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The Disturbance Spectrum

DL-Freq

Reference: Disturbance Theory

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A disturbance level is defined as logarithm of frequency on base 2, so that a wide range of disturbances can be conveniently displayed on a manageable scale,

The frequency of yellow light is 5.8 x 1014 Hz = 249 Hz. Therefore, the disturbance level of yellow light is referred to as DL49.

The Disturbance Level is calculated as, DL = log (frequency) / log 2

The Disturbance spectrum displays the frequencies of electromagnetic radiation and the de Broglie frequencies of mass particles in one place in the form of disturbance levels. Here are some of these disturbance levels.

Radio Waves (3 Hz – 3 GHz) ……………. DL 1.6 – 31

Microwaves (3 GHz – 300 GHz) ………… DL 31 – 38

Infrared (300 GHz – 300 THz) …………… DL 38 – 48.5

Visible (400 THz – 800 THz) …………….. DL 48.5 – 49.5

Ultraviolet (800 THz – 30 PHz) ………….. DL 49.5 – 54.7

X-Rays (30 PHz – 30 EHz) ……………….. DL 54.7 – 64.7

Gammy Rays (> 30 EHz) …………………. DL 64.7 and greater

Electron ……………………………………… DL 66.7

Proton ………………………………………… DL 77.6

Neutron ………………………………………. DL 77.6

Earth ………………………………………….. DL 235.6

This graph plots the levels of any disturbance as a function of frequency. The disturbance levels are defined in terms of the doubling of frequency. The basic disturbance DL0 has a frequency of 1 (20). The subsequent disturbance levels (DL 1, DL 2, DL 3 … DL n.) have frequencies of 21 (2), 22 (4), 23 (8) … 2n. It can be seen from this graph that negative disturbance levels may be postulated to exist with the halving of frequency. The frequency never reaches the zero of ground state. As long as some frequency is present, awareness is also present in some form.

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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?

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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Remedial Physics

CircumhorizonArcAcon

Physical Science 8th grade

The Physics Classroom

Schaum Beginning Physics I

Schaum beginning Physics II

Schaum Modern Physics

Asimov: Understanding Physics Volume 1

Asimov: Understanding Physics Volume 2

Asimov: Understanding Physics Volume 3

Maxwell: A Treatise on Electricity & Magnetism – Volume 1

Maxwell: A Treatise on Electricity & Magnetism – Volume 2

Faraday: Experimental Researches in Electricity – Volume 3

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COMMENTS: Einstein’s 1905 Paper on Relativity (Part 2)

OLYMPUS DIGITAL CAMERA

ReferenceDisturbance Theory

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This is continuation of the examination of Einstein’s postulates underlying his theory of Relativity, specifically, how these postulates were translated into his mathematics.

Einstein’s 1905 paper: http://www.fourmilab.ch/etexts/einstein/specrel/www/#tex2html1

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I. KINEMATICAL PART – § 1. Definition of Simultaneity

“Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the ‘stationary system’.” 

Einstein takes up a system of co­ordinates in which equations of Newtonian mechanics hold well. These he calls inertial frames in which a body remains at rest or moves with constant linear velocity unless acted upon by forces. This property of a body is called inertia.

Inertia represents the resistance to change in motion of a body in space. When this resistance is overcome there is acceleration. We have assumed all along that space is completely permeable to matter. This is not so as evidenced by inertia.

Therefore, matter is ‘stationary’ relative to space when there is no acceleration. All inertial frames in “uniform motion” are actually stationary relative to space. This we identified earlier as the space reference frame (SRF).

“If a material point is at rest relatively to this system of co-ordinates, its position can be defined relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean geometry, and can be expressed in Cartesian co-ordinates.”

A particle is essentially a disturbance propagating through space. This particle of disturbance has a configuration. As the complexity of this configuration increases, the inertia of the particle also increases, and its speed of propagation decreases. A light particle has the simplest configuration and its speed of propagation is ‘c’. An electron is a particle of complex configuration, whose speed is less than 1% of the speed of light. A neutron is a still more complex particle whose speed is thousand times still less.

Einstein’s “material point” refers to a matter particle that has a configuration more complex than that of a neutron. In its most complex configuration a matter particle shall have a speed that is infinitesimal compared to ‘c’. Euclidean geometry and Cartesian co-ordinates apply only to this extreme case of a matter particle. They do not apply to light particles.

All motion considered by Einstein is in reference to matter. This we identified earlier as the material reference frame (MRF). MRF represents a limiting case of a more general SRF that addresses a much wider range of particle configurations.

“If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by ‘time.’ We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, ‘That train arrives here at 7 o’clock,’ I mean something like this: ‘The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events’.”

The natural speed of propagation in space then depends on the complexity of configuration of a disturbance as particle. This we perceive as motion that is balanced by the inertia of the particle. Any change in this balance is perceived as acceleration. Acceleration implies presence of force.

Motion is described by the property of TIME. Time essentially describes the sequence of change. A change is referred back to the previous step in the sequence. Thus, time lies in the continuity of a sequence, and it is unique to the configuration of that sequence.

To compare two time sequences in terms of simultaneity they must have comparable configurations. This is reflected in comparability in terms of inertia of the particles. The property of time shall then be a function of inertia. The “time” that we are used to is tied with the material level of inertia. In other words, our experience of time depends on the inertial characteristic of MRF (material reference frame).

The “time” associated with light shall depend on the configuration of the light particle or its inertia. To consider simultaneity of time for matter and light particles, their relative inertia shall have to be taken into account.

“It might appear possible to overcome all the difficulties attending the definition of ‘time’ by substituting ‘the position of the small hand of my watch’ for ‘time.’ And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or—what comes to the same thing—to evaluate the times of events occurring at places remote from the watch.”

The “time characteristics” of particles of different inertia shall be measurable from a “particle” that has no inertia.  Such a particle may be postulated as “undisturbed space”. We can then assess the “simultaneity” of two particles by determining their “time characteristics” in terms of their inertia.

The complexity of configuration, and thus the inertia of a particle may be measured in terms of “disturbance levels” as described earlier in The Disturbance Theory. On this scale the disturbance level of zero is a frequency of 1. The disturbance level of 77.6 represents a neutron. All higher disturbance levels represent matter. Earth has a disturbance level of about 235.

At the disturbance levels of matter the wavelength, period and speed become infinitesimal; and the sinusoidal variations in time and space become imperceptible. Time and space then acquire an appearance of constancy that does not exist at electrodynamic and quantum levels.

“We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought.”

The idea of observer basically represents the characteristics of the reference frame that is being used to interpret motion. The time measured by Einstein’s clocks follows the inertial characteristics of matter. To combine the velocity of light with material velocity would be equivalent to assuming light to have same inertial characteristics as matter. Any mathematics that combines the velocity of light with material velocity using simple addition or subtraction shall lead to erroneous results. It would be like adding a penny to a dollar and calling it two coins of same magnitude.

Unfortunately, Einstein’s mathematics does just that in the rest of this section. We shall skip this mathematics and focus on those aspects of Einstein’s theory that make correct predictions of physical phenomena. Hopefully, a closer look at such aspects will provide better insight into Einstein’s thinking.

[To be continued…]

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Exercises: Mindfulness (Set 1)

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Reference: Mindfulness Approach

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Mindfulness is seeing things as they are. It provides the discipline for looking and contemplation

The following exercises help you see things as they are. You may do them while sipping coffee in a café, or strolling along a river. You may even find a place where you can sit comfortably for a while without being disturbed, and then patiently observe the world go by.

Desires make one want certain outcomes. This leads to speculations that have no basis other than one’s expectations. But, it is only when you know what is there can you predict future in a reasonable and consistent manner.

Familiarity makes one assume certain things to be there. The visualization is already there in the mind, and it gets superimposed over what is there. However familiar something may be it is never permanent and it may not actually be there.

If something is missing then recognize that it is missing. Do not imagine something in its place. If someone asks you a question and no answer comes up in your mind, then do not feel obliged to make up an answer. Accept that you do not have an answer..

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EXERCISE # 1: Desires and Expectations

PURPOSE:  To discern the influence of desires and expectations on the perception of what is there.

PREREQUISITE:  Review Exercises: Discerning the Environment.

STEPS:

  1. In this exercise you simply become aware of desires and expectations that may influence observation.

  2. Notice the environment and the people in a causal, easygoing manner.

  3. Notice if there is a desire and expectation accompanying your observation.

    For example, you may see a person in priestly robes and have a desire to trust him implicitly. This is one expects from a man of God.

  4. Simply become aware of that desire, and move on. Do not interfere with the desire present. Do not avoid, resist, suppress, or deny any other thoughts or feelings arising in the mind.

  5. If there are extraneous thoughts arising in your mind, notice if they is an underlying desire. Simply become aware of what is there and move on.

  6. If there is uncontrolled thinking going on in your mind, notice if there is an effort to predict something. Simply become aware of what is there and move on.

  7. If there are unanswered questions swirling around, notice if there are expectations attached to them. Simply become aware of what is there and move on.

  8. If a question is really important, and it needs to be resolved, then note it down to be researched later. Do not avoid, resist, suppress, or deny any question. Simply become aware of what is there and move on.

  9. Expand your span of attention to as wide a context as possible, and let the physical and mental perceptions pour in, while doing this exercise.

  10. This exercise is done for 20 minute, which is the normal duration of a session. Several sessions may be given during a day, and over the course of days, until progress is observed.

  11. This exercise is completed when it becomes effortless.

  12. When this exercise is completed you may proceed to the next exercise.

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EXERCISE # 2: Assumptions

PURPOSE:  To discern the influence of assumptions on the perception of what is there.

PREREQUISITE:  Exercise # 1 above.

STEPS:

  1. In this exercise you simply become aware of assumptions that may influence observation.

  2. Notice the environment and the people in a causal, easygoing manner.

  3. As you observe, see if the actual perceptions are different from how they should be according to the ideas in your mind.

    For example, you may see only the profile of a stranger, and see only one ear. But your mind tells you that he has two ears, because “all men have two ears.” He may have two ears but you don’t see them. The chances are slim but this stranger may have only one ear. Those, who are aware of their assumptions, are mindful.

  4. Simply become aware of the assumptions, and move on. Do not interfere with the assumptions present. Do not avoid, resist, suppress, or deny any other thoughts or feelings arising in the mind.

  5. As you observe, see if you are being judgmental about some situation.

    For Example: You may look at a person of certain sex, color, profession or cultural background. This may bring up certain preconceived ideas. Separate the actual perception from the ideas contained in the mind.

  6. Notice the preconceived ideas present one by one. Simply become aware of what is there and move on.

  7. As you observe, see if there is something that does not make sense. Notice if any of your own ideas are contributing to that confusion. Simply become aware of what is there and move on.

  8. Expand your span of attention to as wide a context as possible, and let the physical and mental perceptions pour in, while doing this exercise.

  9. This exercise is done for 20 minute, which is the normal duration of a session. Several sessions may be given during a day, and over the course of days, until progress is observed.

  10. This exercise is completed when it becomes effortless.

  11. When this exercise is completed you may proceed to the next exercise.

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EXERCISE # 3: Something Missing

PURPOSE:  To discern the influence of something missing on the perception of what is there.

PREREQUISITE:  Exercise # 2 above.

STEPS:

  1. In this exercise you simply become aware of something missing that may influence observation.

  2. Notice the environment and the people in a causal, easygoing manner.

  3. Notice something that is puzzling, and about which full understanding is missing. Do not feel obliged to accept the explanations given; instead focus on what is puzzling.

  4. Carefully consider the broad context of the scene, and the purpose of the activity. Notice something specific that really does not make sense. Examine it closely including your viewpoint with respect to it.

  5. Observe your mind imagining reasons to fill the uncomfortable gap in understanding. Simply become aware of what is missing and move on.

  6. Notice questions you have for which satisfactory “answers” are missing. Examine the answers you have and notice what really does not make sense.

  7. Notice the impulse to come up with an answer. If there is no answer then acknowledge the fact. Do not make up an answer. Simply become aware of what is missing and move on.

  8. Repeat the above steps noticing things that are puzzling and for which satisfactory answers re not available.

  9. Expand your span of attention to as wide a context as possible, and let the physical and mental perceptions pour in, while doing this exercise.

  10. This exercise is done for 20 minute, which is the normal duration of a session. Several sessions may be given during a day, and over the course of days, until progress is observed.

  11. This exercise is completed when it becomes effortless.

  12. When this exercise is completed you may proceed to the next exercise.

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