Equation of the force of gravity resulting from the
Planck Energy/Area and wavelength of De-Broglie
without using the Universal Gravitation Constant
Newton.
Rodolfo Sergio González Castro
To cite this version:
Rodolfo Sergio González Castro. Equation of the force of gravity resulting from the Planck
Energy/Area and wavelength of De-Broglie without using the Universal Gravitation Constant
Newton.. 2014. <hal-00947254v2>
HAL Id: hal-00947254
https://hal.archives-ouvertes.fr/hal-00947254v2
Submitted on 19 Feb 2014 (v2), last revised 25 Jan 2014 (v8)
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Equation of the force of gravity resulting from the Planck Energy/Area
and wavelength of De-Broglie without using the Universal Gravitation
Constant of Newton.
Rodolfo Sergio González Castro
Research Institute, University of Tijuana CUT, Av. Lucrecia Borja 1010, Col. Altamira,
Tijuana, Baja California, Mexico. CP 22150.. BA in Psychology, MSc. Administration
General (MBA), MSc. Education, PhD candidate in Education, Theoretical Physicist
Autodidact. Email: [email protected]
Abstract
In this paper I show that it is possible to calculate the force of gravity deriving an
equation of the Planck Energy/Area and wavelength of De-Broglie associated with
particles or massive objects in gravitational interaction without use the universal
gravitational constant of Newton (G).
OAI: hal.archives-ouvertes.fr:hal-00947254
PACS: 04.50.Kd
Newton
Keywords: physics, particles, gravity, gravitation constant,
1. INTRODUCTION
The mathematical physicist Sir Isaac Newton
in 1687 published his book "Philosophiae
Naturalis Principia Mathematica" where he
presented the law of universal gravitation
empirically derived to describe and calculate
quantitatively the mutual attraction of each
particle and massive objects in the universe. In
that document, Newton concluded that the
attraction together two bodies is proportional
to product of their masses and inversely
proportional to the square of the distance that
separates them.
However,
these
must
be
adjusted
proportionalities by introducing a constant
called Universal Gravitation (G) with an
approximate value of 6.67428 × 10-11 N m2
kg-2 units in the International System. Without
the introduction of this constant, the equation,
lose their rationality and is impractical to
calculate the force of gravity without it.
For Newton, gravity is considered a force
exerted on a remote Instant. Moreover, when
the gravity force is exerted by two or more
bodies extremely mass, Newton's law has
serious limitations and then must resort to the
Theory of Relativity General stated by Albert
Einstein in 1915, who says that gravity is not a
force exerted to distance but a contraction of
Space-Time produced by the presence of
matter (1).
However in the final formulation of the
equations of the universe, to make it
compatible with the law of conservation of
energy and principles of general covariance
and minimal coupling, Einstein included
mathematical concepts such as the Ricc i
Tensor and scalar, but mainly the energymomentum tensor, but fails to integrate into
said Energy-Momentum Tensor the constant
Universal Gravitation Newton, as this is
finally out in the second member of the
equation.
While Einstein equation establishes the
relationship between gravity, energy and
geometry distortions spacetime, it does not
define the origin of the relationship.
Subsequently in 1995 Jacobson linked the laws
of thermodynamics to the Einstein equation
and the equation of state correlates with
entropy the energy sector flow (2).
Erik Verlinde published on January 6, 2010,
his work "On the Origin of Gravity and the
Laws of Newton" (3), which proposed that
gravity is a reality entropic force emerging
space. In its formulation, includes reduced
Planck's constant, N as a Screen of information
bits of space, adds a new constant called G,
which ultimately Accounts found to be
equivalent to the Universal Gravitational
Constant. On that basis, Verlinde forecast to
gravity as a fundamental force.
In March 2010, Jae-Weon Lee, Hyeong-Chan
Kim and Lee Jungjai published a paper in
which suggest that the Einstein equation can
be derived from the principle of Landauers on
the Elimination of information causal
horizons, and conclude that gravity has its
origin in quantum information (4). From then
such work is also supported by Jacobson
linking between thermodynamics and the
equation Einstein, as well as on the work o f
Verlinde entropic force.
Thus, we already have a strong linkage
between
energy,
heat,
laws
of
thermodynamics, theory general relativity,
perturbation of the geometry of space-time,
entropy and quantum information, but
somehow linking gravity and electrostatic
force has been fails to integrate in all this work
to finally derive the Einstein equation and the
gravitational constant universal.
From my point of view, crucial to successfully
solve the equations of gravity aspect is the
distribution of Plank area, and both invariance
in all particles and massive objects in the
universe, as discussed in this paper.
Derive a gravity equation that eliminates the
universal gravitational constant and link
strength gravity with the electrostatic force
requires on the one hand make Planck area
invariant, and include in the equation the
length of De Broglie wave.
I.-GRAVITATIONAL ENERGY DERIVED
FROM PLANCK ENERGY/AREA
Newton's equation establishes the relationship
between mass and gravity, while the equation
Einstein relates the Energy-Momentum Tensor
with the modification or distortion of space,
which is more proper perspective proposed
here, including in the case of particles resting
or non-relativistic speeds.
For particles at rest, Einstein's equation defines
the Energy-Momentum tensor in the
coordinate time (t). I mean, you have a single
source of tension, so the above equation
requires the universal gravitational constant
outside the tensor
.
This work is based on the priori hypothesis
that particles resting actually have two sources
of tension at different times (t) with different
effects in terms of pressure on space. The first
source of tension generated electrostatic force,
while the second source of tension is the cause
of the gravitational force.
To explain this I have to consider the existence
of a hypothetical particle whose Plank energy
distribution in space is the area of a perfect
square:
Y=
=
=
1,0155241E-34 m
X=
=
= 1,0155241E-34 m
electrostatic effects and Gravity effects are
"visible" to outside observers.
In other words, the ratio of Planck Area is
invariant in all of the particles and objects
mass of the universe when they are at rest or
non-relativistic speeds.
Here graphically proportional representation of
an electron according to Planck Energy/Area:
Y=
=
4,2504295E-57 m
Both the axis (X) and the axis (Y)
corresponding to the Planck length. Both faces
of the square axes exert pressure on space, or
in terms of Einstein, Energy-Momentum
produce tensor. In the Axis (X) the EnergyMomentum tensor is exactly the same as
Einstein or “first source of tension”, but for
axis (Y) still corresponds to “second source of
tension” or gravity source.
However, in the case of the hypothetical Plank
particle, because both axes or faces have equal
length, and in the case of (Y) perpendicular
pressure is negative and therefore, the two
pressures or two source of tension cancel each
other. In terms of the De Broglie wavelength
to be exactly equal in length and amplitude but
opposite to each other, they cancel each other,
so that an external observer can´t capture the
presence of the Planck particle in electrostatic
or gravitational terms. It is then a "Null
particle" or "Space Empty".
By the law of conservation of the area, or a
hypothetical "law of conservation of space”,
an electron or any other particle in the universe
always retain the same area of Plank. if the (X)
axis is lengthened, then proportionally axis (Y)
will be shortened. But also at the time at which
the lengths (X) and the lengths (Y) are
different, they stop cancel each other and the
X=
=
= 2,4263178E-12 m
Note: The graph of the rectangle is not
exactly proportional to the scalar
quantities for obvious reasons.
As will be seen, in the electron, because (X) is
too extension with respect to the length of
Planck, then (Y) is proportionally shortened
and wavelength being excessively small but
sufficient to generate gravitational effects of
the electron.
In other words, the particles are like strings or
threads whose extension in the X axis is much
longer compared to the Planck length, but the
width, height or thickness (Y axis) is very
short.
In this sense, the present work of the a priori
hypothesis that all the specific objects universe
and all clusters of material occupying a
particular area of space, whether electrons,
protons, atoms, planets, stars and galaxies, all
can be considered as "particles" whose
distribution of energy per occupied space area,
rigorously meet the total Planck energy
distributed in the Planck area or area of the
particle according to the following equation:
=
(1.1)
Where Ep is Planck's energy and N is the ratio
of the rest energy of any particle or object
mass and the Planck energy given by the
equation:
(1.2)
Substituting N into Equation (1.1) then the
energy distribution in an area Planck is given
by:
(1.3)
In this case (E) corresponds to the rest energy
of any known particle or massive object, while
(Eg) in equation described below corresponds
to the "Gravitational Energy" not known so far
(Virtual, dark, pop, entropic or whatever you
want to call) existing in the area occupied by a
visible particle or massive object, which
although is not observable or detectable until
now, its possible existence is the source of
gravitational attraction.
(1.4)
Both the rest energy (E) as the gravitational
energy (Eg), both have a wavelength according
to the associated de Broglie postulates given
by the familiar equation:
That in the case of the gravitational energy, the
corresponding equation is:
Where h is Planck's constant and c is the speed
of light, and where
is the wavelength of
Broglie energy at rest and
is the
gravitational wave length.
2. GRAVITATIONAL COUPLING
Because the two wavelengths originate almost
"simultaneous", the Wavelength gravitational
be coupled to the wavelength of the rest
energy, Generating a factor of coupling to the
gravitational force given by:
(2.1)
Where
is the factor of gravitationa l
coupling. For the electrostatic force, value
coupling is considered constant (Fine
Structure), but, in the case of gravity, said
coupling depends on the ratio of both
wavelengths (and thus Energy) as shown in the
equation 2.1.
3. THE EQUATION OF GRAVITY FORCE
WITHOUT CONSTANT GRAVITATION
Thus if we have defined or calculated the
"Gravitational Energy" derived from the
Planck
Energy/Area,
the
De-Broglie
wavelength
associated
Gravity
and
Gravitational coupling factor, we can then
stating a priori an equation for the
gravitational attraction between two particles
or massive objects identical to or have the
same amount of mass:
( 1.5)
=
The product of two wave lengths,
corresponding to the wavelength of Planck:
(3.1)
And for the case of two different particles or
objects mass:
(1.6)
=
(3.2)
Then comes to be a general equation for
calculating the force of gravity without the use
of the gravitational constant of Newton and
based on Planck Energy/area, and Wave length
De Broglie.
Moreover, due to the existence of a constant in
this equation, it is possible to reduce it further.
In this case the product of the energy (E) for
its associated wavelength is constant:
1.986451698E-25 joules per meter
(3.3)
4. DERIVATION OF EQUATION OF
CALCULATION OF FORCE
ELECTROSTATIC
About the same arguments above, the
calculation of the electrostatic force between
two particles is still simpler due to electrostatic
coupling constant or fine structure. In this
case, we carried a broad general shall term a
priori constant Electrostatic Universal
Constant:
1.4495849660E-27 joules
per meter
Which in turn we reduce as in the case of
Planck's constant:
3.1615287E-26 joules per meter
(3.4)
Thus we can write a new equation for
calculating the gravitational force between two
equal mass particles or objects:
=
=
(3.5)
And for the interaction between two particles
or different massive objects:
(4.1)
No matter how much rest energy of the
particle, the electrostatic force is always the
same and will vary only based on the distance.
That is, the calculation of the electrostatic
force between two identical or different
particles is given by the general equation:
=
=
(4.2)
Where E is the energy at rest,
the
wavelength of de Broglie,
coupling
constant or Fine structure, d is the distance
between the two particles. But it is possible to
reduce it to eliminate (2 Pi) in the equation:
=
=
(3.6)
(4.3)
That is my general equation for calculating the
electrostatic force between two identical
particles or different. This equation is
equivalent to Coulomb's law:
Thereupon
=
=
(3.7)
It is my final general equation for calculation
of the force of gravity between two particles or
objects mass.
For the case of two particles in load
electrostatic interaction.
=
=
=
Again, I must point out here that the develop
equations for calculating the force of gravity
are for particles or massive objects at rest or in
non relativistic speeds. My next job will be
related to cases of relativistic velocities
integrated into the Einstein Tensor.
5. CONCLUSION
Having proven naturally and clean that gravity
is possible to calculate from the Plank
energy/area and De Broglie wavelength
without using the gravitational constant
Newton, paves the way for a unified theory of
everything, and in that sense can assert a
priori:
1.-That to calculate the electrostatic force of
gravity in terms necessarily need to include the
concept of "Gravitational Energy" derivative
of the Planck energy/area.
2.-That the electrostatic force and the force of
gravity can be calculated from the Planck
Energy/area.
3.-That because the wavelength of the energy
at rest and the wavelength of the "Energy
Gravitational" originate form virtually
"simultaneously" because this, the wavelength
Gravity be coupled to the variable length of
electrostatic wave form, which so far had
hampered their electrostatically calculation.
4.-Developed here that the equation for the
calculation of the force of gravity, is actually
an equation electrostatic force, instead of using
the fine structure constant, must use the
variable gravitational coupling due to the
argument of the previous paragraph.
5.-And I can finally conclude a priori, due to
the equations presented here that the force of
gravity It is also modulated by the variable
electrostatic force of gravitational coupling.
REFERENCES
1.
Wald RM. General Relativity. University of Chicago Press; 1984. Available
from: http://bibliovault.org/BV.landing.epl? ISBN=9780226870335
2.
Jacobson T. Thermodynamics of Spacetime: The Einstein Equation of State.
arxiv.org. 1995;Phys. Rev.(qr-qc/9504004v2):1–9.
3.
Verlinde E. On the Origin of Gravity and the Laws of Newton.
2010;(arxiv:1001.0785v1):1–29.
4.
Lee J, Kim H, Lee J. Gravity from Quantum Information.
2010;(arXiv:1001.5445v2).