"Action is curvature of the World"
Pavel D. Ouspensky, A New Model of the Universe, 1911
"At any conditions the action is just the number"
Herman Weyl, Gravitation and electricity, 1918
The epigraph disclosure the technology for time
rate control in general, and I hope that the paper allow to use the mathematical
tool I found in 1989 and use it with well-known Plank's conclusion about
quantum of action. New interpretation for the notion of the Time let us
to develop new branch of the physics: the physics of space-time engineering.
Several
examples of new Natural Law (discovered by the author in 1990) are demonstrated
here. It was found that natural mass-objects are described by whole
number value of the curvature. This property allow to consider
the space-time as secondary induced 4-dimensional resonance effectof
mass process. The concept can be used as applied tool for energy-mass and
mass-energy transformations, gravitational propulsion systems and
experimental research work on the chronal technologies.
r1 = 1/R [ 1/m ] F. 1
where R is radius and r1 is linear curvature.
Process of motion for the line will create the dynamical surface, i.e. two-dimensional space-time (sphere), and the resonance parameter for it is the two-dimensional curvature (it also disclosed in any mathematical textbook):
r2 = 2/R [ 1/m ] F.2
Let's introduce the spatial curvature by similar arguments:
r3 = 3/R [ 1/m ] F.3
It is new special parameter of resonance process of the dynamical structure of any three-dimensional object.
It is possible to use radius as description of periodical process in one-dimensional self-closed space (a circumference) only. On the next level, some value of radius that is measured in ( N+1) space is period of time for processes in dynamical N-space. The "time axis" as radius of the circumference is some direction which is placed out of circumference line. It is new direction, next dimension.
The dynamical structure of 4-dimensional objects can be created as change of 3-dimensional structure in next direction. The parameter is 4-curvature:
r4 = 4/R [1/m ] F.4
So, the principles are clear.
This understanding of the time nature allow to suppose
some methods of local time control. In any case it is necessary to change
density of energy in space. For one-dimensional space (line) it is linear
density of energy, for example: well-known density of electric
current. For surface it is energy of electromagnetic wave.
Also it is possible to change 3-dimensional density of energy (electromagnetic
energy in volume or density of matter in volume) to create local time effect.
For this case, the electromagnetic energy is longitudinal wave energy.
In 1923 L. de Broglie supposed that mass - particles must have the wave properties. He used formulation E=hf and E=pc, where p is impulse, h is Planck constant, f is frequency, m is mass, c is speed of light. Then he joined both parts in equation hf=pc. For wave-length L=c/f this formula is known as L=h/p [1].
There is other logical branch of this idea and we can offer for consideration new concept of mass:
Instead of E=pc, by de Broglie, let us take the formula "energy of mass"
E =mc2 F.5
Energy of electromagnetic field energy (wave energy) is
E = hf F.6
In strength of the wave-particle duality we can offer the equation:
mc2 = hf F.7
and mass can be represented as result of some electromagnetic oscillations
h
m = -------- f
F.8
c2
where (h/c2) is new constant between mass m and frequency of oscillation f. Let's named it as chronal constant (it is original notion) because it demonstrates mass and time correlation:
h 1
m = ------- ------
F.9
c2 T
where T = 1/f is period of oscillations.
In other words, product of mass and period is constant value
h
mT = ----- = const
F.10
c2
The chronal constant is ratio of elementary quantum of action ( h ) to the square of the velocity of light ( c2 ) and it is equal to 0.73725 10 -50 [Js2/m2].
In other words, there is no time separately from mass, by F.10. Main masses of our time-system are masses of the Sun system and our Galaxy.
Then, taking into consideration the Heizenberg's formula
h = Dp Dx F.11
the proposed mass-time equation can be represented in new view
Dp Dx
m T = -----------
F.12
c2
Let's check the measures correctness in this equation
[kg][m][m][s2]
[kg][s] = ------------------- = [kg][s]
F.13
[s][m2]
So, F.9 is true equation that demonstrate the correlation between some mass and period of electromagnetic wave oscillations and next conclusion is obtained: Mass of particle is result of electromagnetic energy oscillations.
By such sort approach the frequency can be calculated by F. 8 for any known mass value, for example, proton has frequency value about 8,1 1026 [Hz].
Interesting conclusions for velocity of motion can be obtained
from F.12
Dp Dx
m Du Dx
mT = --------- = --------------
F.14
c2
c2
We can remove "m" from F.14 and obtain the next formulation
DuDx
T = ------------
F.15
c2
For velocity u=c the wave-length
c c Dx
L = cT = ---------- = Dx
F.16
c2
It is photon state of energy: the wave-length value of the object determine the size (scale) of local area (i.e. the space) of the object.
For velocity in the range 0 < u < c, the wave-length of the object is lesser than possibility of determination of the object position Dx
L = (u/c)Dx F.17
It means that object has some space of positions, object can be moving between different positions since all area of its positions can be determined. It is the nature of space itself for some material object that is moving with u < c (value of its mass is some real mass m)
For velocity u > c, formula F.17 can be represented as
DuDx
(c + u)Dx
T = ---------- = -----------------
F.18
c2
c2
and then we can see the wave-length L=c T
(c + u) Dx
L = c T = ----------------
F.19
c
In result the wave-length formula demonstrate that in this case the size of the object (its own wave-length L) is more that possibility of determination of the object position Dx:
L = (1+ u/c) Dx F.20
Demonstration (detection) of such sort "over-light speed objects" in
real space has some analogy with potential fields since change of
energy density of the object take place in all space at the same moment.
Also we have to suppose possibility of detection of the objects in two
or more places of real space at the same moment of time.
Before the continuation let us assume that the theory of similarity for microcosm and macrocosm is true, hence any planet can be considered as elementary particle in certain sense.
Substitute in matter wave-length formula
L = h/(mu) [ m ] F.21
where h is Plank's constant, m is mass and u is velocity, parameters of our planet to calculate the value:
L = 3,725 10 - 63 [ m ] F.22
Due to our previous supposition, speed of light in 4-space is only factor 4, and the formula is:
E3 = m3 c2 = 9 m3
F.23
and
E4 = m4 c2 = 16 m4
F.24
where m3 is mass of 3-space and m4 is mass for 4-space description.
Note important supposition: The total energy of system is the same independently of its dimensionality description. It means that the same amount of energy ( but in different form of energy) should be considered in 3-space and 4-space description for one certain system. In other words, total net energy of the Universe is always the same, independently of dimensionality of measurement system which is used by observer.
So, we have to write:
E1 = E2= E3 = E4 =... F.25
and in our case 9 m3 = 16 m4 F.26
According to F.21 mass is equal to
m = h/(Lu) F.27
Now we have the correlation
(16 h )/( L4 u)= (9h)/(L3u) F.28
where L3 is wave-length in 3-space, and L4 is wave-length is 4-space. As the system is the same , as velocity is the same. So, there is simple ratio:
L4 = 16 L3 / 9 F.29
Substitute L3 value from F.22 in F.29 and obtain L4 value
L4 = 66,22 10- 64 [ m ] F.30
that conform to curvature
r4 = 1/L4 = 151,00 10 60 [ 1/m ] F.31
Note: it is whole number value.
On the other hand, the period of planet rotation around Sun is equal to 31557600 seconds, that conforms to the oscillation frequency value
f = 1/T = 3,16886 10 - 8 [ 1/s ] F.32
It is own resonance frequency of our planet.
The wave-length of this electromagnetic oscillation is
L em = c/f = 9,46 10 16 [ m ] F.33
and curvature ( radius of resonator ) is equal to whole number value also:
rem = 1057,00 10- 20 [ 1/m ] F.34
The correlation for two results obtained in F.31 and F.34
(rem/ r4)=7 10-80 F.35
The mathematical connection between two different descriptions of the
same natural object (planet ) is the confirmation of true Whole Number
Value of Curvature Law. This Law is valid for any natural system element.
Let us demonstrate this Law in other examples.
The curvature of the Bohr's radius R = 0,52917 Angstrom is
r = 1/R = 3,0075 10 9 [ m ]
F.36
According to F.3 the linear curvature for Bohr's atom is equal to unit:
r1 = r3 /3 = 1,0025 109 [ m ] F.37
and it is right, since it is simple atom, unit matter engine.
Some deviation k = 1,0025... is demonstration of non-ideal resonance state
in real system.
To calculate the wave-length of proton let's use formula F.9
h
h c
h
m = ------
f = ------ --- = --------
F.38
c2
c2 L
c L
h
or L = -------
that is version of de Broglie wave-length for velocity u
= c.
mc
So, for proton m = 1,6726231...10-27 kg, the wave-length L=0,75676739... (mathematical degree is omitted) and curvature is equal to
r = 1/L = 132141,000... F.39
It is whole number value up to third sign that demonstrate particle
proton as some spatial resonance process.
Another example is DNA helical molecule. The unfolded spire-length period
of it is about
71,4417 Angstrom, that conforms to a curvature value
rDNA = 14,0000 10 7 [ 1/m ] F.40
This is very good resonator since it is whole number value up to fourth sign. This accuracy is the basis of supposition about resonance mechanics of energy transformation and information telecommunication on the molecular level in biosystems. The nature of Time Effect is 4-dimensional motion only and resonance structure of DNA-molecule elements superposition allow to use this motion as free energy source and information receiver for biosystems.
Note, that information is not spreading in this case with some velocity but all 3-space is changing at the moment when curvature of 3-space is changing. So, spatial orientation of such sort receiver is not important. Information signal is change of energy density in space.
Now let's make calculation of displacement between two spiral DNA-molecule branches. Two branches have period 34 Angstrom and displacement 23,8 Angstrom. In other words, the 'back wave' is displaced relatively to the 'direct wave' on 0,7 of the wave lenght. It is equal to 50,0 Angstrom and correspond to some whole number value of curvature:
r2 = 2 108 [ 1/m ] F.41
If we'll take into consideration the two-dimensional structure of the spire, so the curvature value is unit value
r1 = 1 108 [ 1/m ] F.42
So, branches of DNA molecule have unit value shift (by the
curvature measurements method) from the zero-state. In this zero
state (theoretically) both branches are join together. Code structures
of each branch are contra-directional to each other. There is very interesting
analogy here with The World of Elementary Particles, that can help
us to disclose the secret of the electron-positron pair creation process.
It would be premature to say about the validity of this concept since the assumptions underlying it are opened to question. It is necessary to make the experimental verification of this approach to the resonance nature of matter and vacuum. Physical sense of the action is the motion in some direction that is placed outside of the object. The natural actions are whole numbers, it is demonstartion of natural discrete counter of space-time, which is created by this simple method of elementary actions. The Law of Whole Number Value of Curvature is operating for any natural element of matter, and it is new mathematical tool for different technologies. In case of its practicable the control on rate of time and curvature of space, on stability of matter (mass - energy transformations) and vacuum (energy - mass transformations) is not a fantasy but the technology.
Also this Law show that any natural system, for example, the planet, atom or DNA molecule can be used for calculation and definition of the "meter/sec" system units.
I believe now you have clear view to the action as curvature and the action as the number.
Alexander V. Frolov
Scientific Expert of Russian Physical Society
P.O.Box 37, 193024, St.-Petersburg, Russia
This paper was published at first in Proceedings of International Scientific Conference "New Ideas in Natural Sciences", June 1996, St.Petersburg, p.123-135, "PiK" Co.,1996. Copyrigth 1996-1999 Alexander V. Frolov. All rights reserved.