Warping to the deep space...
Courtesy
of Fran De Aquino
It
is known that photons have null inertial mass (mi
= 0 ) and that they do not absorb others photons (U = 0 ).
So , if we put mi = 0 and U =
0 in Eq.(1.04),
the
result is mg = 0. Therefore photons have null gravitational
mass. Let us consider a point source of radiation with power P ,
frequency
f and radiation density at distance r given by D = P /4p r2
Due
to the null gravitational mass of the photons, it must be possible to
build a shield of photons around the source, which will impede the
exchange of gravitons between the particles inside the shield and the
rest of the Universe. The shield begins at distance rs from the
source where the radiation density is such that there will be a photon in
opposition to each incident graviton . This critical situation occurs when D
= hf 2 / Sg ,
where Sg is
the geometric cross section of the graviton. Thus rs
is given by the relation, rs = (rg / f )( P/h)1/2
We
then see that the ELF radiation are the most appropriate to produce the shield.
It can be easily shown that, if f << 1mHz , the radiation will
traverse any particle . It is not difficult to see that in this case, there will
be "clouds" of photons around the particles inside the shield.
Due to the null gravitational mass of the photons , these "clouds"
will impede the exchange of gravitons between the particle inside the
"cloud" and the rest of the Universe. Thus, we can say that the
gravitational mass of the particle will be null with respect to the Universe,
and that the space-time inside the shield (out of the particles) becomes flat
or euclidean . It is clear that the space-time which the particles
occupies remains non-euclidean.
In
an euclidean space-time the maximum speed of propagation of the
interactions is infinite
because , as we know, the metrics becomes from Galilei.
Therefore,
the interactions are instantaneous . Thus , in this space-time the speed
of photons must be infinite, simply because they are the quanta
of the electromagnetic interaction. So, the speed of photons will be
infinite inside the shield.
On
the other hand , the new relativistic expression for mass, Eq.(2.06),
shows
that a particle with null gravitational mass isnīt submitted to the increase of
relativistic mass, because under these circumstances its gravitational
mass doesn't increase with increasing velocity .i.e., it remains null
independently of the particle's velocity. In addition , the gravitational
potential
 for
the particle will be null and, consequently , the component
 of
the metric tensor will be equal to -1.
Thus
, we will have
where t' is the time in a clock moving with the particle , and ds2
= c2 dt2 where
t is the time indicated by a clock at rest ( dx = dy = dz
= 0 ).
From
the combination of these two equations we conclude that
t' = t .This means that the particle will be not more submitted to
the relativistic effects predicted in Einstein's theory. So, it can reach and
even surpass the speed of light . We can imagine a spacecraft with positive gravitational
mass qual to (m) kg , and negative gravitational mass ( see System-G in
appendix A) equal to -
(m - 0.001) kg . It has a shield of photons , as above mentioned.
If the photons, which produce the shield , radiate from the surface of
the spacecraft , then the space-time that it occupies remains non-euclidean ,and
consequently , for an observer in this space-time , the total gravitational
mass of the spacecraft, will be
 .
Therefore , if its propulsion system produces F=10N (only) the spacecraft
acquires acceleration
( see Eq.(2.05)).
Furthermore,
due to the "cloud" of photons around the spacecraft its gravitational
interaction with the Universe will be null , and therefore, we can say that its
gravitational mass will be null with respect to the Universe. Consequently, the
inertial forces upon the spacecraft will also be null, in agreement with Eq.2.05
( Machīs principle ).This means that the spacecraft will lose its inertial
properties . In addition, the spacecraft will can reach and even surpass the
speed of light because , as we have seen , a particle with null gravitational
mass will be not submitted to the relativistic effects.
See
also :
Reference
documents :
The
Gravitational Spacecraft by Fran De Aquino
( physics/9904018 )
Gravitation
and Electromagnetism: Correlation and Grand Unification
by Fran De Aquino ( gr-qc/9910036 )
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