Planets And Electromagnetic waves
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Printed in India
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Planets And Electromagnetic waves By Dr. C. Ganesa Moorthy M.Sc., M.phil., PhD., P.G.D.C.A Professor of Mathematics Alagappa University
& G. Udhaya Sankar M.Sc., Department of Physics Alagappa University
IDEA PUBLISHING WWW.ideapublishing.in
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About the authors Dr. C. Ganesa Moorthy is working as a professor in department of mathematics, Alagappa University, and has academic experience about 34 years in teaching and in research. He has published 57 articles in highly reputed journals and published 2 books. He solved a 50 year old open problem for his doctor of philosophy degree, and the solution was published in “Mathematika” in 1992. He is being a renowned theorist in India.
[email protected]
G. Udhaya Sankar is a most promising young scientist in India. He got his B.Sc degree (Physics) in Thiagarajar College, Madurai, and he got his M.Sc degree (Physics) in Alagappa University. Now, he is being a research scholar in Alagappa University. He is very much interested in theoretical physics as well as applied physics and he has published 15 research articles in International Journals.
[email protected] https://www.facebook.com/udhaya.sankar.1848
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About the book Explanations have been given for some breakthroughs in fundamental physics, more specifically in the theory of Electromagnetic Waves. First breakthrough: Only one of the waves, electric field wave and magnetic field wave, emerges as component of an electromagnetic wave. Second breakthrough: All electrons in any rotating planet cause the existence of the magnetic field in the planet. Third breakthrough: Rotating velocity, orbital velocity, escape velocity, and critical velocity are the major factors for existence of atmospheres and winds in planets. Fourth breakthrough: Maximum possible diameter of molecules in our universe may be at most of order 10 power (-7) meters. Explanations have been given with many figures.
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Preface There was a need to provide clarifications for the arguments given in the following essays of C. Ganesa Moorthy, G. Udhaya Sankar, and G. RajKumar. 1. Rotating bodies do have magnetic field. 2. Global magnetic field strengths of planets from a formula. 3. What is the polarity of an electromagnetic wave? 4. A velocity index for existence of atmosphere in a planet. 5. A design for charging sections of electrostatic precipitators by applying a law for electric field waves. 6. LIGOs detected magnetic field waves; not gravitational waves. 7. Simplified interpretation for Einstein’s energy mass relation. 8. Two expressions for electrostatic forces and for magnetic forces to classify electromagnetic waves. 9. Why do distant planets have speedy winds? 10. Temperature of black holes and minimum wavelength of radio waves. This book provides some possible explanations for the arguments used in these articles. An interpretation for Einstein’s energy-mass relation is explained. An interpretation for Planck’s equation ix
for energy is explained. Reasons for existence of magnetic fields, atmospheres and winds in planets are explained. A method to find maximum possible diameter of molecules in our universe is explained. A method to find an average diameter of an electron, a proton and a neutron is explained. Its direct relations and indirect relations with electromagnetic waves are explained. A justification for an electromagnetic wave to have only one component, either electric field wave or magnetic field wave, is explained. A method, to find a length number w=1.063 mm (approximately) such that every electromagnetic wave with wavelength less than w is an electric field wave and such that every electromagnetic wave with wavelength greater than w is a magnetic field wave, is explained. The penetrating capacity of a magnetic field wave with high wavelength is explained. A reason for observations of magnetic field waves with long wavelengths by LIGOs is explained. Students who know some fundamental physics can read this book. Only differentiation and integration are required for mathematical part. The portion about the least squares principle given in chapter 1 is not applied and a reader may skip that portion. Although big size planets and small size electrons have been discussed, the main aim of this book is to provide explanations for the existence of the length number w = 1.063 mm (approximately), in connection with electromagnetic waves.
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Contents Chapter -1 :: Laws of Newton and Kepler
1-6
Chapter -2 :: Energy – mass relation of Einstein
7-12
Chapter - 3 :: Solar system and atom
13-16
Chapter- 4 :: Magnetic fields of planets
17-28
Chapter- 5 :: Atmospheres and winds
29-42
Chapter- 6 :: Electromagnetic waves
43-48
Chapter- 7 :: Stored and released energies
49-54
Chapter- 8 :: Gravitational waves
55-60
Chapter- 9 :: Electric field waves and magnetic field waves
61-64
Chapter- 10 :: A law for light waves
65-72
Chapter- 11 :: A classification for electromagnetic waves
73-76
Chapter- 12 :: Cosmic Microwave Background and classification of electromagnetic waves
77-80
Chapter- 13 :: Diameters of molecules
81-86
Chapter- 14 :: Approximate diameters for electrons, protons and neutrons
87-90
Chapter- 15 :: Different Planck’s constant for Magnetic field waves
91-94
Bibliography
95-96
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C. Ganesa Moorthy & G. Udhaya Sankar
Chapter 1 Laws of Newton and Kepler Theoretical physics cannot omit the laws of Newton. Let us also begin with the laws of Newton, namely, the three laws of motion and the law of gravitation. All of them were known directly or indirectly before the period of Newton. But the mathematician cum physicist Sir Issac Newton (1642-1727) could understand that they are the fundamental laws of nature. The mathematician Newton developed calculus and he was not particular in claiming that he did it. The physicist Newton observed these laws by using his logical thinking as well as his mathematical thinking. The laws can be expressed in terms of mathematical symbols even though they were derived indirectly from known data. There are methods in mathematics to derive such rules. For example, let us consider the following method based on least squares principle in mathematics to derive mathematical equations by using data. Let us assume that some intelligent student guessed that there is a rule in the form: y = F(a,x), where „x‟ is the independent variable, „y‟ is the dependent variable, „F‟ is a fixed function, and when „a‟ is the parameter which is 1
Planets and electromagnetic waves
unknown and which is to be determined. Suppose that the student got the following data: (x1, y1), (x2, y2), … (xn,yn). This means that the value xi for x gives an observed value yi for y, for each i = 1, 2, … n. The student has to find a suitable „a‟ so that these data approximately satisfy the expression y = F(a,x). Here yiF(a,xi) gives an error for the i-th observation when y = F(a,x) is used, because yi is the exact observed value for y when F(a,xi) is the value determined for y from the rule y = F(a,x). Then ∣yi-F(a,xi)∣ gives an absolute error for the i-th observation. So, the student has to find „a‟ such that the sum of the absolute errors∑ ( ) is minimized. It is possible to find such „a‟ by trial and error method by using a computer. In a period when a computer was not available, mathematics proposed another approach to find „a‟. Instead of minimizing the sum of the absolute errors, let the student minimize the sum of the squares of errors∑ ( ) . So, the student has to find „a‟ which minimizes the sum of the squares of the errors, when the student follows the least squares principle. The calculus helps the student for this purpose. To minimize the sum of the squares, the derivative with respect to „a‟ should be zero. So, ∑
(
)
(
)
.
The values of (xi,yi) may be substituted and equation may be solved by the student to determine value for „a‟. Once the value „a‟ is determined, student gets the rule y=F(a,x). This means that 2
the the the the
C. Ganesa Moorthy & G. Udhaya Sankar
student can determine the value y* for y without conducting experiment corresponding to the conditional value x* for x. There are some classical methods in mathematics to derive rules from data. As it was mentioned in the previous paragraph the student should be able to guess „F‟. This means that just mathematical approaches are not sufficient to derive rules of nature. Newton was a brilliant researcher who could understand the nature of rules, beyond mathematics. First law of motion: Any body continues in its state of rest or of uniform motion along a straight line unless it is compelled by an external force to change that state. Second law of motion: The rate of change of momentum of a body is directly proportional to the external force applied on it and the change in momentum takes place in the direction of the force. Third law of motion: For every action there is an equal and opposite reaction. Law of gravitation: Every particle of matter in the universe attracts every other particle with a force which is directly proportional to the masses and 3
Planets and electromagnetic waves
inversely proportional to the square of the distance between them. We have to consider the laws of Kepler which were derived before the period of Newton. The following sentences may be found in section 21 and its appendices in the book [G.F. Simmons, (1972)]. “When the Danish astronomer Tycho Brahe died in 1601, his assistant Johannes Kepler (1571-1630) inherited great masses of raw data on the positions of the planets at various times. Kepler worked incessantly on this material for 20 years, and at last succeeded in distilling from it his three beautifully simple laws of planetary motion, which were the climax of thousands of years of purely observational astronomy.” “Kepler’s first law: The orbit of each planet is an ellipse with the sun at one focus.” “Kepler’s second law: The radius vector from the sun to a planet sweeps out equal areas in equal intervals of time.” “Kepler’s third law: The squares of the periods of revolution are proportional to the cubes of their mean distances.” “Show that Kepler‟s first two laws in the form of equations (8) and (15) imply that m is attracted toward 4
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the origin with a force whose magnitude is inversely proportional to the square of r. This was Newton‟s fundamental discovery, for it caused him to propound his law of gravitation and investigate its consequences.” “In his dynamics and celestial mechanics Newton achieved the victory for which Coopernicus, Kepler, and Galileo had prepared the way.” Let us observe the followings from the previous comments given by G.F. Simmons. Only because of incessant work of Kepler, he had an achievement within 20 years. This period was a very short period in the beginning of the seventeenth century, when there was no sophisticated computer for quick calculations. The Kepler‟s laws were “beautifully simple” in nature. Although things are complicated in nature, one appreciates the laws of nature only when they are simple. Newton got ideas from these Kepler‟s laws to derive the Newton‟s gravitational law. Although the Kepler‟s laws were verified by Kepler by using data, he could guess laws before he framed them. All the things observations.
depend on data
The final conclusion is that observations implied the theory.
5
obtained
experiments
from and
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Chapter 2 Energy – Mass Relation of Einstein Mass is equivalent to energy. Every physicist agrees to this statement. But, only few can give meaning for this statement. What is the interpretation for energy-mass equivalence relation of Einstein? When this question was asked to a professor of physics, the answer given by him was the next sentence. If a mass M having a linear velocity c collides on a non-moving body then the complete energy released by the mass M on the body is Mc2. Let us interpret the same in a different way with an agreement to reserve the notation c for the velocity of light in vacuum. Before modifying his answer let us recall the fundamental assumption in the theory of special relativity: No particle moves with a speed that is greater than the speed of light c. It is understood that no energy wave also move in a speed that is greater than the speed of light c. Here c refers to the speed of the light in vacuum. Suppose an object with mass M is radiated by means of elementary particles with elementary masses dm. Let each elementary mass dm reach the maximum possible velocity c. Then the total energy of all 7
Planets and electromagnetic waves
elementary masses dm released on different bodies is Mc2. This interpretation is equivalent to the one given by the professor of physics, because when all the elementary masses dm are collected together to form the mass M, the corresponding energies of dm should also be collected to consider the energy released by M when it moves with speed c. The meaning of the phrase “total energy of all elementary masses” is to be explained by means of mathematical expressions. Sometimes, words are not sufficient to understand a physical meaning. Let M = initial mass of an object at time zero, m = mass of the object at a general time, v = velocity of the object at a general time, F = force applied on the object, x = distance travelled by the object at a general time, t = a general time, c = velocity of light in vacuum (a constant), and E = total energy that is to be derived from M. Before proceeding further, let us recall the Newton‟s second law of motion in the conventional form ( ) . It is not assumed in the form . (
)
The form is also usually assumed in the special theory of relativity. With this assumption, let us 8
C. Ganesa Moorthy & G. Udhaya Sankar
proceed further for a derivation of the Einstein‟s energymass relation E=Mc2. Note that (
)
. With v = c, a constant, this relation becomes
.
So, if E is the total energy emitted through radiation when the initial mass M is reduced to the zero mass, then the following relations are true, because E coincides with the corresponding work done. ∫
∫
.
This completes a derivation for the Einstein‟s energy-mass equivalence relation E=mc2. This derivation is based on the interpretation by means of radiation. There are articles which use this type of interpretation (for example [A. Rainville et. al., (2005)]). It seems that an interpretation as well as a derivation be completed. But, it is not so, because one has to understand more about the word “equivalence”. Suppose a wooden piece is burnt. Some parts of the mass of the wooden piece are converted into heat energy as well as light energy. Although it is not verified, let us assume that sun light energy is converted as some parts of masses in plants. So, there is a possibility to convert energy into a mass (or a matter). Scientists claim that 9
Planets and electromagnetic waves
fusion happens in the sun, and energies are converted into masses. There are articles which claim through particle collisions that new particles are generated (for example [O.J. Pike, et al., (2014)]), that is, kinetic energies of colliding particles create new matters. Thus masses may be converted into energies and energies may be converted into masses. Practically, not all masses can be converted into energies and not all energies can be converted into masses. However, it is assumed with an imagination that all masses are converted into energies and all energies are converted into masses. The word “equivalence” also assumes theoretical conversions of masses into energies and energies into masses. Why should we believe that the mass-energy relation of Einstein is correct? Let us modify the question. Why should we believe that no particle can move with a velocity greater than c? If the fundamental assumption in the special theory of relativity fails to be true, then one may not accept the formula, because there is no experimental verification for exactness of this formula. However, present technologies use variations of electric fields and of magnetic fields on charged particles. These variations have at most speed c. So, present technologies are not sufficient to create a velocity in a particle that is greater than c. One more question arises. Lorentz transformation is derived from the fundamental assumption of the special theory of relativity. Then this Lorentz transformation is applied to derive the energy10
C. Ganesa Moorthy & G. Udhaya Sankar
mass equivalence relation in classical special theory of relativity. In this chapter a new derivation of the energymass equivalence relation has been derived by applying an interpretation; without applying Lorentz transformation directly or indirectly. So, the new question is the following. Is the derivation presented in this chapter correct? It is correct, and the derivation is an indirect form of interpretation. Strictly speaking, derivations are not necessary, and only interpretations are necessary. Let us justify this statement. If a bullet is fired from a gun, the energy released by the explosive matter of the bullet should also be taken into account to calculate the total energy for the bullet. Similarly, when the elementary masses dm get some kinetic energies (1/2) (dm) c2, the collective mass M gets a kinetic energy (1/2) Mc2. But this kinetic energy can be obtained only by spending an equal amount of “binding energy” (1/2) Mc2. Thus the total energy hidden in the mass M is (1/2) Mc2 + (1/2) Mc2=Mc2. So, Newtonian mechanics for kinetic energy, the fundamental assumption of the special theory of relativity, and interpretations are sufficient to understand the energy-mass equivalence relation of Einstein. The final observation: the entire classical special theory of relativity depends on the fundamental assumption, Lorentz transformation derived from the fundamental assumption, and the classical Newtonian mechanics. 11
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Chapter 3 Solar System and Atom Big size planets are to be discussed and small size electrons are also to be discussed in all parts of this book. So, they are discussed from here. One theory for the origin of our solar system is described in the following way. Long ago, there was a big cloud of gaseous particles. The entire cloud looked like a plate and that cloud rotated itself about a point in a plane. During the rotation, the particles were consolidated at some places to form the sun as well as the planets around the sun. The important thing is that the sun and the planets had self-rotation, and the planets rotated around the sun. Newton observed that the force which made apples to fell down was the reason to make the moon to go around the earth. Apples fell down to the earth, but the moon did not fall down to the earth. Newton‟s first law of motion made the moon to go away from the earth since from the origin of the earth, but the gravitational force did not permit the moon to go away, and finally the moon began to go around the earth as a combined effect. Newton knew all these things. Newton generalized the gravitational law to form a universal 13
Planets and electromagnetic waves
gravitation law applicable for any two bodies. There is no satisfactory theory for existence of gravitational fields. Some scientists attribute the existence of gravitational field to some sub particles having gravitational fields. There is no significance in differentiating existence of gravitational fields in a body and in parts of the body. If one can produce gravitational field by means of experiments, then we may be able to understand reasons for existence of gravitational fields. Let us wait for an experiment which may be conducted in future. This book provides reasons for existence of magnetic fields, atmospheres and winds in planets. On the other side for small particles, we have an accepted theory for atoms. An atom consists of neutrons, protons and electrons. Neutrons and protons are at the center like the sun. The electrons go around the neutrons and protons in their orbits, like planets. No one did see anything about an atom. Although all protons in the center of atom have same type of positive charges, nothing is said about repulsion between two protons in the same center. The reason is not known. Do protons and electrons create magnetic fields inside an atom? Nothing is known. There are many such obvious questions without answers. One may go beyond a single atom to raise questions about molecules. What is the pattern in movement of an electron in a molecule? If a current passes through an electric wire, do protons forget to put electric fields around them to dominate moving electrons? This fundamental question again raises another question about the single atoms. There are two 14
C. Ganesa Moorthy & G. Udhaya Sankar
fields of attraction between a proton and an electron in an atom. They are the gravitational field and the electric field. Which field is the cause for rotation of an electron around a proton? If it is only the gravitational field which make an electron to rotate around a proton (a nucleus), then the protons in a current passing wire do not dominate the electrons moving from molecules to molecules, by means of electric fields. It is assumed in this chapter that the electric fields of the protons do not influence the electric field of a rotating electron in an atom, in connection with rotation. However, it may be true that electric fields of protons nullify the electric fields of electrons inside the orbits, when outside electric fields of electrons are not disturbed. The universal gravitation law gives an expression as the magnitude of the gravitational attracting force between two bodies with distance r and with masses m1 and m2. Here G is the usual universal constant. The derivation was based indirectly on the data used by Kepler. This expression to find gravitational force between two bodies was useful to guess an expression for electrostatic forces between two charges. Experiments were conducted with two collections of charges (not with two single charges) and the forces between two groups of charges were observed.
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Planets and electromagnetic waves
It was found that the force between two charges q 1, q2 placed at a distance r is , when ε0 is a universal constant, The following Coulomb‟s law was guessed from Newton‟s law of gravitation and from his experiments in 1785. Coulomb’s law: The force of attraction or repulsion between two point charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them. The direction of forces is along the line joining the two point charges.
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Chapter 4 Magnetic Fields of Planets Planets were compared with electrons in the previous chapter. Electrons in planets are to be considered in this chapter. There were some discussions in connection with protons and electrons in the previous chapter about their unknown behaviors. It is assumed in this chapter that if an electron moves, it creates a magnetic field. For example, consider an object sliding over an inclined plane. Then all the electrons e in the object also move in the direction of movement of the object A. So, these electrons create a magnetic field.
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Planets and electromagnetic waves
If water flows through a tube, then water molecules move and hence the electrons in the molecules move in the direction of flow of water. These moving electrons create a magnetic field around the water tube.
One may create further examples. One may also raise the following question. Why should we believe that this argument could be correct? Nothing can be seen inside an atom. No one realized so far an observable magnetic field around a water tube. Consider two water tubes in parallel. Let water flow in one direction in only one tube. 18
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Let the other tube contain non-moving water at an initial time. The moving water of the first tube should make the water in the second tube to move, by means of gravitational attraction. No one recorded such an observation. One may argue that the gravity of the earth does not permit (and the friction does not permit) to get an observable movement; and he/she may argue that the movement may happen in the outer space of the earth. Another one may ask about the reason for discussing gravity when we are discussing about magnetic field. The reason is a comparison purpose.
Now we can observe that the magnetic field created by water flow in a tube may not be observable, in view of the magnetic field of our earth. There may be other obvious reasons for non-observable situations. But, these non-observable situations alone cannot justify the existence of magnetic fields around the water tube in which water flows, in view of moving electrons. Let us begin with the right hand palm rule for a justification. 19
Planets and electromagnetic waves
Classical Right Hand Palm Rule: Consider a coil connected to a battery that gives a direct current. If the coil is held in the right hand so that the fingers point in the direction of the current in the windings, then the extended thumb points in the direction of the magnetic field. This rule is applicable even for a single current loop carrying current. But the direction of the conventional current is the reverse direction of the movement of electrons. The figures 4.8 and 4.9 explain the meanings. When an electron moves in a direction, something happens to the shape or the orientation of the electron so that there is an orientation for the magnetic field or the magnetic field lines. The directions of lines of a magnetic field are associated with magnetic poles. Two magnetic poles were already identified (or defined) by means of attraction and repulsion properties by scientists. By convention, it was assumed that magnetic lines begin from the north magnetic pole of a bar magnet and ends at the south magnetic pole.
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In our earth the geographic North Pole is near to the magnetic South Pole, and the geographic South Pole is near to the magnetic north pole. Consider the equator plane that contains the equator circle. Now consider any circle C that lies on a plane parallel to the equator plane 21
Planets and electromagnetic waves
so that the centre lies in the axis of rotation. Consider the materials on the circle C. These materials contain electrons. Consider the movement of these electrons on C. That is, consider the rotation of the earth and thereby the rotation of electrons on the circle C about the axis of rotation of the earth. Now, let us apply the right hand thumb rule (for single loop) for these movements of electrons to get magnetic lines. Collect these imaginary lines by means of intuition. Then we understand that the magnetic north pole is near to the geographic South Pole. This is a good justification for our electronargument for existence of magnetic field in our earth. Let us observe few things from our earlier arguments. The number of electrons need not follow a uniform distribution. So, the magnetic field need not be uniform on the earth. The movements of molten parts inside the core part of the earth may create their own magnetic fields, and these fields may affect the strength and the direction of the magnetic field on the surface of the earth locally. The orbital movement of the earth around the sun may also affect the magnetic field of the earth. Speedy movements of gases in parts of the sun may create magnetic field, sun spots, and magnetic field waves (to be described in chapter 9, and partly in chapter 6). The magnetic field waves of the sun as well as some other cosmic waves may affect the magnetic field of the 22
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earth. Let us ignore or forget all these possibilities for disturbances to the magnetic field of the earth for simplicity. We need this simplicity for comparison of magnetic field strengths in different planets. Before using this simplicity, let us make a statement without repeating explanations: Self-rotating bodies do have magnetic field. Consider a self-rotating planet with radius R and with a uniform electron density ρ, when electron density here refers to the number of electrons in a unit volume. Let T be the fixed time required for one complete (self) rotation about its axis of rotation. Suppose the axis of rotation lies in the z-axis and the equator circle lies in the xy-plane with the center at the origin of the xyzCartesian coordinate space. Consider a circle C on the upper semi sphere which also lies on a plane that is perpendicular to the axis of rotation. Suppose the line joining any point on C with the origin makes an angle θ with the xy-plane (angle with the perpendicular projection of line in the xy-plane). Then the radius of the circle C is R cos θ.
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By the expression (5.40) given in the book [D.J. Griffths, (1999)] and its limitations given as a footnote in [D.J. Griffths, (1999)], the total gravitational field generated by the electrons in the elementary disc containing C is directly proportional to ( )
∫
Here s is used for varying circles in the disc containing C. Observe that
is the angular velocity for the
rotation. If we now vary the elementary discs by varying θ from to , then we conclude that the total magnetic field created by all electrons in the entire planet is directly proportional to ∫
(∫
( )
)
(
24
) (∫
)
C. Ganesa Moorthy & G. Udhaya Sankar
Thus the total magnetic field of the entire planet is directly proportional to ( ), where D is the diameter of the planet. So, the total magnetic field strength of the planet is equal to k ( ), where k is a universal constant applicable for all (spherical) planets with uniform electron density ρ. The following table provides the calculated total magnetic field strengths of the planets in our solar system. Here the moon refers to the moon of the earth. Data for T and D are known (available in standard websites). Rotating
2 Electron D /T Period (T) Density (ρ) (D) (km) (unknown) (km2 /hour) (hours) Diameter
Planets
Magnetic Field 2 Strength kρ(D /T)
Mercury 4879
1407.6
ρ1
16911.5
kρ1*(16911.5)
Venus
5832.5
ρ2
25119.0
kρ2*(25119.0)
6808181.4
kρ3*(6808181.4)
12104
Earth
12756
23.9
ρ3
Moon
3475
655.7
ρ4
18416.4
kρ4*(18416.4)
Mars
6792
24.6
ρ5
1875254.6
kρ5*(1875254.6)
Jupiter
142984
9.9
ρ6
2065093359.0 kρ6*(2065093359.0)
Saturn
120536
10.7
ρ7
1357843673.0 kρ7*(1357843673.0)
Uranus
51118
17.2
ρ8
151921507.2
Neptune 120536
10.7
ρ7
1357843673.0 kρ7*(1357843673.0)
Pluto
10.7
ρ7
1357843673.0 kρ7*(1357843673.0)
120536
25
kρ8*(151921507.2)
Planets and electromagnetic waves
Let us observe the following conclusions. 1. It was assumed that the planets have perfect spherical shapes and they have uniform electron density. 2. All other simplifications mentioned when we discussed existence of magnetic fields are applicable in evaluation of the magnetic field strengths. 3. The expression k ( ) gives the field strength at the poles. There are complications in extending the calculations for magnetic field strengths on the surfaces and above the surfaces. 4. If the electron densities are assumed to be equal for all planets of our solar system, then the previous table provides a comparison for the global magnetic field strengths for planets. Observe from the previous table that the moon also possesses a weak magnetic field. The theory proposed in this chapter is based on the movements of electrons along with movements of bodies containing electrons. There are other theories in literature for existence of magnetic field in planets. But none of them justifies the direction of magnetic lines in our earth. The most popular theory is the geo-dynamo theory [G. Rudiger and R Hollerbach, (2004)]. This theory says that the molten parts of our earth move in the core of the earth and these movements create electric currents and 26
C. Ganesa Moorthy & G. Udhaya Sankar
thereby the magnetic fields in the earth are created. But this theory is certainly not applicable to the moon, because there is no moving part in the core of the moon. According to this geo-magneto theory there is no magnetic field in the moon. However, the existence of magnetic fields in the moon and the existence of magnetic fields in the planet Mars were observed during space research projects; and there are articles in literature which report about experimental observations for magnetic fields of self-rotating bodies, which are not planets.
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Planets and electromagnetic waves
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Chapter 5 Atmospheres and Winds If there are air molecules to a considerable height in a planet, then it is said that the planet has an atmosphere. If there are movements in the atmosphere in a planet, then it is said that the planet has winds. Almost all planets (not all) have water in the poles in the ice form. Sun rays may convert them into water-air-molecules. This is just an example. There are many reasons for production of air molecules at the surfaces of planets. Planets may get air molecules at the surfaces. If they are retained around the surfaces, then the planets have atmospheres. If the air molecules get movements by some means and they are retained around the surfaces, then winds are produced. There are many reasons for retaining atmosphere and there are many reasons for existence of winds. Only very essential parameters will be considered in this chapter to discuss retaining atmospheres and existence of winds. These simplifications are sufficient to understand the nature of 29
Planets and electromagnetic waves
atmospheres and winds to some extent. Our first discussion will be on atmospheres. For this purpose, let us discuss about escape velocity. Each planet is associated with an escape velocity. The escape velocity is the minimum velocity with which a body must be projected vertically from the surface of a planet in order that it may escape from the gravitational pull of the planet. This is a formal definition. However, we can understand from the definition that if the gravitational force is uniform at all points of the surface of a planet, and then the escape velocity is a constant for the planet. Average escape velocities for planets (including the moon of our earth) have been evaluated by using formulas, and these values may be found in some websites. Let us consider an air molecule as a body. Every planet in the solar system moves around the sun. Every air molecule on a planet has inertia. If the planet moves around the sun with an orbital velocity v, then the maximum possible apparent velocity of the air molecule in the reverse direction is also v, because of inertia of the air molecule.
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Thus, if the escape velocity of the planet is less than v, then some air molecules begin to escape. Thus, if →
then the air molecules begin to
escape. Table 1 Orbital velocity (km/s)
Escape velocity (km/s)
→
Mercury 47.4
4.3
11.023
Venus
35.0
10.4
3.365
Earth
29.8
11.2
2.661
Moon
1+29.8
2.4
12.833
Mars
24.1
5.0
4.820
Jupiter
13.1
59.5
0.220
Saturn
9.7
35.5
0.273
Uranus
Planets
6.8
21.3
0.319
Neptune 5.4
23.5
0.230
Pluto
1.3
4.7
3.615
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The data given in this table 1 for orbital velocities and escape velocities are known ones, which may be found in different websites. 1 km/s is the orbital velocity of the moon around the earth and 29.8 km/s is the orbital velocity of the earth around the sun. Both of them should be taken into account for the apparent velocity of an air molecule on the moon. For this purpose the orbital velocity of the moon is taken as (1+29.8) km/s. This is a maximum possibility, and an imagination is required in addition to the figure 5.2
We have the following observations from the table 1. 1. The distant planets Jupiter, Saturn, Uranus and Neptune hold atmospheres firmly, because →
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2. The moon and the Mercury cannot have atmospheres, because the values of are not just greater than 1, the values are greater than 10. The other planets Venus, Earth, Mars, and Pluto also have chances to lose atmospheres. However, since the Venus and The Earth are near to sun and there are many ionized molecules (in ionospheres) in these two planets, and these ionized air particles may not permit atmosphere air molecules to leave the planets. Mars is more away from the sun than the earth, and hence ionized molecules are less in number. So, Mars is losing its atmosphere. Pluto is far away from the sun, and hence it lost the capacity to retain its atmosphere. An indirect observation: We have to protect the ionosphere of our earth. Let us now consider one more parameter in determining capacities to retain atmospheres. That parameter is the self-rotating speed w of a planet at the equator. If an air molecule touches the surface of a planet at the equator, then the air molecule can get a maximum possible speed w which coincides with the rotating speed at the equator. The gained velocity w may be in the direction of a tangent to the equator circle. So, there is a chance for an air molecule to gain a maximum velocity w+v to escape 33
Planets and electromagnetic waves
from the planet, where w is the rotating speed of the planet at the equator and v is the orbital velocity of the planet around the sun.
Let us now introduce a velocity index applicable to each planet.
If the velocity index of a planet is less than 1, the planet has atmosphere. If the velocity index of a planet is greater than 1 then there is a chance to lose atmosphere. Look at the table 2.
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Table 2
Planets
Escape velocity Orbital velocity Rotating speed at Velocity equator (km/h) Index (km/s) (km/s)
Mercury 4.3
47.4
10.8937
11.02
Venus
10.4
35.0
6.5226
3.37
Earth
11.2
29.8
1677.4140
2.70
Moon
2.4
1+29.8
16.6561
12.84
Mars
5.0
24.1
867.7317
4.87
Jupiter
59.5
13.1
45391.7170
0.43
Saturn
35.5
9.7
35404.3900
0.55
Uranus
21.3
6.8
9340.4651
0.44
Neptune 23.5
5.4
9668.2600
0.34
Pluto
4.7
48.5884
3.63
1.3
Unit conversion should be done before calculating velocity indices. One may give interpretations which are similar to the earlier interpretations. Observation: The primary parameters are “orbital velocity” and “escape velocity”. A secondary parameter is “rotating speed”. We had this observation, because introduction of the new parameter “rotating speed” did not change interpretations. Note that we did not consider the collisions of two air molecules. But, we can still get good conclusions. Let us now begin discussions on winds. An earlier interpretation was that the distant planets (excluding the 35
Planets and electromagnetic waves
planet Pluto) Jupiter, Saturn, Uranus and Neptune hold atmospheres firmly. The planets which are far away from the sun of our solar system can receive small amounts of energy from the sun. The planets which are near to the sun receive more sun energies than the sun energies received by the planets which are far away from the sun. The speeds of the winds in the distant planets are much greater than the speeds of the winds in the planets, which are nearer to the sun. Researchers had a belief that the surfaces of the distant planets received internal energies from the core parts of the planets, and these energies helped to create high speed winds in these planets. The ultimate logic is that energies received create high speedy winds, by means of local variations in temperatures. It assumes that internal energies have been continuously used in distant planets to create high speed winds in case of variations in temperatures. But, these planets should have cyclically stable temperatures, at present, on the surfaces in view of their ages, and internal energies cannot change at present cyclically stable temperatures on the surfaces. So, there is a need to find a correct reason for existence of high speed winds in distant planets. The reason is given in terms another index called index of idleness. For this purpose we have to recall the critical velocity in a planet. The escape velocity of a planet with a constant gravitational force G at the surface and with radius R is√ . The escape velocity is a fixed one at all points on
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the surface of the planet. But, the critical velocity of a planet at a point depends on the latitude at which the point is located. If a body on a point at a latitude gets a tangential velocity (tangent to the circle which describes the latitude on the planet) just greater than the critical velocity then the body moves almost in a circular path subject to gravity, and it does not move if it does not get a velocity greater than the critical velocity. In any case the velocity of the body should not exceed the escape velocity. The critical velocity at the equator is √
or
√
. Let us now evaluate
the critical velocity at latitude given by the angle θ.
37
Planets and electromagnetic waves
The radius of the circle C on the surface defined by the latitude angle θ is given by R Cosθ. The corresponding gravitational force component parallel to the plane containing C is G cosθ. Thus the critical velocity at any point in C is√ . Let ω be the √ angular velocity of the planet. Let us observe the followings: √
√
.
This relation provides a universality of the ratio. Let us now define the index of idleness by: √
Let us now discuss about the interpretation for the index of idleness. If the rotating velocity at the equator exceeds the critical velocity at the equator in a planet, the (condensed matter) particles at the equator should go out, and it will disintegrate the planet. That is, a planet cannot exist such that the rotating velocity at the equator exceeds the critical velocity at the equator, provided the planet contains condensed matters. This statement can be verified as a correct statement by using the data given in the table 3. This is not the required interpretation. If the index of idleness is less than 1, then particles may go out. To retain particles on the surface the index of idleness must have a high value. If an air molecule on the surface goes out, then it may be a part of 38
C. Ganesa Moorthy & G. Udhaya Sankar
a wind in the sense of the next sentence. If an air molecule is retained nearly on the surface, then the inertia of the air molecule will make the air molecule to move apparently in the reverse direction of the direction of the rotation of the planet, when the friction is considerably low. That is, for low index of idleness one may expect a high speed wind movement of air molecules on the surface. This surface level movement should affect the wind generation in the atmosphere. Table 3 Planets
Critical velocity at the Equator (km/s)
Rotating speed at the Equator (km/s)
Index of idleness
Mercury
3.04101839
0.0300833
1010.86596
Venus
7.35502122
0.00181111
4061.07958
Earth
7.92079208
0.465
17.0339615
The moon (of the earth) 1.69731259
0.004626873
366.837946
Mars
3.53606789
0.24055556
14.6995891
Jupiter
42.079209
12.6619444
3.32328168
Saturn
25.106082
10.233333
2.45336314
Titan (of the Saturn)
1.86633663
0.01175139
158.818372
Uranus
15.0636492
4.1094444
3.66561699
Neptune
16.6195191
2.6997222
6.15601083
Pluto
0.91937765
0.034225
26.8627509
The Titan of the Saturn has atmosphere. But the moons of our earth and the planet Mercury have no atmospheres. The index value 366.83 for the moon can 39
Planets and electromagnetic waves
be interpreted such that air molecules appeared on the surface of the moon can move very slowly against the very slow self-rotation of the moon. The very low indices of the distant planets Jupiter, Saturn, Uranus and Neptune favour for speedy winds. Comparison between the indices for the earth and the Mars reveal that the winds in the Mars have more speed than the winds in the earth. The index of Venus is very high and it corresponds to slow movements of air molecules on the surface. These things agree with existing data. Although it is not perfectly correct, let us assume that an increase in temperature of the surface of a planet corresponds to an increase in friction. So, a parameter “temperature” should also be included in the calculation of index of idleness. The table 4 is prepared based on the following inclusion of temperature in evaluation of indices. Idleness of wind at a place of the surface = (Index of idleness) x (Temperature of the surface at that place) Table 4 Planets
Average surface Temperature (in Kelvin)
Average Idleness of Rank for wind molecules at average Surface (in speeds of Kelvin) winds
Mercury
440
444781.022
10
Venus
730
2964588.09
11
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C. Ganesa Moorthy & G. Udhaya Sankar
Earth
287
4888.74695
7
The moon (of the earth) 253
92810.0003
9
Mars
218
3204.50866
6
Jupiter
120
398.793802
4
Saturn
88
215.895956
1
Titan (of the Saturn)
98.3
15610.8931
8
Uranus
59
216.271402
2
Neptune
48
295.48852
3
Pluto
37
993.921783
5
Interpretations similar to the previous ones may be provided. Let us next get into the main parts of the book, namely, electromagnetic waves and classifications.
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Planets and electromagnetic waves
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Chapter 6 Electromagnetic Waves Physicists can understand almost everything. If it is said that light is propagated in a straight line, they can understand. If it is said that light is propagated in a wave form, they can understand. If it is said that light energy is propagated by means of photons, they can understand. If it is said that light energy released obeys the formula E=hν, then they can understand, when h is the Planck‟s constant, E is the energy, and ν is the frequency. If it is said that a light wave has polarity, then they can understand. But, they may not understand everything, because the nature is complicated. They do not know about amplitude of a light wave. Some physicists may say that light waves are electromagnetic waves, by means of their definitions for electromagnetic waves. Some physicists may raise the question, “Is it possible to consider a light wave as an electromagnetic wave?”, based on their definitions for electromagnetic waves; and some physicists may answer that “both light waves and electromagnetic waves have speed c in 43
Planets and electromagnetic waves
vacuum, and hence a light wave may be considered as an electromagnetic wave”. But, all physicists used to agree to the figure 6.1 as a representation for spectrum for electromagnetic waves.
Sometimes, figures help readers to understand concepts. Sometimes, figures make the readers not to raise questions, as if the figures give complete explanations. Let us see the figure 6.2.
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Almost all physicists used to agree to consider the figure 6.2 as a representation for electromagnetic waves, because the Maxwell‟s theory says that the electric field and the magnetic field are orthogonal to each other in the place of generation of these fields. Since it is difficult to draw four dimensional coordinate systems, physicists are forced to imagine wave propagation such that the electric field wave and magnetic field wave jointly move in the x-coordinate direction, for example, as given in the figure 6.3.
Let us imagine a suitable polarizer is placed in perpendicular to the x-axis and parallel to the yz-plane as given in the figures 6.4 and 6.5.
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Planets and electromagnetic waves
It may happen that only one of the electric field wave or the magnetic field wave may come out from the polarizer. This means that there is a chance to have separate electric field waves with absence of magnetic field waves, or, there is a chance to have separate magnetic field waves with absence of electric field 46
C. Ganesa Moorthy & G. Udhaya Sankar
waves. Does this statement contradict the Maxwell theory? No. The simultaneous wave equations derived from the Maxwell equations, when varying current flows in a wire (or, a base matter), support simultaneous wavetype oscillations of the magnetic field as well as oscillations of the electric field. That is, the periodic variations may happen for y values as well as z values for these fields when time t varies as given in figure 6.6.
But, only one wave, either electric field wave or magnetic field wave, may increase its value in xdirection along with increase in time t. That is, only one of the electric field wave and the magnetic field wave is propagated, when the other one may oscillate without propagation. Only a philosophical argument has been presented now. Actual justifications are to be given. The followings should be repeated again. The Maxwell equations give wave differential equations. 47
Planets and electromagnetic waves
Wave differential equations give solutions leading to wave-type oscillations. Wave differential equations need not give solutions leading to wave propagations. For example, if a tight string with two fixed ends is pulled aside and released from rest, then its oscillation movement in the subsequent time is described by a wave differential equation. But, the string does not give wave propagation.
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Chapter 7 Stored and Released Energies Electrical energy is stored as chemical energy and then stored chemical energy is released as electrical energy in batteries. In a ruby laser, there is an elliptic-cylindrical mirror, there is a tube type light emitting source in one focus line and there is a ruby rod in another focus line. Light emitting source emits light, these light energies reach ruby rod, ruby rod creates new light rays of its own wavelength, they are reflected inside again and again, and then a laser is released from the ruby. There are such things in science about transforming energies. Two known technical terms in connection with transforming energies are “ground state of electrons” and “excited state of electrons”. Sometimes one may say that an electron moves from one orbit to another orbit, when energy is absorbed or released. Someone may say that electrons spin after gaining energies. Nothing is seen. One more comfortable theory is to be proposed in this chapter to release energies by means of electrons. 49
Planets and electromagnetic waves
All planets follow gravitational law and move without collisions in our solar system. Similarly, electrons in an atom or in a molecule follow the laws for electrostatic forces and move or take positions. If an atom or a molecule accepts some energy, then the electrons may change their positions; and electrons may come close so that there may be an increase in electrostatic forces between at least two electrons or between an electron and a proton, by means of repulsion or attraction. This is something like compressing or elongating a normal spring. Once the spring released from its strained position, the spring releases a kinetic energy. Similarly, strained electrons may release the force in the form of energy, like alpha rays, beta rays and gamma rays. Let us state the conditions more specifically. Consider a current passing wire resistor. Consider two successive free electrons which move. If the first electron moves in one direction, then the second electron tries to reach the first electron in the same direction, because of current flow. But, two successive electrons repel each other because of electrostatic forces. So, the repelling electrostatic force between the two electrons increases. This increased force becomes after some stage as electric field waves (Figure 7.1).
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Similarly, let us consider a superconductor wire in which a high voltage current passes through it. Consider two nearby electrons which move in parallel in the wire in the same direction. Then these two electrons create magnetic fields which are supposed to be naturally attracted, but electrons repel each other, and hence there is a force against natural attraction. This force becomes after a stage as magnetic field waves (Figure 7.2).
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Planets and electromagnetic waves
Let us observe again that magnetic fields are created by electrons moving in parallel, and then these attracting magnetic fields are disturbed because of repelling electrons. In the previous model (Figure 7.1), magnetic fields are created by electrons need not be attracted, and they need not affect naturally repelling electrons. These two models given in the figures 7.1 and 7.2 also give the following conclusion. There is no energy wave with two components, one an electric field wave with wavelength λ and another one a magnetic field wave with wavelength μ. Let us consider again two parallel water tubes through which water uniformly flow in opposite directions. The theory developed in chapter 4 reveals 52
C. Ganesa Moorthy & G. Udhaya Sankar
that the moving electrons in water create magnetic fields around the two tubes with opposite orientations (Figure 7.3).
These two magnetic fields around the tubes may create a force and it may create magnetic field waves, which may not be observable by us. However, two giant bodies rotating in opposite directions for which axes of rotations are parallel to each other in the space outside of our earth may have strong magnetic fields, and when they come very close to each other, there is a possibility to produce magnetic field waves, and these waves may reach our observatories. The ultimate conclusion is the following. Strained forces may become energies, and strained forces may become electromagnetic waves.
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Planets and electromagnetic waves
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C. Ganesa Moorthy & G. Udhaya Sankar
Chapter 8 Gravitational Waves Let us consider again two water tubes through which water flow uniformly in opposite directions (Figure 8.1).
The water flow in the first tube should attract the water in the second tube by gravitational force in the direction of the water flow in the first tube. Similarly, the water flow in the second tube should attract the water in the first tube by gravitational force in the direction of the water flow in the second tube. So, these two forces in 55
Planets and electromagnetic waves
reverse directions may create an energy wave or these two forces in reverse directions may increase the strength of magnetic field waves discussed in the previous chapter. Do two bodies rotating with reverse orientations and with parallel axes of rotation create a new energy wave called gravitational wave, when they come close, by means of gravitational forces? (Do they increase strengths of existing magnetic field waves?). Einstein believed that a new type of energy waves, called gravitational waves, may be created when two big bodies (like black holes) collide with each other, by means of gravitational forces. But, if two rigid bodies go away from each other, then the gravitational forces between them can make energy waves for a while. Collisions of two bodies cannot create energy waves by means of gravitational forces (Figure 8.2). So, there is a need to change existing theory on existence of gravitational waves.
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A high level technical observatory to detect gravitational waves was first established Weber in 1960s. His model contains a suspended heavy aluminum based metal bar, which is maintained at a very low temperature. It was believed that the gravitational waves could affect the aluminum bar and thereby the gravitational waves could be detected. In this connection let us recall Meissner‟s effect. When a material makes the transition from normal to superconducting state at a low temperature; it actively excludes magnetic fields from its interior. In particular, the material at a very low temperature is repelled by magnetic fields. Let us assume without verification that a material that can be made into a super conducting material at a low temperature is disturbed by a magnetic field wave in that temperature. That is, the aluminum bar in the Weber‟s model can be disturbed by magnetic field waves and the instrument can be used to detect magnetic field waves reaching our earth from the outer space. Another big project should also be discussed in connection with gravitational waves. Two LIGOs were installed in distant places Hanford and Livingston of USA. Each LIGO contains two perpendicular arms, which are metal tubes (or tunnels) covered by concrete walls. It was designed with an assumption that arms would be disturbed by gravitational waves received and laser beam passing through tubes would detect gravitational waves through 57
Planets and electromagnetic waves
interferences. Magnetic fields of rotating giant bodies can create magnetic field waves and these magnetic field waves can disturb metal arms and thereby they can be detected by LIGOs. It was reported that both LIGOs detected gravitational waves almost simultaneously on 14th September 2015. It can be concluded from the earlier discussions that magnetic field waves could have been detected on 14th September 2015 by both LIGOs. Since all magnetic field waves which reached on 14th September 2015 had same polarity, the arms of LIGOs should be two pairs of almost parallel arms.
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Big technologies are essential for LIGOs, but they did not detect gravitational waves of two objects. Moreover, only meaningless understandings exist about space-time contractions and space-time expansions for meaningful connections with observations by LIGOs.
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Planets and electromagnetic waves
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C. Ganesa Moorthy & G. Udhaya Sankar
Chapter 9 Electric Field Waves and Magnetic Field Waves The components of electromagnetic waves were known as electric field waves and magnetic fields waves. It was mentioned in chapter 6 that an electromagnetic wave contains only one of the two waves, namely, an electric field wave and a magnetic field wave. These two technical terms were used in the chapters 7 and 8. These two chapters also explained methods to produce energy waves. Let us first fix a definition for electromagnetic waves for our discussion. Let us recall that c refers to the speed of light in vacuum.
Definition: An energy wave which has the speed c in vacuum is called an electromagnetic wave. Alpha rays, Beta rays and Microwaves are not electromagnetic waves according to this definition because they do not have speed c in vacuum. The 61
Planets and electromagnetic waves
“gravitational waves” observed by LIGOs on 14th September 2015 had speed c, and hence they should be electromagnetic waves, according to this definition. Light rays and radio waves have speed c in vacuum, and hence they are also electromagnetic waves according to this definition. Electric field waves are considered (defined) as electromagnetic waves created by forces induced directly by electric fields. Magnetic field waves are considered (defined) as electromagnetic waves created by forces induced directly by magnetic fields. Fields around electrons and protons are electric fields. Consider a tungsten bulb. If a current passes through the tungsten bulb, then we have to refer to the figure 7.1 given in chapter 7. So, light rays produced by a tungsten bulb are electric field waves and hence they are electromagnetic waves. We do not know the fundamental things which happen inside fire flames and CFL bulbs to produce light rays. That is, the ways by which electric fields are involved to produce light rays in fire flames and CFL bulbs are unknown. Without knowing these fundamental things, it is declared that all light rays are electric field waves. So, we have another way to consider light waves as electromagnetic waves, by considering light waves as electric field waves. The reason for existence of light rays with different wavelengths will be discussed later. 62
C. Ganesa Moorthy & G. Udhaya Sankar
Consider a conducting wire-coil and a current flowing through the coil. Then we have to refer to the figure 7.2 given in chapter 7, for the possibility of existence of magnetic field waves, because the magnetic field around the coil may produce magnetic field waves. Maxwell equations and the corresponding wave differential equations were derived only for this situation, and it was understood by the Maxwell theory that both magnetic field waves as well as electric field waves are produced. But, our claim is that only magnetic field waves may be propagated, and electric field may oscillate but not propagated as a wave. Someone may observe heat radiation from the coil, but this one may not be coupled with magnetic field waves. Although some explanations were already provided, we shall give some more explanations for our claim. Our next claim is that electric field waves and magnetic field waves are the only electromagnetic waves. The ultimate claim is that there is a length number w (= 1.063 mm approximately) such that any electromagnetic wave with wavelength less than w is an electric field wave and any electromagnetic wave with wavelength greater than w is a magnetic field wave. However, initial conditions are unknown for existence of electric field waves and magnetic field waves. For example, necessary and sufficient conditions for current, voltage and resistance are unknown to produce light rays from a tungsten blub and to produce radio waves from a 63
Planets and electromagnetic waves
coil. Another unknown thing is about existence of an electric field wave created by electric fields around protons.
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Chapter 10 A Law for Light Waves A law for electric field is framed, interpreted and applied in this chapter. But, this law is framed under the assumption that electric field waves are created by forces induced by electric fields around electrons; as discussed through figure 7.1 in chapter 7. It is believed that all electric field waves are created only by means of forces induced by electric fields around electrons. One reason for this assumption is that protons are almost fixed at the center of an atom and electrons in the orbits of an atom are subjected to natural changes for movements. However, it is justified in this chapter that many laws agree with this law for light waves. So, heat energy also obeys a law that is similar to the law for light waves.
First law: If an electric field wave (or a light wave) strikes a free electron of a molecule of a material, it tries to repel the electron in the direction of the wave. 65
Planets and electromagnetic waves
Second law: If heat energy is applied to a material, the free electrons of the molecules of a material which receive the energy are repelled. It is expected that an electric field wave (created from forces induced by electric fields around electrons) may affect the electrostatic field of an electron, and so the first law is proposed. Since heat energy is associated with light waves, the second law for heat is proposed. The second law will also be justified through known examples.
Justification 1: A classical solar cell consists of two semiconductors; one is an n-type semiconductor and another one is a p-type semiconductor. When light rays fall on the n-type semiconductor, by the first law, these rays push free electrons of molecules of n-type semiconductor toward the adjacent p-type semiconductor. The p-type semiconductor receives these free electrons and there is a potential difference between outer surfaces of the different types of semiconductors. It seems that p-type semiconductors are acceptors of free electrons through “holes” and n-type semiconductors are donors of free electrons of molecules. One may search for donors and acceptors from materials used for cathodes and anodes of electrochemical cells, and from materials used for thermo couples. 66
C. Ganesa Moorthy & G. Udhaya Sankar
Justification 2: The second law can be applied to explain current production in case of a thermo couple. There are two conductors (wires) and they are connected at two ends. One end is kept in a heat source and another end is kept in a cool place. One conductor is an acceptor and other conductor is a donor. In the end kept at the heat source by the second law, donor repels free electrons and acceptor receives free electrons. In the cool end, the procedure is reversed. That is, donor accepts electrons and acceptor repels electrons, when the temperatures of the metal wires kept at the cool source are higher than the temperature of the cool place. Thus, there is a potential difference. This effect of getting current in a thermo couple is called Seebeck effect. The Peltier effect is a converse effect of the Seebeck effect. The Peltier effect is the effect of getting heat and absorbing heat in a thermo couple through which a direct current passes in. Again a thermo couple is considered. But the ends are not kept at a heat source and a cool place. An electro motive force is applied. The end in which electrons move from the donor to the acceptor evolves heat. The end in which electrons move from the acceptor to the donor absorbs heat (and it becomes a cool end).
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Thus the second law takes the following form when an acceptor and a donor are joined. If the joining is kept in a heat source, then the donor tries to repel electrons toward acceptor. Conversely, if electrons move from the donor to the acceptor, then the heat energy is produced. If the joining is kept in a cool place, then the acceptor tries to repel electrons toward the donor. Conversely, if the electrons move from the acceptor to the donor, then the heat energy is absorbed (and the joining becomes cool). The second law can be used to explain the Thomson effect. Consider a donor rod (for example, a copper rod) with ends A and B and with midpoint C. Suppose conventional direct current flows from A to B. That is, electrons flow from B to A. Now, let us heat the midpoint. Then the heat repels the free electrons to both ends A and B. Since the current electrons flow from B to C, they meet heat flow electrons in the part CB and the heat energy is evolved. Since the current electrons flow from C to A, let us imagine that current protons flow from A to C, and they meet heat flow electrons in the part CA, and the heat energy is absorbed. This explains Thomson positive effect. To explain Thomson negative effect, an acceptor rod AB with midpoint C (for example an iron rod) should be considered. As in the previous case, let the 68
C. Ganesa Moorthy & G. Udhaya Sankar
current electrons flow from B to A. Let the midpoint C be heated. Then, we should imagine that the protons are repelled from the midpoint C toward the ends. Then we can conclude that the part AC evolves heat and the part CB absorbs heat. The simple rule applied here is the following. If an electron meets an electron (from opposite directions) heat energy is produced, and if an electron meets a proton the heat energy is absorbed. It was mentioned in chapter 7 (Figure 7.1) that when an electron tries to meet another electron from opposite direction, then electric field waves are produced. Roughly speaking, energy of an electric field wave (or, a light wave) is equivalent to heat energy.
An application: In a vacuum diode a metal sheet connected with the cathode end point of a direct current source is heated by means of an electric coil, receives the heat energy as well as the electric field waves from the coil. These energies (by the first law and the second law) push free electrons from the sheet connected with the cathode end. These electrons reach another part connected with the anode end of the direct current source. This vacuum diode principle can be applied in designing charging sections of electrostatic precipitators. What is an electrostatic precipitator? An electrostatic precipitator consists of a charging section, 69
Planets and electromagnetic waves
which charges one part positively and another part negatively. Air with dust particles passes through these charged portions. The dust particles are charged in one part, attracted by another part and deposited in the other part. The deposited charged dust particles are then removed by a mechanism, and the air is cleaned by this procedure with the help of electrostatic charges. In a classical design for electrostatic precipitators, charging section receives a high voltage current with high volt and low ampere. This creates a corona of charges in one end, the dust particles of the air receive charges from this corona and become charged particles, these charged particles reach the other end of the charging section, the charged particles are deposited in the other end, and then these deposited charged particles are removed by another mechanism.
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In the new design proposed in Figure 10.1, the negatively charged cylindrical metallic tube is subjected to electric field wave radiation and heat radiation by heating a resistor-coil placed outside of the negatively charged tube connected to the cathode of a direct current source. When the air with dust particles is sent through this negatively charged cylindrical tube having a cloud of electrons, the dust particles are negatively ionized. These negatively ionized dust particles are attracted by positively charged rotating circular meshes connected to the anode of the direct current source, and the dust particles are deposited on the meshes and these deposited dust particles may be collected by another mechanism. In the new design mentioned by means of 71
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an electric coil, a low voltage current with low volt and medium ampere can be applied. The advantage is there is no need to handle a high voltage current. Let us observe that both laws are applicable in forming a cloud of electrons in this new design.
Another type of electric field waves: When an electron comes near to an electron, then there is a chance of producing an electric field wave, which was under discussion so far. When a proton comes near to a proton, then again there is a chance of producing an electric field wave, and let us call it a p-type electric field for discussion purpose. One law may be stated for these ptype electric field waves. These p-type electric field waves should attract free electrons of molecules, if these waves exist. The existence of such events was not reported so far. So, let us assume that electric field waves are the electric field waves created by forces induced by electric fields of electrons. All these things are applicable for our universe. If we imagine another unknown universe in which positive charges go around negative charges in atoms of that universe, then p-type electric field waves may exist in that imaginary universe.
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Chapter 11 A Classification for Electromagnetic Waves There are two types of electromagnetic waves, namely, electric field waves and magnetic field waves. Although it was not established in chapter 6, one can guess from the polarity argument that there should be a gap between the collection of wavelengths of electric field waves and the collection of wavelengths of magnetic field waves, because a sudden perpendicular change in polarity of these two collections seems to be a meaningless change. It is to be established in this chapter that the gap is a single point w. That is, there is a length number w such that any electromagnetic wave with wavelength less than w is an electric field wave and such that any electromagnetic wave with wavelength greater than w is a magnetic field wave. To establish the existence of the length number w, we have to consider two known expressions given in standard text books for electromagnetic waves. Refer to the figures 7.1 and 7.2 given in chapter 7 for continuation. 73
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The following two expressions have been verified experimentally by physicists. The first expression gives the electrostatic force (in vacuum) applied by one electron with charge e upon another electron; when they are placed at a distance x. This first expression is
Here 𝜀0 is the usual electric constant. The second expression is
This second expression is the magnetic force (in vacuum) applied by one electron with charge e applied on another electron; when the electrons are moving in parallel in same direction with a constant velocity v; when there is a constant distance x between the electrons; and when x is the perpendicular distance between the straight line paths of the electrons. Here 𝜇0 is the usual magnetic constant. Note that the speed of light c (in vacuum) coincides with the electrodynamics constant
√
. If these moving electrons reach the
constant velocity c, then the second expression becomes 74
C. Ganesa Moorthy & G. Udhaya Sankar
𝜇
𝜇 𝜀 𝜇
𝜀
Since the maximum possible value of v is c, the maximum possible magnetic force between the electrons moving in parallel coincides with the electrostatic force between two stationary electrons; while the electrons have distance x between them. So, the energy released by the maximum possible magnetic force corresponds to the energy released by the electrostatic force; when dual changes happen. Electrostatic forces described above are repelling forces. The maximum possible magnetic forces described above are attracting forces. If one electron is brought close to another electron against the repelling electrostatic force, it is expected that energy is released in the form of electric field waves. Similarly, if the distance between electrons moving in parallel in same direction is increased against attracting magnetic force, it is expected that energy is released in the form of magnetic field waves. Thus dual changes lead to the conclusion that the supremum (or maximum) of the wavelengths of electric field waves should coincide with the infimum (or minimum) of the wavelengths of magnetic field waves. This common value is the constant w described above. Mathematics students can understand the arguments given above easily, if they are familiar with linear programming problems and the dual 75
Planets and electromagnetic waves
problems for these linear programming problems. A minimum feasible solution of a linear programming problem coincides with a maximum feasible solution of the corresponding dual problem; in the theory of linear programming in mathematics. Two methods will be proposed to find the values of w. Infra-red rays are electric field waves and all radio waves are magnetic field waves. So, w should be near to the length value 1mm.
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Chapter 12 Cosmic Microwave Background and Classification of Electromagnetic Waves Once there was a big bang, all stars, planets and dust particles began to move with a fixed high temperature, and then the universe began to expand from a central point. When the things moved from the central point and the universe expanded, the heat energies were distributed, and the dust particles were cooled. The present observed minimum temperature of the background in space is 2.726 Kelvin, which was observed through microwaves received from the space [D.J. Fixsen, (2009)]. This temperature of the cosmic microwave background is observed and it is being applied to find the age of our universe. Let us view this temperature in a different way. There is no possibility to decrease the temperature of the cosmic microwave background beyond 2.726 Kelvin. This statement is made with an assumption that there is a stability in the temperature of the cosmic microwave background, 77
Planets and electromagnetic waves
because of very old age of our universe. That is, no radiation happens when an object reaches the temperature 2.726 Kelvin. In particular, it is assumed that emission of electric field waves is just stopped at 2.726 Kelvin. This particular view is to be applied to find a length value of w discussed in the previous chapter. For this purpose we need another law, called Wien‟s distribution law. Let λm be the wavelength of the waves for which the intensity of a black body radiation is a maximum for a radiating black body with temperature T. It was found empirically that the following relation is true (see section 4.5 in [H. Semat and J.R. Albright, (1972)]). Wien’s distribution law: λm T = b, where b is a universal constant, whose value is b = 2.8978 x 10-1 cm K. Since b is a universal constant, this empirical relation is assumed to be universally true in this chapter. Hypothetically, let us assume that λm corresponds to maximum possible wavelength of electric field waves. Then, we can take T = 2.276 K in the relation λm T = b, because the temperature of the black body decreases, when wavelengths of radiating waves increases, and because 2.276 K is the minimum possible temperature of 78
C. Ganesa Moorthy & G. Udhaya Sankar
a black body to stop all radiations. Thus, the maximum possible wavelength of electric field waves is m, when we assume that the temperature of the cosmic microwave background is the minimum possible temperature of a black body to stop all its radiations. That is, w = 1.063022744 x 10-3 m (approximately). This means that any electromagnetic wave with wavelength less than 1.063022744 mm is an electric field wave, and any electromagnetic wave with wavelength greater than 1.063022744 mm is a magnetic field wave (see figure 12.1).
So, we have reached our ultimate aim. But, let us proceed further for by products. 79
Planets and electromagnetic waves
Black Hole: It is a spherical type object or planet or star, which does not permit energy waves to escape. If we follow this as the definition for black holes, the earlier discussions lead to the conclusion that the temperature of any black hole should be at least 2.726 K (see figure12.2).
We shall discuss about diameters of molecules and electrons as consequences of chapter 7, chapter 11 and chapter 10.
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Chapter 13 Diameters of Molecules Let us begin with the figure 7.1 given in chapter 7. Let us use the notations e, x, ε0, μ0 and w described in chapter 11. Let us also consider the subsequent discussions given in chapter 11. Let us propose another method to find w. Suppose one electron is fixed and a second electron moves towards the first electron along x- axis. Let us consider the distance between the centers of these electrons, and let the center of the first electron be the origin. Let x0 and x1 be two positions of the second electron from the origin with velocities v0 and v1, respectively, at time t0 and t1. Suppose x0 < x1 in the xaxis and the second electron moves from x1 to x0 to release an energy equal to
where h = 6.62607004x10-34
m2Kg/s2 is the Planck‟s constant. Let
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Planets and electromagnetic waves
where m = 9.109x10-31 Kg is the mass of an electron with charge e. Then, the value of K can be evaluated as K = 253.5693929 m3/s2, by substituting known values for e, ε0, and m. Note that (mK)/x2 is the electrostatic force on the second electron at the position x from the origin. Then the energy released gives the relation (for half wave length) ∫
.
This implies that . If T is the time required to move the second electron from position x1 to position x0, then the wavelength of the electric field wave is 2Tc. The length value of w is then the maximum possible value of 2Tc. To fix this maximum possible value of 2Tc, one has to fix suitable x0 and x1 subject to the condition . Note that the theory is being developed only for creation of a half wave. It is being difficult to develop a model for remaining half wave. The following equations are derivable. Let us begin with an equation for force and let us use
. 82
C. Ganesa Moorthy & G. Udhaya Sankar
∫
∫ (
)
(
) (
√ ∫
√
(
)
)
In the last integral, one may take t0=0, t1=T and v0=0, and to minimize the integral one may replace (
) by
, in view of the relation (
)
. This is done with an understanding that the movement of the second electron is stopped at the position x0 and it reaches the velocity 0 for half wave length, and the energy is released when a minimum possible time is taken to reach position x0 from x1. With these substitutions, the last integral gives the relation 83
Planets and electromagnetic waves
(
)√
(
. Thus,
)√
is the final
relation to calculate T and 2Tc gives the corresponding wavelength for suitable values for x0 and x1. The suitable value of x0 is “a width” of the molecule of the material (of the wire) through which the two electrons move. Here “a width” means the maximum possible distance between two electrons which share the same “outer orbit” in the “molecule”. If this x0 is substituted in , then x1 can be found and hence the wavelength 2Tc can be found. Thus each width (possibly varying) of the molecule corresponds to a wavelength of an energy wave released. So, we can have electromagnetic waves with different wavelengths. For four values of x0, the table provides calculated wavelength. Here “width” is replaced by “diameter”, and “wavelength” is replaced by “largest wavelength”. Here “diameter” means “maximum width”. x0=diameter of a molecule Corresponding largest wavelength for electric field
waves
10
-10 m
0.00000000031887210764733642 m
-9 10 m
0.000000031887210806892721572 m
-8 10 m
0.00000318872112183326958022 m
-7 10 m
0.000318872153347330226406122 m
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C. Ganesa Moorthy & G. Udhaya Sankar
If one can find the maximum possible diameter x0 of molecules in our universe, then it should imply 2Tc as the maximum possible wavelength w of electric field waves. It is reported in the article [D. Veldhuis, (2011)] that a stable molecule was produced with diameter almost equal to 10-8 m. Since we know the value of w, we can reverse the calculation procedure to find the value of x0, which is the maximum possible diameter of molecules in our universe. Thus, if we take w=1.063022744 x 10-3 m, then we can conclude that the maximum possible diameter of molecules in our universe is 1.825841138 x 10-7 m, approximately. In particular, our universe has no molecule with diameter 10-6 m. Use the value c = 2.9979250 x 108 m/s for calculations.
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Chapter 14 Approximate Diameters for Electrons, Protons and Neutrons The minimum possible mass of black holes is equal to 1.474 times of the mass of the sun, when the mass of the sun is 1.989 x 1030 kg. This is a Chandrasekhar‟s limit given in the article [S.P.S. Anand, (1965)]. It is assumed that such black holes have highest possible density. These black holes have lost almost all atomic energies and all nuclear energies. That is, they have no energies which may lead to alpha rays, beta rays, and gamma rays. That is, they almost consist only of electrons, protons, and neutrons without other energies or equivalently all molecules do not have spaces between any two of the fundamental particles, namely, electrons, protons, neutrons. So, density ρ of such black holes should be equal to
(
)
(
)
, where me, mp,
and mn are masses of an electron, a proton and a neutron, respectively, and when re, rp and rn are radii of an 87
Planets and electromagnetic waves
electron, a proton and a neutron, respectively. Note that (
)
(
)
gives the density of a matter which
contains an election, a proton, and a neutron without any space gap. This number coincides with ρ, the density of the black holes having maximum possible density, because these black holes contain almost integer multiples of the combined set {one electron + one proton + one neutron} without gap; which is true because every atom contains equal number of electrons, protons and neutrons. The masses of electrons, protons and neutrons have been standardized (see Appendix I in [H. Semat and J.R. Albright, (1972)]). Mass of an electron = me=9.109559x10-31 kg; Mass of a proton = mp = 1.672614 x 10-27 kg; Mass of a neutron = mn = 1.674920 x10-27 kg. Let r be a number such that (
). Let us call r as the cubic
average radius. This r is common for electrons, protons and neutrons, for the purpose to understand their radii. Thus, (
) (
)
.
Let G be the universal gravitational constant 6.67 X 10-11 m3/ (kg s2). Consider a black hole with mass M and radius R. Its escape velocity is (2GM/R)1/2. It should be 88
C. Ganesa Moorthy & G. Udhaya Sankar
greater than c, because the black hole does not permit light waves to escape. That is, (2GM/R) > c2 or (M/R) > c2/ (2G) = 0.673729708 x 1027 kg/m, approximately. For the limiting case and for the smallest possible mass M which is 1.474 times of the mass of the sun, 0.673729708 x 1027 kg/m = (M/R) = (1.474 x 1.989 x 1030 kg)/R, R = 4351.575959 m, and hence the maximum possible density (
)
( )( )
kg/m3,
approximately. Thus, { (
) (
}
)
This gives the value of r as 1.413374432 X 10-15 m. This provides a somewhat common approximate radius for electrons, protons and neutrons. Observe that if the values of radii of electrons, protons, and neutrons have been standardized, then the calculation procedure can be reversed to find a best Chandrasekhar‟s limit.
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Chapter 15 Different Planck’s Constant for Magnetic Field Waves Let us recall the following sentence from chapter 11. “So, the energy released by the maximum possible magnetic force corresponds to the energy released by the electrostatic force; when dual changes happen”. Let us also recall the length value w = 1.063022744 mm found in chapter 12. Consider the Planck‟s equation E=hν, where h is the Planck‟s constant. Here E is the energy completely transferred when an electric field wave with the frequency ν (or, the wavelength c/ν) strikes a matter for one second. Here h is the energy of any electric field wave segment with the length equal to the wavelength. Sometimes h may be considered as the energy of a single photon. The value of h was used only in this context in chapter 13. The sentence mentioned above from chapter 11 induces us to propose a formula for magnetic field waves in the form: E = ⓗλ, where E is the energy 91
Planets and electromagnetic waves
completely transferred when a magnetic field wave with the wavelength λ strikes a matter for one second. Here ⓗ is a universal constant. The same sentence from chapter 11 induces one more thing. One has the relation hν = ⓗλ, for λ = (c/ν) = w. Then ⓗ
( (
) ( )
(
) )
(approximately). Nothing has been verified experimentally. However, it is understood that the energy which can be released in one second by an electric field wave increases as its wavelength decreases. But, the energy which can be released in one second by a magnetic field wave increases as its wavelength increases. So, the “penetrating capacity” of an electric field wave increases as its wavelength decreases, and the “penetrating capacity” of a magnetic field wave increases as its wavelength increases. X-rays are electric field waves with small wavelengths. They penetrate our bodies. If we expect a magnetic field wave to penetrate our bodies, it should have a long wavelength. A magnetic field wave with long wavelength can penetrate the concrete wall of an arm of LIGOs (see chapter 8) and it can reach inner metal tunnels. It is another reason to believe that LIGOs detected only magnetic field waves on 14th September 2015. We did not do experiments so far to generate 92
C. Ganesa Moorthy & G. Udhaya Sankar
magnetic field waves with long wavelengths, near LIGOs. We have to do experiments for limitations of wavelengths for non-harmfulness of magnetic field waves to our bodies, in connection with cell-phone towers and body scanners. However, it can be calculated from the theory and the values given above that an electric field wave with wave length 10-10 m (for x-ray) has an energy equal to the energy of a magnetic field wave with wavelength 11300 m, approximately, when energies are calculated for one second collisions. In general, an electric field wave with wavelength 10-10-n m (for n satisfying 0