ICRANet Seminar ICRANet Pescara 7 November 2019, Pescara, Italy Speaker: Orchidea Maria Lecian Author: Orchidea Maria Lecian, University of Rome La Sapienza Title: Quantum-systems investigations vs optical-systems ones Abstract: The features of quantum systems, quantum-optical-systems and optical systems can be outlined according to the possibility for the study of the properties of matter fields and of the gravitational field. Quantum properties of particles and of the background gravitational field at quantum scales, at the semi-classical regime and at the classical level are analyzed by quantum systems and optical-systems devices, for which the experimental features of the research are compared. Investigation in cosmology and in early cosmology can be envisaged. The features of quantum operators to be evaluated by these techniques are pointed out. The properties of relativistic objects are this way examined. The features of the Einstein fi eld equations and of their initial conditions are de fined. The degrees of freedom available for the Einstein field equations and their initial conditions are characterized. Website: http://www.icranet.org/index.php?option=com_content&task=blogcategory&id=89&Itemid=781

1. Quantum-systems investigations vs
optical-systems ones
O.M. Lecian
Sapienza University of Rome, Rome, Italy
Based on: OML, Alternative Uses for Quantum Systems and Devices,
Symmetry 2019, 11(4), 462,
Special Issue ’Cosmological Inflation, Dark Matter and Dark Energy’
7 November 2019
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

2. Abstract
The features of quantum systems, quantum-optical-systems and optical systems can
be outlined according to the possibility for the study of the properties of matter fields
and of the gravitational field. Quantum properties of particles and of the back- ground
gravitational field at quantum scales, at the semi-classical regime and at the classical
level are analyzed by quantum systems and optical-systems devices, for which the
experimental features of the research are compared. Investigation in cosmology and in
early cosmology can be envisaged. The features of quantum operators to be evaluated
by these techniques are pointed out. The properties of relativistic objects are this way
examined. The features of the Einstein field equations and of their initial conditions
are defined. The degrees of freedom available for the Einstein field equations and their
initial conditions are characterized.
Based on:
OML, Alternative Uses for Quantum Systems and Devices, Symmetry 2019, 11(4), 462, Special Issue ’Cosmological
Inflation, Dark Matter and Dark Energy’;
OML, Semiclassical length measure from a quantum-gravity wave function, Technologies 2017, 5(3), 56, Special
Issue ’Quantum Gravity Phenomenology and Experimental Implications’ [arXiv:1708.07895];
OML, Measuring gravity in the vicinity of the Earth: spectral analysis and related modular structures after further
experimental devices, 4th International Conference and Exhibition on Satellite and Space Missions- Session:
Shaping the Future with Latest Advancements in Satellite and Space Missions, June 18-20, 2018, Rome (Italy);
https://satellite.conferenceseries.com/eposter-presentation.php
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

3. Summary
• Particles to be detected and their interactions
• Quantum optical systems
• Optical systems
• Weak anisotropic gravitational fields
• Interferometers
• Cosmological implementation
• Semiclassical tests: spectral analyses
• non-gravitational contributions
• gravitational contributions
• Spectral analyses for geodesics measurements
• Spectral analyses for particle energy levels
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

4. Particles to be detected
Berry geometrical phase
for a broken O(3) 3-dimensional space symmetry, the
wave-function Φ(x) of Hamiltonian Hλ ≡ Hλ(λ1, λ2, ..., λn)
Φ(x) = e−iΦG (x)
ϕ(x),
- λi , i = 1, ..., n slowly changing parameters - ΦG (x) the gravitational
part of the wavefunction,
ΦG (x) = −1
4
x
P
dzσ
(γασ,β(z) − γβσ,α(z))[(xα
− zα)kβ
− (xβ
−
zβ)kα
] + 1
2
x
P
dzσ
γασkσ
- kα
plane-wave momentum for kα
kα = m2
k
- the broken O(3) is therefore obtained unless strong fine tunings are
imposed on ϕ(x);
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

5. Weak-Gravitational-Field Anisotropies
broken O(3) space symmetry
- velocity-distribution function for the velocities characterizing the
wavepackets
fv =
1
8π3det[(ςv )2]
exp −
1
2
(v − v⊙)T
ς−2
v (v − v⊙) (1)
for quantum states describing asymptotical (−∞) KLSZ states;
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

6. -for a weak gravitational field, the velocity distribution for particles
v in the laboratory frame departs from that calculated on
Minkowski flat spacetime as
fv = 1
8π3det[(ς(v))2]
exp −1
2(v − v⊙)T ς−2
v (v − v⊙) where - the
velocity (v) dispersion tensor ς(v) is diagonal,
- ς(v) ≡ diag[ςx , ςy , ςz ],
- v⊙ the Earth orbital velocity around the Sun,
- encodes the solution to the EFE’s and their initial conditions through
its metric-tensor components as the velocity anisotropy β(r)
- the velocity anisotropy is defined as
β(r) ≡ 1 −
ς2
y +ς2
z
2ς2
x
- the velocity anisotropy can be detected by a ionization chamber
able to recover the track parameters (X, Y , Z, θ, φ, S).
J. Billard, F. Mayet, C. Grignon, D. Santos, Directional detection of dark matter with
MIMAC: WIMP identification and track reconstruction, J. Phys. Conf. Ser. 2001,
309, 012015.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

7. Tachyonic fields
Tachyionc fields Y are characterized as
- non-renormalizability of the operator term Y (even) on
Minkowski spacetime
- their propagation is consistent with the Lorentz invariance only in
one space direction:
the little group for tachyonic fields O(2, 1), which admits only a
one-dimensional representation.
Several mechanisms have been postulated to assure the stability of such
a field in vacuum in an Einsteinian setting:
- it can have a cosmological implementation for the analysis for the
particular potentials which can rule the dynamics, - the stability of
tachyonic field can be connected with particular features of the
gravitational field which can imply a modification, by adding extra
degrees of freedom, of the phase space, for any kinds of interactions;
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

8. - cosmological implementation can be compared with the presence
of the operator Y without violating local Lorentz invariance:
- the operator Y can be kept tamed in several models
- within the Poincar´e symmetry, the little group O(2, 1) can be
realized in only one space direction (say, the direction individuated
by the interferometer arm).
B. Fazlpour and A. Banijamali, Non-minimally Coupled Tachyon Field in Teleparallel
Gravity, JCAP 1504 (2015) no.04, 030.
G. Gabadadze, R. Kimura and D. Pirtskhalava, Vainshtein Solutions Without
Superluminal Modes, Phys. Rev. D 91 (2015) no.12, 124024.
K. Koyama, G. Niz and G. Tasinato, Effective theory for the Vainshtein mechanism
from the Horndeski action, Phys. Rev. D 88 (2013) 021502.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

9. Weak Gravitational Field
For the detection of dark matter, given a WIMP, χ of mass mχ,
from parameter space (mχ, ςi ) it is possible to evaluate the
WIMP-nucleon cross section σW −nucleon
.
- a model-independent cross section of dark matter on protons ςi,p
is found as ςi ≃ 10−3pb
- for scintillators targeted of CsI(Tl),
- 19 F.
F targets were studied for Earth-based experiments to analyze
atmospheric-origin particles.
Detectors for anisotropic ultraenergetic cosmic rays of galactic
origin have been also considered.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

10. Sparticles
in a weak gravitational field
mass dispersion relation ∆mij for masses mij
∆m2
jk
m2
0
=
λj λ∗
k
π2
ln
MPl
MG
, (2)
• λi factorizes the (requested) coupling constant
• m0 is the mass of the common (standard-model) scalar (normalized
to Planck mass MPl )
• MG is the mass for a (massive) gravitational mode.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

11. • after the breach of higher-dimensional structures,
non-perturbative degrees of freedom give rise to
Compton-length waves (particles) whose masses MC are
comparable with Planck mass MPl
• they interact very weakly and gravitationally;
• masses MC are of order MC ≃ R/MPl ;
with R the lower bound on the compactification (energy) scale:
their gravitational interaction can modify ordinary Newtonian
gravity;
• verifications of MC can be achieved by cantilever detectors
and/or silicon-based microelectromechanical systems.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

12. Fractional charges
An instrument aimed at detecting fractional-charge particles is the
rotor electrometer. It was designed as a Faraday container with an
arbitrary high-impedance amplifier, endowed with copper pads, for
which different charges reach the container walls at different
velocities, such that the time of flight can be calculated, i.e., after
a tuning the impedance suited for the charge to be detected.
The existence of fractional quantum numbers n has also been
postulated.
J.C. Price, W.R. Innes, S. Klein, M.L. Perl, The rotor electrometer: A new instrument
for bulk matter quark search experiments, Rev. Sci. Instrum. 1986, 57, 2691.
W.R. Innes, M.L. Perl, J.C. Price, A rotor electrometer for fractional charge searches,
In Proceedings of the 4th International Conference on Muon Spin Rotation, Relaxation
and Resonance, Uppsala, Sweden, 23–27 Jun 1986; pp. 1–2.
V. Mathai, G. Wilkin, Fractional quantum numbers via complex orbifolds,
arXiv:1811.11748.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

13. Fifth-Force interactions
The Fifth-Force potential can be parameterized as
V5 =
α∞;i,j
r
e−
MPL
λ
r
R ,
- α∞;i,k factorizes the Newton gravitational constant at ∞ G∞:
is a function of the Fifth-Force numbers αi and αk of the neutrino νi and the other
particle considered
- R the distance on which the interaction is considered
- β corresponds to the other coupling constant for the Fifth Force (normalized by the
Planck Mass) connected to the parameter λ by numerical values describing the
interaction within this ranges in the constant α∞;i,k
α can be therefore factorized as
α ∼ GNα0αi αk
- αj the Fifth-Force numbers relative to the particles
- α0 a numerical constant useful for relating the range of the Fifth Force with the
gravitational constant GN
such that
V5 =
α ∼ GNα0αi αk
r
e−
MPL
λ
r
R ,
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

14. The angular deviation is maximal when the interaction is supposed as
occurring between two particles, such that, at the end of the
measurement, the trajectory path of the two particles deviates from the
purely-gravitational one of a deviation ∆(x5), both in the case of massive
neutrinos and in that of massless neutrinos.
The displacement is calculated by majorizing the integral of the potential
on a flat Minkowski background, i.e. at an interferometer arm length L,
as
∆(x5) =
α∞;i,k
α0αi αk
1
L5
e−
MPL
β ,
-with β with the dimensions of [mass].
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

15. Semiclassical descriptions
Quantum optical corrections for Maxwell equations are predicted
for short-distance experiments, for which a Fock occupation space
can be defined for the quantum optical system, and for which
quantum-gravitational corrections can be present only in the
field-perturbation-part of the solution of the field equations, as
their minimal length takes place at scales larger than the Plank
scale.
Such corrections can be framed within models interpreting the
statistical correlations as the outcome of theories with local hidden
variables.
An experiment with correlated light beams in coupled
interferometers allows for semiclassical-limit analysis.
M. Faizal, D. Momeni, Universality of short distance corrections to quantum optics,
arXiv:1811.01934.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

16. Laser-frequency measurements help calibrate frequency absolute
and the long-term stability of a fiber Fabry-P´erot interferometer.
For low temperatures, i.e., for a spectrum of 1–3 ms−1
,it is possible
to characterize the Doppler radial velocity shifts at the 1 ms−1 of
exoplanets.
Laser interferometers have proven efficient in detecting particle
interactions linearly in g, such as spin-gravity coupling, and P- and
T-violating interactions from an astrophysical point of view.
It may also apply to (integral-spin) dark-matter searches, as well as
other kinds of investigations.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

17. Quantum optical systems
for spatially non-Gaussian states of light [?]: - the output modes are
characterized as superpositions of Laguerre-Gauss (LG) modes for
numerically-generated orbital-angular momentum (OAM) degree-of-freedom
under the hypothesis of external noise also for models of radial mode
index both for a deep neural network and for a convolutional neural network-
varying the integer l -the argument of the Laguerre-Gauss (LG)
polynomials corresponds to one 2π phase oscillation with different
radial-mode index p: twisting superpositions
| Ψl,−l
p (r, φ) |2
LG ≃ r2|r| 2r2
w2
exp
2r2
w2
(1 + cos (2 | l | φ − θ)) (3)
| Ψn,−n
p (r, φ) |2
BG ≃ J|n|(βr)2
exp
2r2
w2
(1 + (−1)n
cos (2 | n | φ − θ)) . (4)
for LG polynomials and Bessel-Gauss (BG) polynomials
- with J the corresponding Bessel function.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

18. - the numerically-generated external noise not specified whether to
be ascribed with gravitational effects and/or quantum-gravitational
effects or interactions;
- applications in metrology are ensured by the validity of the
analysis for many kinds of interferometers, including hybrid
interferometers.
S. Lohani, E.M. Knutson, M. ODonnell, S.D. Huver, and R.T. Glasser, Applied Optics
Vol. 57, Issue 15, pp. 4180-4190 (2018).
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

19. Semiclassical experiments
Semiclassical structure of the spacetime
- investigating the properties of macroscopic materials: reflection and
refraction specificities
- comparing the atoms and molecules constituting the solid-state
structure, either crystalline or amorphous
extreme approximation of the corresponding potential wells (as
black-hole-like potentials):
the chosen interacting particle (photon) is small enough with
regard to the potential wells and the Planck scale
- the experiment is conducted at length sizes larger than the
Planck scale.
The overall gravitational regime of the lab system is still
Minkowskian:
- there exists a valid paradigm to discriminate and calibrate
interaction(s) between the system and the external environment.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

20. Photon transit in a (macroscopic) block of
diaelectric material
- supposed to cause a (photon) momentum transfer
- there exist appropriate temperatures at which a momentum change
caused by the diffractive diaelectric index: the momentum transferred to
the block can produce appreciable (position) reaction shift of the block
as the photon exits the block
- diffractive diaelectric properties, caused by its solid-state structure, can
be approximated to the effects of a lattice of (small-size) black holes,
which can account for quantum-gravitational properties of the spacetime
inside the block and, in particular, its semiclassical features
Photon crossing: a block of diaelectric material crossed by a photon is displaced
as ∆Xk at the exit of the photon after k double reflections
∆Xk = L1
hω
2π ˜Mc2
(n − 1 + 2k) (5)
- ˜M mass of the block,
- V ˜M = L1L2L3 volume of the block,
- nref refraction index evaluated after the absolute value of the Poynting vector,
- ω frequency of the photon.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

21. Modifications to the measured displacement ∆Xk has to be
ascribed to quantum-gravitational phenomena,
which can manifest -in the modification of the photon energy,
- in the modification of the diffraction index of the diaelectric block,
- and/or after the spacetime semiclassical structure modifies the potential
of the solid-state structure, photon energy, and their interaction.
J.D. Bekenstein, Is a tabletop search for Planck scale signals feasible, Phys. Rev. D
2012, 86, 124040.
J.D. Bekenstein, Can quantum gravity be exposed in the laboratory? Found. Phys.
2014, 44, 452.
O.R. Frisch, Contemp. Phys., 7, 1965, 45-53.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

22. Verifying New Particles by Alternative Experiments
Detectors for Earth-based experiments can be appropriate to look
for WIMP’s of mass mW , mW 80Gev scattering on smaller
particles:
- interaction signals happening in the Sun can be considered as well;
- the main differences between generic light scalars and axions are
discussed on the basis of P and T violations;
- the regions of the parameter space available for axions exclude, by
electric dipole moment bounds, those for a Fifth-Force recognition as
spin-dependent and mediated by an axion-like particle; nonetheless, for a
generic scalar unaffected by CP violation, a Fifth-Force description is still
possible;
- the signal containing a spin-flipping effect calculated after the cross
section of the absorption by a scanning Fabry-P´erot interferometer as a
function of a ’relaxation time’; can be ’cleaned’ and analyzed to obtain a
bettered description of the emission rate and the absorption one;
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

23. - for a beam of electrons prepared for a Fabry-P´erot interferometer
according to a required velocity distribution precision and
(three-dimensional space) radial resolution, for Thomson scattering of
laser electrons from an electron beam, Doppler-shifted wavelength of
photons backscattered under 180 degrees, velocity distribution radially
resolved in space, absolute electron energy, and the degree of
space-charge compensation can be measured
- measurement of longitudinal and transverse electron temperature is
determined up to a lower bound for the ratio, respectively, and it has an
upper bound (of 10/2) for velocity distribution
- it further reveals fractional space-charge compensation;
- is suited for higher laser intensity, i.e., by appropriate placement and use
of the cavity mirrors of a confocal resonator;
- this technique provides nondestructive measurement of velocity
distribution in an electron beam radially resolved in space.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

24. The results comprise the direct measurement of the absolute
electron energy and the degree of space-charge compensation
in the electron beam:
- the determination of an upper bound of 10/2 for the ratio of
longitudinal-to-transverse electron temperature implies the first
direct measurement of flattened velocity distribution;
- look for new predicted particles by adapting previously
proposed experiments and apparati for the required tasks;
- noise-minimization techniques involve changing mirror disposition
for Michelson interferometers;
- nonlinear interferometers, optical switching (for example, but not
only, of mirrors) can be obtained via cross-phase modulation of a
lossy (particle-beam) line, i.e., for a Sagnac interferometer.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

25. The Sagnac effect can be explored by studying the role of
spin-rotation coupling for circularly polarized light to testify on the
photon-helicity coupling to rotation:
for this, an analogous experiment of neutron interferometry can be
performed:
the frequency shift and a constant optical phase shift for the prepared beam of
neutrons can be tested
to obtain helicity-rotation phase shift
∆Φ = 2Ωl/c
as the same phase shift predicted in the rotating frame at the detector, with
- Ω angular velocity,
- ∆t = l/c the time of flight of a photon between two interferometers ends.
The presence of different particles in the (Earth-based) lab system
can be revealed by a different helicity-rotation phase shift
˜∆Φ:
their gravitational interaction and other kinds of interaction with
neutrons in the prepared beam would modify the neutron kinetic
energy Kn.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

26. - velocities v correspond to the average of the wavepacket of the prepared neutron
beam; in the case of neutrons interactions, their velocities after interaction(s),
v′ = vn interact = v
can have changed, i.e., in any case of inelastic scattering interaction(s):
the helicity-rotation phase shift(s) can be measured by evaluating
- the requested time for end-to-end interferometer path covering, ∆˜t,
- their velocities vn interact = vn i ≡ c2ki /ωi , - their velocity distribution, being
Φ ≡ Φ(k) and Φ′ ≡ Φ(kinteract ). In the case of a weak gravitational field, the velocities
of the new interacting particles (not prepared in the neutron beam) in the experiment
environment would be further modified, for which different helicity-rotation phase
shift(s) ˜∆Φ ′′ would be detected.
The presence of different kinds of particles would be predictable in the case of
different values for ˜∆Φ ′′.
The effectiveness of a gravitational (but not necessarily only Berry) phase for the
neutron wavefunction (from which the neutron wavepacket is prepared), would lead to
two different results, ˜∆ΦG
′′′ and ˜∆Φ ′′′ for the measures of the helicity-rotation
phase shift(s) according to whether the new particles interact gravitationally or not.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

27. Features of spectral analyses at the semiclassical level
- quantum-gravitational models for the Planck-scale description of the
spacetime as a most general expansion of the white noise for each
measure of displacement δx
δx ≥ δxi + h
c
2L
mδxi
as powers of the Planck length, whose peculiarities can account for those
a particular quantum-gravity model;
- the power spectrum ρ of the frequency ϕ of the strain noise, according to its most
general features for the detection of quantum features of the spacetime, is
ρ ≃
n≥0
˜ρn
LP
c
ϕn
with ˜ρn numerical coefficients; - inverse powers need not be included, as they are
inconsistent with the theoretical classical limit LP → 0;
- the total uncertainty of an experimental measure having to depend on the sum of
the uncertainty of the initial and final position, which cannot be smaller than the
eigenvalue spacing (i.e., the Planck length);
- modifications about the errors in measuring lengths can be obtained by considering
the quantum nature of extended bodies instead of their macroscopic length-ruler
feature such as macroscopic clocks (systems);
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

28. - each anisotrpy degrees of freedom departing from Minkowskian
spacetime at the semiclassical level is calculated as
ˆL(γxa (t2 − t1))
ˆL(γxb
(t2 − t1))
∼ 1 + ǫ(fa − fb) + ǫfab
lPl
Λ
for segments of length γxa < Λ evaluated along two of the three space
directions γxa < Λ evaluated along two of the three space (coordinate)
directions xa, xb = x, y, z in the time interval t2 − t1,
with ±ǫ in the case both curves are evaluated on the Planck length;
- the request ±ǫ englobes the normalization with respect to the length
ˆL(γxb (t2 − t1)) in the series expansion at the Planck length:
it factors out any proper time dependence of the length measure;
- the non gravitational degrees of freedom are contained in the functions
fi , i ≡ a, b;
- the gravitational degrees if freedom are contained in the functions fab;
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

29. - for quasi-Minkowskian spacetime, the expectation values for the
length operators evaluated on different geodescics (quasi-)
coordinate directions in vacuum ˆX(t), ˆY (t) differs at most as
ˆX(t)
ˆY (t)
≃ 1 −
ˆx1(t − 2L/c) − ˆx2(t − 2L/c)
ˆY (t)
,
Xα
Xβ
≃ 1 − ̺
Fα − Fβ
Xβ
as functions of the F’s, i.e., the (correspondingly-normalized)
differences in in the expectation values, with ̺ a numerical factor
with the dimensions of [length].
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

30. - deviations must be found within the experimental error, for which
the uncertainty is not second order
- a measured length L for a (coordinate) length Lcoord would
correspond to
L =
1
0
qab(c(t)) ˙ca
(t) ˙cb
(t)
1/2
∼ Lcoord + ∆Θ + f (g)
- any (quantum) fluctuation related with an emerging Minkowski
spacetime is related to ∆Θ;
- and any further non-Minkowski contribution is encoded as a
function of the anisotropic metric tensor g;
- differently, strong fine-tuning phenomena must be hypothesized.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

31. Spectral analysis for wavefunctions
The quantum-mechanical implementation of the gravitomagnetic
Hamiltonian requires the wavefunctions
Ψ±(t, β) = Ae−iβe− i
E±t
invariant as
Ψ(t, β) = Ψ(t + T±, β + 2π), E± = ±2π
T±
, T+ − T− = 4πa .
Any corrections to the energy levels must be at least one order
greater than those to the phase.
∆E =
n
a0n
an dnfρ
dmρ
n
+
n
b0n
bn
LP
dnfρ
dpρ
n
- an terms refer to the non-relativistic corrections.
- bn terms to the relativistic ones.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

32. analysis of the corrections
• variation of the (fundamental) cosmological constant wrt time,
˙G: from term 1geometrical correction of a as (L2
P/(G )1/3)a1
constraining α0 and β0 and by keeping φ∗0 fixed;
the remaining parameter range available to determine the
dynamics of φ∗0 from b1.
• quadrupole moment Φ2 parameter for a gravitational mass ¯M
has the same functional expression (also as a function of the
Kerr rotation parameter ˜j) both for circular orbits and
(slightly-perturbed) non-circular ones: possible to discriminate
between two Kerr black holes or two Kerr disks from the 1 a
term, as LP/(c G)a1, as Φ2 ∼ c−4 in the static limit (by
neglecting the secular mass ¯M change);
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

33. • a1 must contain also the most stringent constraints on the
anisotropies in the electron spin (i.e. also those arising from
cosmological origin); in vacuum, a large part for the contributions to
a1 can still be available; in presence of matter, the constrains are
very close to the definition of a Planck mass MP , s.t. the difference
is at most Oh(
− 1) for a2 or the next-order terms; a remaining
addend defining b1 must also ensure Wigner-Barman features for
particles, the discrepancy from them being given by
b1/(C2
1 + C2
2 )1/2
and b1/C3 + O(L−2
P ) in the bi ’s, i ≥ 2: the order
of the discrepancy can therefore be looked for at b4 for the
conservation of the momentum;
• small charged superconductor experimenting gravitomagnetic effect,
the possible non-Riemannian contribution contained in as
(Z0/(Ω − Z0)) in a0n; it can correspond to the possible
contributions due to teleparallel gravity within the an terms at
O(c−4
) to compare at least with a Schwarzschild solution in
presence of a test particle of negligible mass:
for a massive particle, starting from Oc−2
in the bi , the same order
in the time corrections of the gravitomagnetic Hamiltonian at
3-5PPN, i.e. for which (L2
P /(c ))2/3
b2.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

34. • the effects of imposing Q = 0 for Kerr-Newmann spacetimes have
been proven not to be defining for non-charged test particles, as,
from neutron experiment, they have been observed t be
distinguishable (on the two arms of an interferometer), as labelled
by internal states, i.e. by the different harmonic(s) expansion (of
their deBroglie lengths) generated by their energy-momenta.
• the precisions at which arcosecond errors in position in modern
astrophysical position observation for contributions associated to
(also, outside) Solar system sources can be compared only at 1PN,
and 2PN order for precision required about light deflection by the
Sun, due to the difference of velocities at which the Sun and the
extra-Solar-System sources. It is possible to improve the accuracy of
the numerical simulation(s) by calculating the remainder of star
position parallaxes expansions. The correlation in the measurements
acquires efficiency by being enhanced by both the brightness of the
considered celestial bodies and the distance distributions.
For this, the evaluation of the remainder on the second PN formalism for the
motion for the (Earth) moon has been calculated does not produce any such
detectable effect either on Earth-based experiments or on Earth satellite ones.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

35. O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

36. For the analysis of cosmic anisotropy for electrons, a spin
interaction Hamiltonian HC
HC = HC (C1 = C2 = C3; σ) ≡ C1σ1 + C2σ2 + C3σ3
, constrains (C2
1 + C2
2 )1/2 < 3 · 10−20 eV and C3 < 7 · 10−19 eV by
requiring agreement between spin-spin interaction consistency
within the preferred reference frame.
Time-varying gravitational constant For a running Newtonian
gravitational constant G in vacuum
G = G∗A2
0(1 + α2
0)
- G∗A2
0 corresponds to the low-energy limit of further gravitational
theories
- G∗A2
0α2
0 corresponds to the so implied long-range forces of
non-gravitational origin, due to an equivalence-frame scalar field
φ∗0,constrained within the Solar System as α2
0 < 10−5.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

37. Outside the solar system, the time variation of G rate, ˙G/G
˙G
G
= 2α0 1 +
α0
1 + β0
2
˙φ∗0(8a).
- further constraints on β0 (after binary systems observations, and,
in particular, after, binary pulsar observations) as β0 > 4.5.
In presence of matter, the (particle) nature of the associated
corresponding scalar field φ∗0 can be determined by the analysis of
the variation (and, in particular, the dumping) of the gravitational
waves determined to the scalar field φ∗0 also a comparison with
the occurrence of quintessential distribution(s).
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

38. Spectral analysis for the Gravitational constant:
Gravitational constant and Fith Force
- to compare G and the newtonian constant GN in
Fifth-force-mediated interactions:
at the end of the interferometer arm length L, one imposes
V5L
α∞αi αk
≃ 1
and the first correction to the gravitational constant G ≡ GN is formally
estimated as
−
V5L
α∞αi αk
mPl
λ
≤ O
1
c2
- the two inequalities are to be further constrained by analyzing any geodesics
deviation(s) ascribed to the non-composition Fifth Force, and where the last
minorization order has been obtained by the symmetries of the neutrino interactions.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

39. The gravitational constant implied in the fifth-force interaction GFF
admits, in four spacetime dimensions, a spectral analysis as
G
GFF
≃ 1 + O
1
c2
+ O
1
ln1
PL
+ O
1
ln1+1
PL
Indeed, the need to include also the next-to leading orders O 1
c2 and
O 1
l
n2
PL
ensures one that the corrections are to be ascribed to
non-composition Fifth-force interaction rather to other phenomena.
The first correction to the gravitational constraint on the geodesic displacement
∆(x5) ≡ (LLPl )n1 evaluating of the order of the correction in the Plank length LPl .
by expressing the geodesics deviation in Plank lengths, i.e. , with L a numerical
dimensionless constant, and the exponent n1 a dimensionless number, the following
results are found
- for the leading-order correction to the gravitational constant G ≡ GN as
n1 ≃
1
L
log lPl
α∞;i,k
L5
and the next-to-leading order n2 ≡ n1 + 1
n2 ≡ −
1
L
log lPl
α∞;i,k
L5
mPl
β
,
with the proper constraints on β.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

40. Spectral analysis for the Fifth-Force constant(s)
factorization of the Fifth-Force non-composition coupling constant
α0 vs GN,
i.e. α∞; i, k ≡ Gα0αi αk,
after verification of the Gravitational constant GN , i.e. if α0 ≡ α0(GN ):
by utilizing the angular deviation to impose that the Fifth-Force be more
debile than the gravitational interaction, and by minorizing δβ ≤ 10−6
from the angular resolution:
α0
α0(GN)
= 1 +
Ln1
+
mPl
β
10−6
+ O(ln2
Pl ).
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

41. Weak-field gravitational limit
The weak-field limit of GR on the Earth for a ¯v moving charged
mass can produce gravitomagnetic corrections ¯cBg to the α1β2
bein projections of the Ricci tensor as ¯cBg ≤ ¯vgc−2 in the case of
a test mass (for which the tetradic projection is proportional to a δ
projection O(c−3), and ¯cBg ≤ O ¯vgc−2 in the case of a massive
particle,
Bg being the considered gravitomagnetic field Bg ∝ v × j/c2, j being the current for
the Coulomb force.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

42. Spectral analysis for the GR terms
From black holes in an inspiralling compact binary system,
correction terms available at Earth (vicinity) are the long range
effects ΨF2
3.5PN = ... + ΨF2
∞ (10)
ΨF2
∞ ≡ ΨF2
∞ (v; m, ν, ξi ).
F2∞ takes into account non-spinning, spin-orbit, quadratic-in-spin, the
cubic-in-spin contributions but not the black-hole absorption of the horizon
fluxes;
PN energy flux F∞ available reaching still at infinity is
F∞ ≃ 32
5 ν2v10O(v8): with numerical calculations comparable with
a Kerr geometry at 3.5PN order.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

43. Non-axisymmetric azimuthal perturbations of bh’s produce quasi-periodic
oscillations, which stay stable wrt successive perturbations, and induce
accretion matter for the black hole in a quasi-periodic oscillating-in
frequency manner, differently wrt the bh geometry and bh matter
distribution than the equatorial horizon flux absorption F2∞, but does
not modify the bh nature: its ΨF2′
∞ can compare at most O(v8
) with
higher-order corrections of O(v9
) at 3.5PN order, ΨF2
az ∞(ν′
), with ν′
= ν.
Inverse control: F∞(ν′
) must be absent in the cubic-in-spin (CC )
compact-object binaries calculations at leading PN order for circular
-orbit description of spin-aligned at 3 − 2 PN order up to O(c−4
); any
different FCC
∞ (˜νCC ) can be at most starting from O(c−5
); F∞(˜ν) from
quadratic in- spin contributions at 3PN order, the cubic-in-spin terms
3.5PN order, and, and the spin-orbit coupling at 4PN order; for
non-precessing inspiralling binaries, by using generic spins gs, spin
contributions gs in the frequency domain and in the phase domain at
2PN order addends have been found estimated as O(c−5
), such that any
Fgs
∞(νgs) must be looked for at least as O(c−6
).
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

44. Further references
D. Molteni, G. Toth, O.A. Kuznetsov, Astrophys.J. 516 (1999).
N.R. Sibgatullin, R.A. Sunyaev, Astron.Lett. 26 (2000) 699.
J.M Cohen, B. Mashhoon, Phys. Lett. A 181, (1993), 353-358.
R.J. Adler, P. Chen, Phys. Rev. D, 82 025004 (2010).
L.S. Hou, W.-T. Ni, Y.C. M. Li , Phys. Rev. Lett., 90, 201101(2003).
S. Suzuki, K. Maeda, Phys.Rev. D55 (1997) 4848.
T. Tanaka, Y, Mino, M. Sasaki, M. Shibata, Phys.Rev.D54:3762 ,1996.
K.S. Thorne, Rev. Mod. Phys. 52, 299 (1980).
A.G. Shah, Phys.Rev. D90 (2014) 044025.
A. Riazuelo , J.P. Uzan, Phys.Rev. D62 (2000) 083506.
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones

45. Thank You for Your attention!
O.M. Lecian Sapienza University of Rome, Rome, Italy Based on: OML, Alternative Uses for Quantum SystemQuantum-systems investigations vs optical-systems ones