Download influências da expansão do universo na evolução do - Cosmo-ufes

SEMINÁRIO UFES
Vitória, agosto 2013
The quantum-to-classical transition of
primordial cosmological perturbations.
Nelson Pinto Neto
with Grasiele Santos and Ward Struyve
CBPF
ICRA
THE STANDARD COSMOLOGICAL MODEL
(FRIEDMANN-1922)
Copernicus Principle: space homogeneous and isotropic.
 1
2
2
2
2
2
2
ds  dt  a  t  
dr  r d  r sen  d 
2
 1  Kr

2
2
2
K
 a  8 G
i  2

  
3
a
a
2
a
4 G

   3P 
a
3
But where the structures come from?
• In the standard Friedmann model the Universe was always decelerated:
• p=λρ, λ > 0  a=tq with q<1 (λ=0, q=2/3; λ=1/3, q=1/2)
• Scales of different structures grow with a: lphys = a l
• Curvature scale grows with a1/q: H-1 = RH  t  a1/q
ln(lphys) = ln(l) + ln(a)
In the past, observed large scales where much greater then the
curvature scale.
Impossible to justify initial spectrum in terms of local physical
arguments, unless there is an inflationary phase in the past or a bounce
/
/
/
/
/
/
Evolution of scalar perturbations:
Φ(x) is the inhomogeneous perturbation, related to theNewtonian
potential in the nonrelativistic limit, δφ is the scalar field perturbation.
Mukhanov-Sasaki variable
→
Hamiltonian for the perturbations from GR →
Equations of motion
→
IN TERMS OF THE
FOURIER MODES
The classical
solutions
QUANTIZATION
In the Schroedinger picture:
Ψ(y,η) = <y|0,η>
=
THE PROBLEM
|0> is homogeneous and isotropic,
and so is <0|y(x)y(x)|0> (= <0|y(x+δ)y(x+δ)|0>)
Attempts for solving the problem:
squeezing  positive Wigner distribution in phase space
quantum distribution looks like classical stochastic distribution of
realizations of the Universe with different inhomogeneous configurations.
decoherence: avoids interference among realizations.
Severely criticized by Sudarsky and many others:
The state is still homogemeous and isotropic;
In the standard interpretation, different potentialities are not realities;
How ONE of the potentialities become our real Universe?;
What makes the role of a measurement in the early Universe?
(we cannot collapse the wave function because we could not exist without stars!)
The de Broglie-Bohm interpretation
The guidance relation allows the
determination of the trajectories
(different from the classical)
If P(x,t=0) = A2 (x, t=0), all the statistical
predictions of quantum mechanics are recovered.
However, P(x,t=0) ≠ A2 (x, t=0), relaxes rapidly to P(x,t) = A2 (x, t)
(quantum H theorem -- Valentini)
Born rule deduced, not postulated
SOLUTION OF THE MEASUREMENT PROBLEM:
de Broglie-Bohm: particles and fields have actual
trajectories, independently of any observation
(ontology). One trajectory enter in one branch and
singularize it with respect to the others.
Measurement problem:
position in configurations space determines
choosen branch (depends on X0)


Some remarks
a) Q is highly non-local and context dependent!
It offers a simple characterization of the classical limit:
Q=0
b) Probabilities are derived in this theory. The
unknown variable is the initial position.
c) With objective reality but with the same statistical
interpretation of standard quantum theory.
d) One postulate more (existence of a particle trajectory)
and two postulates less (collapse and Born rule) than
standard quantum theory: 1-2 = -1 postulate
QUANTIZATION
In the Schroedinger picture:
Ψ(y,η) = <y|0,η>
=
The de Broglie-Bohm solution
The existence of an actual field configuration breaks
translational and rotational invariance.
It obeys guidance equations.
 Its initial condition satisfies Born rule at initial time.
The quantum-to-classical transition
y(η) α |f(η)| α f(η)
In terms of the quantum potential
FOR THE BOUNCE
Statistical predictions:
the two point correlation function
V - CONCLUSION
Bohm-de Broglie interpretation is very
suitable for quantum aspects of cosmology!
It explains in a very simple way a very old
controversy concerning cosmological
perturbations of quantum mechanical origin.
What about the other interpretations?
"To try to stop all attempts to pass beyond the
present viewpoint of quantum physics could be
very dangerous for the progress of science and
would furthermore be contrary to the lessons
we may learn from the history of science.
This teaches us, in effect, that the actual state
of our knowledge is always provisional
and that there must be, beyond what is actually
known, immense new regions to discover."
Louis de Broglie
THE PROBLEM OF INTERPRETATION
The problem of quantum measurement
Wave function of system + apparatus : interaction ->
bifurcation: but only one branch is observed.
Copenhaguen interpretation:
Actual facts take place in the classical world.
The classical apparatus realizes the collapse of
the wave function and turn the quantum potentialities
into actual and unique facts.
We would like that quantum theory could help cosmology!
Within the Copenhaguen interpretation we are stuck:
no further developments.
Contemporary quantum theory … constitutes an optimum formulation
of [certain] connections … [but] offers no useful point of departure
for future developments.
Albert Einstein.
Fortunately, there are alternative quantum theories!
Many Worlds
Consistent Histories
Spontaneous collapse
de Broglie-Bohm
..........
Decoherence: explain why we do not see macroscopic
superpositions, but...
IT DOES NOT EXPLAIN THE
UNICITY OF FACTS!
FOR THE UNIQUE FACT:
A COLLAPSE OF THE WAVE
FUNCTION IS POSTULATED!
X
MANY WORLDS
(Everett, DeWitt, Deutsch)
All possibilities are realized,
but they are not aware of each other.
THERE IS NO UNIQUE FACT!
SPONTANEOUS COLAPSE
(Pearle, Ghirardi, Rimini, Weber, Penrose)
Non linear evolution suplemented to Schrödinger.
THE DE BROGLIE-BOHM THEORY
“The kinematics of the world, in this ortodox picture, is given by a
wave function for the quantum part, and classical variables
-variables which have values - for the classical part:
(Ψ(t,q ...), X(t) ...). The Xs are somehow macroscopic. This is not
spelled out very explicitly. The dynamics is not very precisely
formulated either. It includes a Schrödinger equation for the
quantum part, and some sort of classical mechanics for the
classical part, and `collapse’ recipes for their interaction.
It seems to me that the only hope of precision with the dual (Ψ,x)
kinematics is to omit completely the shifty split, and let both Ψ and x
refer to the world as a whole. Then the xs must not be confined to
some vague macroscopic scale, but must extend to all scales.”
John Stewart Bell.
Bell in Speakable and unspeakable in quantum mechanics
“In 1952 I saw the impossible done. It was in papers by David Bohm.
… the subjectivity of the orthodox version, the
necessary reference to the ‘observer,’ could be eliminated. . . . But why
then had Born not told me of this ‘pilot wave’? If only to point out
what was wrong with it? Why did von Neumann not consider it? . . .
Why is the pilot wave picture ignored in text books? Should it not be
taught, not as the only way, but as an antidote to the prevailing complacency?
To show us that vagueness, subjectivity, and indeterminism,
are not forced on us by experimental facts, but by deliberate theoretical
choice?” (Bell, page 160)
“I have always felt since that people who have
not grasped the ideas of those papers. . . and unfortunately they remain
the majority . . . are handicapped in any discussion of the meaning of
quantum mechanics”. (Bell, page 173)