"The Concept of Mass-Process"

by Alexander V. Frolov

Scientific Expert of the Russian Physical Society
P.O.Box 37, 193024, St.-Petersburg, Russia
Tel: 7-812-2747877
Email: frolov@mail.dux.ru

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The truth of the matter wave theory is now widely recognized. Attractive as this theory may seem at first sight, it is open to one serious objection: the wave superpositions are unstable and must be disintegrating. To solve this problem, enable it with the supposition that mass particle may be represented as stable dynamical superposition of wave packets that have place for a resonance condition.

In this paper, it is demonstrated how to calculate the resonance parameters of certain mass-object which are described by means of a spatial curvature function. Several examples demonstrate that natural mass-objects are described by a whole number value of resonator curvature. This property allows us to consider the space-time as a secondary induced effect of the mass process. Mass and the gravitation field around it are balanced energy systems. The concept can be used as an applied tool for energy-mass and mass-energy transformations in energetic and gravitational propulsion systems.

This is a new approach to the definition of the nature of time which allows us to develop applied experimental research work in chronal technologies.

Time as the Radius of a 4-dimensional Resonator:

Let's consider the motion of a point along a closed trajectory. This process creates a dynamical one-dimensional space-time which is the line. It is a process and there is some period. If the line is closed, there is a resonance phenomenon and the parameter for it is radius R. Curvature is defined as 1/R:

F. 1   r1 = 1/R [ 1/m ]

where R is the radius and r1 is the linear curvature.

The process of motion for all lines creates the dynamical surface that is two-dimensional space-time. If it is a closed surface (sphere), the resonance parameter for it is two-dimensional curvature:

F. 2   r2 = 2/R [ 1/m ]

By similar arguments the spatial curvature can be obtained:

F. 3   r3 = 3/R [ 1/m ]

It is the parameter for the resonance processes of the dynamical structure of three-dimensional objects.

It is possible to use the radius as a description for periodical processes in one-dimensional closed space of circumference only. But periodical space of any dimensionality includes the circumference as a projection. So, some value of a radius that is measured in (N+1) space is the period of time for processes in dynamical N-space. Time as a radius for circumference is a direction that has moved out of line. It is a new direction, the next dimension.

The dynamical structure of 4-dimensional objects is created as a change of 3-dimensional structure in the next direction. The parameter for it is 4-curvature:

F. 4   r4 = 4/R [ 1/m ]

This understanding of the time nature allows us to suppose some methods to create a local rate of time. In any case, it is necessary to change the density of energy in space. For one-dimensional space (line) it is a linear density of energy, for example: the well-known density of electric current. For surfaces it is the energy of electromagnetic waves.

Also it is possible to change the 3-dimensional density of energy (electromagnetic energy or density of matter) in a volume of space to create a local time effect.

Electrodynamic Nature of Mass-Effect:

In 1923 L. de Brogle supposed that mass-particles must have wave properties. He used the formulations E=hf and E=pc, where p is the impulse, h is the Planck constant, f is the frequency, m is the mass, c is the light velocity. Then he joined both parts in the equation hf=pc. For a wave-length = c/f this formula is known as = h/p [1].

There is another logical branch for this idea and this leads to a wider concept of mass. Instead of E=pc, by de Broglie, let us take the formula for energy of rest mass:

F. 5   E = mc2

The energy of electromagnetic field energy (wave energy) is:

F. 6   E = hf

In strength of wave-particle duality, write the equation:

F. 7   mc2 = hf

and mass can be represented as electromagnetic oscillations:

F. 8   m = (h / c2) f

where (h/c2) is a new constant between mass (m) and frequency of oscillation (f). Let's call it the chronal constant because it demonstrates mass and time correlation:

F. 9   m = h/c2 x 1/T

There T = 1/f is the period of oscillations.

In other words, the product of the mass and period is a constant value:

F. 10   mT = h/c2 = const

The chronal constant is the ratio of the elementary quantum of action (h) to the square of the velocity of light (c2) and is equal to 0.73725 10 x-50 [Js2/m2].

In other words, there is no time separately from mass, by F.10. Large masses of out time-system are the planets and Sun.

Taking into consideration the Heisenberg formula:

F. 11   h = p x

the mass-time equation can be represented in a new view:

F. 12   mT = p x / c2

Let's check the measures' correctness in this equation:

F. 13   [kg][s] = [kg][m][m][s2] / [s][m2] = [kg][s]

So, F.9 is a true equation that demonstrates the correlation between some mass and the period of electromagnetic wave oscillations. The next conclusion is obtained: The mass of particle is the result of electromagnetic energy oscillations.

Let's consider some problem and find the solution for it: by F.9 the increase of mass corresponds to a decrease of time period, but in the macro-world we can observe that the gravitation field of the body (of the star, for example) is the reason of the increase of the photon's oscillation period ("red shift").

This is the pre-condition for the supposition: Space of some mass is created as a balanced structure like paired forces by Newton. Local areas of high frequency electromagnetic oscillations, those that produce localized in space mass-effect M, must be compensated by some change of structure of space around mass M, i.e. some field (the field is an area of action of some force) must be produced (induction phenomenon), and this field is also electromagnetic oscillations. This induced compensation field is the gravitation field of mass.

The mass and gravitation field of this mass are two mutual-compensating processes themselves, but they are separated in space and in time: the mass of the object is localised in some three-dimensional area of space and the gravitation field of this mass is localized in some period of time, i.e. the gravitation field of the mass particle has a certain period of oscillation, wave-length and frequency. In strength of the symmetry, the mass particle is not localised in time (it is moving in time from past to future) but the gravitation field is not localised in space (it is dispersed in all of the Universe from the source of the field to infinity). The situation above is described by Heisenberg's formula F. 11.

To solve the question about the "red shift" of the photon that is travelling in a gravitation field of some planet, for example, let's assume that there is a balance of the positive and negative time functions: (f > 0) inside of the mass corresponds to (f < 0) outside of the mass. Time (t+ > 0) inside of the mass and time (t- < 0) around the mass.

In other words, it is a chronal version for Newton's action and reaction law. Any body produces a t+ process for itself and a t- process (gravitation field) around itself.

So, if body M produces a negative time value in space around mass M, the spectrum (wave length) of light beam that is travelling near M must be changing into a longer time period area ("red shift"). Any object that is placed in the gravitation field of another mass object has its own plus-time (t+), but in external minus-time (t-) the total time rate t is calculated as the difference of plus-time and minus-time, Fig.1.

Mass M
Gravitation field of
mass M oscillations
f > 0 f < 0
t > 0 t < 0


F. 14   t = t+ + t-

or in another form:

F. 15   t = tm - tg

where tm is the positive inner time of the mass and tm is the negative external time of the other mass.

Note: The rate of time t=0 means a zero-state of energy oscillation, i.e. the period of the process (T) is equal to infinity, and the frequency (f) is equal to zero.

The answer for the question above is: For a photon that is moving in a gravitation field of some massive body and for a body that is placed in an area of a gravitation field produced by other mass, total time effect is a summed result of its own positive time and negative time of the external gravitation field. The decrease of its own time in result of this summarising is demonstrated as the "red shift" of a photon's wave-length.

It corresponds to a decrease of the photon's electromagnetic mass. The mass of body that is placed in a gravitation field of another body is decreasing also. It is possible to obtain zero or a negative sum for t. Such sort of situation is known as a black hole.

What is f<0 for oscillations of electromagnetic energy? What is the type of this oscillation? There is an example for this situation in radioelectronics. If some frequency (f1 is a carrier and some frequency f2 is the modulation frequency, in an ordinary case f1 > f2, i.e. the signal (f1) is changing with a frequency of modulation (f2). Measurements are measured for one point of space, i.e. the amplitude, phase or other parameter of electromagnetic wave is changing as the time function for one point of space.

If f1 < f2, the modulation of the signal is possible but all structure of the signal at one moment of time must be changing by the modulation law with f2 in all points of the signal. The signal is not a wave in this case but is a stress field like an electrostatic or gravitation field.

The example above is a relative case for f1 and f2. If f1=0, the value of frequency f2 can be more than zero or less than zero. So, f2 can be considered as a positive or negative frequency of electromagnetic energy oscillations.

So, inside of a mass there is an ordinary electromagnetic wave process (f > 0; t > 0), but it is compensated by external (f < 0; t < 0) oscillation of electromagnetic energy density in all points of space around the body possible for an electrostatic field. Value f is the same for both cases.

By such an approach the gravitation field around some mass particle is an electrostatic high frequency field. The frequency can be calculated by F. 8 for any known mass value, for example, a proton has a frequency value of about 8.1 x 1026 [Hz]. This electrogravitation unification allows us to produce control of the gravitation. An example of similar technology is disclosed in H. Hooper's USA patent number 3,610,971 of 1971, "All -electric Motional Field Generator," and demonstrated in his experiment that used high frequency electric fields changing in one direction only (from zero to some potential, but the field was not an alternating field, polarity of potential was not changing).

Over-Light Velocity:

An interesting conclusion for velocity of motion can be obtained from F.12:

F. 16   mT = p x / c2 = m u x / c2

We can remove "m" from F.16 and obtain the next formula:

F. 17   T = u x / c2

For the velocity u=c, the wave-length is:

F. 18   = cT = c c x / c2 = x

It is the photon state: the wave-length value of the object determines the size of the local area (space) of the object.

For a velocity 0 < u < c, the wave-length of an object is lesser than the possibility of determination of the object position x.

F. 19   = (u/c) x

It means that the object has some space of positions, the object can move between different positions since all of the area of positions are determined. It is the nature of space itself for material objects moving with u < c. For a velocity ut > c, formula F.19 can be represented as:

F. 20   T = ut x / c2 = (c + u) x / c2


F. 21   Tc = cf = = (c + u) x / c

In result, the formula for wave-length demonstrates that the size of the object (wave-length) allows the possibility of determination of the objects position x:

F. 22   = (1+ u/c)

The demonstration of such objects in real space has some analogy with potential fields since the change of energy density of the object takes place in all space at the same moment.

Energy and Time:

The physical sense of the constant h is described by Heisenberg's formulation also as h = E t. In this general formulation, if the period of observation (T) is large, the energy of the system is known, and if the period (T) is very small, the energy has a spectrum of energy levels. Such a property is demonstrated by elementary particles.

Formula E = hf = h/T can be transformed to;

F. 23   E = (E t)/T


F. 24   E / E = t / T

It is an asymmetry of energy and time notions. Time and energy are not the same, but they are complementary notions. Let's formulate the experimental goal: Ordinarily the system has one constant level of energy. But it is possible to create a system that have wide spectrum of energy states in any short period (at the moment) of observation.

Constant of Photon Spreading as a Dimensionality Factor:

Now let's appeal to the simplified model for the space-time relation that is established:

F. 25   f = c/ [ 1/s ]

where f is the frequency of oscillation, c is the constant of spreading, is the wave-length. As the period (T) is inversely proportional to the frequency:

F. 26   T = 1/f [ s ]

as for the sake of the symmetry, it is necessary to consider the fourth parameter which is inversely proportional to the wave length:

F. 27   r = 1/ [ 1/m ]

Since R= is a resonator property, the formula F.25 can be represented as F.28:

F. 28   f = cr [ 1/s ]

Formulas F.1 and F.3 lead to the correlation:

F. 29   r3 = 3r1

and the formula of F.28 is now:

F. 30   f = 3r1

By this sort of approach the velocity of light can be considered as a factor of summarising in F.29. The mathematical power 108 m/s can be omitted here since it is the scale of measurement only. In any case, the electromagnetic wave in a vacuum is moving on 3 units of space per one unit of time: 3 decimetre per one microsecond.

So, the frequency of oscillation for any process is a curvature. The frequency of electromagnetic oscillation is a 3-curvature that corresponds to F.3. Electromagnetic oscillation of energy is the process for creation of dynamical three-dimensional space by means of two-dimensional structure (photon). From this point of view, the structure of reality appears as a dynamical process and can be designed as a local space-time by means of electromagnetics.

Conclusion: the time period for process in 3-space is:

F. 31   T = 1/f = 1/3r1 = 1/r3

The equivalent radius for spatial resonator is demonstrated as a time effect:

F. 32   T = R/3 [ m ]

and measurement of time is possible in spatial units, i.e. in meters. The constant of spreading for different types of energy waves can be equal to n, where n = 1,2,3,4... is the number of dimensions. In strength of this reason, space itself is a result of the energy transformation process only. Dimensionality for space is determined by the type of this process. Energy (by Greek "energy" means "action") is a quantitative description for different forms of motion. Hence space and chrona "time effect" are created as a result of motion. Dimensionality of space is the result of the type of motion.

Planet Curvature Value:

Before continuing, let us assume that the theory of similarity for microcosm and macrocosm is true, hence the planet can be considered an elementary particle in certain sense.

Substitute in the matter wave-length formula:

F. 33   = h/(mu) [ m ]

where h is Plank's constant, m is the mass and u is the velocity parameter of our planet, to calculate the value:

F. 34   = 3,725 x 10 -63 [ m ]

In strength of the supposition that the velocity of light for 4-space is only factor 4:

F. 35   E3 = m3 c2 = 9 m3

F. 36   E4 = m4 c2 = 16 m4

where m3 is the mass of 3-space and m4 is the mass for 4-space description. Note this important supposition: The total energy of a system is the same independent of different dimensionality descriptions. It means that the same amount of energy (but in different forms of energy) must be considered in 3-space and 4- space descriptions for one certain system. In other words, the total net energy of the Universe is the same independently of the dimensionality used by the observer. So, we must write:

F. 37   E1 = E2 = E3 = E4 =...

and in our case:

F. 38   9 m3 = 16 m4

According to F.33 the mass is:

F. 39   m = h/(u)

Now we obtain the correlation:

F. 40   (16 h )/(4u) = (9h)/(3u)

where 3 is the wave-length in 3-space, and 4 is the wave-length is 4-space. As the system is the same, the velocity is the same. So, there is a simple ratio:

F. 41   4 = (16/9)

Substitute the value for 3 from F. 34 in F.41 and you obtain the value:

F. 42   4 = 66.22 x 10-64 [ m ]

that conforms to a curvature:

F. 43   r4 = 1/4 = 151.00 x 1060 [ 1/m ]

Note that it is a whole number value. On the other hand, the period of planet rotation around the Sun is equal to 31,557,600 seconds, which conforms to the oscillation frequency value:

F. 44   f = 1/T = 3.168861 10 x -8 [ 1/s ]

The wave-length for electromagnetic oscillation in this case is:

F. 45   em = c/f = 9.46 x 1016 [ m ]

and the curvature for this length (radius of the resonator) is equal to a whole number value also:

F. 46   rem = 1057.00 x 10-20 [ 1/m ]

The correlation for the two results obtained in F.46 and F.43is:

F. 47   rem / r4 ) = 7 x 10-80

The mathematical connection for the results of two different descriptions of the same natural object (planet) is the confirmation for the Whole Number Value Law. This Law is valid for any natural system element. Let us demonstrate this Law in other examples.

Bohr's Atom Space-Time:

The curvature for Bohr's radius R = 0.52917 Å is:

F. 48   r = 1/R = 3.0075 x 109 [ m ]

According to F.29, the linear curvature for Bohr's atom is equal to the unit:

F. 49   r1 = r3 /3 = 1.0025 x 109 [ m ]

This is correct since it is a simple atom, unit matter engine. Some deviation k = 1.0025... is a demonstration of non-ideal resonance state in a real system.

Space-Time of a Proton:

To calculate the wave-length of a proton, let's use formula F.9:

F. 50   m = (h/c2)f = (h/c2)(c/) = (h/c )
or = h/mc, which is the version of the de Broglie wave-length for the velocity u = c. So, for a proton m = 1.6726231... x 10-27 kg, the wave-length = 0.75676739... (mathematical degree omitted) and curvature are equal to:

F. 51   r = 1/ = 132141.000...

It is a whole number value up to the third sign that demonstrates a particle proton as some spatial resonance process.

DNA-molecule Space-Time:

Another example is the DNA helical molecule. The unfolded spire-length period of it is equal to 71.4417 Å, which conforms to a curvature value of:

F. 52   rDNA = 14.0000 x 107 [ 1/m ]

This is very good resonator since it is a whole number value up to the fourth sign. This accuracy is the base for the supposition about resonance mechanics for energy transformation and information telecommunication on the molecular level in biosystems. The nature of the Time Effect is a motion only and resonance structure of matter elements. The superposition for the DNA molecule allows us to use this motion as a power 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 some curvature of 3-space has taken place. So, orientation for such a receiver is not important. The information signal is a change of energy density in space.

Now let's make calculation for the displacement of spiral DNA branches. Two branches have a period of 34 Å and a displacement of 23.8 Å. In other words, the ‘back wave' is displaced relative to the ‘direct wave' on 0.7 of the wave period. It is equal to 50.0 Å and corresponds to a curvature value of:

F. 53   r2 = 2 108 [ 1/m ]

If you take into consideration that for the two-dimensional structure of the spire, the curvature value is unit:

F. 54   r1 = 1 x 108 [ 1/m ]

So, branches of DNA molecules have a unit value shift from the zero-state. In this zero state, theoretically both branches are joined together. Code structures of each branch are contra-directional to each other. There is a very interesting analogy here with the elementary particle world. Creation - annihilation of virtual pairs of electron-positrons or photon-antiphotons in a vacuum is proposed in many concepts as zero-point energy source. By means of the methods disclosed in this paper it is possible to find the resonance condition for the generation of stable particles from a vacuum.


It would be premature to talk about the validity of this concept since the assumptions underlying it are open to question. It is necessary to make the experimental verification of this approach to the resonance nature of matter and vacuum. The Law of Whole Number Value for the curvature of natural elements of matter, demonstrated in this paper, is a mathematical tool for different technologies. The case of its practicality, the control on the rate of time and curvature of space, on the stability of matter (mass-energy transformations) and vacuum (energy-mass transformations) is not fantasy but technology.

Also, this Law shows that the absolute natural system for calculation is the decimal system and the absolute natural system for measurement is the "meter/sec" system. There is the possibility of establishing a new standard metre definition.

Since absolute systems are impossible in accidental phenomenon, the Law of Whole Numbers for curvature values of elements of matter shows that the material World is created. This is the main conclusion of this paper.


1. Cooper, Leon N. (1974), An Introduction to the Meaning and Structure of Physics, Harper & Row, Publishers, New York, Evanston, London, 1968. p.136 by Russian Edition (1974).