LHC as Time Machine (Adventures in Extra-Dimensions) Tom Weiler - - PowerPoint PPT Presentation

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LHC as Time Machine (Adventures in Extra-Dimensions) Tom Weiler - - PowerPoint PPT Presentation

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LHC as Time Machine (Adventures in Extra-Dimensions) Tom Weiler Vanderbilt University Nashville. TN Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010 Syllabus: * Closed Timelike Curves (CTCs) *

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

LHC as Time Machine

(Adventures in Extra-Dimensions)

Tom Weiler Vanderbilt University

  • Nashville. TN

µ

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

Syllabus:

*

Closed Timelike Curves (CTCs)

* Goedel, van Stockum,Tipler- planes

* Spacetime metrics, warped space

*

From 5D to 6D (un-compactified) * and back to 5D (compactified)

*

Energy distribution, energy conditions (if time)

*

Conclude

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

CTCs defined

Superluminal travel means signaling faster than speed of light,

 e.g. LSND/MiniBooNE and sterile neutrinos taking

shortcuts through Xdim bulk

 (Paes, Pakvasa, Weiler, hep-ph/0504096)  (Hollenberg, Micu, Paes, Weiler, 0906.0150)

More challenging is to receive a signal BEFORE it leaves! “Closed Timelike Curve” or CTC

 e.g. (Paes, Pakvasa, Dent, Weiler, gr-qc/0603045)

Hawking’s Chronology Protection Theorem simply asserts that this is too pathological to be permissable.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Open strings = SM brane particles, Closed strings = singlet bulk/brane particles

Our context:

  • I. Stringy Model where gauge charges live on the ends of open strings,

and stick these SM “particles” to our brane; gauge-singlets are then closed strings, free to explore the bulk

 (e.g., graviton, sterile neutrinos)  (higgs singlets produced/detected at the LHC?)

  • II. Einstein’s GR, where geometry is destiny.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Godel-Tipler-vonStockum spacetimes

.

Distortions of the “lengths” phi and t in the radial direction is an example of warping.

And an example of time-warping is the Robertson-Walker big-bang metric.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Negative time:

.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Lightcone slopes:

.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

GTvS - the good, bad, and ugly

.

Text

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

CTCs (PPDW)

  • PRD80, 044008 (2009)

and gr-qc/0603045

Phys.Rev.D80:044008,2009. e-Print: gr-qc/0603045 Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

A linear path off the brane

.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Causal properties (continued) :

.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

CTC condition(s) :

We show (Heinrich’s perseverance) that a metric with two branes in the (u,v) dimensions, with relative motion (thereby hardwiring a boost), admits CTCs (see the pub for the somewhat complicated metric)

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

Fig: boosted branes

fig: Dent

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Energy (philosophic discussion)

.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

CTCs in N+1, N=2,3,....

We have seen GTvS CTCs in N=2 (phi,r). Therefore, we expect metrics in N=3,4,... with CTCs. Eqn (22) shows that this is so. The mathematical recipe that emerges from Eqn (22) is simply:

(i) allow gxx to change sign as a function of another spatial variable; (ii) take gtx nonzero; (iii) arrange a suitably “fast” return path. AND, there is an aesthetic input: choose a metric that is physically motivated.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Compactified 5th Dim and Higgs Singlets (at the LHC?)

This time actually solving for the geodesic!

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

Consider metric

[CM Ho ansatz]

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

geodesic solutions:

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

Got and not-Gott

This new metric resembles Gott’s 3+1 for spinning cosmic strings and associated CTCs (but without his infinite-energy, infinite red/blue shifting pathologies).

E.g., a well-known Thm says low-dimensional metrics are conformal to Minkowski space, i.e. locally Minkowskian but topologically complicated. For the Gott metric the identifications bring the form to locally Minkowski space away from the strings, but subject to the global identifications But, Gott’s metric violates all energy conditions but W(eak)EC.

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

Local Minko, Global Time Machine

With the redefiniton

  • ur metric becomes locally Minkowskian too,

but subject to the global boundary condition i.e.

Being everywhere Minkowskian, on and off the brane (after redefining u), the Einstein eqn gives 0= and so all energy conditions are (trivially satisfied). [Since matter fields must be added only to the brane, we expect the geodesics for bulk travel to be little affected by matter.]

i.e., compact u => periodic time !

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

Implications for LHC

I f h i g g s e s a r e m a d e , d

  • u

b l e

  • s

i n g l e t m i x i n g m a y m e a n ( i . e . “ r i g h t ” m e t r i c ) w e a r e a l l c

  • n

n e c t e d b y

  • n

e d e g r e e

  • f

s e p a r a t i

  • n

,

  • u

r p a s t a n d f u t u r e 5

  • v
  • l

u m e s . M a y f i n d s p

  • n

t a n e

  • u

s a p p e a r a n c e

  • f

K K m

  • d

e s

  • f

s i n g l e t s , p e r i

  • d

i c i n f u t u r e a n d p a s t t i m e s , s t a b l e i n t h e b u l k , b u t d e c a y i n g ( v i a h i g g s m i x i n g ) a s t h e y t r a v e r s e t h e b r a n e . T h e s e s i n g l e t s m a y h a v e b e e n m a d e b y u s a t t h e L H C N O W ,

  • r

i n t h e L H C F U T U R E , O R , b y O T H E R C I V I L I Z A T I O N S s i g n a l i n g u s N O W .

F

  • r

t h e f i r s t t i m e i n h u m a n h i s t

  • r

y , w e h a v e t h e m a c h i n e s a n d d e t e c t

  • r

s t

  • t

a l k t

  • e

x t r a

  • t

e r r e s t r i a l s

  • O

K , w e n e e d s

  • m

e m

  • r

e e n g i n e e r i n g a n d p h y s i c s t

  • s
  • r

t i t

  • u

t . [ S . H a w k i n g s a y s t h i s i s t

  • b

i z a r r e t

  • h

a p p e n ; a n d i f i t d

  • e

s h a p p e n , r u n a n d h i d e ! ]

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

What it really, really looks like, in true colors!

.

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

* GTvS CTCs easily generalize to more dimns

(general CTC conditions on metric given)

* There exist spatially warped metrics in infinite

6D (not 5D) exhibiting CTCs * There exist spatially warped metrics in compact 5D exhibiting CTCs

*

These CTCs challenge “chronology protection”, and may enable iner-temporal communication

*

Intriguing energetics, zero or positive on brane, zero or negative in bulk

*

More implications, more models to investigate

Summary

Monday, May 10, 2010

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Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University

Extra Slides

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

.

Product of lightcone slopes:

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Lightcone slopes

  • .

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Stress-energy tensor and energy conditions

.

.

Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Energy figure

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Monday, May 10, 2010

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Madison Pheno,10 May 2010 Tom Weiler, Vanderbilt University, USA

Energy conditions:

.

Monday, May 10, 2010