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Negative energies and time reversal in QFT and GR grqc 0404110

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Allow the exact cancellation of vaccuum divergences and cosmological constant terms ... It is possible to get exact cancellations as in SR ... – PowerPoint PPT presentation

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Title: Negative energies and time reversal in QFT and GR grqc 0404110


1
Negative energies and time reversal in QFT and
GR (gr-qc 0404110)
  • Frederic Henry-Couannier
  • henry_at_cppm.in2p3.fr
  • CPPM/RENOIR Marseille

2
Plan
  • Introduction 
  • Negative energies and time reversal in
    Relativistic Quantum Field Theory
  • Negative energies and time reversal in GR
  • Schwarzschild and cosmological solutions
  • Outlooks and Conclusion

3
Negative energies
  • The Lorentz Group has negative energy
  • representations
  • Why not Elt0 -hn, -mc2, -(g-1)mc2 -1/2 mv2
    (vltltc)?
  • Usual answer
  • Stability issue
  • Never observed particles

4
Motivation for negative energies
  • Solutions of all relativistic field equations
  • Generated through time reversal in classical
    relativistic physics
  • Possibly a solution to many outstanding enigmas

5
Outstanding enigmas
  • Gravity
  • Galaxy formation and rotation
  • Gravitational lensing
  • Pionner deceleration
  • Universe acceleration
  • F lat universe
  • RG singularities
  • Vaccuum divergences
  • Cosmological constant
  • All interactions
  • UV loop divergences
  • Weak interactions?!
  • C, P asymetries

6
Stability of free scalar fields
  • Positive energy Action
  • Negative energy Action
  • Stability is also all right for a free negative
    energy field which maximises its action

7
Stability of negative energy matteralone
  • Negative energy photons ? reversed Coulomb Law
  • Negative energy fermions
  • ? In the fermions and photons gas
  • Negative energy atoms appear
  • Most probable states have maximal energies
  • Entropy and temperature are negative and entropy
    decreases
  • Stability is also all right for a free negative
    energy field which maximises its action

8
Uncoupled positive and negative energy worlds are
stable
               
 
9
Leading idea
  • Rehabilitation of negative energies in QFT and GR
    should lead to a new picture where
  • Positive and negative energy worlds interact only
    through gravity
  • Stability is insured

10
Positive and negative energy Fields, Actions and
Hamiltonians
11
Unitary time reversal
  • Energy reversal
  • I and f states not interchanged

12
Vaccuum energies
  • Vaccuum energy of the positive energy Quantum
    Field
  • Vaccuum energy of the negative energy Quantum
    Field
  • ?Vaccuum divergences are exactly opposite

13
Why believe in the Unitary Time Reversal scenario
  • Most natural way to cancel vaccuum divergences
  • Unitary as for all usual symetries (Parity,
    Lorentz )
  • No more time reversal paradoxes
  • (E,p) behaves as (t,x) as for all usual symetries
  • Only possibility in classical physics

14
Actions under time reversal
  • We already have (unitary choice)
  • But we also need
  • In order to get
  • ? No way in SR!!

15
Time reversal conjugated metrics and Actions
  • Postulate
  • T keeps discrete in GR
  • Two conjugated metrics but no extradimension

16
Scalar action under general coordinate and
discrete transformations
  • The T-conjugated worlds are not coupled
  • But the T-conjugated metrics are necessarily
    linked
  • ? The gravitational interaction (only) will
    connect the two worlds

17
Requirements for a relation between the
conjugated metrics
  • Agree with GR in the well tested domain (PN)
  • Generate negative energy sources from each metric
    point of view
  • Allow the exact cancellation of vaccuum
    divergences and cosmological constant terms
  • Avoid instability issues
  • ? A simple solution exists!?

18
A priviledged coordinate sytem
  • is not covariant
  • There is a priviledged coordinate system to be
    determined
  • We assume it is global
  • But it might be global for cosmology local for
    perturbations
  • ? Need for other criteria symetry principles,
    isometries

19
Modified Einstein equationin the priviledged
coordinate system
  • Objects living in the same metric attract each
    other
  • Objects living in different metrics reppel each
    other ? This is a stable picture!

20
Vaccuum energy and cosmological constant
  • Cosmological constant terms vanish if
  • Vaccuum energy terms vanish if
  • ? It is possible to get exact cancellations as in
    SR

21
In the linear approximation( )
  • ?Energy and momentum of matter_radiation
  • Energy of the gravitationnal plane wave

22
Time reversal effects in GR
  • Energy reverses
  • Momentum is invariant
  • Mass and speed are invariant
  • ? This speed involves a flowing time which arrow
    is not reversed under time reversal
  • ? Coherent with the unitary time reversal picture

23
The Schwarzschild Solution
  • In our priviledged coordinate system, both
  • are stationary and isotropic
  • We neglect possible background effects (from the
    cosmological solution)
  • We get In GR
  • No more coordinate singularity in the most
    natural coordinate system (isotropic system)
  • ? It is possible to get exact cancellations as in
    SR

24
The Cosmological global priviledged coordinate
system
  • In our priviledged coordinate system, both
  • are homogeneous and isotropic
  • ? The metric is spatially flat
  • Postulate the priviledged coordinate system is
    Conformal_Newtonian
  • Allows to study in a simple way Gauge invariant,
    Newtonian_like Scalar perturbations.
  • Time-Space symetry (tachyon ltgtbradyon ?)
  • ? It is possible to get exact cancellations as in
    SR

25
Cosmological Equations
  • At high pressures we expect matter exchanges
    between the two metrics to be non-negligible
  • ? Difficult task to predict the evolution of
    however

26
An exact cosmological solution
  • The space-space equation in the cold-cold phase
  • ( )
  • ?
  • ? ? In comoving time units
  • ( )

cold
radiative
radiative
We are here
27
An approached cosmological solution
  • With the time-time equation
  • (1) Assuming no matter exchange (
    )
  • ? ?
  • ? (1) is quite a good approximation in some
    cold-cold phases but there are matter exchanges!
    (center of stars or galaxies, radiative era)

28
Magnitude vs redshiftSNA test (SCP 2003)
  • In the constant acceleration phase
  • Assuming a law
  • Fit a and normalisation only

?249. (54 ndof)
? 1.60.3(stat) ? q0-0.380.07 (5?)
SCP 2003 Statistical error only
29
Magnitude vs redshiftSNA test (RIESS 2004)
  • Same fit on RIESS 2004 compilation (gold sample)

? 1.430.13(stat) ? q0-0.300.03
?2 181.(156 ndof)
30
Ages
  • A constant acceleration
  • ? Universe age
  • ? Old galaxy (z5) age
  • ? Expansion rate was slower in the past

31
Outlooks and conclusion
  • Stability must be fully adressed in quantum
    gravity but the classical context is already very
    favorable.
  • If the model is right
  • A new window opens with rich and fascinating
    phenomenological and theoretical outcomes!

32
Stability of paths for a positive kinetic energy
mass point
  • Action
  • dS0 ?
  • S has no maximum due to the positive kinetic term
  • The extremum we find is a minimum

33
Stability of paths for a negative kinetic energy
mass point
  • Action
  • dS0 ?
  • S has no minimum due to the negative kinetic term
  • The extremum we find is a maximum
  • ?The fundamental principle is that of stationary
    (dS0) action. In all cases, paths are stable

34
Anti-Unitary time reversal
  • No energy reversal
  • Initial and final states interchanged

35
A priviledged coordinate sytem
  • is not covariant
  • The priviledged coordinate system might be
  • Global
  • ? SEP violation (very small magnitude?)
  • ? Most easy way
  • ? Which one?
  • Local
  • May be no SEP violation
  • Which one at each space-time point ?
  • Global for cosmology, local for perturbations
  • ? Need for other criteria symetry principles,
    isometries, null gravitational energy,
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