Fundamentals of Physics

  1. Faraday: On the Conservation of Force
  2. Einstein: 1905 Paper #1 on Light Quanta
  3. Einstein: 1905 Paper #2 on Molecular Dimensions
  4. The Quantum
  5. Newtonian Concepts for Quantum Age
  6. The Spectrum of Substance 
  7. “Energy” in Quantum Mechanics
  8. “Force” in Quantum Mechanics
  9. “Motion” in Quantum Mechanics
  10. Newton’s Fourth Law
  11. “Charge” in Quantum Mechanics
  12. Feynman on Quantum Behavior
  13. Higgs Mechanism

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“Motion” in Quantum Mechanics

Reference: Fundamentals of Physics

In Classical Mechanics, we are looking at the motion of objects that have a precise center of mass (CM). Therefore, their position can be represented by a dimensionless point in space. Their speed can be measured by the relative motion of this dimensionless point. We are familiar with this as Galilean relativity.

But in Quantum Mechanics, we are looking at the motion of particles with no CM. An electron or photon cannot be pinpointed with accuracy because it has no CM. They cannot be treated as dimensionless points. The concept of motion is very different for such particles; and it cannot be visualized like the motion of material particles.

Electron and photons are built of cycles of motion. Their size and speed as a particle is determined by the frequency of their cycles.

The idea of mass comes from particles that make up the nucleus of an atom, such as, neutrons and protons. These particles are extremely small and made up of an extremely high frequency of cycles. They represent “mass.” The largest stable nucleus of an atom consists of 83 protons and 126 neutrons. But the size of this nucleus is still so small that it can be approximated as a point.

Mass may be looked upon as extremely high frequency of cycles packed in an extremely small size. 

We may say that an atom has its nucleus as its CM. When the atoms are arranged in a fixed configuration in a solid object, then that object has a CM. Even liquid and gaseous objects made of atoms will have a CM that can be determined statistically. This is classical mechanics. But in Quantum mechanics the situation is quite different.

An electron is 1836 times loosely packed with “mass” as a proton. We may visualize that proton to be embedded at the center of the electron in a hydrogen atom. This makes an electron to be roughly of the size of the hydrogen atom. We may not be able to measure sizes accurately at atomic level; but we can say with certainty that the size of an electron is much bigger than the size of a proton. 

The size of an electron is roughly thousands of time bigger than the size of a proton.

The relative sizes of quantum particles may be estimated by the ratios of their wavelengths. Since the speed of light is a universal constant, this ratio will be inverse of the ratio of their frequencies. Therefore, the smaller is the frequency the larger would be the size of a quantum particle. Using the data from The Spectrum of Substance, we may say that

An electron is 2000 times bigger than a proton.

A photon of visible light is more than 200,000 times bigger than an electron.

A proton appears as a point in classical space. The electron may appear as a point in a classical space expanded 2000 times. Similarly, the photon may appear as a point in classical space expanded 400,000,000 times.

A particle’s speed is zero relative to itself in its own space. Therefore, an electron’s speed will be zero relative to itself in “electron space”. Similarly, the speed of a photon will be zero relative to itself in “photon space”.

All this adds up to “absolute speeds” of particles being in a ratio that is inverse of the ratio of their frequencies. The higher is the frequency the lower will be the absolute speed. This appears to be valid when we calculate the ratio of the frequency of the proton to the frequency of the photon.

The desired ratio =  277.6 / 249  =  228.6  =  4 x 108

This is of the same order as the speed of light in the inertial frame of matter. This value is higher because the frequency of neutron is slightly higher than the average frequency of matter.

We may say that the “absolute speed” of a particle is inversely proportional to its frequency.

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Definitions

MOTION
Motion is self-actuated and inherently free aliveness as observed in the motion of light and the electrons. It is infinite when it is free. Motion becomes bounded and finite when it is cyclic. With the increase of cycles, the motion becomes increasingly centered. It then takes force to move it away from that centeredness. That resistance of motion to being changed is called inertia. Pure motion is an absence of cycles and inertia.

PARTICLE
A particle is a unit of substance whose size is proportional to its wavelength. Electron as a particle is 2000 times bigger than a proton. Photon as a particle is more than 200,000 times bigger than an electron. The boundary of a particle is determined by the cycles of motion of which it is constructed. A particle has the property of centeredness, which is proportional to its frequency. This centeredness is manifested as inertia when attempt is made to change its inherent motion.

SPEED
The concept of speed applies to a particle. The measure of absolute speed of a particle is inverse of its centeredness. Since the “particle” of gravity is least centered, its speed is infinite. This means that the particle of gravity is manifested instantly at any location in the universe. Thus, speed has the sense of the rapidity with which a particle is manifested at a location in the universe after being manifested at another location.  

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BUDDHISM: The Eightfold Path

Reference: Buddhism

[NOTE: In color are Vinaire’s comments.]

The result of right concentration is not simply a new philosophy of life; but a regeneration: change into a different kind of creature, who experienced the world in a new way.

The Buddha’s approach to the problem of life in the Four Noble Truths was essentially that of a physician. He began by examining carefully the symptoms that provoke concern. If everything were going smoothly, so smoothly that we noticed ourselves as little as we normally notice our digestion, there would be nothing to worry about and we would have to attend no further to our way of life. But this is not the case. There is less creativity, more conflict, and more pain than we feel there should be. These symptoms the Buddha summarized in the First Noble Truth, with the declaration that life is dukkha, or out of joint. The next step was diagnosis. Throwing rites and faith to the winds, he asked, practically, what is causing these abnormal symptoms? Where is the seat of the infection? What is always present when suffering is present, and absent when suffering is absent? The answer was given in the Second Noble Truth: the cause of life’s dislocation is tanha, or the drive for private fulfillment. What, then, of the prognosis? The Third Noble Truth is hopeful: the disease can be cured by overcoming the egoistic drive for separate existence. This brings us to prescription; how is this overcoming to be accomplished? The Fourth Noble Truth provides the answer. The way to the overcoming of self-seeking is through the Eightfold Path.

The Fourth Noble Truth provides the prescription to the overcoming the egoistic drive for separate existence, which throws life out of joint.

The Eightfold Path, then, is a course of treatment. But it is not an external treatment, to be accepted passively by the patient as coming from without. It is not treatment by pills, or rituals, or grace. Instead, it is treatment by training. People routinely train for sports and their professions, but with notable exceptions like Benjamin Franklin, they are inclined to assume that one cannot train for life itself. The Buddha disagreed. He distinguished two ways of living. One—a random, unreflective way, in which the subject is pushed and pulled by impulse and circumstance like a twig in a storm drain—he called “wandering about.” The second, the way of intentional living, he called the Path. What he proposed was a series of changes designed to release the individual from ignorance, unwitting impulse, and tanha. It maps a complete course; steep grades and dangerous curves are posted, and rest spots indicated. By long and patient discipline, the Eightfold Path intends nothing less than to pick one up where one is and set one down as a different human being, one who has been cured of crippling disabilities. “Happiness he who seeks may win,” the Buddha said, “if he practice.”

The cure comes about when the Eightfold Path is practiced.

What is this practice the Buddha is talking about? He breaks it down into eight steps. They are preceded, however, by a preliminary he does not include in his list, but refers to so often elsewhere that we may assume that he was presupposing it here. This preliminary step is right association. No one has recognized more clearly than the Buddha the extent to which we are social animals, influenced at every turn by the “companioned example” of our associates, whose attitudes and values affect us profoundly. Asked how one attains illumination, the Buddha began: “An arouser of faith appears in the world. One associates oneself with such a person.” Other injunctions follow, but right association is so basic that it warrants another paragraph.

The preliminary step is right association.

When a wild elephant is to be tamed and trained, the best way to begin is by yoking it to one that has already been through the process. By contact, the wild one comes to see that the condition it is being led toward is not wholly incompatible with being an elephant—that what is expected of it does not contradict its nature categorically and heralds a condition that, though startlingly different, is viable. The constant, immediate, and contagious example of its yoke-fellow can teach it as nothing else can. Training for the life of the spirit is not different. The transformation facing the untrained is neither smaller than the elephant’s nor less demanding. Without visible evidence that success is possible, without a continuous transfusion of courage, discouragement is bound to set in. If (as scientific studies have now shown) anxieties are absorbed from one’s associates, may not persistence be assimilated equally? Robert Ingersoll once remarked that had he been God he would have made health contagious instead of disease; to which an Indian contemporary responded: “When shall we come to recognize that health is as contagious as disease, virtue as contagious as vice, cheerfulness as contagious as moroseness?” One of the three things for which we should give thanks every day, according to Shankara, is the company of the holy; for as bees cannot make honey unless together, human beings cannot make progress on the Way unless they are supported by a field of confidence and concern that Truthwinners generate. The Buddha agrees. We should associate with Truthwinners, converse with them, serve them, observe their ways, and imbibe by osmosis their spirit of love and compassion. 

We should associate with Truthwinners, converse with them, serve them, observe their ways, and imbibe by osmosis their spirit of love and compassion. 

With this preliminary step in place we may proceed to the Path’s eight steps proper. 

1. Right Views. A way of life always involves more than beliefs, but it can never bypass them completely, for in addition to being social animals, as was just noted, human beings are also rational animals. Not entirely, to be sure—the Buddha would have been quick to acknowledge this. But life needs some blueprint, some map the mind can trust if we are to direct our energies purposively. To return to the elephant for illustration, however great the danger in which it finds itself, it will make no move to escape until it has first assured itself that the track it must tread will bear its weight. Without this conviction it will remain trumpeting in agony in a burning wagon rather than risk a fall. Reason’s most vociferous detractors must admit that it plays at least this much of a role in human life. Whether or not it has the power to lure, it clearly holds power of veto. Until reason is satisfied, an individual cannot proceed in any direction wholeheartedly. 

Until reason is satisfied, an individual cannot proceed in any direction wholeheartedly. 

Some intellectual orientation, therefore, is needed if one is to set out other than haphazardly. The Four Noble Truths provide this orientation. Suffering abounds, it is occasioned by the drive for private fulfillment, that drive can be tempered, and the way to temper it is by traveling the Eightfold Path.

The Four Noble Truths provide this orientation.

2. Right Intent. Whereas the first step summoned us to make up our minds as to what life’s problem basically is, the second advises us to make up our hearts as to what we really want. Is it really enlightenment, or do our affections swing this way and that, dipping like kites with every current of distraction? If we are to make appreciable headway, persistence is indispensable. People who achieve greatness are almost invariably passionately invested in some one thing. They do a thousand things each day, but behind these stands the one thing they count supreme. When people seek liberation with single-mindedness of this order, they may expect their steps to turn from sliding sandbank scrambles into ground-gripping strides. 

People who achieve greatness are almost invariably passionately invested in some one thing. 

3. Right Speech. In the next three steps we take hold of the switches that control our lives, beginning with attention to language. Our first task is to become aware of our speech and what it reveals about our character. Instead of starting with a resolve to speak nothing but the truth—one that is likely to prove ineffective at the outset because it is too advanced—we will do well to start further back, with a resolve to notice how many times during the day we deviate from the truth, and to follow this up by asking why we did so. Similarly with uncharitable speech. Begin not by resolving never to speak an unkind word, but by watching one’s speech to become aware of the motives that prompt unkindness.

Begin not by resolving never to speak an unkind word, but by watching one’s speech to become aware of the motives that prompt unkindness. Same with untruth.

After this first step has been reasonably mastered, we will be ready to try some changes. The ground will have been prepared, for once we become aware of how we do talk, the need for changes will become evident. In what directions should the changes proceed? First, toward veracity. The Buddha approached truth more ontologically than morally; he considered deceit more foolish than evil. It is foolish because it reduces one’s being. For why do we deceive? Behind the rationalizations, the motive is almost always fear of revealing to others or to ourselves what we really are. Each time we give in to this “protective tariff,” the walls of our egos thicken to further imprison us. To expect that we can dispense with our defenses at a stroke would be unrealistic, but it is possible to become progressively aware of them and recognize the ways in which they hem us in. 

Once we become aware of how we do talk, the need for changes will become evident. Be what you truly are.

The second direction in which our speech should move is toward charity. False witness, idle chatter, gossip, slander, and abuse are to be avoided, not only in their obvious forms but also in their covert ones. The covert forms—subtle belittling, “accidental” tactlessness, barbed wit—are often more vicious because their animus is veiled.

The second direction in which our speech should move is toward charity.

4. Right Conduct. Here, too, the admonition (as the Buddha detailed it in his later discourses) involves a call to understand one’s behavior more objectively before trying to improve it. The trainee is to reflect on actions with an eye to the motives that prompted them. How much generosity was involved, and how much self-seeking? As for the direction in which change should proceed, the counsel is again toward selflessness and charity. These general directives are detailed in the Five Precepts, the Buddhist version of the second or ethical half of the Ten Commandments:

Understand your behavior more objectively before trying to improve it. Any change should proceed toward selflessness and charity as spelled out in the Five Precepts below.

Do not kill. Strict Buddhists extend this proscription to animals and are vegetarians.
Do not steal.
Do not lie.
Do not be unchaste. For monks and the unmarried, this means continence. For the married it means restraint in proportion to one’s interests in, and distance along, the Path.
Do not drink intoxicants. It is reported that an early Russian Czar, faced with the decision as to whether to choose Christianity, Islam, or Buddhism for his people, rejected the latter two because both included this fifth proscription.

5. Right Livelihood. The word “occupation” is well devised, for our work does indeed occupy most of our waking attention. Buddha considered spiritual progress to be impossible if the bulk of one’s doings pull against it: “The hand of the dyer is subdued by the dye in which it works.” Christianity has agreed. While explicitly including the hangman as a role society regrettably requires, Martin Luther disallowed usurers and speculators. 

One’s occupation should not pull against one’s spiritual progress.

For those who are intent enough on liberation to give their entire lives to the project, right livelihood requires joining the monastic order and subscribing to its discipline. For the layperson it calls for engaging in occupations that promote life instead of destroying it. Again the Buddha was not content with generalizing. He named names—the professions of his day he considered incompatible with spiritual seriousness. Some of these are obvious: poison peddler, slave trader, prostitute. Others if adopted worldwide would be revolutionary: butcher, brewer, arms maker, tax collector (profiteering was then routine). One of the number continues to be puzzling. Why did the Buddha condemn the occupation of caravan trader? 

Engage in occupations that promote life instead of destroying it. 

While the Buddha’s explicit teachings about work were aimed at helping his contemporaries decide between occupations that were conducive to spiritual progress and ones that impeded it, there are Buddhists who suggest that if he were teaching today he would be less concerned with specifics than with the danger that people forget that earning a living is life’s means, not life’s end.

Earning a living is life’s means, not life’s end.

6. Right Effort. The Buddha laid tremendous stress on the will. Reaching the goal requires immense exertion; there are virtues to be developed, passions to be curbed, and destructive mind states to be expunged so compassion and detachment can have a chance. “‘He robbed me, he beat me, he abused me’—in the minds of those who think like this, hatred will never cease.” But the only way such crippling sentiments can be dispelled, indeed the only way to shake off fetters of any sort, is by what William James called “the slow dull heave of the will.” “Those who follow the Way,” said Buddha, “might well follow the example of an ox that marches through the deep mire carrying a heavy load. He is tired, but his steady gaze, looking forward, will never relax until he comes out of the mire, and it is only then he takes a respite. O monks, remember that passion and sin are more than the filthy mire, and that you can escape misery only by earnestly and steadily thinking of the Way.” Velleity—a low level of volition, a mere wish not accompanied by effort or action to obtain it—won’t do.

Reaching the goal requires immense exertion; there are virtues to be developed, passions to be curbed, and destructive mind states to be expunged so compassion and detachment can have a chance.

In discussing right effort, the Buddha later added some after-thoughts about timing. Inexperienced climbers, out to conquer their first major peak, are often impatient with the seemingly absurd saunter at which their veteran guide sets out, but before the day is over his staying pace is vindicated. The Buddha had more confidence in the steady pull than in the quick spurt. Stretched too taut, a string will snap; a plane that ascends too sharply will crash. In China the author of the Tao Te Ching made the point with a different image: “He who takes the longest strides does not walk farthest.”

The Buddha had more confidence in the steady pull than in the quick spurt. 

Because the West has found the last two steps in the Eightfold Path of special importance for the understanding of the human mind and its workings—there are several meditation centers in the United States, catering disproportionately to mental health professionals, that are dedicated exclusively to their practice—these will be discussed at greater length. 

7. Right Mindfulness. No teacher has credited the mind with more influence over life than did the Buddha. The best loved of all Buddhist texts, the Dhammapada, opens with the words, “All we are is the result of what we have thought.” And respecting the future, it assures us that “all things can be mastered by mindfulness.” 

All we are is the result of what we have thought. All things can be mastered by mindfulness.

Among Western philosophers, Spinoza stands closest to the Buddha on the mind’s potential. Spinoza’s dictum—“to understand something is to be delivered of it”—comes close to summarizing his entire ethic. The Buddha would have agreed. If we could really understand life, if we could really understand ourselves, we would find neither a problem. Humanistic psychology proceeds on the same assumption. When “awareness of experience is fully operating,” Carl Rogers writes, “human behavior is to be trusted, for in these moments the human organism becomes aware of its delicacy and tenderness towards others.” The Buddha saw ignorance, not sin, as the offender. More precisely, insofar as sin is our fault, it is prompted by a more fundamental ignorance—most specifically, the ignorance of our true nature. 

Insofar as sin is our fault, it is prompted by a more fundamental ignorance—most specifically, the ignorance of our true nature. 

To gradually overcome this ignorance, the Buddha counsels such continuous self-examination as to make us wilt (almost) at the prospect, but he thought it necessary because he believed that freedom—liberation from unconscious, robot-like existence—is achieved by self-awareness. To this end he insisted that we seek to understand ourselves in depth, seeing everything minutely, “as it really is.” If we maintain a steady attention to our thoughts and feelings, we perceive that they swim in and out of our awareness, and are in no way permanent parts of us. We should witness all things non-reactively, especially our moods and emotions, neither condemning some nor holding on to others. A miscellany of other practices are recommended, some of which are these: The aspirant is to keep the mind in control of the senses and impulses, rather than being driven by them. Fearful and disgusting sights are to be meditated on until one no longer experiences aversion toward them. The entire world should be pervaded with thoughts of loving-kindness. 

The aspirant is to keep the mind in control of the senses and impulses, rather than being driven by them. Fearful and disgusting sights are to be meditated on until one no longer experiences aversion toward them. The entire world should be pervaded with thoughts of loving-kindness. 

Out of the semi-alertness that comprises the consciousness of the average human being, this seventh step summons the seeker to steady awareness of every action that is taken, and every content that turns up in one’s stream of consciousness. The adept becomes aware of the moment when sleep takes over, and whether breath was coming in or going out at that moment. Obviously, this takes practice. In addition to working at it continuously to some extent, special times should be allotted for undistracted introspection. Periods of complete withdrawal for the purpose must also be built into one’s schedule. 

This seventh step summons the seeker to steady awareness of every action that is taken, and every content that turns up in one’s stream of consciousness.

Here is a Western observer’s description of monks in Thailand practicing this seventh step: 

One of them spends hours each day slowly walking about the grounds of the wat in absolute concentration upon the minutest fraction of every action connected with each step. The procedure is carried into every single physical act of daily life until, theoretically, the conscious mind can follow every step that goes into the generation of a feeling, perception or thought. A fifty-year-old monk meditates in a small graveyard adjoining his wat, because he’s undisturbed there. He seats himself, cross-legged and immobile but with his eyes open, for hours on end—through the driving rain at midnight or the blistering heat of noonday. His usual length of stay is two or three hours. 

Through this practice one arrives at a number of insights: (1) Every emotion, thought, or image is accompanied by a body sensation, and vice versa. (2) One discerns obsessive patterns in what arises in one’s mind and how these patterns constitute our misery (dukkha). For some it is a nursing of old grievances; others find themselves preoccupied with longings and self-pity, and still others simply feel at sea. With continuing practice the obsessive grip of these patterns loosens. (3) Every mental and physical state is in flux; none is solid and enduring. Even physical pain is a series of discrete sensations that can suddenly change. (4) The meditator realizes how little control we have over our minds and our physical sensations, and how little awareness we normally have of our reactions. (5) Most important, one begins to realize that there is nobody behind the mental/physical events, orchestrating them. When the capacity for microscopic attention is refined, it becomes apparent that consciousness itself is not continuous. Like the light from a light bulb, the on/off is so rapid that consciousness seems to be steady, whereas in fact it is not. With these insights, the belief in a separate self-existent self begins to dissolve.

With this close examination of one’s nature, one starts to realize that there is no separate self-existent self.

8. Right Concentration. This involves substantially the techniques we have already encountered in Hinduism’s raja yoga and leads to substantially the same goal. In his later years the Buddha told his disciples that his first intimations of deliverance came to him before he left home when, still a boy and sitting one day in the cool shade of an apple tree in deep thought, he found himself caught up into what he later identified as the first level of the absorptions. It was his first faint foretaste of deliverance, and he said to himself, “This is the way to enlightenment.” It was nostalgia for the return and deepening of this experience, as much as his disillusionment with the usual rewards of worldly life, that led him to his decision to devote his life completely to spiritual adventure. The result, as we have seen, was not simply a new philosophy of life. It was regeneration: change into a different kind of creature, who experienced the world in a new way. Unless we see this, we shall be unequipped to fathom the power of Buddhism in human history. Something happened to the Buddha under that Bo Tree, and something has happened to every Buddhist since who has persevered to the final step of the Eightfold Path. Like a camera, the mind had been poorly focused, but the adjustment has now been made. With the “extirpation of delusion, craving, and hostility,” the three poisons, we see that things were not as we had supposed. Indeed, suppositions of whatsoever sort have vanished, to be replaced by direct perception. The mind reposes in its true condition.

The result of right concentration is not simply a new philosophy of life; but a regeneration: change into a different kind of creature, who experienced the world in a new way. Suppositions of whatsoever sort vanish, to be replaced by direct perception. The mind reposes in its true condition.

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“Force” in Quantum Mechanics

Reference: Fundamentals of Physics

Quantum mechanics started with the study of black body radiation. It is, therefore, the mechanics of radiative energy. It not only applies to the radiative energy inside the atom, but also to the radiative energy out in the broad universe. Quantum mechanics’ object of study is much wider than the classical study of matter. 

As we have already established, the concept of force is more basic than the concept of energy. This concept originated in the context of matter. We now want to understand force in the context of the universe. 

Force comes about when there is a change in momentum, as in slowing, curving or reflecting of motion. This requires the universe to have a boundary where motion is slowed, curved or reflected. The universe is, therefore, finite with a boundary. We have explained elsewhere that the universe implies awareness. Beyond the universe there is non-awareness.

When motion slows, curves or reflects, it means that the motion is cyclic. The cycles have a frequency. The frequency could be extremely slow or extremely high.

Force gets its meaning from cyclic motion, as in E = hf, where E has the sense of force with substance.

Thus, more basic than force is the concept of cyclic motion, which has the property of frequency.

Force comes about when there is a change in motion, such as in the case of an impact. Change in motion occurs in terms of change in the frequency of cycles. This is seen as acceleration or deceleration in classical mechanics.

Force comes about in an impact because motion has the property of “centeredness” and it resists being changed. That means motion has a tendency to maintain its frequency. This tendency is referred to as inertia in classical mechanics.

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Definitions

FORCE
Force is the manifestation of acceleration or deceleration in motion caused by a change in frequency. This is sensed in our very being. It underlies all our physical senses. All our perception is based on force. Any sense of substantialness comes from impacts on our sense organs. The impact is always in the form of force. This is what defines any substance. 

This was Faraday’s view of force. Maxwell defined it mathematically as “the tendency of a body to pass from one place to another,” that depended upon “the amount of change of tension which that passage would produce.” Unlike Faraday, Maxwell did not relate force directly to the nature of substance.

INERTIA
Inertia is the tendency of the motion to continue in its course. Any effort to change that course is met with resistance. Inertia is caused by the cyclic nature of motion. The cycles make the motion centered and finite. As the cycles increase in frequency, the motion becomes more centered and finite. This increases the inertia of motion. In fact, inertia may be measured in terms of frequency of motion.

Inertia is manifested only when the course of motion changes, as during an impact. There is an acceleration or deceleration of motion. This phenomena of inertia underlies the sense of touch. It also underlies during any contact, such as, between the eye and light. 

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“Energy” in Quantum Mechanics

Reference: Fundamentals of Physics

Energy is a classical concept that applies to Newtonian mechanics as “the capacity for doing work.” But this same word “energy” has gone through a fundamental shift in its meaning in Quantum Mechanics.

The word QUANTUM means, “quantity or amount”. It refers to the smallest quantity of radiant energy, equal to Planck’s constant times the frequency of the associated radiation (E = hf). “Quantity of radiant energy” means that radiant energy is a substance that can be collected and measured. This is a revolutionary thought. 

Quantum refers to “the smallest quantity of substance,” where substance means “something substantial enough to be sensed.” 

The basis of substance is impact, which comes from a change in momentum. This is the classical definition of force. Light has momentum. Light can have impact and force. Therefore, light is substance. It was for establishing the reality of quantum as quantity of substance, which he demonstrated through the phenomenon of photoelectricity, that Einstein got a Nobel Prize.

The classical sense of energy is derived from force as the product “force x distance.” Thus, energy is a mathematical concept, much like the “lagrangian” and “hamiltonian” functions. But force is a real concept that can be experienced. The concept of “energy” in Quantum Mechanics is closer to the sense of force and substance.

Quantum is closer to the basic sense of FORCE as in the “impact of substance” than to ENERGY as in the “capacity for doing work.”

It was Faraday who first articulated that the concept of force is more basic than energy in his thesis: On the Conservation of Force. Maxwell, who applied mathematics to Faraday’s ideas, disagreed with Faraday on his notion of force (see Faraday & Maxwell). But Einstein, who kept a picture of Faraday on his wall, did understand the notion of force as Faraday intended.

Thanks to Faraday and Einstein, that we can visualize a broad spectrum of substance today (see The Spectrum of Substance). The concept of substance translates into having an atom-less consistency and not just atomic mass. The concept of inertia is not just limited to mass, but it applies to consistency as well.

Mass is, essentially, “frozen inertia” as in the case of the nucleus of atom. It is more like “liquid inertia” as in the case of electrons; and it is “vaporized inertia” as in the case of radiant energy. The property of inertia is the core of substance as it generates sensation.

Underlying substance, mass, consistency and inertia is the concept of FORCE.

This force is proportional to frequency.

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Definition

ENERGY
Energy is a mathematical concept derived from force. It is a mathematical function, much like the “lagrangian” and “hamiltonian” functions. 

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