Lorentz transformation

lorentz

Reference: Disturbance Theory

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From Wikipedia,

“In physics, the Lorentz transformations are coordinate transformations between two coordinate frames that move at constant velocity relative to each other. The transformations are named after the Dutch physicist Hendrik Lorentz.

“Frames of reference can be divided into two groups: inertial (relative motion with constant velocity) and non-inertial (accelerating in curved paths, rotational motion with constant angular velocity, etc.). The term “Lorentz transformations” only refers to transformations between inertial frames, usually in the context of special relativity.”

“Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame.”

Thus, the earth provides one reference frame, and the Sun provides another. Since the earth is moving relative to the sun, one would expect the velocity of light to be slightly different in the two reference frames. However, this difference is practically undetectable from the experiments conducted so far. This resulted in the assumption that speed of light is independent of the reference frame.

Is the assumption that the speed of light is independent of the reference frame, correct?

This assumption will definitely be correct if the speed of light is infinite. But the measurements show that the speed of light is 3 x 108 meters /second. It takes sunlight an average of 8 minutes and 20 seconds to travel from the Sun to the Earth. Why is the speed of light finite?

From the essay, The Inertial Frame and Space,

“The truth seems to be that matter cannot move freely through space.  Matter encounters resistance when pushed through space. This resistance is INERTIA.”

The speed of light is finite because its propagation through space is not without resistance. Light has a limiting speed because its acceleration is balanced by inertia.

The speed ‘c’ of light is the result of a balance of forces.

We know that the earth is always accelerating toward the sun; but it has hit a limiting speed because this acceleration is balanced by its inertia. This may be the case with the speed of all heavenly bodies.

A heavenly body has a limiting speed because its acceleration is balanced by its inertia.

It is the resistance between space and the moving object that limits the speed; therefore, we may use space as the common reference frame for both matter and energy.  This is the SRF (space reference frame) mentioned in The Inertial Frame and Space.

In SRF, the naturally balanced speeds of objects and radiation shall depend on their inertia. Light has a very high speed because its inertia is very small. The speed of the earth is likely to be very small because its inertia is very large. The speed of the sun shall be smaller still because its inertia is much larger than that of the earth.

This means that the speed of light shall be different relative to the earth and the sun.

The speed of light ‘c’ remains a universal constant in SRF. But it is not a constant in the reference frames of material origin.

The assumption that the speed of light is independent of the reference frame (of material origin) is theoretically incorrect.

This brings into question the usefulness of Lorenz transformations that are based on this assumption. This also brings into question those aspects of the Theory of Relativity that utilize Lorentz transformations.

Lorentz transformations have only a limited application.

There cannot be matter traveling at speeds that are significant fractions of the speed of light. Only sub-atomic particles with very small inertia can have speeds anywhere near the speed of light. But in that range more useful than velocities are frequencies, where the ratio of wavelength to period is ‘c’.

In Cosmology, Lorentz transformations may provide good approximations only for relative speeds that are very small compared to the speed of light. That happens to be the case in explaining the aberration of light.

In my opinion, the Theory of Relativity only resolves those difficult problems in physics, where the speeds are relatively very small compared to the speed of light. For larger relative speeds in the material realm, the speed of light cannot be held as a constant.

Lorentz transformations may provide good approximations only for relative speeds that are very small compared to the speed of light.

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June 15, 2017 – 9:03 AM Categories: Uncategorized | Post a comment

The Problem of Aether

Stellar_aberration_versus_the_dragged_aether
Reference: Disturbance Theory

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James Bradley’s (1729) explanation for aberration of light became unacceptable in 1804 because light was established to be a wave. It was no longer looked upon as corpuscular, which was assumed earlier by Newton. So, the medium of light (aether) became an issue.

The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of the observer.

Pre-1800 Corpuscular theory of light – Light was considered to be made up of particles that had inertia and they traveled in straight lines. Aberration of light was explained very simply by James Bradley using this model for light. It was shown that the telescope had to be tilted to capture a vertically descending light particle because earth moved. This created the angle of aberration.

1804 Thomas Young – He proved the wave nature of light through the famous double-slit experiment. This revived investigation into the nature of the medium through which light moved. This medium was viewed as aether that filled all space. It was completely elastic as it could transmit light over infinite distances.

1810 François Arago – He expected the speed of light to be different as corpuscles of light were supposed to be affected differently by the gravity of different stars. But light from different stars produced the same refractive index, and, therefore, had the same velocity. This negated Newton’s corpuscular theory of light, and supported a uniform medium of aether.

1816 Augustin-Jean Fresnel – Since the speed of light was constant in aether, he expected it to have different values relative to earth as earth changed its directions. However, Arago’s results negated that. Therefore, Fresnel postulated that earth’s velocity did account for the aberration of light, but aether was partially dragged at the point of measurement to maintain a constant velocity of light. Fresnel calculated an aether drag coefficient based on the refractive index that seemed to explain the inconsistency.

1887 Michelson & Morley – Earth was expected to have a velocity relative to aether in order to explain the aberration of light. However, the velocity of light was found to be constant regardless of the direction in which earth moved. This created the same inconsistency as the Arago’s experiment, but on a much larger scale.  This could not be explained by Fresnel’s partial ether drag hypothesis.

1905 Albert Einstein – He explained the inconsistency by dropping the aether model and returning to the corpuscular theory of light. This generates questions about the very nature of light. Light cannot be a wave. It cannot be a particle with significant inertia either. The questions now become,

  1. If light is made up of particles that do not require a medium to travel, then how do these particles coordinate their motion?

  2. Matter has relative speeds. Light seems to adjust its speed to ‘c’ relative to any matter. So, how does light and matter coordinate their motion?

  3. Are light particles made up of electromagnetic fields? Do they exist within larger fields? If not, then what do we have?

The theory of relativity is too mathematical and does not seem to answer these questions

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June 9, 2017 – 1:11 PM Categories: Science | Comments (1)

Aberration of light in SRF

Reference: Disturbance Theory

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Problem: Celestial objects have apparent motion. (See https://en.wikipedia.org/wiki/Aberration_of_light )

What is true position of the celestial objects?

ra_and_dec_on_celestial_sphere

Mean Equator and Equinox of J2000.0: This coordinate system is oriented with its xy-plane parallel to the mean Earth equator at epoch J2000.0, and its z-axis pointing toward the mean north celestial pole of J2000.0. The x-axis points toward the mean equinox of J2000.0. This coordinate system is used for expressing the positions of stars in catalogs and planets in basic solar system ephemerides.

Right Ascension: Angular distance on the celestial sphere measured eastward along the celestial equator from the equinox to the hour circle passing through the celestial object.

Declination: Angular distance on the celestial sphere north or south of the celestial equator. It is measured along the hour circle passing through the celestial object.

Distance: The distance from the center of the Earth to the Solar System object, given in astronomical units (kilometers for the Moon). Distance is not calculated for stars.

Celestial Sphere: An imaginary sphere of arbitrarily large radius, concentric with Earth. All objects in the observer’s sky can be thought of as projected upon the inside surface of the celestial sphere, as if it were the underside of a dome or a hemispherical screen. The celestial sphere is a practical tool for spherical astronomy, allowing observers to plot positions of objects in the sky when their distances are unknown or unimportant.

Shouldn’t there be a motion?

The celestial sphere does not rotate with the earth. But it moves around the sun with earth. This may affect the observation of true position.

Annual aberration — a deflection caused by the velocity of the Earth’s motion around the Sun, relative to an inertial frame. This is independent of the distance of the star from the Earth.

Light-time correction is a displacement in the apparent position of a celestial object from its true position (or geometric position) caused by the object’s motion during the time it takes its light to reach an observer.

Is the aberration of light constant for all celestial objects?

It appears to be so for stars. For objects in the solar system their speeds become relevant.

Why is James Bradley’s (1729) explanation not adequate for the aberration of light?

Bradley conceived of an explanation in terms of a corpuscular theory of light in which light is made of particles that do not require a medium. His classical explanation appeals to the motion of the earth relative to a beam of light-particles moving at a finite velocity, and is developed in the Sun’s frame of reference. However, once the wave nature of light was better understood, a medium needed to be accounted for.

The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of the observer.

Let a star be at distance ‘d’ from earth. Light takes time = ‘d/c’ to reach earth from the star. If earth is moving at velocity ‘v’, then it has moved a distance ‘v.d/c’ during the time star light reaches earth. The ratio of these two distances is ‘v/c’. This is the angle of aberration.

In SRF, the only motion visible is acceleration. Uniform motion is indistinguishable from ‘rest’. Earth is always accelerating toward the sun, so this motion shall be visble in SRF. Earth’s velocity ‘v’ is the result of balanced acceleration.

Light’s velocity ‘c’ is also the result of balanced acceleration. It is a limiting velocity. Light has velocity ‘c’ because it cannot be accelerated anymore.

The motion visible in SRF is balanced acceleration. So, the explanation given above for angle of aberration based on ‘v’ and ‘c’ shall be valid in SRF.

In SRF, the motion of planets shall be perceived as if they are moving in a groove carved in space. Light is moving, similarly, in a groove carved in space.

Conclusion:

James Bradley’s (1729) explanation for aberration of light became unacceptable in 1804 because light was established to be a wave. It was no longer looked upon as corpuscular as was assumed earlier by Newton. So, the medium of light (aether) became an issue.

In SRF (space reference frame), the aether is the space itself. From SRF point of view, the change in view of light from corpuscular to wave would not have created an issue in 1804 with the earlier 1729 explanation for aberration of light.

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June 8, 2017 – 7:09 AM Categories: Uncategorized | Post a comment

The Faraday Atom

Loop ball

Reference: Disturbance Theory

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The fundamental principles that Maxwell helped isolate are:

1.    A changing electric field produces a magnetic field of force

2.    A changing magnetic field produces an electric field of force

The next step is to generate a model based on these principles that we may visualize through Faraday’s lines of force.

When a current flows in a wire the magnetic lines of force loop around it. Similarly, when a magnet is moved through a wire loop, a current is generated in that loop. This gives us a basic structure as follows:

The electrical and magnetic lines of force may be visualized as two circular loops at right angles to each other, such that each loop passes through the center of the other loop.

If we model an atom based on Faraday’s lines of force, the entire atom shall consist of electrical and magnetic lines of forces coupled as above. There would be no sub-atomic particles. Such coupling can get quite complex as atoms grows in complexity.

Since the nucleus of an atom is positive, the electric lines of force in the atom would be mostly radial, and the magnetic lines of force would be mostly circumferential.

The atom is overall neutral. A neutral configuration shall consist of coupled electric and magnetic loops that are symmetrical. Symmetrical loops shall be circular. An asymmetric configuration shall consist of elongated loops resulting in charged or magnetized atom.

Under electrical induction, the electrical loop shall elongate producing positive and negative charge displacement. Under magnetic induction, the magnetic loop shall elongate producing North and South polarization.

When atoms are aligned in the plane of elongated electrical loops we shall have storage of electrical energy as in a capacitor. When atoms are aligned in the plane of elongated magnetic loops we shall have storage of magnetic energy as in a magnet.

It would be easy to distinguish between electric and magnetic lines of force.

When the opposite charges or poles exist in two separate objects situated close to each other, the elongated loop must pass through space from one to the other object. Here we have lines of forces that venture out in space but they always originate from and end in material atoms.  The displacement or polarization occurs in the atoms and not out in the space.

The “space medium” does not act like a dielectric as Maxwell assumed.

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The electromagnetic phenomenon, such as light, may exist in space by itself as follows.

  1. The lines of forces are traveling through space as pulses.
  2. They exist as simple loops without atomic configuration.
  3. The electric and magnetic loops are symmetrical.

A free charged particle, such as a free electron shall be one end of the stretched loop of electric line of force. The other end of this loop may be attached to an atom (a positive ion) or simply extended into infinity.

The atom as a neutral particle is not really isolated. The lines of force extend from the atom into surrounding space to other atoms.

The atoms may appear discrete but they are never isolated unto themselves. They all connected as a continuum of lines of force.

Please note that this is only a working model of “Faraday atom”. The electrical and magnetic lines are always transforming into each other at a certain frequency.

All lines of forces are dynamic.

The nucleus of the atom is also made up of lines of force. These are extensions of the electromagnetic lines of force, but they have much higher frequency.

The nuclear lines of force have characteristics different from electromagnetic lines of force.

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June 4, 2017 – 9:14 PM Categories: Physics | Post a comment

A Study of Maxwell

Maxwell Cover

Reference: Disturbance Theory

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Maxwell (1831 – 1879) constructed his theory of Electromagnetism based on the inspiration he got from the experimental research of Michael Faraday (1791 – 1867); but there was a fundamental difference. Faraday believed in the idea of a continuum of the force of nature permeating all space.  But Maxwell ended up siding with the idea of isolated entities moving through a void of empty space.

Maxwell didn’t intend it that way for he writes in the preface of his major work “A Treatise on Electricity & Magnetism”:

“Faraday, in his mind’s eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance: Faraday saw a medium where they saw nothing but distance: Faraday sought the seat of the phenomena in real actions going on in the medium, they were satisfied that they had found it in a power of action at a distance impressed on the electric fluids.”

Maxwell seems to have tried his best to unlock the mystery of action going on in the medium that Faraday sought, but he did not quite understand what Faraday meant by “force of nature”. Michael Faraday was quite clear in saying that his ideas involving “lines of force” were an alternative to the aether theory. But Maxwell couldn’t move beyond the mechanical view of nature as presented in the theory of aether.

The excellent article “Why Maxwell Couldn’t Explain Gravity” points out where Maxwell was influenced by the aether theory and diverged from the ideas of Michael Faraday.

“Maxwell’s understanding of the electrical force that exists between charged particles was based on the idea that even the ‘empty space’ of the vacuum is actually permeated with some kind of substance, called the ether, which consists of individual parts that can act as dielectrics… In simple terms, he pictured ordinary empty space, when devoid of any electric field, as consisting of many small pairs of positive and negative charge elements, and in the absence of an electric field the two opposite charges in each pair are essentially co-located, so there is no net change or electric potential observable at any point. If an electric potential is established across some region of this medium (e.g., empty space), it tends to pull the components of each pair apart slightly. Maxwell termed this an electric displacement in the medium. Of course, the constituent parts of the dielectric pairs attract each other, so the electric displacement is somewhat like stretching a little spring at each point in space.”

The article goes on to say,

“It’s interesting that this theory, which supposedly denies the intelligibility of distant action, nevertheless ends up invoking (albeit on a very small scale) what appears to be elementary attraction between distinct and separate entities.”

Maxwell was thus unable to unlock the mystery of action going on in the medium because he assumed charges to be discrete. Discreteness implies separation and, thus, action at a distance.

Thus, Maxwell could not provide a solution to the problem of “action at a distance” that Faraday sought with his “lines of force”. However, Maxwell’s work did pave the way that could lead one out of the limitations imposed by ideas, such as, the aether theory based on discrete particles.

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The most important conclusions that I draw from a study of Maxwell are as follows:

  1. A changing electric field produces a magnetic field of force

  2. A changing magnetic field produces an electric field of force

Thus, both electric and magnetic phenomena have to do with change and force. Change in one phenomenon seems to create force in another phenomenon. Therefore, each phenomenon seems to act as the potential for the other phenomenon. This is the bottom line in the conservation of energy.

This happens with light in space in the absence of discrete charge and mass. What part does charge and mass play? Is light the product of charge and mass, or is charge and mass the product of light? Or, is light, charge and mass the product of space?

  1. Per dimensional analysis provided by Maxwell, a charge has same characteristics as mass.

[M] = [Q] = [L3T -2] = Area x acceleration

Is the acceleration of two dimensional wave front of space in the third dimension somehow responsible for the production of light, charge and mass?

The questions asked in this essay shall be dealt with in subsequent essays.

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June 4, 2017 – 6:08 PM Categories: Physics | Comments (1)