompar'd to man's making a mor regular mekanism by desIning a longer train of kog-wyls, that slows down the ful fors of the main-spring to unwind mor gradualy and uniformly. That way, the klok is les liabl to gain tw much wen fuly wound up and to lws tw much as it runs down. )

So, the solar system was adopted as a mor regular natural klok. This is kal'd efemeris tIm. Efemeris tabls giv the positions of the planets at given tIms. The most konvenient planetary pointer for so teling the tIm, but not the most akurat, is the mwn. Thus, tIm is a konvention that depends on the most regular availabl tIm-pys.

Efemeris tIm was swn super-syded by a konvention bais'd on atomik periodisity. ( On the very smal skail of the atom, gravitational disturbanses ar neglijibl. ) But it remains a pointer in Julian Barbour's quest for the tru natur of tIm. The solar system is a litl univers in itself. Indyd, by the start of the third milenium, man's teknikal ability skarsly ryches to its limits. Barbour sujests that if tIm is mor akuratly mesur'd by a graduation from diurnal tIm to efemeris tIm, then the ultimat tIm-pys is nothing les than the univers itself.

Mach's prinsipl says tIm only maks sens in terms of motion and motion is relativ to the motions of al the mases of the univers, on wich tIm, therfor, ultimatly depends.

Universal gravity is its 'main-spring' wich spins houl galaxys in its train. ( The aktual train of the stelar klok-work mekanism, or wich kogs konekt with wich, also mIt be yus'd as a fansiful analojy to Barbour's idea of 'best matching'. )

By definition, the univers is every-thing that ther is. It wud be ilojikal to think of a god, out-sId it, tIming its run, with a stop-watch. But that is esentialy wat the notion of 'absolut tIm' is, in klasikal fysiks. Barbour wishes to promot Ernst Mach's belyf in a self-referential univers, from wich tIm is a konvenient derivation but no mor than that. The very konveniens of the konsept of tIm may mak it a most powerful ilusion. But basikly tIm is just an ilusion, Barbour thinks. Hens, the tItl of his bwk.
The obvius presedent for this way of thinking is how fysiks over-turn'd the konvenient fiktion that the sun travels round the erth, rather than vice versa.

The shaip spas of triangl land.

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Barbour sets out to show how the notion of tIm may emerj from a univers konsider'd myrly as the relations betwyn al its objekts. To do this, he imajins a model of the simplest of universes, konsisting of thry objekts. Thry objekts hav a triangular relationship and he kals this univers 'triangl land'. If thys ar masiv objekts, ther relations wil be govern'd by the law of gravity.

But ther is no-uon runing a stop-watch to gaij the tIm it taks for the thry bodys to chanj ther positions relativ to ych other. Ther is no absolut tIm. Nor is ther an 'absolut spas': thes bodys ar not spatialy mesur'd with respekt to the sIds of a box of ko-ordinats, the lenth, bredth and hIt of som kyub-shaip'd rwm.

Barbour's triangl land is a univers suficient to itself. So, it must fashon any ko-ordinats, such as it may hav, in its own terms. In praktis, this myns taking the thry bodys in uon konfiguration at a tIm. That is uon diferently shaip'd triangl at a tIm, with the bodys at its thry korners. Barbour kals ych of thys triangls 'tIm-instants'. They ar lIk fotografs or snaps of the bodys at uon instant of tIm.

Al the posibl konfigurations for thry bodys kan be represented by al the posibl shaips of a triangl. The jeneral jeometry of triangls is, in efekt, the struktur of the spas, or the 'konfiguration spays', within wich thys thry bodys must mov.
For the posibl relations betwyn 4 bodys, the jeometry of a tetrahedron land, in six dimensions, wud aplI, analjusly. And so on, for greiter numbers of bodys, in hujly multi-dimensional konfiguration spases.

Hapily, the simpl 'univers', of positions for thry bodys, kan be visualis'd in thry dimensions. Ther thry ko-ordinats ar AB, BC and CA. Thys represent the lenths of ych sId of a given triangl. Ych triangl is then pin-pointed akordingly within this box of ko-ordinats. Uon korner of this box is taken as the orijin, myning the point representing a triangl, al thry of hws sIds ar zero. This is the unyk point at wich al thry bodys, konfiguring a triangl, myt. Barbour sujestivly kals this the alfa point.

From that korner, the thry rwm-ejes of lenth, bredth and hIt extend. A 'triangl' pin-pointed exaktly on ko-ordinat AB, BC or CA is just a greiter or shorter lIn AB, BC or CA, respektivly.

The jeometrik propertys of triangls limit the area of the box that may be fil'd with positions for posibl triangl shaips. Uon triangl sId kan not be longer than the sum of the other tw. This limitation removs som points in the box as posibl positions to represent triangls. The borders of this limit ar deskrib'd by a regular thry-korner'd pyramid, hws apex is at the orijin of the box.
The pyramid's thry ejes, to its bais korners, extend at 45 degrys to the thry ko-ordinats AB, BC, CA. Thys pyramid-ejes represent triangls, tw of hws thry korners koinsId, uon of ther sIds being zero lenth. This stands for tw out of thry bodys myting. They ar the next most unyk positions to the orijin or alfa point. ( Diagrams ar given in Barbour's bwk! )

It dos not mater how far the ejes of the pyramid extend or how larj is the bais triangl of the pyramid. Yu kan kut the pyramid into triangular kros-sektions. Ych kros-sektion is, in efekt, a mor or les brod bais to the pyramid. Thys kros-sektions al revyl the saim patern of information about the jeometrikal natur of the triangls that al the positions on ther surfases represent. Thys kros-sektions ar kal'd 'shaip spas'. Independently of skail, shaip spas kontains positions for every posibl shaip of triangl.

Notis that the jeometrik myning, of the pyramid's ejes, is retain'd in the kros-sektions of shaip spas, konsider'd as the bais korners, that the ejes extend-to from the pyramid apex. The bais lIns of the pyramid, wich ar also the sIds of shaip spas, ar the positions for al triangls, in wich the lenth of uon sId equals the sum of the other tw sIds.
Also, the very senter of ych kros-sektion is the uon position in shaip spas marking an equilateral triangl. It is perpendikular to the pyramid apex, wer thry bodys ar zero distans from ych other. The apex or alfa point is lIk an equal-sIded triangl, wer al thry sIds ar zero lenth.

( A potential enerjy kontur map kan be drawn over shaip spas. Potential enerjy is inversly proportional to separation, so the potential enerjy rises lIk kanyon wals over the shaip spas's thry korners, ych representing tw of the thry mases koinsiding. Indyd, the potential enerjy only depends on the relativ konfiguration of mases. It is independent of a fraim-work of absolut spas and absolut tIm, and so is a suitabl mesur of chanjes from plas to plas, in platonia, as mention'd, below. )

A fuler analysis of the shaip spas of triangl land revyl'd the folowing. Thry lIns, that kros at the senter to mak perpendikular bisektions with the thry sIds of ych kros-sektion, mark the only positions for isoseles triangls ( wer tw of the sIds ar equal ).
It turn'd-out that rIt-angl'd triangls' positions wer found only on thry lIns konkaiv to the thry sIds of shaip spas. The thry 'lens' areas, in betwyn, represented positions for triangls with an obtus angl ( greiter than 90 degrys ). The remaining sentral area of shaip spas designated akut-angl'd triangls: al angls les than 90 degrys.

The moral is that even the simplest of platonias or relativ konfiguration spases, konsisting of thry bodys' posibl positions, has a jeometrik struktur. Wer-as, absolut spas is tryted as absolutly uniform. No point in absolut spas is regarded as diferent from any other. It is esentialy a transparent abstraktion. Julian Balfour belyvs that the extrymly komplex struktur of a platonia of the ryl univers wil be shown to gId the aparent 'arow of tIm', wich givs us the impresion of being kaut on a present flow of tIm out of the past into the futur. But the mathematikal demonstration of Barbour's konjektur is liabl to be extrymly difikult.

The nouts of his bwk mention kolaboration on a dynamik jeometry to remov komplytly the konsept of absolut distans. This wud be analjus to the way shaip spas removs over-al skail from triangl land. But, as wel as that, the ratios of lenths of sIds wud no longer be relevant. ( Barbour's web sIts promis'd nws: www.julianbarbour.com or platonia.com ).

Shortest paths in triangl land.

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We must remember that triangl land has no out-sId observer timing a sequens that thys triangls mIt mak, as a myns to determining the distanses betwyn them. The so-kal'd 'relativ konfiguration spas', that maks up triangl land, konsists of nothing mor than a jumbl of triangls. 'Platonia' is Barbour's naim for al such relativ konfiguration spases for any given number of bodys, up to the totality of the univers itself.

But it is stil posibl to mesur a 'distans', in platonia, betwyn neiboring triangls, without referens to an out-sId fraim-work.

( The distans mesur for triangl land, yus'd in 'The End Of Time', is lIk Pythogoras' theorem in thry dimensions, but with the hypotenus transform'd into the platonia 'distans' and the thry perpendikular sIds of a thry-dimensional triangl transform'd into the distanses, AA*, BB*, CC*, betwyn the respektiv korners of tw triangls in triangl land.
If the thry bodys, at the korners, hav diferent mases, this may be alow'd-for by weiting this kalkulation.
In other words, if a, b, c, ar the mases of thry objekts, in tw diferent triangular konfigurations, ABC and A*B*C*, then the platonia distans, squar'd, equals a tIms (AA*) squar'd plus b tIms (BB*) squar'd plus c tIms (CC*) squar'd. )

Any tw such triangls kan be mov'd relativ to ych other, so that ther distans, represented by neiboring points in platonia, is at a minimum. This minimum distans is term'd ther 'intrinsik diferens' and, as such, is said to represent ther best-matching position. ( The formula for intrinsik diferens is modifI'd by a funktion of potential enerjy, aktualy the squar rwt of minus the potential, akording to Barbour. But this modifikation, 'the aktion', dos not afekt the argument. ) It kan be found for any tw distributions of mater, such as astronomers mIt observ, at any tIm, in any arbitrary relation to ych other.

Thys shortest paths, in platonia, ar lIk the jeodesics in jeneral relativity. In that theory, lIt apyrs to bend or kurv under gravitational atraktion, bekaus it is aktualy folowing a shortest path, determin'd by the jeometrikal kurving of spas around gravitational mases. Given that platonia kan hav its own jeometrikly determin'd 'lIns of lyst resistans' or jeodesiks, thys ar the most probabl paths for a konfiguration of mases, ploted in platonia.

Richard Lung.

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Barbour's klasikal fysiks part 2.

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