Уткин Владимир Михайлович. The realizability of the Penrose stairs. Part 2. Electromagnetism

THE REALIZABILITY OF THE PENROSE STAIRS.

PART 2.

(ELECTROMAGNETISM)

Vladimir Utkin u.v@bk.ru

INTRODUCTION

The Penrose Stairs is a design of stairs, for which, in the case of moving on it in one direction (for Fig. 1 anti - clockwise), person would unlimited rise, and while moving backwards, would continuously descend. After completing visual route, a person shall be at the same point from which his movement started. The existence of the stairs in the real world is considered impossible to believe. That is an example of the classic optical illusion.

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Fig. 1 The Penrose Stairs

In spite of that, we shell try to create a structure, in which ideas of optical illusion become practically possible. To this end, we shall do:

1. Movement on stairs ("up" or "down")

2: Return to the origin position ("without energy losses transition")

To solve the problem, we choose the decision based on the ideas of committing mechanical work under the electromagnetic interaction.

THE GENERAL APPROACH

It is known, that the bodies cooperating in environment with a magnetic field, can make mechanical work, moving each other. In the elementary case it can be, for example, two permanent magnets. Approaching each other (at appropriating orientation of poles) they will make positive mechanical work.

Besides it can be one magnet and one ferromagnetic, or two coils with currents, or the coil and a magnet, or the coil and ferromagnetic, etc. However, for ease of presentation delivering shall be limited by: a magnet, ferromagnetic and the coil with a current (not considering the other bodies possessing magnetic properties - paramagnetic, diamagnetic and others.)

We wonder: how energy of the magnetic field changes at the fulfillment of the mechanical work?

Let's consider some options.

-- Interaction of two coils with current I1, creating a magnetic field intensity H1 -Fig.1

Fig.2 The fulfillment of the mechanical work on approaching the two coils with currents.

The final energy of the general magnetic field has decreased by half. It is clear: mechanical work has been accomplished, energy of the magnetic field has passed into mechanical work. The current in each of coils has decreased by half (due to the phenomenon of back EMF). Final energy of the magnetic field of the interacted coil has decreased by half from initial energy of magnetic fields of two coils. The magnetic field is spent for fulfillment of the mechanical work! Or, not??? We shall consider the following option.

2. Interaction of the coil with the current I1, creating a magnetic field intensity H1 and a permanent magnet intensity H1 - Fig.3.

Fig.3 The fulfillment of the mechanical work on approaching of the coil with a current and a permanent magnet.

The final energy of the general magnetic field has decreased by half. Again clearly: mechanical work has been accomplished, energy of a magnetic field has passed in mechanical work. The current in the coil has decreased up to zero (due to the phenomenon of back EMF). Final energy of a magnetic field has decreased by half from initial energy due to a zero current in the coil. The magnetic field of the coil was ran out for fulfillment of mechanical work! Or, not??? We shall consider a following option.

3. Interaction of the coil with a current I1, creating a magnetic field

intensity H1 and a ferromagnetic bar - Рис.4.

Fig.4 The fulfillment of the mechanical work on approaching the coil with a current and a ferromagnetic bar.

The final energy of the general magnetic field after fulfillment of mechanical work has not changed, here is a surprise!!! The coil has magnetized ferromagnetic, as a result it changed (has decreased) the current in the coil (due to the phenomenon of back EMF) and final

intensity of the magnetic field has not changed.

If energy of the final magnetic field has not changed, what energy made mechanical work??? We must consider the following option.

4. Interaction of two permanent magnets possessing a magnetic field

intensity H1 - Fig.5.

Fig.5 The fulfillment of the mechanical work on approaching two permanent magnets.

The final energy of the general magnetic field H2, after the fulfillment of the mechanical work, at least, has not decreased, as magnets cannot magnetize each other more almost, than is. If final energy of the magnetic field has not changed, what energy made this mechanical work??? We shall consider a following version of interaction..

5. Interaction of a permanent magnet, creating a magnetic field

Intensity H1, and a ferromagnetic bar - Fig.6.

Fig.6 The fulfillment of the mechanical work on approaching a permanent magnet to a ferromagnetic.

The Final energy of the general magnetic field H2 after fulfillment of the mechanical work has increased, as the permanent magnet could magnetize ferromagnetic bar on value dH during approaching. It turns out, that mechanical work is made, but energy of the magnetic field only increased! Again a surprise!!! If the energy of the final magnetic field has increased only, what an energy made mechanical work??? It is a time to answer this question.

As the energy of the magnetic field during fulfillment of mechanical work can to decrease or to increase itself, or to remain constant, it seems not logical to consider that exactly energy of magnetic field makes mechanical work. The threefold signs of a question putted earlier have appeared quite proved.

So for enigmatic " free energy " makes mechanical work?

Is it necessary to enter new concepts, or it is possible to be limited to old concepts?

POTENTIAL ENERGY

During carrying out, specified above mental experiments, on fulfillment of mechanical work, the general energy balance in several experiments have not been carried out, considered so.

Nevertheless, to enter any new concept of " free energy " it is not required. It is possible to consider such "missed" type of energy as potential energy, due to mechanical work was made, instead of magnetic field energy. Observable "laws" in variation of magnetic field energy were displaying only "by-effects". "By-effects" are responsible for the reduction, increasing or an invariance of intensity the final magnetic field.

Let's try to explain.

Most simply, as will not seem strange, to explain concept of potential energy is possible on the basis of gravitational interaction, whence actually this concept has come.

For this purpose it is necessary to involve concept of " curvature of space ", to illustrate which is possible by accommodation of a certain cargo on the flexible and thin horizontally located membrane. Therefore the membrane is deformed and sags - Fig.7.

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Fig.7 The Illustration of the curvature of the space

Such figurative concept allows to explain the occurrence of two types of energy: energy of the gravitational field and the potential energy.

If the deformed membrane to present as the "compressed spring", energy reserved by the compressed spring can be treated as energy of the gravitational field.

If the deformed membrane to consider as "dug pit", depth of this pit can be treated as potential energy for a body being on its edge.

Consequently, at gravitational interaction of two bodies (at their approaching) and fulfillment a work, energy of the gravitational field does not change (remaining the equal sum energy two cooperating bodies), though locally "spring" is compressed more strongly. That tends to increase depths of "dug pit" for the third body, etc. Thus, potential energy of cooperating bodies decreases (becomes equal to zero at their merge).

Such explanation is very rough, but allows to feel an essence of occurring processes.

A similar curvature of space can be represented and for the magnetic field when the mechanical interaction of two permanent magnets takes place - Fig. 8.

That is, when two magnets make positive work, the energy of the magnetic field does not change. The resulting magnetic field will have the same energy, equal to the sum of the energies of the interacting magnets, potential energy will work.

Therefore, the observed decreases in energy of the magnetic field, previously pointed in mental experiments, not linked to the perpetration of the mechanical work for bodies in the magnetic field.

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Fig. 8 The illustration of the curvature of the space for the magnetic field.

That is, for observed in mental experiments "by - effects", that lead to the reduction of the energy in the final magnetic field, "to response" the other physical processes.

Hence, promising interactions in terms of the realization of the Penrose stairs, you can consider such interactions that lead only to change in potential energy (on stairs), keeping the original value of the magnetic field energy unchanged. As we have seen, it is the interaction of two permanent magnets.

However, we choose not this interaction described between two permanent magnets, but interaction a coil and a ferromagnetic material, as in this case, it is sufficient to simply implementation of "without losses transitions", or "jumps", where we will be in the starting point of the movement (with the initial value of the potential energy).

THE POTENTIALLY REALIZABLE THE PENROSE STAIRWAY

If careful reading the previous sections, you can draw attention to the fact that to create potential energy not consumed any other forms of energy. It is determined solely by the position of the bodies at the beginning of the interaction, i.e. at the time of the magnetic field appears in the surrounding space (for electromagnetic interaction).

Therefore, changing the starting position of the interacting bodies before magnetic field appears, you can change the original value of potential energy, not spending any energy on it.

Potentially realizable Penrose stairway, based on the principles described above, is represented on Fig. 9. Where figures (1) and (2) are displaying the two identical coils, and the gray bar, displaying the ferromagnetic material, moves in to one then to another, depending on the position of the coil with magnetic field, and that producing a mechanical work. Potential energy decays under it, and the energy of the magnetic field is not changing.

Return to the "starting point" of the movement on the "Penrose stairs" takes place by overpumping magnetic fields from one coil to another, through the interim charge to the capacitor - C. Thus, Fig. 9 presents the Penrose stairs when moving "down", moving "up" on Penrose stairs is represented on Fig. 10

At the same time, it is believed that the coils have no ohmic losses (superconductor), and they both have no losses in all elements of the schemes. Start in working process is carried out by, for example, the initial charging of the capacitor - C, with energy which is then converted into the energy of the magnetic field.

Fig. 9 The potentially realizable Penrose stairs when moving "down" the stairs.

Fig. 10 The potentially realizable Penrose stairs when moving "up" the stairs.

Moving "Up" on Penrose stairs means the conversion of the mechanical energy into higher potential energy, if we want to "climb" on the Penrose stairs, the more mechanical energy will be spent - Fig. 10.

In other words, if "descent" on the stairs pulled in the ferromagnetic bar in the coil by himself, but when "lifting", ferromagnetic bar must be pulled out from the coil by the application of the external force.

At the end of the movement the energy of the magnetic field will not changed (as noted earlier), that allow "to transfer" the energy of the magnetic field from one into another coil (without losses transition) and repeat pulling out again.

Two motors were shown for "pulling" on Fig. 10, and their shafts are associated with the ferromagnetic bar. Energy into electric motors fed from an external source (not shown).

BRUSHLESS ELECTRIC MOTOR

Specialists familiar with electrical engineering and, in particular, electrical machines, might guess that the processes described for potentially realizable Penrose stairs, have much in common with processes taking place in the brushless electric motor (stepping motor) - Fig. 11.

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Fig. 11 Diagram of the brushless electric motor (stepper motor).

Difference for the Penrose stairs, described above, and for the brushless electric motor (stepper motor) is only that instead of linear movement, ferromagnetic core commits rotational movement, trying to take a position with the lowest potential energy, which corresponds to the orientation along the axis of the coils pair. Such pairs of coils can be up to four (typically). But, in general, the processes described above are the same.

But in this case of motor, there are no "without losses jumps", meaning "throwing" energy between pairs of coils, that not allows to consider this design the finished Penrose staircase. To bring the brushless electric motor to the level of the Penrose stairs, you must modify the control unit (Controller) in accordance with the principles described above, as well as take care of recharging a capacitor associated with the various losses of energy of the magnetic field. However, these issues are beyond the scope of this work.

ENERGY GENERATION

Unlimited descent on the Penrose stairs should lead to the unlimited process of generating energy. A ball, thrown on the stage, will endlessly roll down, converting the potential energy of steps height into the kinetic energy of motion.

The same should happen in our potentially implemented Penrose stairs.

For utilization the kinetic energy as electricity, one can connect a ferromagnetic bar to the electrical generators through a flexible thread - Fig. 12.

Fig. 12 Unlimited "descent" on the Penrose stairs - energy generation.

Start of this scheme can be implemented by, for example, the initial charge of the condenser - C, with the energy which is then converted into the energy of the magnetic field.

Taking into account the earlier comments (for brushless electric motor), circuit Fig. 12 can take the following form - Fig. 13.

Fig. 13 Unlimited "descent" on Penrose stairs - generation electricity, using brushless electric motor.

If you introduce the notion of "external observer", the energy change of initially charged capacitor-C, in the observation process, it will not be able to determine the energy generated or not, because the average energy on capacitor will remain unchanged.

When a loop compensation of losses for an idealized case (loss less) is not mandatory.

If you introduce the notion of "internal observers" - rating this energy on the output device, it will observe the process of infinite energy generation.

It should be noted, however, for the work of such ladder shall be in it of the Penrose downloaded the initial energy (charge a capacitor), this initial energy only and will be able to watch "external observer".

ENERGY DESTRUCTION

The endless rise on the Penrose stairs should lead to unlimited energy pays, person going up the staircase raises his body higher and higher, spending his kinetic energy and transferring it into potential energy height of steps.

The same should happen in our potentially realizable Penrose stairs - Fig. 14

Fig. 14 Unlimited "lifting" on Penrose stairs - destroying energy.

The scheme can be activated, for example, by the initial charging of the capacitor - C with the energy, which is then be converted into the energy of the magnetic field.

Taking into account the earlier comments (for brushless electric motor), the scheme of Fig. 14 can take the following form - Fig. 15.

At the same time, the direction of rotation for an ordinary AC or DC electric motor in Fig. 15 must be opposite the direction of rotation for the brushless electric motor. Thus, ferromagnetic core "comes out" to a higher level of potential energy, while input energy (for an ordinary electric motor) is destroying. The energy of the magnetic field inside the brushless electric motor remains the same.

Fig. 15 Unlimited "lifting" on the Penrose stairs - destruction of the energy by using the brushless electric motor.

No increases in energy of initially charged capacitor any "outside observers" will not be able to discover. That is, it will not be able to determine the energy comes into the system or not, because the average energy on the capacitor will remain unchanged.

The term "destruction" of the energy selected precisely, because the spent energy will not be convertible into any other type of energy in terms of "outside observer". For "outside observer" it will disappear without a trace. At the same time, the "inner observer" would say that the power constantly comes the system.

Thus, the generation and the annihilation of the energy depends on the direction of the movement on the Penrose stairs. When driving in one way energy is generated, when driving in the opposite direction it is destroyed.

It should be noted that the practical value of the destruction of the energy is no less important than the practical value of the energy generation.

For example, when you want to cool an object and reset the heat. In this case can help energy destroy. Heat of the object transforms into the electricity that turns the electric motors in energy annihilator. Heated body cools itself, without heating the environment.

THE LAW OF THE CONSERVATION OF THE ENERGY

It was shown for potentially realizable Penrose stairs, that any outside observer cannot say generated energy or destroyed. For him, some generation or some destruction of energy is not discoverable.

At the same time, the internal observer will manifest generation or destruction of energy depending on the direction of the movement on the stairs. Moreover, this energy will be real in both cases.

One would like to understand how this is consistent with the law of the conservation of the energy.

First of all, it should be noted that for the law of the conservation of the energy, as well as for any other physical laws, there is an area of applicability determined by the Emma Noether's theorem.

Theorem from 1918 year mathematics Emma Noether asserts that every continuous symmetry of a physical system corresponds to the some conservation law:

Symmetry of the time corresponds to the law of the conservation of the energy,

Symmetry of space meets the law of the conservation of the momentum,

Isotropy of space corresponds to the conservation of the angular momentum,

Gauge symmetry corresponds to the conservation of the electric charge etc.

That is, the first is a symmetry, and then a corresponding conservation law. If there is no symmetry, then you are beyond the area of applicability of the conservation law. Thus, the law of the conservation of the energy is impossible to break fundamentally, because it is the effect, not the cause. However, it is possible to go beyond the area of its applicability violating the relevant symmetry.

We will have interesting symmetry in time.

Symmetry of time means an invariance in choosing the origin on the axis of time. That is, you can choose the origin on the time axis arbitrary, the result of the experiment on this should not be changed unless other conditions have changed.

But, for constant conditions in potentially realizable Penrose stairs "not everything is all right." There are points on the time axis "without losses transition" when on the left from them the body has one potential energy, and on the right the different potential energy. That is, left and right conditions are differ. Thus, to say that potentially realizable Penrose stairs will be located in the area of applicability of the law of the conservation of the energy is not possible. At the same time, the "outside observer" cannot determine any generated or destroyed energy in this device.

However, for starting the device it will need to download some kind of primary energy (to charge a capacitor). An "outside observer' will be able to watch only that energy.

The results do not contradict the law of the conservation of the energy, since it's outside an area of applicability of the Emmy Noether's theorem, which defines as invariance in choosing the origin on the time axis (time symmetry). For the considered potentially realizable device this condition fails because it uses "without losses jumps", leading to the restoration of the potential energy of the body. On the left and on the right from the jumps conditions are different.

CONCLUSION

It was shown a concept of the realizability of the Penrose stairs, based on the mechanical moving bodies in the magnetic field. As a result, the energy of the magnetic field is not changing, but the potential energy is changing for the relative positions of the interacting bodies.

The mere formation for the potential energy for the magnetic field was illustrated based on the curvature of the surrounding space. It is shown that the formation of potential energy does not require additional energy magnetic field itself.

Work against the magnetic field (the increase in potential energy) becomes the equivalent of lifting on the Penrose stairs. Work of the magnetic field (the decrease of potential energy) becomes the equivalent of the descent on the Penrose stairs.

It was shown that after "lifting" or "descent" on Penrose stairs, jumps without losses are available, that means return to the beginning of the journey. After that, the movement on the Penrose stairs can be repeated on a cycle.

As interacting bodies were chosen: a ferromagnetic bar and a coil with a current, because as a result of this interaction does not change the energy of the final magnetic field.

It was shown, that for losses less return (jump) at the beginning of the paths can be used moving the magnetic field relative to ferromagnetic material by "pumping" current from one coil to another (via an intermediate charge a capacitor).

The result of the implementation of the Penrose stairs is the ability to generate and to distract the energy, understandable as emergence from "Nowhere" and vanish into 'Nowhere', rather than the conversion of some types of energy in different energy. Which corresponds to the unlimited descent and the endless rise on the Penrose stairs, respectively.

Generation or destruction of the energy is possible only for "inner observer". At the same time reaffirmed once again justice allegations that the work performed by the body when driving on a closed path in a potential field is zero. That is, "an external observer" would not be able to determine whether the generation or destruction of the energy is in the described device.

The results do not contradict to the law of the conservation of the energy, since it is outside its applicability (area of the Emmy Noether's theorem, which defines as invariance in choosing the origin point on the time axis - time symmetry). For the considered potentially implemented device this condition fails, because it uses losses less jumps, leading to the restoration of the potential energy of the body, on the left and on the right, depends from different conditions.

To start device operation, it is necessary to upload a primary energy (to charge a capacitor). These are the only the energy costs and be able to watch a third party observer.

All reasoning is based on the fact that with the introducing ferromagnetic material in the coil with some current, energy of the magnetic field of such a coil is not changed. If the energy is going to change, then all arguments are not correct.

LITERATURE

ARE ALREADY KNOWN DEVICES

A device based on a theory described above is the Peter Lindemann rotary attraction motor - Fig.16.

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Fig.16 Lindemann rotary attraction motor

Or, its modification with one battery - Fig.17.

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Fig.17 Lindemann rotary attraction motor with one battery.

Another device, based on the described approach should be considered an electric motor boat from Alfred Hubbard - Fig. 18.

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Fig. 18 Electric Motor boat from Alfred Hubbard

Very little information has survived about this device from 1924 onwards. The use of modern transistors and element base Hubbard then couldn't, so everything was organized on the basis of the 'avto' distributor, spark and a heap of wires that can be displayed on copies of photos from old newspapers.

Initial energy came from the battery and after interaction with rotor engine again returned to the battery.

What scheme was used, that is, with one or two batteries, it is rather difficult to say right now.

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Аннотация: Researching of the renewable potential energy. Energy generation and destruction based on it. The law of the energy consevation and the renewable potential energy application. Schematics and are known devices based on this theory delivered.

Уткин Владимир Михайлович : другие произведения.

The realizability of the Penrose stairs. Part 2. Electromagnetism