Title: Integrating Magnetic Force and Frame-dragging Effect (Force) to Establish a Determinative Atom Model
Wanchung Hu
PhD candidate,
National Taiwan University, Johns Hopkins University
Correspondence Email: whu@jhsph.edu; lukluk73_2006@yahoo.com.tw
Abstract
A determinative atom model is proposed considering magnetic force and frame-dragging effect. In the nuclear basal status, protons and neutrons are rotating separately in nucleus in opposite direction. All electrons are rotating in the plane of the middle of proton and neutron rotation plane. Protons’ electric force provides the centripetal force for electrons. There are three reasons for this phenomenon. 1. There is a blocking effect of neutrons to block Coulomb force between electron and proton when electrons deviate from the middle rotating plane. 2. Electrons tend to rotate in the same direction as protons or neutrons due to frame-dragging effect(force) (F=SJmW/r^2). 3. Because of Bremsstrahlung effect (P=uq^2a^2g^6/6piC, g=1/(1-Ve^2/C^2)^1/2), electrons deviating from the middle plane will receive acceleration due to frame-dragging force and radiate energy to fall into nucleus. The centripetal Coulomb force from the electron and proton’s interaction is equal to the centrifugal force due to the electron’s orbital movement. Thus, the electron has least acceleration as possible to prevent from losing energy and falling into nucleus. In addition, electron’s orbiting matches electron’s wave length and constitutes a standing wave to prevent electron from losing energy. Two electrons are in the same orbital position with different spinning direction because different spinning direction makes them to close each other like two small magnets. The magnetic force between the two electrons due to electron spin is F=(Vs^2/c^2)*Kq^2/r^2 (Vs=electron spin’s linear velocity). Magnetic force and electric force are well-balanced. For the interaction of two rotating electrons in the same orbit position, magnetic force provides attractive force against repulsive electric force. Electron linear velocity(Ve) is very close to light speed to overcome the repulsive electric force. The net force is F=(1-Ve^2/c^2-Vs^2/c^2)*Kq^2/r^2. According to Ampere’s law, paired electrons’ spin directions can also be decided. The new atom model can predict the electron position to explain atom magic numbers and release the complete limitation of principle of uncertainty. It can also solve EPR paradox and explain Pauli’s exclusion principle. Magnetic force and frame-dragging effect(force), which were neglected in Bohr’s model, provide insight into better understanding of the atom model.
PACS number: 31.10+z
The most accepted atom model currently was proposed by Dr. Bohr and by Dr. Schrodinger and Dr. Dirac subsequently [1,2]. However, many phenomenons cannot be explained by Bohr’s atom model. He used Coulomb electric force as the centripetal force to explain the rotation of electrons around nucleus. Another very important basic forces, magnetic force and frame-dragging force (spinity) , were neglected and not included in his atom model. In Schrodinger’s atom model, there are problems limiting the formation of correct atom model such as principle of uncertainty, Schrodinger’s cat, and EPR paradox [3,4]. In this study, a new determinative atom model is proposed to explain atomic phenomenon and to solve above puzzles.
According to a previous important research by Professor Ostuka T, protons and neutrons are rotating separately in an opposite direction in nuclear basal status [6]. This phenomenon can also be confirmed by the semi-empirical mass formula from liquid-drop nuclear model:
Eb=alpha(v)A-alpha(s)A^2/3-alpha©Z(Z-1)/A^1/3-alpha(a)(A-2Z)^2/A+delta(A,Z)
In the asymmetric term, the difference of neutron numbers and proton numbers will decrease the nuclear binding energy. This can be explained only when protons and neutrons are packed separately. If they are packed together, there will be no difference in the binding energy. Thus, there are proton subplace and neutron subplace in the nucleus. In addition, when proton group starts to rotate in one direction in nucleus, neutron group will need to rotate in the opposite direction in nucleus based on the conservation of angular momentum. In light atom, proton mass numbers are equal to neutron mass numbers. Thus, proton group angular velocity should be equal to neutron group angular velocity.
Frame dragging force (spinity) is a newly identified force. I propose here that “rest mass produces gravity, spinning mass produces spinity; rest change produces Coulomb electric force, spinning and moving charge produces magnetism”. Frame dragging effect was derived by Dr. Lense and Thirring to describe the procession of an orbiting object using general relativity [7]. Nobel prize winner Dr. LD Landau also derived orbiting object’s lagranian around central spinning mass using general relativity (reference). However, these professors didn’t point out that frame dragging is actually a new basic force which has close relation with gravity. When an object has mass, it will have gravity to attract its parts to the center. In order to overcome this continuously centripetal force, the object needs to spin to produce centrifugal force to balance gravity. When the object spins, spinity occurs. I propose to call this new force “spinity” because it is a combination of “spin” meaning origin of this force and “ity” meaning basic force. Frame dragging means a spinning mass can drag nearby space-time to rotate around the mass, so it is actually a force which can cause peripheral smaller object to orbit around the central mass according to the basic concept of general relativity Below is the summary of Professor Landau’s derivation from general relativity:
Vector g=(2G/c^3)Jr’/r^2 (J:central mass angular momentum ,r’=unit vector)
Lagranian L=-mc*ds/dt=L0+deltaL
deltaL=mc*g*V=(2G/c^2)mJ/r^3*V*r (V=r*W)
Thus, deltaL=(2G/c^2)mJW/r (W=relative angular velocity=Wc(central mass spinning angular velocity)-Ws(peripheral mass orbiting angular velocity))
Because deltaL=F*r
Thus, spinity F=(2G/c^2)mJW/r^2=(2G/c^2)mJV/r^3
Considering the angle theta between orbiting object and the equator plane of central spinning mass, the formula can be adjusted into:
F=(2G/c^2)mJWcosTheta/r^2=ma, S=spinity constant=2G/c^2
How do I know this formula is correct? We can actually confirm it by calculating the moon’s moving away from our earth. Our moon is moving away from our earth about 3.8cm each year by using actuate laser measurement. Current tidal force theory cannot calculate the 3.8cm correctly. I think moon’s moving away from earth is due to the effect of earth’s spinity. Because of earth’s spinity on moon, moon is accelerating in its orbiting and is moving away finally. We can use the following values:( S=2G/c^2=1.48*10^-27, Earth mass=5.9736*10^24, Earth radius=6378km, Earth spinning angular velocity=1/43200(1/sec), Moon orbiting period=27day, Angle thelta=20(cosTheta= 0.94), Moon’s distance from Earth is 384399km). After we get the acceleration a, we can calculate the moving distance by using S’=1/2at^2(t=31536000sec=1 year). Because circumference and radius has a relation (S’=2pi*r’), so r’=S’/2pi. Finally, we get the result r’=3.75149cm which is very close to the laser measurement 3.8cm. Thus, the spinity formula is correct.
While protons and neutrons are rotating separately in nucleus, we can deduct that all electrons are orbital-rotating in the middle of proton and neutron rotating plane due to the following three reasons:
1.Blocking effect of neutrons:
Because protons provide electric force for the centripetal force for electron rotation, all electrons are rotating around protons. Neutrons can only provide gravity for the electrons. Because of the great difference between electric force and gravity, neutrons will have blocking effect on the electrons when electrons deviate from the middle rotating plane. Then, electrons cannot rotate continuously around the nucleus.
2.Protons’ or neutron’s frame-dragging effect(force):
Because protons and neutrons are spinning, they will definitely produce frame-dragging force for the orbital-rotating electrons. The force is given by:
F=SJmW/r^2. (S=frame dragging (spinity) constant=1.5*10^-27, J=angular momentum of protons(neutrons)=2/5MRWc^2, M=protons(neutrons) mass, R=protons(neutrons) radium, Wc=protons(neutrons) angular velocity, W=Wc-Ws=protons(neutrons) spinning angular velocity minus electron orbital angular velocity, r=distance between electron and nucleus)
Thus, electrons will tend to rotate in the same direction as proton rotation or neutron rotation. Thus, it can help to maintain all electrons rotating in the middle plane of protons and neutrons rotating plane. We assume that electrons orbiting direction is the same as protons spinning direction first. Because electrons are orbiting near lightspeed, we need to use special relativity to adjust the relative velocity. We can deduct the net transverse force(Net Ft) when electrons are orbiting in the middle plane of proton group rotation and neutron group rotation. We will show you evidences why electrons need to move in the middle plane of proton group rotation and neutron group rotation..
Spinity F=(2G/c^2)mJW/r^2=(2G/c^2)mJV/r^3
NetFt=Fp-Fn=SmJp(Vp-Ve)/(1-VpVe/c^2)r^3 – SmJn(Vn+Ve)/(1+VnVe/c^2)r^3
(Jp=protons angular momentum, Jn=neutrons angular momentum, Vp=protons rotation linear velocity, Vn=neutrons rotation linear velocity, Ve=electron orbiting linear velocity)
When proton mass is equal to neutron mass and proton group angular velocity is equal to neutron group angular velocity, then Jp=Jn and Vp=Vn and the formula becomes:
NetFt=SmJp*2Ve[(Vp^2/c^2)-1]/(1-Vp^2Ve^2/c^4)r^3
Atom nucleus spins in a angular velocity equal to 10^20(1/sec) to 10^21(1/sec) and Bohr radius for minimal electron orbiting is 10^-11 m.
Vp=Vn=W*r=10^9~10^10m/sec>lightspeed 3*10^8m/sec
Because lightspeed is the maximal information transmission speed, Vp should be near equal to and very slightly less than lightspeed c. Thus, (Vp^2/c^2)-1~0 and NetFt~0
3.Proton’s Bremsstrahlung effect:
Because of the frame-dragging effect, electrons deviating from the middle rotating plane will receive Bremsttrahlung effect. The Bremstrrahlung formula is given by:
P=uq^2a^2g^6/6piC, g=1/(1-Ve^2/C^2)^1/2 (acceleration a is parallel to velocity)
The frame-dragging effect of spinning protons or neutrons will provide acceleration on the electrons. Because protons and neutrons are rotating in the opposite direction, the only possibility that electrons won’t be affected by frame-dragging is that electrons are in the middle plane of protons and neutrons rotating plane. If electrons deviate from the middle plane, they will receive acceleration due to either protons’ frame dragging force or neutrons’ frame dragging force, the electrons will then start radiation and fall into nucleus. Only when electrons rotate in the middle plane, the atom can maintain stable.
Thus, we know that all electrons are rotating in the middle plane of protons and neutrons rotation. According to Bohr’s deduction, electrons are rotating around protons because protons provide electric force as centripetal force. And the centripetal Coulomb force is equal to centrifugal force produced by electron’s orbital rotation movement. Viewing from an inertial reference frame, we find that there is a centripetal force during electron’s orbital rotation. However, we know the example of general relativity’s equivalence principle. Thus, the centripetal force observed from inertial reference frame is actually a centrifugal force acted on the electron itself(acceleration reference frame). In order to maintain the electron’s orbit, the centripetal Coulomb force must be equal to the centrifugal force due to electron’s orbit movement. The balance is very important because the electron’s net acceleration then is zero. Thus, the electron won’t radiate energy and fall into nucleus. We can deduct net inward/outward force: Net Fio.
Fc=KQq/r^2, (K=Coulomb constant=9*10^9, Q=proton charges, q=electron charges, r=distance between electrons and protons)
Net Fio=KQq/r^2-mrW^2= KQq/r^2-mV^2/r=0, (W=electron’s orbital angular velocity)
When angular momentum is quantized, then the formula is given following:
r=nh’/mVe, (n=major quantum number,h’=reduced planck constant=1*10^-34, m=electron mass, V=electron orbital linear velocity)
Thus, we can get:
KQq/r=mVe^2
KQq/nh’=Ve
For example: In hydrogen atom with n=1(innermost orbit) and Q=q=1.6*10^-19coulomb, the value Ve becomes:
Ve=2.3*10^6m/sec
Thus, electron orbital linear velocity is less and close to light speed (3*10^8m/sec).
Even the largest atom’s electron linear velocity is smaller than lightspeed. For the atom118, the Ve becomes(Q=118q and n=1):
Ve=118*2.3*10^6=2.7*10^8m/sec
Because Ve is still smaller than lightspeed, the formula 1-Vp^2Ve^2/c^4 is not equal to zero. Because the denominator is not zero and nominator is zero, the net transverse force is near zero.
Magnetic force plays an important role in the new atom model. In this new atom model, electric force and magnetic force are serving as two balanced force to control electron movement. In this deduction, two electrons rotate as a pair around the nucleus. For the interaction of rotating electrons in the same orbit position, magnetic force provides attractive force against repulsive electric force. The orbital rotation of one electron can produce magnetic field to the other coupled electron by Biot-Salvart Law:
B=(Ve/c^2)xE, E=Kq/r^2, (B=magnetic field induced by one electron, V=linear velocity of electron, x means cross product, E=electric field induced by electron,r=distance between the paired electrons)
The direction of B is vertical to the direction of Ve and the direction of E
The magnetic force on the rotating electron from the other paired electron is:
Fm=qVxB=(Ve^2/c^2)(Kq^2/r^2), (B=magnetic field induced by one electron, Ve=linear velocity of the other electron, x means cross product, q=electric charge of the electron).
According to Coulomb’s magnetic law, the magnetic force induced by two spinning charges is:
Fm=(u/4pi)*qV*qV/r^2=(K/c^2)q^2*V^2/r^2
If the paired electrons are spinning in the opposite direction, the magnetic force between them is attractive.
We can deduct net in-between force Fib:
Net Fib=Fc-Fm=(1-Ve^2/c^2-Vs^2/c^2)Kq^2/r^2 (Vs=electron spin linear velocity)
Electron orbital linear velocity (Ve) is very close to light speed to overcome the repulsive electric force. Thus, the net force between the two electrons is close to zero. Thus, the repulsive force between the two electrons is minimized. Thus, even Ve and Vs both are less than lightspeed c, Ve^2+Vs^2 can be still larger than c^2. Because the two paired electrons spin in the different direction, they can be coupled together like two small magnets. Thus, it can explain Hund’s law why unpaired electrons are arranged in an atom first.
Pauli’s exclusion principle is saying that no two electrons have the exactly the same quantum number [5]. If two electrons are in the same position, their spinning direction must be different. However, Pauli’s exclusion principle suffers from EPR paradox even the principle is effective. The EPR paradox is saying that: If we move away one of two paired electron to a far away distance. If we check one electron’s spinning direction, the other electron’s spinning direction can be decided at once. Thus, it disobeys the principle of locality of physics. In this new atom model, we infer that two electrons are in the same orbital position rotating around the nucleus. In addition, one electron is a little bit above the electron orbital rotational plane and the other one is a little bit below the electron orbital rotational plane.
Electron spin will let them become a small magnet. The spinning direction can decide the direction of magnetism. Thus, the two electrons have different spinning direction, so they can couple together as two small magnets. Thus, EPR paradox is solved. The different spinning direction of two electrons is because they use it to couple each other in the same orbital position. If the two electrons are separated, the spinning direction of the two electrons will be changed. It can explain why Pauli’s exclusion principle is effective.
From Bohr’s deduction:
Etotal=(-13.6eV)1/n^2
Based on the Ampere’s law, we can even know the spinning direction of the two paired electrons. If one electron is orbiting around nucleus, it will become a tiny current. Thus, it will produce a magnetic field around this tiny current according to Ampere’s law. In order to get the lower energy as possible, the other paired electron must be aligned to this magnetic field induced by first electron. Thus, this electron’s spinning direction is decided. In addition, the second electron also produces a magnetic field for the first paired electron. The first electron also needs to align the magnetic field induced by the second electron. Thus, the spinning directions of the two paired electrons are decided. Based on Ampere’s law, the two electrons’ spinning directions are opposite.
From the Etotal equation, we can infer that the relationship between radius and major quantum number (n). When n=1, r is called Bohr radius(r=1^2). When n=2, r=2^2=4 Bohr radius. When n=3, r=3^2=9 Bohr radius. When n=4, r=4^2=16 Bohr radius. We can also infer the radius of electron rotation. Form inner to outer orbit, the radius should be like 1, 4, 9, 16, 25, 36. Two electrons can be in the same orbital position. The circumference is 2r, so the magic numbers can be predicted: 2, 8, 8, 18, 18, 32, 32. It is because that one paired electrons are arranged in a 2 distance, and then another paired electrons are arranged in a distance.
According to the previous researches, four “quantum numbers” have been identified in atom model. Our new model is also consistent with the four quantum numbers. The first major quantum number n is used above to describe the electron radium. The second angular momentum quantum number p can be explained by the degree of ellipse orbits of our new atom model. The magnetic quantum number m can be explained because electrons can rotate in two possible direction(the one is the same as protons rotation direction, the other is the same as neutrons rotation direction) and produce different magnetic moments. The four quantum number s can be explained because paired electrons have exactly two kinds of spinning directions in the atom. Our new model has the advantage without the disadvantage of quantum mechanics.
Heisenberg’s principle of uncertainty said that we cannot predict the exact electron position in the atom because photo will interfere electron’s orbit. Then, Dr. Schrodinger proposed his atom model by using wave probability function. However, the probability has severe limitation. It causes a paradox like Schrodinger’s cat that saying the strangeness and logical problems of the quantum mechanics. And, it is very difficult to imagine electrons can really rotate in strange orbital shapes such as dumbbell or double dounut from Schrodinger’s atom model. It is more reasonable that electrons are rotating in a circular or ellipse shape. Quantum mechanics needs Copenhagen interpretation saying that wave function collapse during observation. It says that subject’s measurement affects object’s physical law and fact. It is not realism and is not truth. In addition, quantum mechanics requires to assume absolute and discontinuous time which should be discarded according to special relativity. Quantum mechanics also allow to disobey conservation of energy which is the most fundamental law of physic. This new atom model proposed here let the atom go back to the classical physics. Principle of uncertainty is a limitation of observational physics, but it cannot be viewed as a law to governing real atom orbit. I believe this new atom model will provide an important insight into the current physics.
References
[1] N. Bohr, Nature 92, 231 (1914)
[2] N. Bohr, Philosophical Magazine 26,1 (1913)
[3] W. Heisenberg, Zeitschrift fur Physik 43,172 (1927)
[4] A. Einstein, B. Podolsky, and N. Rosen Phys Rev 47:777 (1935)
[5] D.J. Griffiths, Introduction to Quantum Mechanics (2nd ed) (2004)
[6] T. Otsuka, Phy Rev Let 71,1804 (1993)
[7] B. Mashhoon, F. W. Hehl, and D. S. Thesis, General Relativity and Gravitation 16, 711 (1984)
[8] L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields (1975)