Quantum reality in the macro-world phenomena

Classical reality emerges from quantum reality provided there is interaction between the micro-objects. So far there is no unified description of classical and quantum realities, though everyone knows that such description is not simply possible, it’s necessary.

Here’s a simple way of describing the macro-world phenomena (inertia, motion, propulsion force, gravitational force, kinetic and potential energies, centrifugal force) relating to classical mechanics through the notions and means of electrodynamics and quantum mechanics. In effect, we are talking about a new quantum-mechanical interpretation of the formulas of classical mechanics.

The first such interpretation became possible after the creation of rhythmodynamic model of the processes which trigger the motion of macro-bodies in space [1].

Rhythmodynamics (RD), a branch of science studying the role of periodic processes in the formation of natural phenomena and their qualities.

The notion of ‘motion’ is known to be present in all formulas of classical mechanics, in one form of the other. There are several kinds of motion but we’ll focus on only two of them: the motion with constant speed (by inertia), and the motion with constant acceleration (free fall).

According to [1]

,                                  (1.00)

i.e. the speed of the body is proportional to the phase displacement between the body’s oscillating elements.

One of the main achievements of rhythmodynamics was finding this relation, the formula of which reflects the processes without which the above-mentioned regimes of motion in wave medium would hardly be possible. Relation 1.00 is the main element of the new way of description of macro-phenomena. It sets a tentative, so far, link between classical and quantum mechanics. From a mathematical point of view, it’s simply a different formulation and interpretation of the laws of classical mechanics. From a physical point of view, we are talking of a qualitatively new vision of the world.

1. Force and acceleration in the field of gravitation

There are several options of deriving the relation describing the body’s free fall in the field of gravitation. Option 1 seems most curious because it originates from the well-known premises.

Option 1 (gravitational red shift)

Einstein predicted phenomenon of gravitational red shift. In earth conditions such shift is insignificant, but they did manage to measure it in an experiment based on the Mossbauer effect.

If a photon with frequency  is emitted at height Í above the surface of the Earth toward its center, at the Earth’s surface level its kinetic energy  increases at the expense of potential energy. Following the law of conservation of energy we formulate:

(1.01)

It assumes that photon’s mass  is constant. So, the receiver encounters a photon with frequency , different from the one it had during its emission by the source. With Í=10 m

Fig.1 In a three-dimensional body one can always find some atoms which are farther from the earth’s surface, and others which are closer.

But what, in the Earth’s gravitational field, will the frequency difference be of similar (fig.1) vertically positioned atoms, with the distance between them of one standing wave, i.e. ?

(1.02)

(1.03)

If frequency difference does depend on acceleration g, then it would be possible to state that it’s the frequency difference which forms acceleration. Let’s rewrite formula 1.03 relative to acceleration g:

(1.04)

(1.05)

There are other ways of obtaining relation 1.05 (one of them is rhythmodynamic) which corroborates the derived dependence of acceleration on frequency difference. Substituting acceleration g in formula   by its new expression, we obtain a new meaning of the notion the force of gravitation:

,                                           (1.06)

but

Then

(1.07)

In 1.07 the force of gravitation applied to the experimental body is proportionate to the frequency difference imposed by gravitational field on the interacting atoms.

Option 2 (rhythmodynamic)

According to classical mechanics:

(1.08)

According to rhythmodynamics:

,                                  (1.00)

but ,

i.e.à                                  (1.09)

or                                    (1.05)

where:

V – velocity of the system of oscillators

ñ – velocity of the waves in the medium (speed of light)

à, g – acceleration of the system of oscillators

– phase displacement between oscillators

– oscillators’ frequency difference

For

Gravitational field imposes a frequency difference on the body’s oscillating elements, thus breaking the system’s natural synchronism. This happens at least at the atomic level of matter organization and leads to the system’s reaction in the form of the body’s self-propulsion with acceleration.

Self-propulsion, internally provoked natural change of the system determined by its contradictions indirectly reflecting external factors and conditions.

2. Wave interpretation of the force of gravitation

Quantum mechanics, a branch of physics studying the ways of description and the principles of motion of elementary particles, atoms, molecules, atomic nuclei, as well as macro-phenomena. Quantum mechanics determines relations of quantities describing particles and systems with the physical quantities directly evaluated in the experiment.

Let’s examine an experiment measuring the force of gravitation affecting an experimental body m. But what triggers this force? The researcher is convinced that the force affecting body m is nothing but a net reaction of the body’s elements to the conditions created by the gravitational field in and around the body (gravitational field makes space heterogeneous). But what exactly changes inside the body, what parameters, and why does the body react to the changes?

Classical mechanics asserts that in the gravitational field body m comes under the effect of force

(1.06)

Earlier it was shown that gravitation g is proportionate to the gravitational red shift, i.e.

,                                       (1.05)

where the frequency difference can be expressed through the speed of light and wave lengths:

(2.01)

Then

,                       (2.02)

and

(2.03)

But quantum mechanics accepts as true the relation:

,                                           (2.04)

then

(2.05)

Taking into account 2.05, we’ll rewrite 2.02 and 2.03

,                                 (2.06)

and

.                            (2.07)

But , and ,

then

,                               (2.08)

or

or          (2.09)

where:

hPlanck’s constant

pwave impulse

Ebody’s overall energy

The left part of formulas 2.07, 2.08, 2.09 has a classical expression of force, while their right part –  a quantum-mechanical expression.

Expressing through the notions and parameters of quantum mechanics () we’ve shown the link between quantum and Newtonian mechanics. In effect, 2.09 is a wave equation revealing a frequency-wave nature of force in general, and gravitational force in particular.

3. Kinetic and potential energies

Kinetic energy, a measure of bodies’ mechanical motion which depends on velocities of their motion in a given inertial frame of reference.

Potential energy, forces hidden in matter which could become effective under certain circumstances.

Considering dependence of speed on phase shift one can take a different look on the notions of kinetic energy and potential energy.

(3.01)

but

(3.02)

then

(3.03)

where:

then

(3.04)

(3.05)

The difference between formulas 3.03, 3.04, 3.05 and formula 3.01 is that their right part reflects directly the gradient-phase nature of kinetic energy, i.e. inner system processes which ensure the presence of such energy. In other words, the phase shift reveals the cause of the system’s propensity to move. If such system is blocked its kinetic energy should be viewed as potential energy seeking to be transformed into kinetic one. Such system has an inner propensity to move, and the energy which actualizes it is called potential energy. Transformation of potential energy into kinetic one takes place if the system is no longer blocked.

If ,  the energy is kinetic, i.e. present in the body and maintaining its motion:

(3.03)

If , i.e. the system is blocked, the very same energy (3.03) is potential:

(3.06)

The common mechanism-cause of kinetic and potential energies lies in the presence of internal phase changes. These changes, if free motion is obstructed, reveal themselves in the form of internal force of propulsion (as propensity to move).

Now we have a deeper understanding of the processes responsible for kinetic and potential energies.

4. Centrifugal force

Centrifugal force, a force with which a material particle moving uniformly on a circular trajectory affects the link.

(4.01)

But                                     (4.02)

then

(4.03)

(4.04)

5. Quantity of motion

Quantity of motion, a measure of inner propulsion force maintaining velocity regime in a wave medium. (Rhythmodynamic interpretation).

(5.01)

but                                     (4.02)

then

(5.02)

According to the motion equation, phase displacement makes the body (system) move at a speed corresponding to this phase displacement. If the body’s (system’s) free motion is obstructed, the force it will exert on the block will be:

(5.03)

Analyzing the obtained expression of force one can see that the change of the system’s velocity regime may be not due to external force, but due to the phase-frequency state of the system’s oscillators. In that case propulsion force emerges, bringing the system in a state of sustained motion.

(5.04)

6. Velocity of the energy flow

Suppose we have two sources of waves whose frequency, respectively,  and  (fig.4), with .

Fig. 4. The observer must move to implement the condition of equal frequencies of the incoming waves and energies emitted from the sources. In this case he registers a standing wave! The energy flow of the standing wave is equal to the wave’s velocity.

In the moving observer’s reference frame we have:

(6.01)

(6.02)

But , therefore

(6.03)

Let’s solve the equation relative to the system’s velocity , in which equality of incoming frequencies and a regular standing wave is observed:

(6.04)

The same, relative to the emitters, is also the speed   of the flow of energy concentrated in the standing wave:

(6.05)

7. Rhythmodynamic and  quantum-mechanical interpretation of the formulas of classical mechanics

The familiar formulas of classical mechanics (1) have acquired rhythmodynamics (2) and quantum-mechanics’ interpretations. What’s important is that the new formulas of classical mechanics have acquired fundamental constants (the speed of light and Planck’s constant), as well as basic parameters used in electrodynamics and quantum mechanics (phase, frequency, wave impulse). The formulas are compiled in Table 1.

Table 1

 Basic parameter, notion Classical mechanics (CM) Rhythmodynamics (RD) New formulas to describe the laws of mechanics 0 1 2 3 Speed Acceleration Acceleration of free fall Force Force of gravitation Quantity of motion, momentum Kinetic energy Potential energy Centrifugal force Work The speed of energy flow ??? ???

The new interpretation allows us to take not the usual formal, but a fresh look at the phenomena and their properties through processes which contribute to the formation of these phenomena and properties. This is a new approach and a new depth of understanding natural phenomena.

The new formulas often contain a relation  numerically equal to  and usually marked as:

In which case some formulas acquire a more compact form, for example:

,

,

,

Conclusions and consequences

The expressions we’ve derived for speed, acceleration, the force of gravitation, kinetic and potential energies, centrifugal force, quantity of motion in their essence contain the elements of quantum mechanics and electrodynamics which points to the phase-frequency causal nature of these phenomena. The new formulas could well replace or go side-by-side along the old ones, especially if we need to switch from one system of notions and ideas to the other.

MIRIT Scientific-Technological Center

Yuri N. Ivanov.

December 13, 2008.

Bibliography:

1. Ivanov Y.N. Rhythmodynamics. New Center Publishers, 1997.

2. Ivanov Y.N. Rhythmodynamics.  Energy Publishers, 2007.

3. Physical encyclopedia. Sovetskaya encyclopedia, 1990.

Books [1] and [2] are freely accessed at http://www.mirit.ru