TeV Gravity at LHC,

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TeV Gravity at LHC,
Hawkings Chronology Protection Conjecture
and Renormalizations Group
I. Arefeva

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PREDICTIONS

• Micro-Black hole production at CERN's Large
  Hadron Collider (LHC)
• Micro-Wormhole/time machine production at LHC

I.A. and I.V.Volovich, Time Machine at the
LHC, arXiv 07102696, Int.J.Geom.Meth.Mod.Phys.
(2008)
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Outlook

• TeV gravity
• TIME MACHINES
• Chronology Protection Conjecture and
  Renormalizations

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Time Machine

• In GR a TM is a region of space-time that has a
  Closed Timelike Curve (CTC)
• CTC suggests the possibility of time-travel with
  its well known paradoxes

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Time Machine. Definition

• Spacetime (M,g), M manifold, g metric.
• Einstein equations for g.
• Time machine is a region of space-time (M,g)
  that has a closed timelike curve (CTC).
• Example. Time is circle

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Causality

Time machines violate the standard causality
condition.
It seems that there is a Chronology Protection
Agency which prevents the appearance of CTCand so
makes the universe safe for historians
Hawking,
Phys.Rev. (1992)
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Causality

• Cauchy problem. Global hyperbolic
• Causality in QFT
• Bogoliubov, Shirkov
• Local commutativity
• Bogoliubov, Tavkhelidze, Vladimirov,
• 
  Whightman,
• Locality in string theory Gross, Veneziano,
  Susskind, t Hooft
• Nonlocality at the Planck scale Bronstein,
• 
  Wheeler, Blokhintzev,
  Markov, t Hooft,
• 
  p-adic space-time

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Time Machine in Special Relativity

• TM is impossible in special relativity.
• Indeed, to make a loop, a curve must somewhere
  leave the null cone as shown in this picture.
• A particle with such a world line would exceed
  the speed of light that is impossible in SR.

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Time Machine in GR

• In general relativity the situation is much less
  trivial.
• According to GR, our spacetime must be a smooth
  Lorentzian manifold
• small regions approximately
  Minkowskian',
• large scale any geometry and topology.
• There may be holes, handles, almost
  whatever one wants.
• A direction of null cones may change.

t
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Solutions of Einstein eqs. with Closed Timelike
Curves (CTC) / Time Machine.

• Godel's solution 1949
• van Stockum-Tipler cylinder 1937, 1974
• Kerr solutions 2 axially symmetric, stationary
  Kerrs
• Gott's time machine
• Wheeler wormholes
• Morris-Thorne-Yurtsever's TM
• Ori's dust asymptotically-flat space-time

Violation of normal chronology is such an
objectionable occurrence that any of such
solutions could be rejected as nonphysical.
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General Relativity and Chronology

• In GR one cannot simply assert that chronology is
  preserved, and causality respected, without doing
  considerable additional work.
• The essence of the problem lies in the fact that
  the Einstein eqs of GR are local equations,
  relating some aspects of the spacetime curvature
  at a point to the presence of stress-energy at
  that point.
• In the small GR respects all of the causality
  constraints of special relativity, but GR does
  not provide any natural way of imposing global
  constraints on the spacetime
• Without imposing additional principles along GR
  is completely infested with time machines

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Paradoxes generated by thepossibility of time
travel
There are two broad classes of paradox generated
by the possibility of time travel

• Grandfather paradoxes Caused by attempts to
  change the past,
• and so modify the conditions that lead to
  the very existence of the
• entity that is trying to modify the
  timestream.
• Information paradoxes bring information to past.

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Proposals

• Make radical alterations to our worldview to
  incorporate at least some versions of chronology
  violation and time travel.
• Permit constrained versions of closed timelike
  curves
• Incorporate quantum physics to intervene and
  provide a universal mechanism for preventing the
  occurrence of closed timelike curves.
• Chronology Protection
  Conjecture
• 
  Hawking

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• There are long debate concerning such principles.
  
• Several people participated in these discussions.
• Wheeler, Tipler, Gott, Visser,
• Hawking, Deser, Jackiw, t Hooft,

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Chronology Protection Conjecture
(Hawking)

• But there are not enough convincing arguments for
  this conjecture
• QG effects might smear out the divergences.
• Moreover, if QG exists, then chronology
  protection should be settled within the framework
  of this theory
• CTC does appear in a semi-classical approximation

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Chronology Protection Conjecture

• It was suggested that large values of expectation
  value of the energy-momentum tensor occur when
  one has CTCs. If one fed this energy-momentum
  tensor into the Einstein eqs. it could prevent
  one from creating a TM.
• Or divergences in the energy-momentum tensor
  occur. These divergences may create space-time
  singularities which prevent one from traveling
  through to the region of CTC

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Hawking's "chronology protection conjecture
Hadamard form
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Hawking's "chronology protection conjecture
Theorem (Kay,Radzikowski,Wald). There are points
on the chronology horizon where the two-point
functions is not of Hadamard form
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Renormalization Group in Curved Spacetime
DeWitt

• Problems with definition of Renormalization Group
  flow
• Scaling of global coordinates or momenta (as in
  Minkowski space) is not well defined
• No preferred vacuum state for Green functions

Proposal
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Mathematical solution of Grandfather paradox

Recent overcoming of the grandfather paradox
There are spacetimes having CTC for which
smooth, unique solutions to the scalar wave eq.
exist for all data on generalized Cauchy surface
I.A., I. Volovich, T. Ishiwatari
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Time Machine
Surgery in the Minkowski spacetime
Make two cuts and glue the left edge of left cut
to the right edge of the right cut and vice
verse,
t
x
This space contains timelike loops
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The Cauchy problem on spacetimes that are not
globally hyperbolic
t
x
Cauchy problem
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t
x
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Example 2 dim scalar wave equation
Theorem Under assumption of minimal singularity
the Cauchy problem has a unique solution
The Cauchy problem for tgtb is not well posed
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Quantization
IR regularization
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Energy density
No new divergences as compare with Minkowski case
Counter example to Hawking's "chronology
protection conjecture
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Conclusion

• TeV Gravity opens new channels BH, WH, TM
• Wheeler foam at
  TeV scale.
• No enough arguments for Hawking's "chronology
  protection conjecture
• WH/TM production at LHC is of the same order
  of magnitude as BH production.
• The important question on possible experimental
  signatures of spacetime nontrivial objects
  deserves further explorations.