Bose-Einstein Condensate and Gravitational Shielding Fran De Aquino
Copyright © 2014 by Fran De Aquino. All Rights Reserved. In this work we show that when possible transform some types of substance into a Bose-Einstein condensate at room temperature, which exists long enough to be used in practice then will be possible to use these substances in order to create efficient Gravitational Shieldings. Key words: Quantum Gravity, Gravitation, Gravitational Shielding, Bose-Einstein Condensate.
The quantization of gravity shows that the gravitational mass mg and inertial mass mi are correlated by means of the following factor [1]: 2 ⎡ ⎤⎫ mg ⎧⎪ ⎛ ⎞ Δ p ⎪ ⎟⎟ − 1⎥⎬ (1) = ⎨1 − 2⎢ 1 + ⎜⎜ χ= ⎢ ⎥ mi 0 ⎪ m c ⎝ i0 ⎠ ⎣ ⎦⎪⎭ ⎩ where mi 0 is the rest inertial mass of the particle and Δp is the variation in the particle’s kinetic momentum; c is the speed of light. In general, the momentum variation Δp is expressed by Δp = FΔt where F is the applied force during a time interval Δt . Note that
there is no restriction concerning the nature of the force F , i.e., it can be mechanical, electromagnetic, etc. For example, we can look on the momentum variation Δp as due to absorption or emission of electromagnetic energy. In this case, we can write that
(2)
where kr is the real part of the propagation
r
r
vector k ; k =| k |= kr + iki ; ΔE is the electromagnetic energy absorbed or emitted by the particle; nr is the index of refraction of the medium and v is the phase velocity of the electromagnetic waves, given by:
dz ω c (3) = = dt κ r ε r μr ⎛ 2 ⎜ 1 + (σ ωε ) + 1⎞⎟ ⎠ 2 ⎝ ε , μ and σ, are the electromagnetic characteristics of the particle ( ε = ε r ε 0 where ε r v=
is
the
relative
electric permittivity and ε 0 = 8.854 × 10 F / m ; μ = μ r μ 0 where μ r is the relative magnetic permeability and μ 0 = 4π × 10 −7 H / m ). −12
2 ⎧ ⎡ ⎤⎫ ⎛ ΔE ⎞ ⎪ ⎪ ⎢ (4) = ⎨1 − 2 1 + ⎜⎜ χ= n ⎟ − 1⎥⎬ 2 r⎟ ⎢ ⎥⎪ mi 0 ⎪ mi 0 c ⎝ ⎠ ⎣ ⎦⎭ ⎩ By dividing ΔE and mi 0 in Eq. (4) by the volume V of the particle, and remembering that, ΔE V = W , we obtain
mg
2 ⎧ ⎡ ⎤⎫ ⎛ W ⎞ ⎪ ⎪ ⎢ n ⎟ − 1⎥⎬ χ= = ⎨1 − 2 1 + ⎜⎜ 2 r⎟ ⎢ ⎥⎪ mi 0 ⎪ ⎝ρ c ⎠ ⎣ ⎦⎭ ⎩ 3 where ρ is the matter density (kg m ).
mg
Equation
(2)
tells
us
(5)
that
F = d(Δp) dt = (1 v) d(ΔE) dt. Since W ≡ pressure then we can write that W=F A=(1v) d(ΔE) dt A=Dv, where D is the power density of the absorbed (or emitted) radiation. Substitution of W = D v into Eq. (5) yields
Δp = nhk r = nhω /(ω / k r ) = ΔE /(dz / dt ) = = ΔE / v = ΔE v (c c ) = ΔEnr c
Thus, substitution of Eq. (2) into Eq. (1), gives
2 ⎧ ⎡ ⎤⎫ ⎛ D 2⎞ ⎪ ⎪ ⎢ = ⎨1 − 2 1 + ⎜⎜ n ⎟ − 1⎥⎬ = χ= 3 r ⎟ ⎢ ⎥⎪ mi 0 ⎪ ⎝ρ c ⎠ ⎣ ⎦⎭ ⎩ 2 ⎧ ⎡ ⎤⎫ ⎛ D ⎞ ⎪ ⎪ ⎢ ⎜ ⎟ (6) = ⎨1 − 2 1 + ⎜ − 1⎥⎬ 2 ⎟ ⎢ ⎥⎪ ρ cv ⎠ ⎝ ⎪⎩ ⎣ ⎦⎭
mg
In a previous paper [2] it was shown that, if the weight of a particle in a side of a lamina is
r r r P = m g g ( g perpendicular to the lamina)
then the weight of the same particle, in the other side of the lamina is
r r P ′ = χm g g , where
χ = m g mi 0 ( m g and mi 0 are respectively, the gravitational mass and the inertial mass of the lamina). Only when χ = 1 , the weight is equal in both sides of the lamina. The lamina works as a Gravitational Shielding. This is the Gravitational Shielding effect. Since P′ = χP = χmg g = mg (χg) ,
( )
we can consider that
g ′ = χg .
m ′g = χm g
or that