Christoph Schiller - Motion Mountain - 6

7/29/2019 Christoph Schiller - Motion Mountain - 6

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the entropy o black holes

. T . H -v , , . H x , x , x , .

Summary o the ourth argument or e tension

T -. N one single object (

), extended ( z ) uctuat-ing ( x ). N - , . N . T f

v . I , discreteness , , z ; q z - , . A x -

zv , q v .

A x , x tube, P . C . T

( ) v , q v .I , x j ,

, , v . W x .Page 134

the en tropy of b lack holes

W .A . S v

- x . I , . S - . T v - v .

T . I , .A v v . I

v m f - S z

r S

=Gm

/c (114)

. A . S , .

T . T S B HRef. 55, Ref. 56 , v

S=kl Pl A=kcG A S=k Gmc (11 )

M o t i onM o un t a i nT h eA d v en t ur e of P h

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p d f l e a v a i l a b l ef r e

e of c h a r g e a t www .m o t i onm o un t a i n .n e t

C o p y r i gh t C h r i s t o

ph S c h i l l er N ov em b er 1 9 9 7 J un e2 0 1 1
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the shape o points

k B z A= r S z .T v .Ref. 118 T v vf - q v : v - . I x , fnite , proportional to the

area z .I v x , f

: f f v v ( ). I v -

: . I , q v f j , . J BRef. 33 j

( ) .T z . W ? T q

Ref. 119 . * A

- v . I , x - j , , .Ref. 121 I ,

N , a, r , v Ref. 122

S(r ) =k 3r Na Na Na r . (11 )T v -

, : x ; v a v . Ex ( 11 ) v

v f : , Na elongation a N , r . I

, x -v , S r . T only exible extended constituents yield an S r

dependence.H v , . F x a N v a N l Pl; , v v

. O , v r .T

v . A v . I v , j f z v z ( v -

j z )Ref. 106 . I , x v P z , v , z . W f x

* T Ref. 120 . H , .


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e xcha nging space p oin ts or pa rticles at pl anck s cal es

.A v f . E ( )

- - q x . T v Ref. 100 G H . B f ,

, x .F , x

- no-hair theorem: , x .

T f .

Summary o the i th argument or e tension

B x . B f v

.

exchanging space points or particles at plancksca les

L x v . W v v v , - , . I

? I x , v , .I , q f

[x , y ] =x y yx = (11 ) x y , . B P , x , [x , y ] =l Pl+... . (11 )

T .* P v xx . I , - - , x P . I , v ,v Ref. 44 x

P .C v

: braids.Ref. 123 T P , z . W f q

v v x .Ref. 123W . A v :

, v , identical . Ex v

* T - G .T P .


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the shape o points

cur ios it ies and fun chal lenges about ex tens ion

N

.

C S zI v , .Q v x , xv . C v ?Challenge 87 s

C v Challenge 88 e x ? I , !

D ( x) vChallenge 89 ny ?

D v ?Challenge 90 ny

I v , v . D Challenge 91 d ?

D q v . A m r q v mPl/m l Pl/r . I , Pl/ . V x q v !V .

- v v . D Challenge 92 s ?

A , . ., v( ) ( ). H ,

x ? I Challenge 93 s ?

D , . A


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checks o extension 7

, v . W x ?Challenge 94 d

C P - z - q v v ?Challenge 95 d

WRef. 125, Ref. 126 x v x .V x . C ?Challenge 96 ny

Gender pre erences in physics

W x ? H not too serious. W v

v , Vol. I, page 271 . T .W ?

F v , q - v , . W

v , v v . I f , , v v f . A

v 2 00 v , v x . I

( ) v .

checks of ex tens ionT x

f . H x ?T v v v . W

theoretical f .

A x without x v - x .

A x invalidating x v x - .Challenge 97 e

Ex any ( - ) -

v P . I v q x v x-

.Page 102 A E W , f .

I unrelated x , x .

F contradicts x


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checks o extension

v v .

B z , f , - f .Ref. 129 I ,

x .

R q v Ref. 130, Ref. 131 , q v v x .

I 1990 , D K - QED F

.Ref. 132 H v x v v - .

A , , v .Ref. 133 I x .

I v Vol. IV, page 131 x -. W x .

A -f , Ref. 134, Ref. 135 - , Ref. 136, Ref. 137 , , ,Ref. 138, Ref. 139 . A

x . S v .Page 299D x , v

. O 19 4 200 .

Superstrings e tension and a web o duali t ies

T ; I .

W S , Macbeth.

Superstrings supermembranes strings membranes x- v jRef. 140 v . T - x , x ( ). T - v , q v . T

v f v q :

. P j extended . O , j


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the shape o points

v , -.T v j x x -

v v . I 5 v .Ref. 145 T v ; f v f v . A v

q L .W

. T j P z . Tz - ,

P , H . H v , H v .

he status o the string con ecture

E G L , . *

F H , Enzyklopdie.H , v 10 not j . T

membranes. A 10 , , . T

.I v 10 000 - v v x

j : z - ,

z - v , z - q .I , , . D v 10 000

- , experimentally measurable v . F x , j -

, v , -. W , none Page 17 v j . T , -

v N P z ,Ref. 146 j .W j , v

x , ? S , , complex v :

v , , v f . I, f

x f . B x .

* N , . H Enzyklopdie der philosophischen Wissenschafen im Grun-

drisse, , 29 .


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C h a p t e r

THE BASIS OF THE STRAND MODEL

W , .

E R

The x v

q f v - x P . f f

f v P , v : simplest

. S , x , v v , v q , v v .

W v f f .

T q unifed P , P , q f , - v . I , ,Page 146 f

v all observations v complete precision.F , q f -. I , f v q

extended . W v . A q v . F , x -

. S , x - . T , x

v . F , x 1/2.B f ; fnal . T q : f unmodifable . A

,Page 148 f , z , , v , f .

Re uirements or a inal theory

I q f , f , v q z . A q . S, . C q


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7 the basis o the strand model

TA BL E 6(Continued) General requirements for a nal and unied description of nature and of motion.

A s p e c t R e q u i r e m e n t s o r t h e i n a l a n d u n i i e dd e s c r i p t i o n

P P , ; .

U , .P limit values (

); f .P f ,

, .P f , .R , O z .B , .

B - equal - , di er P .B , ,

- .C f f , f ,

.A , ; H

.D unde ned P , f .S unde ned P ,

.L similar , .

L q f , .Ev q q v

, q contradicts q -v . T f di ers . A f

q v . , q f v

.O Ref. 148 q ,

simplest Page 149 eatureless uctuating strands . I ,

, * , v , - .

Introducing strands

N v , . Ev v v , , z . S

* I D : , F : f , G : F , I : f .


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the basis o the strand model 7

t 1 t 2

t 1 t 2

A twist :

A twirl :

F I GU R E 11An example of strand deformation leading to a crossing switch (above) and one that doesnot lead to a crossing switch (below).

x . Ev v , - v . v ,

undamental principle:

Planck units f .

T f P Page 135 F 10 .A q f . T

f P natural units . I , P :

Plancks quantum o action / v . T , .

T ( ) Planck length l Pl =G/c . S P v -, v .

T Planck entropy , . ., B z k, - , .

T ( ) Planck time t Pl =G/c5 .C P , -

. Eq v , x f .


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4 7 the basis o the strand model

Elementaryspin 1 boson :

Elementaryspin 1/2fermion :

Vacuum :

Horizon :spin

spin

F I GU R E 13A rst illustration of the basic physical systems found in nature; they will be explored indetail below.

T physical space background space. W

q .Page 150 W , , v z , uctuating strandscontinuous background . W f .

Continuous background space v , v . Ev v -

. B v .

A , assume . L needs - .Page 182 T size

; . I v , , . H v , v P

.

Fluctuations , ; , . H v ,

v .


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TA BL E 7Correspondences between all known physical systems and mathematical tangles.

P h y s i c a l s y s t e m S t r a n d c o n t e n t a n g l e t y p e

V f ,

G f G f H z f , - E ( )

f

C ( )

f

E ( ) f

E ( ) f

A , . F x ,. W v ,

v .

F q .

D q

, . I , v v . T ,

, ., fx .F x v does ,x v not . O

f . B , v v v .W v all physical systems .

v f v v v , z tangles.

A tangle f .

S x v F 1 . W v f

.W v

v v q L qf v . I , v

v , all known interactions v .


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The strand model : Observation :

Nothing

(for longobservationtimes)

Vacuum

time averageof crossingswitches

F I GU R E 14A schematic illustration of the strand model for the vacuum.

T v . T - v f P - , ,

z q , .

Vacuum

W , , , . W .

Vacuum , physicalspace, v .

I , v ; x- .* H v ,

, physical background . I, v ,

. A , .

W v v v , -. Eq v , , v ,

v v , , v

. F 14 v z . v v

.W ( ) v , v

, continuous, orentz invariant unique. T . L v v z v

* W , , .


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;Page 242 x f q v .

W f v v , - v . I ,

. I -, . A

f . O , v ; . T . T v W - .

Obser ables and limits

T f v :

T distance x . L -

f P .

T time interval v x . -

f P .T action v v f

. A - f . P

change .

T entropy . E f . T any large

physical system , , z .

I - v f . I , all v f . W v ,

average . A v , v - P . T -, , , , v v , . C x

v . F , f v P c, , c4/G, k observer-invariant limit v . A

Page 135 q f .

Particles and ields

S f , F 1 :


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Observedprobabilitydensity

Strand model :

crossingorientations

spinorientation

core

phasespositions

phaseposition

tailstime averageof crossingswitches

A fermion

F I GU R E 15The tangle model of a spin 1/2 particle. More details will be given below.

A quantum particle tangle . T core, - , f , , . T tails .

A ,Page 157 f q , , v ,

.B f . I , f , -

Page 198 .

M D qPage 188 vq . S , v , , fnite x ,Page 269 topological type - , x , q , -

. I 19 0 , J W x , , f f . T z

.B , f x .

Curiosit ies and un challenges about strands

T v x f v . A , , v . I , . A , f .Page 202

I ? Y . O , . O ,


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Christoph Schiller - Motion Mountain - 6