594
Discussion concerning the root of Lorentz
Fig. 29.3 Discussion concerning the root of Lorentz
• The special theory of relativity SKT only is defined for v < c
• For v • c particles with a complex mass, but with
a real energy density (according to GRT') would result.
• From the point of view of the theory of objectivity (GOT)
the mass should be taken negative-real (neutrino?).
Mathematical gleanings ________________________________________________ 595
29.3 Discussion concerning the root of Lorentz
Fig. 29.2 forms the basis for the transformation in the domain of the GOT, the general
theory of objectivity, where it plays a role, if a subjectively measured factor should be
converted from the laboratory domain or a relativistic factor according to the SRT or the
GRT'. The given proportionalities thereby should be put in the respective relation. In this
way results the respective valid instruction for transformation on the basis of the root of
Lorentz.
Let's take a critical look at the root of Lorentz. The velocity v occurring in it, of whatever
this may consist, is depending on the field according to equation 28.14 + 28.15. It strictly
speaking wouldn't be constant anymore and wouldn't belong in a general instruction for
transformation at all. Only, what is valid for v, is valid to the same extent for c. Since only
the proportion of v/c occurs in the root of Lorentz every influence depending on field or of
other nature will have no effect on v/c and the value of the root of Lorentz. It in any case
will retain its value. It fulfills for itself the condition of the Lorentz invariance.
According to that in the case of the relative velocity v it doesn't depend on the absolute
value, but only on the relation to the speed of light. In addition the restriction to values of
v < c is normal, if the speed of light is seen as an upper limit. Let's first purely
mathematically draw a case distinction for different velocity domains of v. For v = 0 the
root of Lorentz becomes one and the Lorentz transformation turns into the Galilei
transformation.
Connected to this is the today well-known and technically used domain up to the limit of
v = c. It virtually is impossible to accelerate a mass particle to the speed of light, since
mass, field and energy would grow towards infinity, as is clear from the table (fig. 29.2).
Particles as fast as light, like photons, hence cannot have a mass. At v = c a singularity is
present.
In a field theory, which also deserves this name, however an upper limit must not be
present. Hence also the case for v > c should be required theoretically. Only later we will
be able to judge if this makes sense physically. We at first only want to examine the case
mathematically. Mass, field and energy now again have a finite value, there however
results a complex, purely imaginary mass, a negative field and doing so, as already before
a positive energy and power density.
There sometime has been the textbook opinion that it is physically impossible to fly faster
than sound. This erroneous statement even could be proven ,,scientifically", because such
a supersonic airplane would fly off the observation space and with that wouldn't be real
anymore, thus from a mathematical viewpoint would be complex. Anyone, who in New
York gets off a Concorde, can confirm that everything at any moment of the flight was
real. Only the observer is deceived, if the airplane flies somewhere else, than he perceives
it. Is the speed of light also such a ,,sonic barrier", which by the majority of the scientists
since Einstein until today still is thought to be insurmountable?
How should one physically imagine a complex mass? Let us remember the alternating
current teachings, where it is normal to work with complex values, since the mean values
of the oscillating alternating currents, tension voltages and fields are zero. Calculating
with mean values would result in zero energy and power. Hence complex factors are
introduced and the root mean square values are calculated and measured instead of the
mean values. Could a complex mass analogously not concern an oscillating particle, a
particle, which in addition is faster than the light?
596
Mathematical derivation of the neutrino
• Physical example: ______________________________
neutrino = mean of the oscillating mass zero
RMS value of the complex mass zero
E- and H-field with inverse sign
carrier of positive energy and power
-model: ring-like vortex oscillating from e
-
to e
+
Examples from the general theory of relativity (GRT):
(28.16): length contraction
(6.19): increase in mass
(6.6,28.15) field dilatation
Fig. 29.4: Root of Lorentz for speeds faster than light (v > c)
Mathematical gleanings __________________________________________ 597
29.4 Mathematical derivation of the neutrino
In the domain of speeds faster than light, for v > c, the power series (28.12) does not
converge anymore and every observer theory and every observation (fig. 28.4) will fail,
because particles faster than light run away of their own visible appearances. Every
measurement and every observation inevitably is behind and hardly can be assigned to the
actual cause. That way for instance measured neutrino events are being connected with
celestial observations, with which they haven't got anything to do at all.
If we however describe the domain v > c in the complex plane, then astonishing results
are found, which could be verified physically: a complex length dilatation with increasing
velocity goes along with a loss of complex mass. The oscillating fields, energy and power
density however would be real with negative sign.
Thus there would result particles carrying energy with an oppositely poled field, with an
oscillating mass and if necessary also an oscillating charge. Without static mass and
charge these particles hardly would interact with normal matter, which leads to an
enormous ability of penetration. The only physical particles, which have such a property,
are the neutrinos. With that a usable and an extremely efficient model description has been
found for these particles. Also the energy of these particles can be calculated, which has
considerable orders of magnitude and is available as an energy source everywhere and any
time.
If for instance in a converter for space energy a neutrino should be converted into a resting
charge carrier (with v = 0), then two steps are necessary (see part 2 of this series of
books):
1.
First the neutrino must be slowed down to 1.414 times the speed of light (fig. 28.9).
Doing so energy is spent and not won! The converter for instance can cool down.
2.
Afterwards the characteristic rotation of its own, with which the ring-like vortex
spins around itself by permanently putting its inside to the outside and vice versa,
has to be taken away from the neutrino. In that way the vortex centre is closed and
the particle acquires localization. It becomes a charge carrier.
Even if the representation in the complex plane represents only an auxiliary description,
the model nevertheless seems to be efficient, because despite its complex mass and charge
the neutrino nevertheless carries a real energy. It in any case is represented in that way to
an observer, who measures the relation with the speed of light, who in the relativistic
scheme of things scans the relation.
Today, as already said, even the sonic barrier has become permeable and no scientist dares
to physically deny this fact and even prove his mistake mathematically anymore. No, on
the contrary, he always did know that as an expected consequence the sonic barrier runs
after the supersonic plane. The once physically unthinkable and scientifically fought has
become normality.
What should hinder an oscillating particle, like a neutrino, to be faster than the light?
Some time one also will accustom to that.