The Universal Quantum Fluid

The Universal Quantum Fluid

Fran De Aquino
Maranhao State University, Physics Department, S.Luis/MA, Brazil.
Copyright © 2011 by Fran De Aquino. All Rights Reserved

The quantization of gravity showed that the matter is also quantized, and that there is an elementary quantum of
matter, indivisible, whose mass is kg73109.3 −×± . This means that any body is formed by a whole number of these
particles (quantization). It is shown here that these elementary quanta of matter should fill all the space in the
Universe forming a Quantum Fluid continuous and stationary. In addition, it is also explained why the
Michelson-Morley experiment was not able to detect this Universal Quantum Fluid.

Key words: Quantum Fluids, Quantum Gravity, Quantum Cosmology
PACS: 67.10.-j; 04.60.-m; 98.80.Qc

1. Introduction
Until the end of the century XX,
several attempts to quantize gravity were
made. However, all of them resulted fruitless
[1, 2]. In the beginning of this century, it was
clearly noticed that there was something
unsatisfactory about the whole notion of
quantization and that the quantization
process had many ambiguities. Then, a new
approach has been proposed starting from the
generalization of the action function*. The
result has been the derivation of a theoretical
background, which finally led to the so-
sought quantization of gravity and of matter
[3]. The quantization of matter shows that
there is an elementary quantum of matter
whose mass is kg73109.3 −×± . This means that
there are no particles in the Universe with
masses smaller than this, and that any body is
formed by a whole number of these particles.
Here, it will be shown that these elementary
quanta of matter should fill all the space in
the Universe, forming a quantum fluid
continuous and stationary. In addition, it is
also explained why the Michelson-Morley
experiment found no evidence of the existence
of the universal fluid [4]. A modified
Michelson-Morley experiment is proposed in
order to observe the displacement of the
interference bands.
2. The Universal Quantum Fluid
The quantization of gravity showed
that the matter is also quantized, and that

* The formulation of the action in Classical Mechanics
extends to Quantum Mechanics and has been the basis
for the development of the Strings Theory.
there is an elementary quantum of matter,
indivisible, whose mass is kg73109.3 −×± [3].
Considering that the inertial mass of
the Observable Universe is kgGHcMU
53
0
3 102 ≅= ,
and that its volume is
( ) 3793034334 10 mHcRV UU ≅== ππ , where
is the Hubble constant,
we can conclude that the number of these
particles in the Observable Universe is
118
0 1075.1
−−×= sH
( )
( )110125
min0
particles
m
M
n
i
U
U ≅=
By dividing this number by , we get UV
( )2/10 346 mparticles
V
n
U
U ≅
Obviously, the dimensions of the
elementary quantum of matter depend on its
state of compression. In free space, for
example, its volume is UU nV .
Consequently, its “radius” is mnR UU
153 10−≅ .
If particles with diameter N φ fill all
space of then . Thus, if
then the number of particles, with
this diameter, necessary to fill all is
. Since the number of
31m 13 =φN
m1510−≅φ
31m
particlesN 4510≅
elementary quantum of matter in the
Universe is 346 /10 mparticlesVn UU ≅ we can
conclude that these particles fill all space in
the Universe, forming a Quantum Fluid
continuous and stationary, the density of
which is
( ) ( )3/10 327min0 mkg
V
mn
U
iU
CUF
−≅=ρ
Note that this density is smaller than the

2
density of the Intergalactic Medium ( )326 /10 mkgIGM −≅ρ .
The density of the Universal Quantum
Fluid is clearly not uniform along the
Universe, since it can be strongly
compressed in several regions (galaxies,
stars, blackholes, planets, etc). At the normal
state (free space), the mentioned fluid is
invisible. However, at supercompressed
state, it can become visible by giving origin
to the known matter, since matter, as we have
seen, is quantized and consequently, formed
by an integer number of elementary quantum
of matter with mass . Inside the
proton, for example, there are
(min0im )
( ) 45min0 10≅= ipp mmn elementary quanta of matter
at supercompressed state, with volume
pproton nV and “radius” mnR pp
303 10−≅ .
Therefore, the solidification of the
matter is just a transitory state of this
Universal Quantum Fluid, which can turn
back into the primitive state when the
cohesion conditions disappear.
Due to the cohesion state of the
elementary quanta of matter in the Universal
Quantum Fluid, any amount of linear
momentum transferred to any elementary
quantum of matter propagates totally to the
neighboring and so on, in such way that,
during the propagation of the momentum, the
elementary quanta of matter do not move, in
the same way as the intermediate spheres in
Newton’s pendulum (the well-known device
that demonstrates conservation of momentum
and energy) [5, 6]. Thus, whether it is a
photon that transfers its momentum to the
elementary quanta of matter, then the
momentum variation due to the incident
photon is λhp =Δ , where λ is its
wavelength. As we have seen, the diameter
of the elementary quantum of matter is
. According to the Uncertainty
Principle the variation can only be
detected if . In order to satisfy this
condition we must have .
This means that momentum variations, in the
elementary quanta of matter, caused by
photons with wavelength cannot
be detected. That is to say that the
propagation of these photons through the
Universal Quantum Fluid is equivalent to its
propagation in the free space. In practice, it
works as if there was not the Universal
Quantum Fluid. This conclusion is highly
important, because it can easily explain why
in the historical Michelson-Morley
experiment there was no displacement of the
interference bands namely because the
wavelength of the light used in the Michelson-
Morley experiment was fact that led
Michelson to conclude that the hypothesis of
a stationary ether was incorrect. Posteriorly,
several experiments [
mx 1510−≈Δ
pΔ
h≥ΔΔ xp
mx 14102 −≈Δ≤ πλ
m1410−>λ
m7105 −×=λ
7-13] have been carried
out in order to check the Michelson-Morley
experiment, but the results basically were the
same obtained by Michelson.
Thus, actually there was no
displacement of the interference bands in the
Michelson-Morley experiment because the
wavelength used in the experiment
was , which is a value clearly
much greater than , and therefore,
does not satisfy the condition
derived from the Uncertainty
Principle. The substitution of light used in
the Michelson-Morley experiment by
radiation with is clearly
impracticable. However, the Michelson-
Morley experiment can be partially modified
so as to yield the displacement of the
interference bands. The idea is based on the
generalized expression for the momentum
obtained recently[
m7105 −×=λ
m1410−
mx 14102 −≈Δ≤ πλ
m1410−≤λ
3], which is given by ( )4VMp g=
where 221 cVmM gg −= is the relativistic
gravitational mass of the particle and V its
velocity; the general expression
of the correlation between the gravitational
and inertial mass;
0ig mm χ=
χ is the correlation
factor[3].Thus, we can write
( )5
11 22
0
22 cV
m
cV
m ig
−
=
−
χ

Therefore, we get

3
( )6ig MM χ=
The Relativistic Mechanics tells us that
( )7
2c
UV
p =
where is the total energy of the particle.
This expression is valid for any velocity V of
the particle, including
U
cV = .
By comparing Eq. (7) with Eq. (4) we
obtain
( )82cMU g=
It is a well-known experimental fact that
( )92 hfcM i =
Therefore, by substituting Eq. (9) and Eq. (6)
into Eq. (4), gives
( )10λχ
h
c
V
p =
Note that this expression is valid for any
velocity of the particle. In the particular
case of , it reduces to
V
cV =
( )11λχ
h
p =
By comparing Eq. (10) with Eq. (7), we
obtain ( )12hfU χ=
Note that only for 1=χ Eq. (11) and Eq.
(12) are reduced to the well=known
expressions of DeBroglie ( )λhq = and
Einstein ( ) . hfU =
Equations (10) and (12) show, for
example, that any real particle (material
particles, real photons, etc) that penetrates a
region (with density ρ , conductivityσ and
relative permeability rμ ), where there is an
electromagnetic field ( , will have its
momentum
)BE,
p and its energy U reduced by
the factor χ , where χ is given by[3]:
( )13110758.1121
1121
44
32
3
27
2
00
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛×+−=
=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−==
−
rms
r
ii
g
Bc
f
cm
p
m
m
ρ
σμ
χ
where is the rms value of the magnetic
field
rmsB
B .
The remaining amount of momentum
and energy, respectively given by
( ) λχ hcV ⎟⎠⎞⎜⎝⎛−1 and ( ) hfχ−1 , are
transferred to the imaginary particle
associated to the real particle† (material
particles or real photons) that penetrated the
mentioned region.
It was previously shown that, when the
gravitational mass of a particle is reduced to
a range between iM1590.+ to ,
i.e., when
iM1590.−
159.0<χ , it becomes
imaginary[3], i.e., the gravitational and the
inertial masses of the particle becomes
imaginary. Consequently, the particle disappears
from our ordinary space-time. It goes to the
Imaginary Universe. On the other hand, when the
gravitational mass of the particle becomes greater
than iM1590.+ , or less than , i.e.,
when
iM1590.−
159.0>χ , the particle return to our
Universe.
Figure 1 (a) clarifies the phenomenon of
reduction of the momentum for 159.0>χ , and
Figure 1 (b) shows the effect in the case of
159.0<χ . In this case, the particles become
imaginary and, consequently, they go to the
imaginary space-time when they penetrate the
electric field E . However, the electric field E
stays in the real space-time. Consequently, the
particles return immediately to the real space-
time in order to return soon after to the imaginary
space-time, due to the action of the electric
field E . Since the particles are moving at a
direction, they appear and disappear while they
are crossing the region, up to collide with the
plate (See Fig.1) with a momentum,
λχ
h
c
V
p m ⎟⎠
⎞⎜⎝
⎛= , in the case of a material
particle, and λχ
h
pr = in the case of a photon.
If this photon transfers its momentum
to elementary quanta of matter ( )mx 1510−≈Δ ,
then the momentum variation due to the
incident photon is λχ hp =Δ . According to
the Uncertainty Principle the variation pΔ
can only be detected if , i.e., if h≥ΔΔ xp
( )142 xΔ≤ χπλ
We conclude, then, that the interaction
between the light used in the Michelson-

† As previously shown, there are imaginary particles
associated to each real particle[3].

4
Morley experiment ( )m7105 −×=λ and the
Universal Quantum Fluid just can be
detected, and to produce of the displacement
of the interference bands, if
( )15108 7×≥χ
In order to satisfy this condition in the
Michelson-Morley experiment, we must modify
the medium where the experiment is performed
(for example substituting the air by low-pressure
Mercury plasma), and apply through it an
electromagnetic field with frequency . Under
these conditions, according to Eq. (13), the value
of
f
χ will be given by
( )16110758.1121 44
32
3
27
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛×+−= − rmsr Bc
fρ
σμχ
If the low-pressure Mercury plasma is
at and
[
23 80106 −− =×= mNTorrP .. KT 15.318≅
14], then the mass density, according to the
well-known Equation of State, is
( )17.10067.6 350 −−×≅= mkg
ZRT
PMρ
where is the molecular
mass of the Hg;
1
0 20060
−= molkgM ..
1≅Z is the compressibility
factor for the Hg plasma;
is the gases
universal constant.
1013148 −−= KmoljouleR ...
The electrical conductivity of the Hg
plasma, under the mentioned conditions, has
already been calculated [15], and is given by
( )18.419.3 1−≅ mSσ
By substitution of the values of ρ and σ into
Eq. (16) yields
( )191105471.1121
3
4
17
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−×+−=
f
Brmsχ
By comparing with (15), we get
( )2001037.0
3
4
≥
f
Brms
Thus, for , the ELF magnetic field
must have the following intensity:
Hzf 1=

( )2132.0 TBrms ≥

This means that, if in the Michelson-Morley
experiment the air is substituted by Hg
plasma at and , and an
ELF magnetic field with frequency
Torr3106 −× K15.318
Hzf 1=
and intensity is applied through
this plasma (Fig. 2), then the displacement of
the interference bands should appear.
TBrms 32.0≥
It is important to note that due to the
Gravitational Shielding effect [3], the gravity
above the magnetic field is given by
. This value, extends
above the vacuum chamber for
approximately 10 times its length. In order to
eliminate this problem we can replace the
ELF magnetic field,
28 .108.7 −×≥ smgχ
B , shown in Fig. 2, by
two ELF magnetic fields, and , sharing
the same frequency, . The field, , is
placed vertically through the region of the
experimental set-up. The field, , is also
placed vertically, just above (See Fig. 3).
Thus, the gravity above is given by
1B 2B
Hzf 1= 1B
2B
1B
2B
g21χχ where 111 ig mm=χ and
222 ig mm=χ are respectively, the
correlation factors in the Gravitational
Shieldings 1 and 2, produced by the ELF
magnetic fields and , respectively. In
order to become
1B 2B
gg =21χχ we must make
7
12 10811 ×−== χχ . According to Eq.
(19), this value can be obtained if
and .
Note that the value of is less than the
value of the Earth’s magnetic field
( ). However, this is not a
problem because the steel of the vacuum
chamber works as a magnetic shielding,
isolating the magnetic fields inside the
vacuum chamber.
( ) TBrms 52 10331481522.5 −×= ( ) TBrms 32.01 =
( )2rmsB
TB 5106 −×≅⊕

5






















(a)
* There are a type of neutrino, called "ghost” neutrino, predicted by General Relativity, with zero mass
and zero momentum. In spite its momentum be zero, it is known that there are wave functions that
describe these neutrinos and that prove that really they exist.



















(b)
Fig. 1 –The correlation factor in the expression of the Momentum. (a) Shows the
momentum for 159.0>χ . (b) Shows the effect when 159.0<χ . Note that in both cases,
the material particles collide with the cowl with the momentum ( ) λχ hm cVp = , and
the photons with λχ
h
pr = .
material particle
imaginary particle
associated to the
material particle
real photon
imaginary photon
associated to the
real photon
σρ ,, fE
159.0>χ
λχ
h
c
V
p m ⎟⎠
⎞⎜⎝
⎛=
[ ] λχ hpi −= 1
λχ
h
pr =
[ ] λχ hcVpi ⎟⎠⎞⎜⎝⎛−= 1
λ
h
c
V
pm ⎟⎠
⎞⎜⎝
⎛≅
*0=ip
λ
h
pr ≅
0=ip
material particle
imaginary particle
associated to the
material particle
real photon
imaginary photon
associated to the
real photon
σρ ,, fE
159.0<χ
λχ
h
c
V
p m ⎟⎠
⎞⎜⎝
⎛=
[ ] λχ hpi −= 1
λχ
h
pr =
[ ] λχ hcVpi ⎟⎠⎞⎜⎝⎛−= 1
0=ip
0=ip
λ
h
pr ≅
0=ip

6










































Fig. 2 - The modified Michelson-Morley experiment. The air is substituted by Hg plasma at
Torr3106 −× and K15.318 , and an ELF magnetic field with frequency Hzf 1= and intensity
TBrms 32.0≥ is applied through this plasma, then the displacement of the interference bands should
appear.


Hg Plasma ( Torr3106 −× , K15.318 )
Vacuum
Pump
Movable
Mirror
Fixed
Mirror
Beam splitter Compensator
Detector
Coherent
Light source
Hg
Plasma
Manometer
ELF magnetic Field
Vacuum
Chamber
Hzf 1=
TBrms 32.0≥
B

7









































Fig. 3 – Cross-section of the vacuum chamber showing the magnetic fields 1B and 2B .
1
1
1
01 iL
N
B ⎟⎟⎠
⎞
⎜⎜⎝
⎛= μ ; 2
2
2
02 iL
N
B ⎟⎟⎠
⎞
⎜⎜⎝
⎛= μ


Steel
Vacuum
Chamber
χ1
χ2
gg =21χχ
g
Wire
Region of the experimental set-up
B2
B1
N2
N1
L2
L1

8

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