Detection of quantum decoherence due to spacetime fluctuations

1
Detection of quantum decoherence due to spacetime
fluctuations

• Paolo Bonifacio1
• Charles Wang1,2, Robert Bingham2,3, Tito
  Mendonca2,4
• 1SUPA Dep. of Physics, University of Aberdeen,
  Scotland, UK
• 2Rutherford Appleton Laboratory, Oxfordshire, UK
• 3SUPA Dep. of Physics University of Strathclyde,
  Glasgow, Scotland, UK
• 4Instituto Superior Tecnico, Lisbon, Portugal

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DETECTING QUANTUM GRAVITY?
1/23

• CAN SPACETIME FLUCTUATIONS PRODUCE ANY OBSERVABLE
  EFFECT AT OUR MACROSCOPIC SCALE?
• Einsteins (1905) Brownian motion work of
  inferred properties of atoms by
• observing stochastic motion of
  macrostructures
• Spacetime fluctuations at the Microscopic scale
  can produce stochastic phase
  shifts.
• ?

Diffusion of the wave function
CHALLENGE CAN THIS BE MEASURED AS A DECOHERENCE
EFFECT IN A MATTER WAVES INTERFEROMETER ?
Random walk of a Brownian particle (blue) due to
stochastic interactions with molecules (red).
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2/23
RELEVANT SCALES RANDOM GRAVITY APPROACH
Wang, Bonifacio, Bingham, Mendonca,
arXiv0806.3042v1 (2008)
4
3/23
COSMOLOGICAL CONSTANT AND DARK ENERGY
FOCUS ON VACUUM ONLY
AT THE CLASSICAL SCALE
?
5
4/23
COSMOLOGICAL CONSTANT PROBLEM
S.M. Carroll astro-ph 0004075
6
5/23
VACUUM LORENTZ INVARIANCE PROBLEM
HOWEVER..
MATTER FIELDS STRESS ENERGY TENSOR WILL ALSO
BREAK LORENTZ INVARIANCE (L.I.) OF VACUUM AT THE
CLASSICAL SCALE
Wang, Bonifacio, Bingham, Mendonca,
arXiv0806.3042v1 (2008)T. Padmanabhan,
arXiv0807.2356v1 (2008)
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VACUUM LORENTZ INVARIANCE PROBLEM
6/23
S.W. HAWKING G.F.R. ELLIS, The Large Scale
Structure of Space-Time, 1973
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7/23
EVEN IF JUST THE METRIC FLUCTUATIONS (GRAVITON)
ARE INCLUDED ONE WOULD STILL GET
INDICATION THAT SOME OTHER MECHANISM OR PRINCIPLE
MUST BE AT WORK ?
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CONFORMAL INVARIANCE
8/23
KNOWN PHYSICS IS BASED ON SYMMETRY PRINCIPLES
COVARIANCE, GAUGE INVARIANCE
GR Particles SM
YET AS EARLY AS THE 80s J.D. BEKENSTEIN SHOWED
THAT THE SM ENJOYS AN EXTRA SYMMETRY
CONFORMAL INVARIANCE (C.I.)
PHYSICS MUST BE INVARIANT UNDER LOCAL CHANGE OF
UNITS
Conformal invaraince, microscopic physics, and
the nature of gravitationJ. D. Bekenstein, A.
Meisels, Phys. Rev. D 22(6), 1313 - 1323 (1980)
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CONFORMAL INVARIANCE
9/23
IN A LOCAL UNITS TRANSFORMATION ALL PHYSICAL
QUANTITIES (LENGTHS, TIMES etc.) TRANSFORM BY A
SPACETIME DEPENDENT FACTOR
REST MASS MUST ALSOBE RESCALED
ALL LENGTH MUST BE RESCALED,IN PARTICULAR
COMPTON WAVELENGTHS
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THE GAUGE MASS FIELD
10/23
IF PARTICLES REST MASSES RATIOS ARE CONSTANT,
C.I. IMPLIES THE EXISTENCE OF A NEW MASS GAUGE
FIELD
COVARIANCECONFORMAL INVARIANCEACTION PRINCIPLE

IN ANY CONFORMAL FRAME (i.e. LOCAL SYSTEM OF
UNITS ) WITH CONSTANT MASS FIELD, THIS GIVES
GENERAL RELATIVITY WITH CONSTANT PARTICLE MASSES
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C.I. IN THE RANDOM GRAVITY FRAMEWORK
11/23
IN A GENERAL CONFORMAL FRAME, BY EXPRESSING
THEN THE TOTAL (gravity matter fields) ACTION
IS
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MASS FLUCTUATIONS AS CONFORMAL FLUCT.
12/23
AT THE RANDOM SCALE, THE BEST ONE CAN DO, IS TO
CHOOSE THE SYSTEM OF UNITS IN SUCH A WAY THAT
PARTICLE MASSES ARE ALMOST CONSTANT, APART FOR
SMALL FLUCTUATIONS INDUCED BY THE MASS FIELD
(CONFORMAL) FLUCTUATIONS
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CLASSICAL SCALE LORENTZ INVARIANCE
13/23
UP TO THIS POINT, THE PRESENT THEORETICAL
STRUCTURE CAME OUT NATURALLY BY ASSUMING ONLY
COVARIANCECONFORMAL INVARIANCERANDOM FIELDS
TREATMENT AT THE RANDOM SCALE
OUR MAIN ASSUMPTION IS NOW ONCE AGAIN DRIVEN BY
SYMMETRY PRINCIPLES
AT THE CLASSICAL SCALE, THE EMPTY SPACE STRUCTURE
EMERGING FROM THE QUANTUM VACUUM MUST BE LORENTZ
INVARIANT (L.I.)
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LORENTZ INVARIANT SPECTRUM
14/23
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ROLE OF THE CONFORMAL FLUCTUATIONS
15/23
VACUUM ENERGY BALANCE AND RESTORING LORENTZ
INVARIANCE
LIKE IN CASIMIR EFFECT, THE REGULARAZING
CONFORMAL AMPLITUDE IS INDEPENDENT OF THE CUTOFF
USED IN THE CALCULATIONSN100 IS THE TOTAL
NUMBER OF INDEPENDENT MATTER FIELDS MODES
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PHYSICS OF DECOHERENCE
16/23
MATTER WAVES INTERFEROMETERS MEASURE INTERFERENCE
PATTERN OF MASSIVE QUANTUM OBJECTS
? INTERACTION WITH THE ENVIRONMENT ?
Collisions with ambient particles ? Black
body radiation ? Interaction with its own
components ? Natural vibrations of the
system ? QUANTUM SPACETIME FLUCTUATIONS ?..
FRINGE VISIBILITY IS AFFECTED BY DECOHERENCE DUE
TO
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EFFECTIVE NEWTONIAN POTENTIAL
17/23
TO ESTIMATE DECOHERENCE SUFFERED BY MASSIVE
PARTICLE WE START FROM RELATIVISTIC KLEIN-GORDON
EQUATION WITH FLUCTUATING MASS AT THE RANDOM
SCALE
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DECOHERENCE AND NON-LINEARITY
18/23
THE CONFORMAL FLUCTUATIONS ARE MODELED IN 3D ON
THE BASIS OF THEIR LORENTZ INVARIANT POWER
SPECTRUM ONLY,UPON WHICH THEIR STATISTICAL AND
CORRELATION PROPERTIES DEPEND
A RIGOROUS QUANTUM MECHANICS CALCULATION ON THE
DENSITY MATRIX EVOLUTION REVEALS THAT ONLY A
QUADRATIC NON-LINEAR TERM IN THE EFFECTIVE
POTENTIAL CAN IN INDUCE A DEPHASING WITH THE SAME
EFFECT OF GENUINE DECOHERENCE, i.e. AN
EXPONENTIAL DECAY OF THE OFF DIAGONAL ELEMENTS IN
THE DENSITY MATRIX DESCRIBING THE PROBING
PARTICLE

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DECOHERENCE FORMULA
19/23
THE MAIN RESULT IS THAT
P. BONIFACIO, C. WANG et al. in preparation
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DECOHERENCE OF FULLERENES
20/23
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OBSERV. DECOHER. Vs THEORY (without QG
fluctuations)
21/23
IT IS HIGHLY UNLIKELY THAT THIS LARGE DISCREPANCY
BETWEEN THEORY AND EXPERIMENT FOR LONG DRIFT
TIMES IS DUE TO QG DECOHERENCE
HOW MUCH SHOULD WE EXPECT FROM OUR THEORETICAL
FRAMEWORK ?
Stibor, Hornberger, Arndt et al. Laser Physics,
15, 10 (2005)
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PROBING PARTICLE CUTOFF LENGTH
22/23
THE MAIN RESULT WAS
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SOME ORDERS OF MAGNITUDES
23/23
IN SPACE ONE COULD HOPE TO ACHIEVE DRIFT TIMES OF
1 sec
WITH N 100 OUR FORMULA GIVES
TOO SMALL !!!
IF QG DECOHERENCE IS TO BE DETECTED WE ARE LIKELY
TO NEED SUPER-HEAVY QUANTUM PARTICLES MASSIVE
GOLD CLUSTERS ? ENTANGLED BOSE-EINSTEIN
CONDENSATES ?
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CONCLUSIONS

• Conformal Invariance and the related gauge mass
  field could play a key role in regularizing the
  overall amount of vacuum energy in the Universe
  and yielding a small Cosmological Constant,
• Modeling of quantum gravity at low energies
  within the newly established C.I. random gravity
  framework supports the idea of loss of coherence
  in matter interferometers,
• We have indications that advanced matter
  interferometers experiments in space could be in
  conditions to detect a decoherence signal using
  super-massive quantum particles with M 1010 amu
• Great experimental and technological challenge
  in matter interferometers it is difficult to
  avoid interactions with the environment. The
  challenge is to detect the spacetime fluctuations
  unambiguously.

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COULD THIS BECOME A REALITY IN THE NEAR,
FORESEEABLE FUTURE ?