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Research on Momentum Order **iLATEST VERSIONj**

By KUBOTA Hidefumi

(As specified in the homepage, I exhibited this contents onto the Net on
5th May, 2006.)

index

Chapter 1: The basic theory

Section 1: Bose Einstein condensation and the permanent current

Section 2: Momentum order in the direction of electric current

Section 3: Momentum order in the direction of electromagnetic force

Section 4: The phenomenon which the momentum order in the direction of electromagnetic force causes

Section 5: The phenomenon which the ripple current of high frequency causes

Chapter 2: How to experiment

Chapter 3: About theoretical questions

Chapter 4: The utility of my device

Chapter 5: At the end

Chapter 1: The basic theory

Section 1

Bose Einstein condensation and the permanent current

As for the superconductive condition, it is possible to assume that Bose Einstein condensation is formed. It is thought that the motion of center of gravity of each Cooper pair which composes a permanent current is in the orderly condition which has momentum with a same size like the motion of center of gravity of each atom which forms Bose Einstein condensation. An electron is a fermion and follows Pauli's principle. However, a Cooper pair is supposed to be a kind of Bose particle and to be able to get condensed to a same momentum. This condensation of electron pairs secure the full conductivity of electric resistance zero when becoming a superconductive condition.

Let's think of the momentum of a Cooper pair which composes a permanent current in the direction through which the permanent current making a strong magnetic field of a superconductive magnet flows (hereinafter, abbreviate with " the direction of electric current "). The motion of Cooper pairs in this direction of electric current is the substance of the permanent current. Because of the antiparallel motion of super electrons of Cooper pairs, the momentums of two super electrons which compose a Cooper pair in the ground state are supposed to bePand -P. The momentum of a super electron by adding voltage to the Cooper pair isQ. This Cooper pair has a momentum 2Q. This 2Qconvey the permanent current.

(P+Q)+(-P+Q)=2Q

It is supposed that a magnetic field is given to this permanent current. According to the Fleming's left hand rule, with an outer magnetic field, Lorentz force arises in the direction perpendicular to the direction through which the electric current flows (hereinafter, abbreviate with " the direction of electromagnetic force "). Lorentz force by this magnetic field acts on the permanent current and the momentums of super electrons change. The strength of Lorentz force is proportional to the strength of the magnetic field and the strength of the permanent current. The change of momentum of the super electron which has momentumPis supposed to be˘P. Then, the change of momentum of the super electron which has momentum |Pis supposed to be |˘P. Since the direction of momentumPand -Pis opposite, the directions of Lorentz force acting on super electrons become opposite. Then, the change of momentumQis supposed to beR. The momentum of the Cooper pair in this case becomes 2Q+2R.

(P+˘P+Q+R)+(-P-˘P+Q+R)=2Q+2R

Since the change of momentumPand -Phas been canceled by the antiparallel motion of super electrons, Lorentz force to changePand -Pis canceled as the whole Cooper pair.@However, it is thought that the change of momentumQremains and that this acts on the superconductive coil as electromagnetic force.@Then, to form the condensation of electron pairs, 2Q+2Rof each electron pair must have a same size.@

@Therefore, it is thought that momentum order is effective in both the direction of electric current and the direction of electromagnetic force. Momentum order is that the momentum of Cooper pairs change from a same momentum into the other same momentum and that all pairs change all together when changing.

Section 2

Momentum order in the direction of electric current

First, it is thought of the momentum of Cooper pairs which compose a permanent current in the direction of electric current.

It is supposed that momentum order isn't effective in both the direction of electric current and the direction of electromagnetic force. Since momentum order isn't effective in the direction of electric current, 2Qof each electron pair has different size. Then, it is supposed that a uniform magnetic field is added to this permanent current. Since the magnetic field is uniform, momentum 2Rin the direction of electromagnetic force is proportional to the size of momentum 2Qin the direction of electric current. The size of momentum 2Q+2Ras this whole electron pair is proportional to the size of momentum 2Qin the direction of electric current. Since it is thought that this 2Qof each electron pair has the different size, the size of momentum as a whole is different. Under this condition, the momentum of each electron pair as a whole doesn't have a same size and the condensation of electron pairs can't be formed. Therefore, it is thought that the momentum 2Qof all electron pairs has the same size.

As for a permanent current, an electric current of a constant value flows in a constant direction permanently. It is thought that to form the motion of this constant value each Cooper pair is in the orderly condition that not only the momentum of each Cooper pair as a whole but also the momentum of each Cooper pair in the direction of electric current has a same size. Then, when Cooper pairs which have a same momentum in the direction of electric current change the momentum into another same momentum, all pairs change them all together. When changing apart, Cooper pairs receive resistance while the momentum changes and full conductivity would collapse. It is thought that these secure full conductivity. Therefore, in the direction of electric current, momentum order is effective.

Section 3

Momentum order in the direction of electromagnetic force

Next, let's think of the momentum of Cooper pairs which compose a permanent current in the direction of electromagnetic force.

So far, as for macro quantum effect " momentum order " which takes place with the superconductivity, the direction of electric current has been placed in the mind. It should be thought in the direction where electromagnetic force arises, too.

It is supposed that momentum order is effective in the direction of electric current and that momentum order isn't effective in the direction of electromagnetic force. It is attempted to add an uneven magnetic field to the permanent current of Cooper pairs which have momentum 2Qwith a same size in the direction of electric current. Since the momentum in the direction of electric current has the same size, the size of Lorentz force is proportional to the strength of the uneven magnetic field at some part. According to the strength of the uneven magnetic field of each part, the size of momentum 2Rin the direction of electromagnetic force is different. Since the momentum 2Qin the direction of electric current has the same size, according to the size of momentum 2R, the size of momentum 2Q{2Rwhich electron pairs as a whole have would be different. Under this condition, the momentum which electron pairs have as a whole doesn't have a same size, and the condensation of electron pairs would not be formed. Therefore, it is thought that the momentum 2Rhas a same size. It is necessary to think that momentum order is effective in the direction of electromagnetic force, too.

It is thought that the momentum 2Rby an outside magnetic field follows the momentum order. That is, it is thought that the momentum 2Rof Cooper pairs which compose a permanent current has a same size and that the momentum changes into a same size all together. The momentum order is extended and applied to the direction of electromagnetic force perpendicular to the electric current. By thinking at it this way, the momentum 2Q+2Rof a Cooper pair has a same size in this case, too, and the condensation of electron pairs that Cooper pairs get condensed to a same momentum is formed without a problem.

Therefore, the motion of an electron pair follows the momentum order in the direction of electromagnetic force, too, and conveys electromagnetic force to the material of a superconductive coil.

Let's think of the momentum order in a superconductive magnet by the wave motion of center of gravity of electron pairs. It is thought that in the direction of electric current they form a standing wave whose length of bowstring is equal to the full length of a wire which composes a superconductive coil. The positive integral multiple of wavelength agrees with the length of the bowstring. In the same way, it is thought that in the direction of electromagnetic force they form a standing wave whose length of bowstring is equal to the diameter of the wire which composes the superconductive coil. But, the positive integral multiple of half wavelength agrees with the length of the bowstring. Since the motion of center of gravity of electron pairs is quantized both in the direction of electric current and the direction of electromagnetic force, the motion of center of gravity of electron pairs as a whole is quantized. Then, it is thought that since the momentum which the motion of center of gravity of electron pairs have agrees in the direction of electromagnetic force in addition to the direction of electric current, the momentum which the motion of center of gravity of electron pairs as a whole agrees with a quantized same value and the condensation of electron pairs is formed.

[ Figure 1 ]

An example of simultaneous change of momentum by a magnetic field

Section 4

The phenomenon which the momentum order in the direction of electromagnetic force causes

It is attempted to think of the case to give an outer magnetic field which changes temporally to a superconductive magnet from now.

It is thought that since the momentum order is effective in the direction of electromagnetic force, the following phenomenon will happen. That is, when adding a moving magnetic field which doesn't suit the motion following the momentum order, owing to the regulation by the momentum order, the motion of center of gravity of Cooper pairs acted on by Lorentz force could not change the momentum in the direction of electromagnetic force. It is thought when the moving magnetic field changes temporally and gives magnetic force with different sizes to each place of the superconductive coil, the impulseiforce~timejby Lorentz force which should change the momentum of Cooper pairs of a permanent current can not change the momentum. It is because if supposing that the motion of center of gravity of a Cooper pair changes its momentum just as according to the impulse by this magnetic field, the momentum 2R of Cooper pairs by the outer magnetic field have different sizes with each Cooper pair. Therefore, it is thought that the momentum order regulates 2R's taking such different values and doesn't allow the impulse by Lorentz force to change the momentum. However, it is thought that there is a limit in the regulation by the momentum order, too.

First, it is attempted to think spatially at some time. It is thought of the case where the moving magnetic field give a magnetic field which has different but and above a fixed strength to the motion of center of gravity of electron pairs in each place of the superconductive magnet. In this case, since Lorentz force by the coordinate magnetic field and below the fixed strength is not contrary to the momentum order, there is no problem if the impulse by this Lorentz force changes into the momentum. On the other hand, the momentum order is disturbed when the impulse by Lorentz force changes into momentum just as according to the magnetic field beyond the fixed strength. Therefore, it is thought that the impulse by the Lorentz force of the magnetic field beyond the fixed strength does not have to change into momentum.

Next, it is attempted to add temporal change and think of it. It is thought of the case where the influence of Lorentz force by a magnetic field reaches an impulse and above a fixed size in a fixed time about each electron pair in each place of the superconductive magnet. By this impulse, the momentum and above the fixed size can take place in each electron pair in each place of the superconductive magnet. Therefore, since the coordinate momentum and below the fixed size is not contrary to the momentum order at all, it is thought that each electron pair changes momentum only by the coordinate momentum.

It is because an electron pair is a quantum that it is thought of the fixed value of both impulse and momentum by the impulse. The momentum of one electron pair necessary to change into the momentum of one more quantum number from some momentum in the direction of electromagnetic force is supposed to be "k". It is because the impulse becomes not be able to change the momentum of center of gravity when the impulse doesn't change into the momentum of center of gravity during the fixed time to think of the fixed time. This fixed time is supposed to be "t" second. It is thought that the impulse not having been able to change the momentum cannot change into the momentum of center of gravity of electron pairs but changes into the energy of not electron pairs but each electron. It is thought that specifically the energy is the one of the antiparallel motion of each electron, i.e. the increase ofPand the vibration of each electron. Since it cannot change the motion of center of gravity of an electron pair, it is thought that it changes intoPof each electron and the increase of vibration which can change. Then, it is thought that this energy is slipped outside as heat energy through the scattering of each electron.

It is thought that the impulse and abovekmust be given to all electron pairs in the fixed timetfor the momentums of all electron pairs to change the condition from quantum number 1 to 2. If an electron pair to receive the impulse belowkduring thetsecond exists, the change of quantum number to 2 doesn't take place. It is to think about the nexttseconds. If an electron pair to have received the impulse whose total during thetseconds and the nexttseconds is belowkexits, all the impulses which electron pairs received during the previoustseconds change into the energy of each electron as thetseconds have passed. Then, if an electron pair to have received the impulse belowkduring the 2tseconds exists, the impulse never accumulates in time and the change to quantum number 2 doesn't take place constantly.

Next, it is thought of the case to change into the condition ofn+m("n" and "m" are positive integers) from the condition of the quantum numbern.

As for the change fromnton+m, if there is an electron pair which received only the impulse belowmk, for the momentum order to regulate, the change inton+mdoesn't take place. To change the arbitrary quantum numbernto the arbitrary quantum numbern+m, for the momentum order to regulate, the impulse and abovemkmust be given to all electron pairs.

It is to think of the least impulse given to a certain electron pair in all electron pairs during the fixed timet. It is supposed that this least impulse doesn't fill necessary size (m+1)kto change the quantum number ton+m+1 but fill necessary size mk to change the quantum number ton+m. In this case, since the impulse and abovemkis given to each electron pair in the fixed timet, each electron pair changes the momentum into the quantum numbern+m. However, since the least impulse which an electron pair receives in the fixed time t doesn't fill (m+1)k, for the momentum order to regulate, the change into the quantum numbern+m+1 doesn't take place. The possibility that the impulse beyondmkgiven to each electron pair in the timetchanges into the energy of each electron arises.

It is to think about the nexttseconds. If an electron pair to have received the impulse whose total during the previous timetand next timetis below (m+1)kexists, all the impulses beyondmkwhich electron pairs received during the previous timetchange into the energy of each electron as thetseconds have passed. Then, if an electron pair to have received the impulse below (m+1)kduring the 2tseconds exists, the impulse never accumulates in time and only the change of quantum number to +mtake places. Therefore, all the impulses beyondmkhave changed into the energy of each electron, but the change to +mby the impulse ofmkmay accumulate and can generate electromagnetic force.

As described above, by the regulation by the momentum order, the impulse may change into the heat energy without changing into the momentum of motion of center of gravity and the cancel of electromagnetic force may take place by the impulse which was slipped outside as the heat energy.

[ Figure 2 ]

Waveform of a ripple current

Section 5

The phenomenon which the ripple current of high frequency causes

Let's think of the case where a normal conductor is piled up and fixed on the superconductive magnet and make a ripple current of very high frequency (the waveform is like figure 2) flow through the loop of the normal conductor with taking a coil. The wavelength is made equal to the length of a round of the loop. This ripple current flows and changes its strength temporally from 0 to a fixed size and can give a magnetic field with various strength to each place of the superconductive coil.

It is to think of the speed of the ripple current and the speed of the permanent current. Since the ripple current is made from an alternating current, it may think that the speed of mountains of the ripple current is the velocity of light. On the other hand, since the speed of the permanent current is the one of electron pairs which receive Lorentz force, it becomes later than the speed of the mountains. However, it is thought that the speed of the ripple current faster than the one of electron pairs doesn't make a problem. While the magnetic field of the ripple current gives Lorentz force with different size to each electron pair, it passes by electron pairs. Then, the strength of Lorentz force which electron pairs of the permanent current receive from the ripple current is different according to the strength of the ripple current. Therefore, the regulation by the momentum order works.

And, the ripple current flows intermittently. The time when the electric current flows through and the time when the electric current doesn't flow through appear alternately and they are the same. Therefore, since the wavelength is equal to the length of the loop, in each moment, as for electron pairs in the half part of the superconductive magnet, Lorentz force to receive is zero. Since the impulse with the size zero of Lorentz force exists in each moment, the regulation by the momentum order works. Then, during the time of half period, an electron pair to receive zero of Lorentz force always exists. It is thought that the time of half period is longer than 2t.

All the impulses to act on each electron pair do not reach to the fixed size, and abovesk("s" is equal to or more than 1 integer which is comparatively small) in the fixed time of 2t. The impulse (and abovesk) to make the momentum of an electron pair in the direction of electromagnetic force and above the fixed size does not accumulate. It is thought that the impulses given to electron pairs in each place never reach and above the fixed size (and abovesk) in the 2tbecause of the characteristic of the ripple current. Therefore, it is possible for electron pairs and the permanent current of the electron pairs to change momentum in the direction of electromagnetic force only for (s-1)k. Since an electron pair to have received the impulse with the size belowskduring the 2tseconds exists, the impulse never accumulates in time and the change of momentum equal to the impulse and aboveskdoesn't take place constantly. Then, since it takes time until it accumulates even if the change of momentum for (s-1)kaccumulates temporally and electromagnetic force arises, it arises only intermittently. Then, the electromagnetic force of the superconductive magnet which should arise by the material of the superconductive coil's receiving the momentum from electron pairs doesn't arise or is very small.

As for the ripple current to think of here, it is thought that the time when the Lorentz force which electron pairs receive is zero, i.e. the half period of the ripple current is longer than the 2t. Therefore, it is expected thatsis 1, i.e. the change of momentum is continuously zero.

It is thought that the phenomenon which the ripple current of this very high frequency causes to the superconductive magnet is applied to the industrial technology.