08 / 25 / 2011 - 15:11 — Алекс

**PROOF OF EXISTENCE OF UNIVERSE’S HIDDEN EXTRA DIMENSIONS ****BY INVESTIGATING RESONANT PROCESSES IN LINEAR ELECTRIC CIRCUITS**

**Alexander Antonov, Ph.D., Associate Professor**

**Reseach ****Center of Information Technologies**

*Анализируется существующая теория резонанса в линейных электрических цепях на действительных частотах и показывается ее несовершенство. Предлагается новая теория резонанса на комплексных частотах, полностью свободная от недостатков существующей теории резонанса. Приводятся многочисленные экспериментальные доказательства существования резонанса именно на комплексных частотах. Новая теория резонанса позволяет не только успешно ее применять при решении различных практических задач, но и с ее помощью обнаружить существование скрытых дополнительных измерений Вселенной.*

*Ключевые слова:**электрические цепи, резонанс, переходные процессы, действительные частоты, комплексные частоты, дополнительные измерения вселенной, скрытые измерения вселенной*

*We analyse the current theory of resonance in linear electric circuits at real frequencies and demonstrate its shortcomings. We offer a new theory of resonance at complex frequencies, which is free from the shortcomings of the current theory of resonance. We offer numerous experimental evidence of resonance particularly at complex frequencies. The new theory of resonance allows not only using it successfully to solve various practical tasks; it can be used as a tool for discovering the existence of hidden extra dimensions of the Universe. *

*Keywords**: electric circuits, resonance, transitional process, real frequency, complex frequency, Universe’s extra dimensions, Universe’s hidden dimensions*

**1. ****Introduction**

Resonanceisanimportantoscillationprocess. Nevertheless, despite the fact that resonance in electric circuits was first discovered by Felix Savary (1797 – 1841) in 1826 [1], this physical phenomenon remains largely unexplored. The current theory of resonance in electric circuits at real frequencies is inconsistent and unable to account for these inconsistencies. As for the current theory of electric circuits at complex frequencies, the concept of resonance is not even mentioned.

The present paper suggests a new theory of resonance [2], which, among all, allows extending our knowledge of the structure of the Universe.

**2. ****Investigation****of****resonance****at****real and complex frequencies **

In the theory of electric circuits at real frequencies, resonance is understood as a phenomenon which meets the following conditions:

- a. the amplitude of forced oscillations at resonance frequency takes an extreme value;
- b. forced oscillations at resonance frequency are in phase with the external action oscillations;
- c. resonance frequency equals the frequency of free oscillations.

However, during investigation of LCR-circuits at real frequencies it turned out that the phenomena which are usually referred to as resonance, in fact almost never meet the above conditions [3], [4], [5]. Actually, the conditions ‘a’ and ‘b’, with precise in calculations, are usually fulfilled at different frequencies. Moreover, with precise calculations, very often several frequencies meet the conditions ‘a’ and ‘b’. As for the condition ‘c’, it is never fulfilled. In particular, Russian academician Mandelshtam[6] tried to explain the latter circumstance in the 1^{st} half of the 20^{th} century, but failed. After him, no attempts to further develop the theory of resonance at real frequencies were taken.

**Figure 1 **Electric LCR-circuits under investigation

Indeed, even in the simplest electric LCR-circuits, for example, in the form of series-oscillating circuit given in Fig. 1, not a single, but two resonance frequencies correspond to the first of the above attributes of resonance:

(1a)

where

Two resonance frequencies also correspond to the second of the above attributes of resonance for the same electric LCR-circuit:

(1b)

And, finally, the frequency of free oscillations in the LCR-circuit under investigation is

(1c)

As can be seen from formulae (1), all these frequencies are actually different. Study of other LCR-circuits yields similar results.

Thus, the current theory of linear electric LCR-circuits at real frequencies always uses approximations, which allow obtaining the results allegedly meeting the conditions ‘a’, ‘b’ and ‘c’. The shortcomings of this theory are admitted by all authors of technical literature, who never even attempt to use precise calculations which they will not be able to explain.

The impossibility of eliminating the above shortcomings of the theory of linear electric circuits at real frequencies, obviously, accounts for the development of the theory of linear electric circuits at complex frequencies [7], [8], [9], which is perfect, but only due to the fact that it simply does not deal with the issues which may be arguable and difficult to explain. In particular, it says nothing about resonance. It also does not explain the physical meaning of the concept of complex frequency. Certainly, this reduces the value of this theory.

However, the publications mentioned above [2] ? [5] suggest the new theory of resonance, which completely eliminates the shortcomings of both current theories of linear electric LCR-circuits. The new theory, first of all, gives theoretical and experimental evidence of the physical reality of complex frequencies. It also proves, in particular, using the Cassini ovals, that resonance actually takes place not at real frequencies **W**, but at complex frequencies . The new theory explains the above inconsistencies of the theory of resonance at real frequencies using vector diagrams at complex frequencies. It also describes numerous experiments confirming the existence of resonance particularly at complex frequencies, in particular, at complex frequencies in LCR-circuits under the impact of exponential radio pulses, as well as at complex frequencies in RL- and RC-circuits under the impact of exponential video pulses, which is completely identical to resonance at complex frequencies in LC-circuits under the impact of sustained sinusoidal oscillations. It is shown that resonance at complex frequencies can have a practical application in the development of complex frequencies filters, which enable better signal selection than the current real frequencies filters. Resonance at complex frequencies can be also successfully used to solve other practical tasks [10].

The physical reality of complex frequencies can be proven as a result of investigation of oscillation transitional processes [11], [12].

**3. ****Hidden****extra****dimensions****of****the****Universe **

The new theory of resonance has another important advantage – it allows extending our knowledge of space and time.

Indeed, as mentioned above, this theory proves the physical reality of complex frequencies and other concrete complex numbers – complex resistances and admittances, complex voltages and currents, complex powers and energies, and so on. However, this statement inevitably brings up additional questions which require an answer, for instance, how to verify the physical reality of complex numbers with the help of human sense organs, and how to understand the physical reality of complex numbers.

The answer to the first question is clear – nowise, since people do not have the appropriate sense organs. However, this answer should not be surprising, since human senses are not susceptible to the magnetic field, to the electromagnetic radiation (except for the optical and thermal ranges), to the electric current (if it is small enough), or even to the low-frequency infrasound (perceived by many other living beings). Human sense organs are unable to verify the atomic structure, the molecular structure, the existence of black holes, and many other things. Thus, people believe these phenomena exist based on the results of theoretical and experimental scientific research. Therefore, people should simply believe in the new scientific knowledge on the physical reality of concrete complex numbers.

The answer to the second question is more complicated and more important. In fact, the objective of the present research is to answer this question. The point is that, in accordance with the Euler formula

(2a)

which can be obviously transformed into

(2b)

The exponent on the left contains complex frequency , the physical reality if which has been proven above. Thus, the left part of the formula on the whole, and, thus, its right part, as well, is physically real complex numbers. Therefore, the real component of any oscillation process observed by people is always conjugated with its imaginary really existing component. However, since numbers are a measurement tool, this additional imaginary component is in essence an extra dimension of a process [13], [14], [15].

Since this imaginary component is not felt by people in any way, it can be referred to as the hidden extra dimension, similar to the hidden extra dimensions of the microcosm which are supposed to be discovered during the experiments at the Large Hadron Collider [14]. However, hidden extra dimensions of the Universe described in the present paper are different from the hidden extra dimensions dealt with in [16]. Indeed, since the physical reality of oscillation processes described with formula (2a) holds true for , the revealed hidden extra dimensions apply just as well to sustained oscillation processes of any physical nature, including the rotation of electrons around the atomic nucleus, and the rotation of planets around their stars. In other words, the extra dimensions discovered and described herein apply to any fragments of the Universe, both to the physical world we live in, and to the microcosm and macrocosm, as well.

We do not rule out that other hidden extra dimensions of the Universe can exist, corresponding, for instance, to hypercomplex numbers [17], if, of course, their physical reality is proven.

**4. ****Summary**

Thus, thorough investigation of resonant processes in linear electric circuits allowed not only developing the perfect theory of resonance at complex frequencies, but discovering on its basis the existence of the hidden extra dimensions of the Universe.

**References****:**

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