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

LHC as Time Machine (Adventures in Extra-Dimensions) Tom Weiler Vanderbilt University Nashville. TN µ Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

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 Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

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

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

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

Negative time: . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

Lightcone slopes: . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

GTvS - the good, bad, and ugly . Text Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

CTCs (PPDW) • PRD80, 044008 (2009) and gr-qc/0603045 Phys.Rev.D80:044008,2009 . e-Print: gr-qc/0603045 Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

A linear path off the brane . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

Causal properties (continued) : . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

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

Fig: boosted branes fig: Dent Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

Energy (philosophic discussion) . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

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 g xx to change sign as a function of another spatial variable; (ii) take g tx nonzero; (iii) arrange a suitably “fast” return path. AND, there is an aesthetic input: choose a metric that is physically motivated. Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

Compactified 5th Dim and Higgs Singlets (at the LHC?)  This time actually solving for the geodesic! Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

Consider metric [CM Ho ansatz] Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

geodesic solutions: Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

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. Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

Local Minko, Global Time Machine With the redefiniton our metric becomes locally Minkowskian too, but subject to the global boundary condition i.e. i.e., compact u => periodic time ! 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.] Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

Implications for LHC I f h i g g s e s a r e m a d e , d o 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 o n n e c t e d b y o n e d e g r e e o f s e p a r a t i o n , o u r p a s t a n d f u t u r e 5 - v o l u m e s . M a y f i n d s p o n t a n e o u s a p p e a r a n c e o f K K m o d e s o f s i n g l e t s , p e r i o 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 , o 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 o r t h e f i r s t t i m e i n h u m a n h i s t o 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 o r s t o t a l k t o 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 o m e m o r e e n g i n e e r i n g a n d p h y s i c s t o s o r t i t o u t . [ S . H a w k i n g s a y s t h i s i s t o o b i z a r r e t o h a p p e n ; a n d i f i t d o e s h a p p e n , r u n a n d h i d e ! ] Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

What it really, really looks like, in true colors! . Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

Summary * 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 Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

Extra Slides Madison Pheno, 10 may 2010 Tom Weiler, Vanderbilt University Monday, May 10, 2010

Product of lightcone slopes: . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

Lightcone slopes • . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

Stress-energy tensor and energy conditions . . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

Energy figure . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010

Energy conditions: . Tom Weiler, Vanderbilt University, USA Madison Pheno,10 May 2010 Monday, May 10, 2010