text:
Self-sufficient, self-reliant, and dynamic, the mind expresses knowledge not as content but as capacity.[1]

- Tarthang Tulku

## What is Reality?

At the most fundamental level of reality the Gforce is a dynamic, highly inertial existence that gives rise to the fabric of Aether.  Distinct from the Aether is a vast sea of apparently finite quantity, primary angular momentum, which when absorbed by the Aether becomes onta.  Aether rearranges onta to produce different physical forms.  Through motion, the forms change.  Within the process of change are various manifestations of “flow,” which add to the quality of our experience.

Coinciding with the mechanics and electromagnetism of the Universe is a quality we inherently recognize as mind.  The capacity of the mind directly experiences the physical manifestations of Aether and onta and through a body senses heat, touch, smell, taste, sight, hearing, and emotions.  The mind also has the capacity to create and store impressions of the sensations.  Moreover, through various agencies, the mind can in turn manipulate the Aether and onta.

In reality, there are no individual beings living independent lives, but a grand entity with incredible abilities to fragment itself and regroup in an endless cycle of becoming.  There is no separation of the mind from space, time, and form.  The skin conductance of the human body is a measure of its emotions; the conductance of Aether is the collective emotion.  All experience what happens to one.

Through various agencies, the mind can directly influence the muscles of the body, which in turn can manipulate matter.  However, anomalous events such as the bending of metal by some yet unknown non-material force, and the use of biofeedback machines demonstrate that there are multiple venues for the mind to interact with the material world.  There may yet be venues previously undiscovered.

There is a mind quality associated with individual existence.  Yet there is also a collective mind quality associated with groups of individuals.  Each small community has a mental quality of its own, as do the countries these communities comprise.  Does it stretch the limits of knowledge too much to suggest that there is a mind quality behind all forms of existence?  A scientist might think so, but an artist might think otherwise.

Similarly, the environment in which a body exists affects the body as much as the body affects its environment and other bodies.  We are as much dependent upon our environment as our environment is dependent upon us.

Just as many drops of rain come together to form a river and ultimately a mighty ocean, it seems the purpose of science and spirituality is to return our awareness to the Source.  Our reality is in the truth of our unified existence.

The whole of material existence is based on just four or five specific dimensions; mass, charge, length, frequency, and possibly sphericity.  The presence of four or five specific dimensions, however, suggests that even these dimensions have a common Source.  Moreover, if the dimensions pre-exist time and space, they must come from a Source that shares that timeless and space-less nature.  Western civilization might train a new type of “explorer” who would follow in the traditions of Eastern yogis and mystics.  Practitioners employing the tools of meditation, involving reflection and contemplation, might further explore the physics of dimensions leading toward the Source.

Nevertheless, in this book we have already accepted the premise that the dimensions have a common Source.  From there we progress toward the realm where we exist as human beings (away from the Source) in an attempt to understand as much as we can about our present existence.

Creating taxonomy of reality helps in our understanding.  In table 1 below, we will arbitrarily call the level of dimensions “level 1.”  If in the future we learn to quantify the level preceding level one, we will call it level ½.  The level preceding that will be level 1/3 and so on.

Therefore, level 1 is the level of dimensions.  From the dimensions of level 1, the existence of units develops, which is level 2.  The units include velocity, potential, angular momentum, and all others.  At level 2 the concept of quantity is also introduced so that each dimension, and thus each unit, has a quantum measurement.  The dimension of length produces a quantum measurement equal to the Compton wavelength.  Similarly, the quantum measurement of frequency derives from the empirical speed of light divided by the quantum distance.  The quantum mass has two specific quantities, the mass of the electron and the mass of the proton.  The quantum charges are the electrostatic charge and the strong charges, which derive from the onta angular momentum times the conductance constant.

In level 2 there are sublevels.  The quantum distance and quantum frequency have just one measurement.  The quantum mass has two measurements (electron and proton masses), and the quantum charges have several measurements.

From the units of level 2, the existences of atoms come into being as level 3.  The atoms themselves have several sublevels of existence.  From the atoms of level 3 the molecules come into existence as level 4.  The molecules themselves have a complex system of sublevels.

From the molecules of level 4 there are several more levels of existence before reaching the human level.  Then even beyond the level of humans, there are several more levels of existence dealing with the structures made by humans.  This book is not particularly concerned with what precedes level 1, or what develops after level 4.  It is specifically concerned with the quantum realm where physical existence comes into being.

 Existence Level Description 1/3 …closer to God 1/2 pre-dimension 1 Dimensions 2 Units 3 Atoms 4 Molecules … further levels leading to humans x Humans … further levels extending from humans

Table-1

As part of our physical existence, we experience the phenomena of mind, consciousness, and life “force” (or spirit).  Some sensitive people can directly experience the auras around living beings.  There are also documented cases of such things as the poltergeist[2] effect.

Undoubtedly,many people have not directly experienced the poltergeist effect.  Others would deny that there is a life force, consciousness, auras, or even mind.  Likewise, respectable people also once thought that the world was flat, and that human space travel was impossible.  This chapter avoids the useless effort of trying to make believers out of skeptics, rather, it speaks to those who have directly experienced the paranormal and are seeking a rational explanation for their experiences.

For example, the author has occasionally bent keys (photo of bent keys at right) without any conscious effort to do so.  In one case, a key bent in my hand as I was looking at it.  It felt like the key momentarily turned to soft plastic and after it finished bending it solidified in place.  Similarly, other researchers have witnessed other anomalous events in their everyday lives, events that must have a cause.  And since both the Aether and physical reality begin with level 2, the cause must be explainable at level 2, if the event is real.

The Aether Physics Model predicates on the assumption that dimensions truly exist and that all known phenomena can be quantified with dimensions.  This also means that since the “life force” is real, it is quantifiable.  Similarly, if auras or minds exist, they too will express in dimensions and there will be equations with units to describe them.  That is, of course, if “life force,” auras or mind originate in level 2.  If such things exist prior to level 2 then we will need a new physics based on the qualities of the relevant level(s).

It must be true that any reasonable unit of dimensions has a real world analog.  For example, length times frequency is equal to velocity.  The reverse logic should also be true.  If we have the dimensions of length times frequency we should be able to deduce that this particular combination of dimensions would represent velocity.  Velocity is not a material entity, and yet it has real dimensions.  Therefore, if we stand by the assumption that dimensions are real, then velocity (or motion) must also be real, except that motion is one level of reality removed from its dimensions.  Of course, in this case there is also the possibility that motion is primary to the dimensions of length and frequency, and that motion is the source of those dimensions, which would explain why there is an absolute speed of light.

We must remain open to the possibility that Gforce, primary angular momentum, charge and the speed of light may be primary causes for all existence.

On a more macro level, we think of our body as real.  However, if our organs could talk to us they would say that the body is an illusory construction based on the organs functioning together.  And at a lower level the cells could say that the organ is an illusion, that the real function is the cells working together.  Then we might hear the molecules say that cells are illusions because they are the function of molecules working together.  The atoms would point out that molecules are the function of atoms working together.  And subatomic particles would say that atoms are apparitions caused by the congregation of angular momentum.  And then the dimensions would point out that the angular momentum is merely the appearance of dimensions working together.

Each order of reality would consider the higher order to be an illusion with regard to the grouping of its members.  Even at the level of humans we consider the concept of community to be an illusion created by the congregation of humans.  Yet there may be some form of more complex consciousness among human communities, which communicates with each other and considers humans to be mere components.

It is interesting to look at the level of dimensions and reflect on what a dimension is.  The only way we can experience dimension directly, it appears, is in our mind.  How is it that the most fundamental form of knowable existence experiences only by the mind?

At this point we can conjecture that the more complex a level is from the Source of reality, the further that level is from being real in an absolute sense.  The underlying substance of dimensions is very real, but the forms made from these dimensions are much less real, becoming more transitory in nature with each level of complexity.  Further, it is the perception of the forms, which is the source of their unreal nature.  The dimensions are still there, but instead of seeing the dimensions for what they are, we are seeing them for the bound forms we would rather see.  An in-depth analysis of the nature of perception is the subject for other books and explains quite well in some religious and philosophical traditions.

## Motion

Motion is not merely a characteristic of Aether; it gives the Aether functionality.

The Aether Physics Model shows that onta are contained within a quantum unit of Aether.  Aether is what gives the Universe its fabric of space-time, and onta is the visible matter that occupies it.  The onta do not leave the Aether unit they reside in.  So technically, matter never moves in space or time.  Material matter is as a particle suspended in water.  In order to move the particle, the fluid must move.

All motion is of the Aether.  The onta influences the Aether, but at all times it remains encapsulated by Aether.  That is how Aether donates its electrostatic charge to onta.  It is also how primary angular momentum can interact with Aether to produce strong charge.  So when atoms and molecules move, the Aether encapsulating them also moves.  And since the Aether is formed of force carrier dipoles, which interact with other Aether units, the Aether units between and around atoms and molecules also drag with it.

So wherever an object is perceived, that object has its own Aether associated with it.  That object could be as dense as a gold nugget, the rarefied atmosphere, or even a magnetic field or gravitational field, and the Aether will remain grouped just the same.  Dense objects have more onta than rarefied objects, therefore dense objects also have more Aether density than rarified objects.

Aether behaves like a solid, fluid, and gas all at once.  Because the Aether constructs from reciprocal mass, it is the ability to manifest reality.  If there is nothing denser moving through a region of Aether, it will move with the densest system closest to it.  For example, magnetic, electrostatic, and gravitational forces hold our galaxy together.  The Aether of the galaxy moves as a whole.  Within the galaxy are solar system and dust clouds.  Each of these objects are more dense than the galaxy as a whole and influence the Aether local to these objects.

The solar systems are essentially made of a star, planets, and minor bodies.  The density of the solar system determines how much local Aether it influences.  A planet within that system will be the densest object in the local area and will influence the Aether local to it even more so.  At a given place on the planet, there will be objects denser to the local Aether and they will preponderate.  This pattern of influence continues down to the quantum level of existence.

The Aether associated with each object likely moves similar in nature to a Rubik’s cube.  To move through the Aether would require the displacement of other Aether units.  René Descartes called this type of movement a vortex.  The vortices are not limited to the three axes available to a Rubik’s cube, however, and have much more freedom.  A spaceship passing through the emptier regions of the solar system will push the Aether in front, which will curve back around to fill the wake.  The flow of Aether would look similar in pattern to the magnetic field lines of a magnet, moving from one pole and curving back around to the other pole.  In fact, the relative movement of Aether would appear as a magnetic field in relation to the ship.

## Flow

Flow extends from motion and gives it structure.  A river can be a flow of raindrops.  The Gulf Stream is a flow of ocean current and a segment of Thermohaline Circulation.  An economy is the flow of money and industry is the flow of goods.  The body relies on the flow of air (breath) and blood circulation among other instances of flow.  Reading is the flow of words; traffic is the flow of cars.  There is flow happening everywhere and at all times.

All flow relates to the general concepts of health and sickness.  If the breath or blood circulation is poor, the health suffers.  If the money does not flow, the economy suffers.  Alternatively, if the flow is too strong, such as for a river, then flooding occurs.  Proper regulation is essential to the health of all aspects of the Universe.

The Aether is no exception.  The space-time around us and within us must also flow properly to maintain health.  Western medicine has so far denied the flow of Aether through the body and environment.  This is a natural consequence of denying the existence of Aether in physics.  Nevertheless, ancient literature acknowledges the flow of Aether, which the East acknowledges even today.  Of course, the flow does not name as Aether, but Chi, Ki, Qi, Ku, and prana, among others.  In the West, a similar line of study almost came into existence calling it Orgone.  Controlling the flow of Aether has found its way into the esoteric martial arts, the work of psychics and mentalists, and alternative healing methods.

## Orgonomy

The study of orgone (orgonomy) is one of those “sciences” where qualified researchers have invested their hard-earned degrees trying to quantify something they could not clearly measure.

#### Orgone:

A universal life force hypothesized by Wilhelm Reich[3], supposed to emanate from all organic material that purportedly can be captured with a boothlike device and used to restore psychological well-being.[4]

Aether units have mass and charge, but it is reciprocal mass and charge.  Just as frequency manifests differently than its reciprocal of time, the reciprocal dimensions of mass and charge also manifest differently than mass and charge.

The Aether is dynamic in that its quantum unit is a rotating magnetic field.  The Gforce being the cause of this rotating magnetic field gives the impression that the Aether is alive and somehow self-perpetuating.  The description of orgone seems to be similar to the description of the Aether unit in that both are associated with “aliveness,” appear massless, and are not directly measurable.

No preplanned conception preceded the Aether Physics Model.  Its development resulted from following one empirical lead after the next.  The concepts discussed here are natural consequences of the science.

The discovery of the Unified Force Theory, insights into the atomic binding processes, the true nature of charge, the geometry of the Aether and other key discoveries concerning the physical and non-material world were completely unexpected.  When I was approached by Jim Bourassa to research and write a book on this new theory he suggested we also write about orgone.  I flatly told him that I had no data or other evidence to suggest orgone was real, at that time.

Then as I put the raw notes into book form and began organizing topics and developing the theory, it became clear that every physical process in nature appears to be accounted for in the Aether Physics Model.  It became clear at this point that the mind, the life force, the emotions, consciousness, and other non-material aspects of experience may also be quantifiable, even if not directly measurable.

It also became clear that some aspects of the physical world, such as time, are not directly measurable, but are still quantifiable.  Time infers by observing the frequency of certain regular processes (rotation of the Earth or oscillation of Cesium atoms).  If time measures indirectly, but precisely from its inferred reciprocal of frequency, then there are likely other units of the Universe that measure indirectly.

As I started interacting with orgone researchers and questioning their “data” and instrumentation, I began to suspect that mind might be related to the reciprocal of mass, orgone might be the same thing as Aether, and the aura of the body might be a form of reciprocal strong charge or conductance.  It could also be that there are other dimensions in greater space-time that correlate to these non-material aspects of existence.  Whatever it turns out to be, the Aether Physics Model provides a valid paradigm in which these long unanswered issues might resolve.

I have had many metaphysical experiences of which precognitions, out of body experiences, and lucid dreaming are just a few.  So at a level of direct experience I can relate to the concepts being put forth by researchers such as Wilhelm Reich.  However, this does not mean I necessarily agree with conclusions or observations arrived at without properly acquired data.  If we are to include the non-measurable aspects of experience into our physics, we are still obligated to establish a reliable method for quantifying these experiences.

If there truly is a life force, then it must be quantifiable.  We can make this statement even without first verifying the method for quantifying the life force.  It is a consequence of logic.  If keys truly bend without directly applied mechanical force, then there must be a quantifiable mechanism to explain the phenomenon.  If objects accelerate upward off the floor such as in John Hutchison’s demonstrations[5], then there must be a quantifiable explanation for this effect, too.  The fact that we observe these phenomena before understanding them is part of the natural progression of learning.

## Health and Healing

It is this author’s insight that qualities such as consciousness, mind, and health are quantifiable with the proper interpretations of quantum data.  After all, the Aether Physics Model yields the world’s first and simplest Unified Force Theory.  It is logical that if the physical world sorts out mathematically and geometrically through the Aether Physics Model, then the best chance for quantifying all other characteristics of living experience (consciousness, mind, health, etc) will also follow through this model.

Dale Sumburèru, DrPH, MD, has proposed extending the present health system, which treats only pathogenic disease, to a system also incorporating salutogenic treatment[6].  The essence of Dr. Sumburèru’s theory is that good health quantifies and has cause; just as bad health can be quantified and has cause.  Good health quantifies according to the Cellular Cosmic Signature (CCS) of cells, organs, or organisms, which is a measurement of biophotons.  According to Dr. Sumburèru, the biophotons generate by living beings through the same or similar process as the photons generated by strong charge.  This is just a working hypothesis at this time, but it is the beginning of a much-needed proactive approach to health and healing.

Dr. Sumburèru further suggests that Aether is “accumulated” through sleep and that “the Aether is used by the human organism to facilitate memory, the placebo effects, and spontaneous healing through the autonomic nervous system.”  Perhaps Aether needs to condition through proper flow and accumulate to maintain the life force.  It would appear that the water vortices work of Viktor Schauberger involved the conditioning of Aether in water, Feng Shui is the conditioning of Aether in our environment, and generating a rotating magnetic field would condition the Aether directly.

From the view of the Aether Physics Model, it would appear that health of a body is due in part to the proper flow of Aether through and around it.  This Aether flow can replenish our body through deep breathing, walking, driving, or bathing in Aether conditioned water.  Magnets realign the Aether units of air as the magnetic field passes through it.  Stretching body tissue, as in yoga, would increase the presence of Aether by increasing its flow.  Individuals who have raised the level of Aether in their body could transfer this Aether to others through touch or closeness.

Such healing techniques have been around for thousands of years, but modern Western science does not understand the mechanism of these techniques.  Indeed, how does one measure the presence of properly flowing empty space?  Without acknowledging the existence of Aether, how could modern science ever know about its function in health and healing?

In recent times, Victor Schauberger discovered the process whereby nature uses natural vortices to rejuvenate water.  Nikola Tesla and Georges Lakhovsky experimented with rotating magnetic fields generated by high frequency, using high potential apparatus as a healing mechanism.  Wilhelm Reich developed orgone therapy.  Others have found similar healing techniques involving Aether conditioning.  However, in the West, all went to the dustbin of history because scientists did not know how to quantify the Aether.

The healing techniques of the East, on the other hand, do quantify and understand the need for Aether.  In Eastern systems of medicine, Aether acknowledges as Chi or Qi (Chinese), Ki (Japanese), Prana (Hindu), and Ku (Tibetan).  Other cultures acknowledge Aether in one form or another.  The methods for cultivating the flow of Aether are highly developed in Eastern cultures.

It is ironic that for several hundred years Westerners considered Easterners barbaric, primitive, and uncultured, thinking it necessary to send its missionaries into Eastern cultures and purge them of their knowledge and systems of healthful living, which were supposedly based on superstition and ignorance.  Yet, it might now appear that the dead and lifeless culture of the West was at times the disease and plague to ancient, balanced cultures.  Our inability to measure what others could directly sense is the result of our own ignorance.  Western culture must have caused tremendous suffering for “primitive” cultures by our destruction of natural and healthy ways of living.

Perhaps now that we can quantify Aether, scientific research on it will begin.  Perhaps our advanced technology can identify the causes of imbalance in the daily lives of living beings and our environment, and suggest ways in which to improve living.  As we learn that no single culture has a monopoly on God, perhaps all people will unite as a network of distinct cultures in a greater community of planet Earth, and indeed of the Universe.  Moreover, perhaps the discovery that our ancestors knew more than we gave them credit for will humble us.

## Form and Beauty

The Standard Model cannot describe the simple shape of the electron.  But the Aether Physics Model can not only describe the simple shape of the electron, it can also show how the entire physical realm is a symphony of form, just as Beethoven’s Fifth is a symphony of melody.

In chapter 4 the reader was introduced to Aether numbers.  Examples were given that show how spin position produces various forms.  However, this was just an introduction to a vast field of study that will delight artists of all media.

We showed that $$\frac{{158}}{2}\pi$$ and $$\frac{{16{\pi ^2}}}{2}\pi$$ ranges were relevant to forms produced by half-spin onn in the Aether.  Below, different sequence numbers produce a table of selected forms according to the Aether function $$G\left( {x,y} \right) = \frac{{x + 1}}{2} \cdot \frac{{x + 3}}{2}$$ in the cylindrical coordinate system.

 $$\frac{{53}}{2}\pi$$ $$\frac{{3 \cdot 53}}{2}\pi$$ $$\frac{{39}}{2}\pi$$ $$\frac{{4 \cdot 39}}{2}\pi$$ $$\frac{{31}}{2}\pi$$ $$\frac{{5 \cdot 31}}{2}\pi$$ $$\frac{{27}}{2}\pi$$ $$\frac{{6 \cdot 27}}{2}\pi$$ $$\frac{{23}}{2}\pi$$ $$\frac{{7 \cdot 23}}{2}\pi$$ $$\frac{{19}}{2}\pi$$ $$\frac{{8 \cdot 19}}{2}\pi$$

Notice that when the number of sides or points the shape has multiplies the base number of the image, it produces a seed or “bell pepper bottom” shaped image.  It is as though the seed geometry or “bell pepper bottom” geometry is a primary form of some kind.  As far as the seed shape goes, nearly all plant and animal life begins as a seed or ovum.

It would seem that the “bell pepper bottom” geometry is peculiar to an even number of sides or points in the shape, and the seed geometry is peculiar to the odd number of sides and points.

More of the primary set images follow below.  Notice the near perfect symmetry of the stars.  Perhaps it would not be surprising if all the stars had an even number of points.  However, most of the stars have an odd number of points.

 $$\frac{{63}}{2}\pi$$ $$\frac{{5 \cdot 63}}{2}\pi$$ $$\frac{{45}}{2}\pi$$ $$\frac{{7 \cdot 45}}{2}\pi$$ $$\frac{{59}}{2}\pi$$ $$\frac{{8 \cdot 59}}{2}\pi$$ $$\frac{{35}}{2}\pi$$ $$\frac{{9 \cdot 35}}{2}\pi$$ $$\frac{{43}}{2}\pi$$ $$\frac{{11 \cdot 43}}{2}\pi$$ $$\frac{{73}}{2}\pi$$ $$\frac{{13 \cdot 73}}{2}\pi$$

The fact that so many non-repeating images could appear in the primary set, and with such precision of form, is astounding.  It is further awe inspiring that these forms are, in fact, the forms of living things as reflected in flowers in particular, plants in general, and sea creatures to name a few.

 Cylindrical Coordinates Spherical Coordinates $$\frac{{16{\pi ^2}}}{2}\pi$$ $$\frac{{16{\pi ^2}}}{2}\pi$$ $$\frac{{8{\pi ^2}}}{2}\pi$$ $$\frac{{8{\pi ^2}}}{2}\pi$$ $$\frac{{4{\pi ^2}}}{2}\pi$$ $$\frac{{4{\pi ^2}}}{2}\pi$$

In the above images, using the Aether constant of $$16{\pi ^2}$$ and its divisions, we further generate interesting images.

The $$4{\pi ^2}$$ constant, which is the constant of a toroid, indicates that the perception of three angular dimensions of length in the form of a cube is the result of toroidal onta.  This would explain why the Cartesian coordinate system best explains our human perception of space, while the cylindrical and spherical coordinate systems best explain the way onta experience space.

This book also demonstrates the effect of $$Phi$$ and $$phi$$ numbers and their relationship to physical constants such as the g-factors.  We can set $$G$$ to be a function of the $$Phi$$ and $$phi$$ numbers:

$G\left( {x,y} \right) = \frac{{\left| {\sqrt x } \right| + 1}}{2} \cdot \frac{{\left| {\sqrt y } \right| + 3}}{2} \tag{11.1}$

In this case, since $$5$$ is already known to be a full cycle with $$Phi$$ and $$phi$$ numbers, we set the range to be $$5\pi$$ and the surface plot appears as nearly a sphere:

Not covered here are many other interesting observations made from the $$Phi$$ and $$phi$$ contour plots.

The Gforce manifests through the Aether unit.  Presented earlier was the reduction of reality down through to the level of dimensions.  Now we see the profound relationship of Aether spin positions to the general forms of living and growing things.  Taken together, a picture is emerging that shows the method and harmony of all things as evolved from an all-pervading God.  Of course, there is a need to expand the detail of the method and harmony, but this is a start.

## God

The physical vacuum is a manifestation of conscious Spirit, and material science has correctly recognized that it is all-pervading and full of infinite energy.  However, physicists are at a loss to explain how the vacuum came to exist in the first place, so it is viewed - like God - as eternal.  The new physics is on the right track, but unfortunately it is considering the physical vacuum to be the final cause of existence rather than what it actually is; the last link in a causative chain that extends from God, through the action of Spirit, to the material creation[7]. – Brian Hines

Since Aether units are independent units of 2-spin rotating magnetic field, without any solid substance of their own, and eternally dynamic in nature, then there must be more to Aether than mere empty space.  The existence of an all-powerful, all pervasive God supports by the presence of the Gforce in the Aether constants, by the existence of the dimensions and the principle of reductionism.

One cannot study the Aether without developing an appreciation and awe for the beauty of the Creator and the Creator’s manifestations in all that exists.  Even if the world were some sort of elaborate illusion, we still see the witnesses to God all around us.  With all the evidence for an ordered existence arising out of the mind-like qualities of dimensions, even the most skeptical among us could understand the rational logic for the existence of God.

With the Aether Physics Model, we can also learn how to separate the truth of what God is from the myth imbued by the culture surrounding a given religion.  For example, the physics do not support the concept of male superiority (or female superiority for that matter), neither does the theory single out a specific name or a specific geographic location for God.  Nevertheless, the science clearly supports the qualities of the Creator as an all powerful, all pervading, living and dynamic force.

Perhaps by understanding physical existence with the assistance of the Aether Physics Model, humans will better be able to appreciate God and learn that we all share the same universal heritage and the same destiny.  Perhaps we will see the benefit to all life that comes from balancing the flow of Aether and all physical existence.

## Consciousness

In chapter 3, the Gforce was shown to be the single force from which all forces arise.  The Gforce is enormous and acts through each quantum Aether unit.  Whatever the Gforce is, and wherever it comes from, the Gforce pre-exists physical existence and gives rise to it.

It is probably not possible to quantify something that pre-exists the physical Universe.  In addition, whatever it is that pre-existed the physical Universe, it must have a non-material quality.  Several of the world’s major religions and cultures generally refer to enlightened mind as some kind of non-material, pre-existing, all-powerful, and creative force of the Universe.  In this book, we accept this non-material, creative Gforce as a postulate and accept it as “pure, enlightened Mind,” or “God.”  Each quantum Aether unit is structure of a more complex order of God, or mind.  The sum of all quantum Aether units or any quantity of Aether units has the identical properties of its parts.  This “God Mind” thus postulates to be present throughout the visible Universe and to apply equally to all objects, regardless of their size, constitution, and structure.

Having postulated a Universal Mind of God, based in part on empirical observations, we can now attempt to quantify the individual consciousness of this Universal Mind as perceived through a human body’s senses.

Each order of physical reality is matter, bound within an environment, but in a more complex form than the previous level.  Just as the Gforce evolves into the electromagnetic, electrostatic, and gravitational forces, and ultimately into various other manifestations of force, the living God Mind evolves into complex manifestations as well.  Masaru Emoto shows evidence that water possesses a quality of mind.  We suspect that cells possess a quality of mind.  We accept that our complex human form possesses a quality of mind.  If the Gforce is the God Mind, and water and cells possess a quality of mind, as do humans, then what logic would allow for the other levels of existence to not possess a quality of mind?  It is reasonable to conclude that the God Mind evolves (or devolves) into the consciousness we are familiar with, just as onta evolves into the human form.

From the physical perspective, the Aether as seen through “God’s eyes” exists as a 2-spin, space-resonance domain.  The physical body, composed from onta, exists in a ½ spin, space-time domain.  God consciousness thus exists in at least one more dimension than physical-based consciousness.

As far as this discussion goes, God consciousness only describes as the basis for physical consciousness (ego).  One can only know or feel the direct meaning of God consciousness since the source of God consciousness pre-exists the physical Universe.  The methods for setting aside physical consciousness so that God consciousness can be known and felt are well documented in Buddhism, Hinduism, A Course in Miracles, and other systems of thought.  This section is concerned primarily with quantifying the physical consciousness in such a way that we can develop an understanding of how physical consciousness relates to the physical Universe.  In general, when referring to consciousness, we will be referring to individual consciousness (or ego) and not God consciousness.

Psychophysiology is the branch of physiology dealing with the relationship between physiological processes and thoughts, emotions, and behavior[8].  The primary tool for measuring the thoughts, emotions, and behavior with regard to our physical body and physical environment is a device that measures electrodermal activity (EDA).  EDA is another way of saying “skin conductance.”  Therefore, it is intended that the devices used by psychophysiologists today measure skin conductance.

According to the Standard Model, the reciprocal of the conductance unit is the resistance unit.  However, data clearly shows that skin conductance does not have a linear relationship to the skin resistance.  According to the Aether Physics Model, the reciprocal of conductance is the magnetic flux unit.  Moreover, as presented earlier, evidence exists that shows a linear relationship between conductance and magnetic flux.  Thus, there is already sufficient evidence to show that the reciprocal of conductance is magnetic flux, and not resistance.

If the Aether Physics Model is correct, then conductance is not equal to current divided by potential, as the Standard Model shows.  In the APM, conductance is equal to frequency divided by potential:

$Cd = \frac{{freq}}{{potn}} \tag{11.2}$

Conductance is also equal to charge per angular momentum:

$Cd = \frac{{chrg}}{h} \tag{11.3}$

Properly designed equipment will calculate conductance based on the frequency per potential between a pair of electrodes.  The conductance between two points can produce useful data, but the ultimate device for measuring and observing conductance would produce a surface color map of all cell conductances (or conductances for any particular order of reality).  The Aether Physics Model predicts this is possible.  Essentially, a device that produces a color map of conductance over the surface of a body would give a view of the body’s aura.  We could then explore the reading of the aura as an accurate medical diagnostic tool.

If we wanted to see the body’s aura in terms of light (ligt) then we would have to accelerate the strong charge per conductance of the measured body:

$ligt = \frac{{chrg \cdot accl}}{{Cd}} \tag{11.4}$

Is there such a process that could map the body’s conductance by accelerating the strong charge and presenting a map in the form of light?

In 1939, the same year that Reich claimed to have discovered bioenergy in the form of orgone, a Russian scientist, Semyon Kirlian discovered a novel form of photography that, for the first time, appeared to show unmistakable evidence of just such a field – a field that Russian scientists called bioplasmic energy.  Kirlian’s invention makes use of the Tesla coil – a high-voltage, high-frequency electrical device – to photograph living tissues.  Experimenters have used frequencies between 20,000 and 3,000,000 cycles per second, and voltages between 20,000 and 50,000 volts, to generate electric fields that cause electrons to be pulled out of the surface of living tissue such as human skin.  The process is not destructive or painful but it does enable the pattern of electrons, in turn, to generate light that can expose a photographic plate[9].

Kirlian photography appears to be a valid science, or at least there are equations that predict it.  Perhaps we need to do more research to better develop the Kirlian photographic method.

In the Aether Physics Model, as we simplify within the various orders of reality, we pass from molecules, to atoms, to units, to dimensions, and ultimately to God.  As the order of reality reduces in complexity, we get closer to the ultimate truth.  Progressing toward the more complex levels of reality, we get further away from God, but the level of sophistication in our experience becomes more detailed.  Therefore, the two aspects of our mind, the God consciousness and the ego consciousness, tend to evolve mutually exclusive of each other, even though we view ego consciousness through the God consciousness.  Furthermore, it would appear that there are other measurable and knowable levels of consciousness allowed, based upon the different orders of reality.

We can postulate that the God consciousness is a given, but ego consciousness must exist due to physical laws since it perceives the physical world.  Many philosophers, ancient and modern, have wondered how it is that the mind interfaces with the physical world.  The Aether Physics Model offers a solution to the problem.

The physical matter making up a human body can identify more or less as something isolated from its environment, although this is a misperception.  The distinction between what constitutes the body and its environment is not entirely clear because we are constantly exchanging molecules with our environment through breathing, drinking, eating, defecating, urinating, and perspiring.  Furthermore, Aether always encapsulates onta.  Yet at any given time we can say “this is my body and it has certain characteristics apart from other objects and apart from the environment.”  The characteristics we are primarily concerned with are the molecules in the brain and blood, though ultimately all the molecules in our body contribute to our present state of ego consciousness.

At the quantum level, we have defined the Aether unit and postulated that the God consciousness dwells within it.  We also know that as angular momentum spins through the conductance of the Aether unit, the Aether produces strong charge.  Angular momentum interfacing with Aether conductance presents a physical experience to the Aether consciousness.  At the quantum level, the Aether consciousness experiences all electrons and protons in the same way.  However, at the atomic level, the total geometry of the atom presents a different experience to the Aether consciousness for each type of atom.  Similarly, at the molecular level, that geometry is much more complex.  The Aether consciousness experiences the complex geometrical structures quite differently.  Therefore, it seems that the consciousness of a given collection of molecules is associated with the total molecules of the entity, even though there is also consciousness at the level of each individual onn.  In other words, there are different levels of consciousness in a complex entity, each occurring at the various levels of reality.  Hence, at the human level of reality, we perceive individual human consciousness, but awareness also exists of group consciousness and global consciousness.

## Truth

For some, truth is what we believe in.  This sounds good at first, until we question what is doing the believing.  In this book, we show the various orders of reality within the physical world.  We also show evidence that each order of reality animates by a living force, a living substance, and in a living environment.  More specifically, the self associated with our body is a level of consciousness peculiar to our experience at the level of the body.

The self we are familiar with is the consciousness of a particular group of organs, cells, molecules, atoms, and onta, which compose the body and its environment.  When the self says, “I believe,” it is the group consciousness of that limited portion of the Universe, which is making the statement.  Therefore, the perception and belief in that truth reflects those limitations.

There is another kind of truth, which reveals to us.  We do not have to interpret it to make it true, although we may have to interpret our sensations in order to understand it.  The Gforce and dimensions are what they are.  Since we are thinking with consciousness associated with the body, our knowledge of the Gforce and dimensions comes through our senses.  Knowledge that comes through the senses needs interpretation since it arrives to our awareness as sensations.  Nevertheless, the underlying truth, which the body senses, is what it is.  Therefore, there is an absolute truth, which we can know and interpret correctly.

## War and Peace

When the Standard Model was developed, the United States was at war.  Scientists were under pressure to produce more powerful and destructive weapons.  Thus, the “mass equals energy” paradigm was quite attractive to the military industrial complex.  After all, the winner of a war is the one who strategically commands the most energy.

Ironically, the cause of the wars was also about strategically commanding energy.  Energy, like money, has corrupted individuals and entire cultures.  There is nothing wrong with money or energy.  They are good, and they are essential to the structure of civilization.  However, money and energy are not the only foundation of civilization.

Civilization is a collection of living beings, each of which exists at various levels of existence.  Science should not only be about killing beings, if it even should be about killing at all.  Science has an obligation to further all aspects of society so that health, harmony, and individual satisfaction are the purpose for the existence of science.

The needs of living beings are not met merely by the provision of comforts for the body, and a safe community, with fairness for all.  These are essential, yes, but the need for purpose in life is just as important.  Each living individual must have a purpose, a reason for existing in the first place, if any of the creature comforts are to be meaningful.

The “mass equals energy” paradigm is not only fallacious; it is also empty.  How will science ever truly fulfill the needs of living beings with a paradigm, which enlists false equalities and false logic?  Even though the data behind the Standard Model is good, that does not mean the theory that explains the data is good.  If we expect our citizens to abide with common sense and fidelity, then our science and religion must set the example.

Visualize a paradigm, based on the empirical data, which clearly shows the development of the physical Universe from a living God.  Imagine a model that children can understand and conceptualize, which illustrates for them a simple and common sense explanation of how an all-pervading, eternal Gforce gave rise to the world into which they were born.

A physics model that gives a clear conduit of development from God to the learner creates a link between the Creator and the creation.  This link gives a sense of belonging, and develops a sense of purpose in life.  And what could our purpose be other than to create the conditions that will further our understanding of the Source of all life and all existence?

There are generations who are thankful they won their wars, regardless of the cost, and perhaps rightly so.  However, the present generation’s gratitude is better spent being thankful that no more wars need be fought.  We have before us now a new opportunity to establish balance and harmony within civilization through the marriage of science and spirituality.  We now have a tool that not only increases the knowledge of our physical world, but also can help us find common ground in our spiritual paths.

Perhaps for the first time ever, pure knowledge reveals, not this time to the priests and their chosen initiates, but now to all humans.  And even more fortunate, this knowledge is not about technologies of war, but of technologies of peace.

The Aether Physics Model is about truth in science, but it is also undeniably about truth in spirituality.  Whatever spirituality may be, and whatever we call it, nearly everybody acknowledges that it exists.  Perhaps spiritual reality is merely a quality of mind; perhaps it is much more than that.  However, whatever truth is, we must all seek it together, not in war, but in peace.

[1] Tarthang Tulku Knowledge of Time and Space (Dharma Publishing, Dharma Press Berkeley, CA, 1990) 327

[2] "POLTERGEIST  [Ger.,=knocking ghost], in spiritism, certain phenomena, such as rapping, movement of furniture, and breaking of crockery, for which there is no apparent scientific explanation. " "Poltergeist ," The Columbia Encyclopedia , 6th ed.

[3] REICH, WILHELM, 1897–1957, Austrian psychiatrist and biophysicist. For many years a chief associate at Freud's Psychoanalytic Polyclinic in Vienna, he later broke with Freud and the psychoanalytic movement. Forced to leave Nazi Germany, he resettled in New York City in 1939 to continue independent research in biophysics. He taught (1939–41) at the NewSchool for Social Research, and in 1942 he founded the Orgone Institute. According to Reich's theories the universe is permeated by a primal, mass-free phenomenon that he called orgone energy; in the human organism the lack of repeated total discharge of this energy through natural sexual release is considered the genesis not only of all individual neurosis but also of irrational social movements and collective neurotic disorder. Reich invented the orgone box, a device that he claimed would restore energy but that was declared a fraud by the Food and Drug Administration. In 1956 he was tried for contempt of court and violation of the Food and Drug Act and sentenced to two years in a federal penitentiary, where he died.

[4] Definition quoted from The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2003 by Houghton Mifflin Company.

[5] The Hutchison Effect http://www.hutchisoneffect.org/

[6] “The construct of Salutogenesis is proposed as a unifying theory for medicine, health and healing.  It is posited as a spectrum from the most subtle nuances of health to the most adverse medical issues where all interventions at our disposal would fit within this model.  The primordial aether is assumed to be the underpinning function and the model relies on and maximizes the placebo effect for efficacy.”  D Sumbureru, Salutogenesis I: A Unified Theory on Medicine, Health and Healing, Subtle Energies & Energy Medicine, vol 14, #2, pp175-199

[7] Brian Hines, God’s Whisper, Creation’s Thunder (Threshold Books, Brattleboro, VT, 1995)148

[8] The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2003 by Houghton Mifflin Company.

[9] Richard Milton, Alternative Science: Challenging the Myths of the Scientific Establishment (Rochester, Vermont, Park Street Press, 1996) 70-71


text:
# Flight Instrument Gauge Visualization for a Drone

Import and visualize a drone flight log using 3-D animations and flight intrument gauges. This example obtains a high level overview of flight performance in MATLAB® using Flight Instruments (Aerospace Toolbox) functions in Aerospace Toolbox™. Then, to view signals in a custom interface in Simulink® , the example uses the Flight Instruments (Aerospace Blockset) blocks from Aerospace Blockset™

The example extracts the signals of interest from a ULOG file and plays back the UAV flight trajectory in MATLAB. Then, those signals are replayed in a Simulink model using instrument blocks.

### Import a Flight log

A drone log file records information about the flight at regular time intervals. This information gives insight into the flight performance. Flight instrument gauges display navigation variables such as attitude, altitude, and heading of the drone. The ULOG log file for this example was obtained from an airplane model running in the Gazebo simulator.

Import the logfile using ulogreader. Create a flightLogSignalMapping object for ULOG files.

To understand the convention of the signals, the units, and their reference frame, inspect the information within the plotter object. This information about units within log file becomes important when connecting the signals to flight instrument gauges.

plotter = flightLogSignalMapping("ulog");
info(plotter,"Signal")
ans=14×4 table
SignalName          IsMapped                                                                                SignalFields                                                                                FieldUnits
_____________________    ________    __________________________________________________________________________________________________________________________________________________________________________________________________________    ___________________________________________________

"Accel"                   true       "AccelX, AccelY, AccelZ"                                                                                "m/s^2, m/s^2, m/s^2"
"Airspeed"                true       "PressDiff, IndicatedAirSpeed, Temperature"                                                                                "Pa, m/s, degreeC"
"Barometer"               true       "PressAbs, PressAltitude, Temperature"                                                                                "Pa, m, degreeC"
"Battery"                 true       "Voltage_1, Voltage_2, Voltage_3, Voltage_4, Voltage_5, Voltage_6, Voltage_7, Voltage_8, Voltage_9, Voltage_10, Voltage_11, Voltage_12, Voltage_13, Voltage_14, Voltage_15, Voltage_16, RemainingCapacity"    "v, v, v, v, v, v, v, v, v, v, v, v, v, v, v, v, %"
"GPS"                     true       "Latitude, Longitude, Altitude, GroundSpeed, CourseAngle, SatellitesVisible"                                                                                "degree, degree, m, m/s, degree, N/A"
"LocalNED"                true       "X, Y, Z"                                                                                "m, m, m"
"LocalNEDTarget"          true       "XTarget, YTarget, ZTarget"                                                                                "m, m, m"
"LocalNEDVel"             true       "VX, VY, VZ"                                                                                "m/s, m/s, m/s"
"LocalNEDVelTarget"       true       "VXTarget, VYTarget, VZTarget"                                                                                "m/s, m/s, m/s"
"Mag"                     true       "MagX, MagY, MagZ"                                                                                "Gs, Gs, Gs"

### Extract Signals of Interest

To visualize the drone flight using instrument gauges, extract the attitude, position, velocity, and airspeed at each timestep. Specify the appropriate signal name from the info table in the previous step. Call the extract function with the appropriate signal names. The time vector element of signals are adjusted so they start at 0 seconds.

% Extract attitude and roll-pitch-yaw data.
rpy = extract(plotter, data,"AttitudeEuler");
rpy{1}.Time=rpy{1}.Time-rpy{1}.Time(1);

RollData = timetable(rpy{1}.Time,rpy{1}.Roll,...
'VariableNames',{'Roll'});
PitchData = timetable(rpy{1}.Time,rpy{1}.Pitch,...
'VariableNames',{'Pitch'});
YawData = timetable(rpy{1}.Time,rpy{1}.Yaw,...
'VariableNames',{'Yaw'});

% Extract position and xyz data.
Position = extract(plotter, data,"LocalNED");
Position{1}.Time = Position{1}.Time-Position{1}.Time(1);

X = timetable(Position{1}.Time,Position{1}.X,...
'VariableNames',{'X'});
Y = timetable(Position{1}.Time,Position{1}.Y,...
'VariableNames',{'Y'});
Z = timetable(Position{1}.Time,Position{1}.Z,...
'VariableNames',{'Z'});

% Extract velocity data.
vel = extract(plotter, data,"LocalNEDVel");
vel{1}.Time=vel{1}.Time-vel{1}.Time(1);

XVel = timetable(vel{1}.Time,vel{1}.VX,...
'VariableNames',{'VX'});
YVel = timetable(vel{1}.Time,vel{1}.VY,...
'VariableNames',{'VY'});
ZVel = timetable(vel{1}.Time,vel{1}.VZ,...
'VariableNames',{'VZ'});

% Extract Airspeed magnitude data.
airspeed = extract(plotter, data,"Airspeed");
Airspeed = timetable(airspeed{1}.Time,airspeed{1}.IndicatedAirSpeed,...
'VariableNames',{'Airspeed'});

### Convert Units and Preprocess Data for Gauges

Our flight log records data in SI Units. The flight instrument gauges require a conversion to Aerospace Standard Unit System represented by English System. This conversion is handled in the visualization block available in attached Simulink model for the user. The turn coordinator indicates the yaw rate of the aircraft using an indicative banking motion (which differs from the bank angle). In order to compute the yaw rate, convert the angular rates from body frame to vehicle frame as given below:

$\stackrel{˙}{\psi }=\frac{\mathrm{qcos}\left(\varphi \right)+\mathrm{rsin}\left(\varphi \right)}{\mathrm{cos}\theta }$

The inclinometer ball within turn coordinator indicates the sideslip of the aircraft. This sideslip angle is based on the angle between the body of the aircraft and computed airspeed. For an accurate airspeed, a good estimate of velocity and wind vector is required. Most small UAV's do not possess sensors to estimate wind vector data or airspeed while flying. UAV's can face between 20-50% of their airspeed in the form of crosswinds.

${\mathit{V}}_{\mathit{g}}$- ${\mathit{V}}_{\mathit{w}}$=${\mathit{V}}_{\mathit{a}}$

To compute sideslip and turn, extract wind and attitude rate data directly from the log file.

% Extract roll, pitch and yaw rates and an estimated windspeed.
[p,q,r,wn,we] = helperExtractUnmappedData(data);

% Merge timetables.
FlightData = synchronize(X,Y,Z,RollData,PitchData,YawData,XVel,YVel,ZVel,p,q,r,Airspeed,wn,we,'union','linear');

% Assemble an array for the data.
FlightDataArray = double([seconds(FlightData.Time) FlightData.X FlightData.Y FlightData.Z FlightData.Roll ...
FlightData.Pitch FlightData.Yaw,FlightData.VX,FlightData.VY,...
FlightData.VZ,FlightData.p,FlightData.q,FlightData.r,FlightData.Airspeed,FlightData.wn,FlightData.we]);

% Ensure time rows are unique.
[~,ind]=unique(FlightDataArray(:,1));
FlightDataArray=FlightDataArray(ind,:);

% Preprocess time data to specific times.
flightdata = double(FlightDataArray(FlightDataArray(:,1)>=0,1:end));

### Visualize Standard Flight Instrument Data in MATLAB

To get a quick overview of the flight , use the animation interface introduced in the Display Flight Trajectory Data Using Flight Instruments and Flight Animation (Aerospace Toolbox) example. The helper function helperDroneInstruments creates an instrument animation interface.

helperDroneInstruments;

The Airspeed indicator dial indicates the speed of the drone. The Artificial Horizon indicator reveals the attitude of the drone excluding yaw. The Altimeter and Climb Rate indicator reveal the altitude as recorded within the barometer and the climb rate sensors respectively. The Turn Coordinator indicates the yaw rate of the aircraft and sideslip. If the inclinometer skews towards left or right, this denotes a slip or skid situation. In a coordinated turn, the sideslip should be zero.

In Simulik, you can create custom visualizations of signals using intrument blocks to help diagnose problems with a flight. For example, voltage and battery data in log files can help diagnose failures due to inadequate power or voltage spikes. Extract this batter data below to visualize them.

% Extract battery data.
Battery = extract(plotter,data,"Battery");
% Extract voltage data from topic.
Voltage = timetable(Battery{1}.Time,Battery{1}.Voltage_1,...
'VariableNames',{'Voltage_1'});
% Extract remaing battery capacity data from topic.
Capacity = timetable(Battery{1}.Time,Battery{1}.RemainingCapacity,...
'VariableNames',{'RemainingCapacity'});

Open the 'dronegauge' model, which takes the loaded data and displays it on the different gauges and the UAV animation figure.

open_system('dronegauges');

Run the model. The generated figure shows the trajectory of the UAV in real time and the gauges show the current status of the flight.

sim('dronegauges');

Get trial now

format: plain


text:
# But the average roll is 3.5

Discrete Mathematics Level 4

Suppose I have a line of squares, labelled $$0,1,2,3,4, \ldots$$ and so on. I place a counter on the square 0. On every turn, I roll a fair die (with the numbers 1 to 6) and move forward as follows: if I was on square $$P$$ before the roll and I get a $$x$$ then I move to square $$P+x$$. Let $$X_n$$ be the chance that I land on the square labelled $$n$$. Find

$$\text{max}(X_n)? \space\space ( n \in \mathbb{N})$$

and submit your answer as $$n$$.

×


text:
I'm studying the notion of a a $\mathcal{V}$ category $\underline{\mathscr{A}}$ which is powered or compowered over $\mathcal{V}$. I'm having trouble finding a proof that powering/copowering gives a $\mathcal{V}$ functor $\underline{\mathcal{V}} \otimes \underline{\mathscr{A}} \to \underline{\mathscr{A}}$. (Add "op" as necessary.)

In Riehl's Categorical Homotopy Theory, she gives some indication of the proof, but I'm having trouble parsing it. In particular, see these two pages. The claim here appears to be the following:

Proposition: [Edit: I believe I have interpreted the text wrong, because this seems to be incorrect] Let $\underline{\mathscr{A}}$ and $\underline{\mathscr{B}}$ be $\mathcal{V}$ categories, with underlying categories $\mathscr{A}$ and $\mathscr{B}$. Let $L:\mathscr{A} \leftrightarrows \mathscr{B}: R$ be an adjunction with unit $\eta: 1_\mathscr{A} \Rightarrow RL$. Let there be a given isomorphism $\underline{\mathscr{A}}(a,Rb) \cong \underline{\mathscr{B}}(La, b)$ whose image in the underlying categories is the natural isomorphism of the adjunction. Let $R$ be the underlying functor of a $\mathcal{V}$ functor $\mathbf{R}:\underline{\mathscr{B}} \to \underline{\mathscr{A}}$. Then there is a $\mathcal{V}$ functor $\mathbf{F}:\underline{\mathscr{B}} \to \underline{\mathscr{A}}$ agreeing with $F$ on objects and with action on hom objects given by $$\mathbf{F}: \underline{\mathscr{A}}(a,a') \xrightarrow{(\eta_{a'})_*} \underline{\mathscr{A}}(a, RLa') \cong \underline{\mathscr{B}}(Fa, Fa')$$ $\mathbf{F}$ is the $\mathcal{V}$-adjunct of $G$.

I can't seem to show functoriality of $\mathbf{F}$. (See this link where I've drawn the diagrams out.) Maybe someone can help.

It could be that I'm misunderstanding the claim she's making.

Edit: Just considered the possibility that there's something special about $\underline{\mathcal{V}} = \underline{\mathscr{A}}$, which seems to be the case she's dealing with exclusively. Let me see if I can make that work.

Edit 2 The statement in Kelly is

When [the forgetful functor] is conservative--faithfulness is not enough--the existence of a left adjoint $S_0$ for $T_0$ implies that of a left adjoint $S$ for $T$.

So I think I must be misunderstanding Riehl's text here. Perhaps someone can help me.

• If you are actually missing a hypothesis, I think it might be that the components $\underline{\mathscr{A}}(a,Rb) \cong \underline{\mathscr{B}}(La, b)$ satisfy the property of being enriched natural isomorphisms between the enriched (co)representable functors. – Vladimir Sotirov Aug 18 '16 at 15:50
• @VladimirSotirov As you can see, a Yoneda Lemma argument is used to show $\underline{\mathcal{V}}(u \otimes v, w) \cong \underline{\mathcal{V}}(u, \underline{\mathcal{V}}(v,w))$. I can't see how to conclude from that that this is a natural (in $u$ and $w$) $\mathcal{V}$ isomorphism of bifunctors. Can you? – Eric Auld Aug 18 '16 at 16:27
• I don't think she claims that it is a $\mathcal V$-natural isomorphism of functors. I think the claim is that powers and copowers are enriched functors that are ordinary adjoints to the appropriate representables. ($\mathcal V$-natural transformations aren't even defined at this point in the text, so I think when she says left/right $\mathcal V$-adjoint, she means a left or right adjoint that is $\mathcal V$-enriched, not a $\mathcal V$-adjunction which is what I think Kelly is talking about). – Vladimir Sotirov Aug 18 '16 at 17:55
• @VladimirSotirov Thanks for the response. This is really helping. I guess I'm just not understanding how to show her claim that an enrichment of the (ordinary) right adjoint gives me an enrichment of the left adjoint. Even in the case of $-\otimes v \dashv [v,-]$, I can show that $-\otimes v$ is enriched directly, but I don't see how it follows from the enrichment of $[v,-]$ (even using her tip to postcompose with the unit). – Eric Auld Aug 18 '16 at 19:25

Let me start by stating clearly the unenriched version of the result whose enriched version I was trying to evoke here. This appears as Proposition 4.3.4 in Category Theory in Context which is available here:

Category Theory in Context

Prop. Consider a functor $G\colon B \to A$ so that for each $a \in A$ there exists an object $Fa \in B$ together with an isomorphism

$B(Fa,b) \cong A(a,Gb)$ that is natural in $b \in B$.

Then there is a unique way to extend the assignment $F \colon obA \to obB$ to a functor $F \colon A \to B$ so that these isomorphisms are also natural in $A$.

The proof is by the Yoneda lemma (see the cited notes).

Now I claim that the same result is true for $V$-categories $A$ and $B$, a $V$-functor $G \colon B \to A$, and a family of isomorphisms $B(Fa,b) \cong A(a,Gb)$ in $V$ that are $V$-natural in $b \in B$.

The given isomorphisms in $V$ can be used to define a canonical map in $V$

$A(a,a') \to V(B(Fa',b), B(Fa,b))$

for each $b \in B$. Not only is this canonical but it's uniquely determined if you want the iso to be $V$-natural in $A$ in the end.

Moreover these maps are (extra-ordinarily) $V$-natural in $B$. What this means is that you actually get a map into the enriched end

$A(a,a') \to \int_{b \in B} V(B(Fa',b), B(Fa,b))$.

(These are defined in section 7.3.) Now one version of the $V$-Yoneda lemma tells you that

$\int_{b \in B} V(B(Fa',b), B(Fa,b)) \cong B(Fa,Fa')$

so this map is the map you seek.

In the definition of tensors I should have asked that the isomorphisms

$M(v\otimes m,n)\cong V(v, M(m,n))$

were $V$-natural in $n$. (Vladimir's comment is correct.) In any case it was absolutely my intention to define tensored to mean that the hom bifunctor has a left $V$-adjoint. Apologies for the confusion!


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# Subbase for a Topology

Let $\left( {X,\tau } \right)$ be a topological space. A sub-collection $S$ of subsets of $X$ is said to be an open subbase for $X$ or a subbase for topology $\tau$ if all finite intersections of members of $S$ form a base for $\tau$.

In others words, a class $S$ of open sets of a space $X$ is called a subbase for a topology $\tau$ on $X$ if and only if intersections of members of $S$ form a base for topology $\tau$ on $X$. The topology obtained in this way is called the topology generated by $S$.

Example:

Consider the Cartesian plane $\mathbb{R}$ with usual topology. The ${\rm B}$ is the base for the topological space $\mathbb{R}$, then the collection $S$ of all intervals of the form $\left] { - \infty ,b} \right[$, $\left] {a,\infty } \right[$ where $a,b \in \mathbb{R}$ and $a < b$ gives a subbase for $\mathbb{R}$. Since the finite intersection of all such intervals gives the members of the base of $\mathbb{R}$, i.e., $\left] { - \infty ,b} \right[ \cap \left] {a,\infty } \right[ = \left] {a,b} \right[$.

Example:

Let $X = \left\{ {a,b,c,d} \right\}$ with topology $\tau = \left\{ {\phi ,X,\left\{ a \right\},\left\{ c \right\},\left\{ d \right\},\left\{ {a,c} \right\},\left\{ {c,d} \right\},\left\{ {a,d} \right\},\left\{ {a,c,d} \right\}} \right\}$
${\rm B} = \left\{ {\left\{ a \right\},\left\{ c \right\},\left\{ d \right\},X} \right\}$
$S = \left\{ {\left\{ {a,c} \right\},\left\{ {c,d} \right\},\left\{ {a,d} \right\},X} \right\}$ is a subbase for $\tau$.

Theorems

• Let $S$ be a non-empty collection of subsets of $X$. Suppose that $X = \cup S$, then $S$ is a subbase for some topology on $X$.
• Let $X$ be any non-empty set, and let $S$ be an arbitrary collection of subsets of $X$. Then $S$ can serve as an open subbase for a topology on $X$, in the sense that the class of all unions of finite intersections of sets in $S$ is a topology.


text:
# Minimalist C++?

This topic is 4351 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

I'm working with C but I want to get the big picture stuff on C++ without having to delve into the myriad arcane corners of the language. What are the absolute core features of C++ (beyond the C base) to get the most bang for your buck? That is, what are the "can't really do without" parts of C++ that add the most power, etc. Or should C++ be an all-or-nothing sort of affair? Of course different people will have different responses but that's ok.

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Start with the standard C++ library, and build from there. std::string and std::vector, for example.

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I'm not sure I understand the question, but the features of C++ that make me want to use it OVER C are the following:

exceptions
templates
single-inheritance OOP (I don't like to truck with multiple inheritance)
class methods

There isn't alot more in C++ that's not in C, but this should illuminate, that while C is C++, there is alot of C++ that's not C.

Besides exceptions and templates, there is nothing in C++ that can't be easily emulated or worked around in C (easily meaning straight-forward, not that it's actually easy to implement VFTs).

Even templates can be managed with the C preprocessor, but the result lacks strong typing, which in my opinion is 50% of the reason to use them in the first place.

But, where does it get you? my old prof. used to say, that C++ is as fast as C + epsilon (where epsilon is very small until you use multiple inheritance). But using the features that I've mentioned, my C++ code is typically half the length of my equivalent C code. This is measuring primary implementation code, not all the support libraries.

Finally, creating support libraries is very comfortable with C++, encapsulation using namespaces and classes is a breeze.

Hope this is enlightening

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Quote:
 Original post by Ned_KI'm working with C but I want to get the big picture stuff on C++ without having to delve into the myriad arcane corners of the language. What are the absolute core features of C++ (beyond the C base) to get the most bang for your buck? That is, what are the "can't really do without" parts of C++ that add the most power, etc. Or should C++ be an all-or-nothing sort of affair? Of course different people will have different responses but that's ok.

Templates provide a replacement for macros. They provide:
* Type safety
* They can be properly debugged.
* They dont have to be inlined and instantiation can be controlled.

STL means that you'll never have to write another dynamic array again.

OO features such as classes and inheritence. Although C++ is a multi-paradigm language the OO parts it provides are a very natural way of coding.

There are exceptions to all of these but they hold true for 95% of cases.

Like anything C++ is a tool and to say C++ is slow is just a workman blaming his tools. Get a good C++ book, there are loads out there. I could recommend a few, to start: Meyers, Effective C++ and Alexandrescu, Modern C++ Design.

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Ned_K, I think you have the right idea about learning C++. So many people complain about it being so hard to learn when they try to memorise every possible aspect of the language before they're even comfortable with it. Meanwhile, C++ is designed to be C with extra features you can use if you feel like it, and ignore otherwise.

First thing you need to know for C++ is to write functions and expressions. The basic C stuff. A few things are nicer in C++, such as the fact that you can overload functions. This means that you can have two functions with the same name, but with different argument lists.

Then it's nice to start using classes. Easy - just like structs, but with methods and privacy. And constructors and destructors.

Then you can make you can make your life a little easier by using std::string for strings instead of character arrays.

At this point you probably will benefit from the standard template library. Learn how to use std::vector, std::list, std::set, std::map - they all work basically the same way, so it's hardly any work. Learn iterators too, so you can use these things in for-loops.

Use what you know until you're comfortable. Then, when you feel like it, try out inheritance. Not too hard. If you want polymorphism, simply make your methods virtual. Don't forget virtual destructors.

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Quote:
 Original post by Ned_KWhat are the absolute core features of C++ (beyond the C base) to get the most bang for your buck? That is, what are the "can't really do without" parts of C++ that add the most power, etc.

Without a doubt, the feature I can't be without in Cplusplus that is not available and cannot be emulated in C, C#, Java, or any other language I've programmed in (not to say I've used 'em all) is something handily referred to as RAII.

RAII requires the use of objects, which are instantiations of classes, and takes advantage of the object constructor and destructor to guarantee certain invariants are true during the lifetime of the object, and that certain pre- and post-conditions are met.

For example, an object encapsulating a file I/O stream can use RAII to guarantee that while the object exists, the file stream is opened and writeable or readable, and that when the object is destroyed the file stream is flushed and closed.

So, if you want to start using Cplusplus, learn the basics of classes, constructors, destrutors, and assignment operators (the rule of three), understand class invariants, and master the use of RAII.

From there, learn how to use exceptions to guarantee class invariants, then learn the standard library (streams, strings, containers, iterators, algorithms, in that order) so you can do something useful with your objects.

After that, learn about inheritance, virtual functions, and how to do Java-style multiple inheritance in Cplusplus. Learn about functors and smart pointers.

The esoteric thing you don't need to learn right away are how to write templates and do metaprogramming, RTTI (run-time type identification), and the more arcane things like fancy ways of newing objects (custom new operators, placement new) etc. Most of boost or tr1. Cplusplus0X.

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For many years, C++ compilers weren't very good. Hence people tended to avoid features that would cause problems in portable programs:

- RTTI
- Exceptions
- Nontrivial templates

Now, C++ compilers are a lot better than they used to be. They're more consistent and more features are implemented "correctly".

I still don't think it's necessary to know every feature of C++ - to be honest, I don't think very many C++ programmers do.

If you read "Thinking in C++", you'll see that some features, especially OO, constructors, destructors, RIAA and exceptions, are quite helpful to the language and make things a lot easier, especially when it comes to error handling.

Templates are useful in some circumstances, but I find that I don't implement them very often, I just use the standard ones (i.e. STL) instead.

Mark

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Quote:
Original post by Bregma
Quote:
 Original post by Ned_KWhat are the absolute core features of C++ (beyond the C base) to get the most bang for your buck? That is, what are the "can't really do without" parts of C++ that add the most power, etc.

Without a doubt, the feature I can't be without in Cplusplus that is not available and cannot be emulated in C, C#, Java, or any other language I've programmed in (not to say I've used 'em all) is something handily referred to as RAII.

I wouldn't go so far as to say it "can't be emulated". It's quite easy to have RAII in C#, for instance, by simply having a using statement:

using (ResourceObject resObj = new ResourceObject(@"C:\texture.tga")){  // do stuff}// resObj is destroyed and properly disposed of

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Other than MFC there is little reason for me to use C++. I mostly use C because that's all I need in most cases. The minimalist C++ would be object based programming.

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Quote:
 Original post by JDOther than MFC there is little reason for me to use C++. I mostly use C because that's all I need in most cases. The minimalist C++ would be object based programming.

MFC is not affiliated with C++. MFC is a Windows only set of classes (a feature of c++) used for Windows-only development. C++ can and has been used on many, many platforms and hardware environments. It is a general purpose systems programming language.

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# zbMATH — the first resource for mathematics

On the $$L^ 2$$-index of Dirac operators on manifolds with corners of codimension two. I. (English) Zbl 0881.58071
The purpose of this paper is to generalize the Atiyah-Patodi-Singer index theorem to compact manifolds with corners. A manifold with corners can be defined as a topological manifold $$X$$ with boundary together with an embedding $$\iota: X\hookrightarrow \widetilde X$$ into a closed $$C^\infty$$ manifold for which there exists a finite collection of functions $$\rho_i\in C^\infty (\widetilde X)$$, $$i\in I$$, such that $$\iota(X) =\{x\in \widetilde X\mid \rho_i (x)\geq 0$$, $$i\in I\}$$ and for each subset $$J\subset I$$, the $$d\rho_i$$, $$i\in J$$, are linearly independent at each point $$x\in\widetilde X$$ where all $$\rho_i$$, $$i\in J$$, vanish. The boundary of $$X$$ is the union of embedded hypersurfaces $$Y_i$$, $$i\in I$$.
Let $$Y_{i_1 \dots i_k}= Y_{i_1} \cap \cdots \cap Y_{i_k}$$, $$i_j\in I$$. Then we say that $$Y_{i_1 \dots i_k}$$ is a corner of codimension $$k$$. Let $$X$$ be endowed with a metric which is a product near all hypersurfaces and also near all corners. Let a Dirac operator on $$X$$ be adapted to the product structure near the boundary. Then the goal is to generalize the Atiyah-Patodi-Singer index theorem to this case. In this paper only manifolds with corners of codimension $$\leq 2$$ are considered.

##### MSC:
 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 58J20 Index theory and related fixed-point theorems on manifolds
Full Text:


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Loss of ladder line: copper vs CCS (DXE-LL300-1C) – KN5L’s measurement 11/2020

DXE sell a nominal 300Ω ladder line, DX Engineering 300-ohm Ladder Line DXE-LL300-1C, and to their credit they give measured matched line loss (MLL) figures.

Loss of ladder line: copper vs CCS (DXE-LL300-1C) – revised for 25/07/2018 datasheet was a revision of an earlier article based on an updated datasheet from DXE. I noted that the specification data had artifacts that one would not expect of such a line, and I questioned whether the datasheet was credible.

John, KN5L, recently purchased, measured and published measurements of a 10.06m (33′) section of new DXE-LL300-1C which provide an independent dataset that might cast some light on the matter.

The chart above plots:

• DXE’s datasheet MLL figures (converted to dB/m);
• MLL calculated from KN5L’s S11 open and shorted measurements; and
• theoretical MLL for round copper conductors of the same gauge as specified for the LL300 (dielectric loss is assumed insignificant).

The theoretical line is based on well developed skin effect and $$MLL \propto \sqrt f$$, resulting in a straight line on the log-log graph.

KN5L’s 100 point measurement dataset is for the most part smooth and quite credible, though it shows departure from ideal homogenous conductors with well developed skin effect… and for good reason, these are not homogenous conductors and skin effect is only developed at higher frequencies.

At 60MHz, KN5L’s measured MLL is a little worse than theoretical, quite probably due to the fact that these are 19 strand conductors, and the cladding thickness may be just too little to deliver copper like performance even at 60MHz. At lower frequencies, MLL is better, but a good deal worse than the theoretical MLL for copper conductors.

Whilst the MLL might seem small, these types of line are commonly used in scenarios with high VSWR. Let’s calculate the loss under mismatch of a scenario used for some recent articles.

The scenario then is the very popular 132′ multi band dipole:

• the famous 40m (132′) centre fed dipole;
• 20m of feed line being parallel RG6/U CCS quad shield with shields bonded at both ends;
• 7MHz where we will assume dipole feed point impedance is ~4000+j0Ω.

We will consider the system balanced and only deal with differential currents.

Taking the MLL of the LL300 as 0.018dB/m, the calculated loss under mismatch is 2.3dB. It is not huge, but any assumption that the loss in open wire line is insignificant is wrong.

Lets evaluate the loss using a home made open wire line of 2mm copper conductors spaced 150mm. The calculated loss under mismatch is 0.114dB, a lot better than the previous case.


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# Financial indicators of Holcim (Romania) for 2007

7 Februarie 2012

### Bucharest

Although the turnover of Holcim (Romania) increased by 28% in 2007 as compared to 2006, the gross profit (before tax) of the company decreased by 33%. The decrease of the profit before tax was due to the higher increase of operational costs than net sales, on one hand, and, on the other hand, by the excessive depreciation of local currency against the euro towards the end of 2007, which generated a financial loss (due to different exchange rates applied for the debts expressed in euro). In addition, in 2006 the registered financial profit was also generated by the higher appreciation of local currency against the euro.
 Type of financial situation 2006 2007 Balance Sheet Indicators lei lei < TD>Fixed assests - Total 860,678,446 1,445,955,431 Current assets -Total, out of which 146,141,657 207,630,425 Stocks (materials, ongoing production, half-finished products, finite products, goods, etc) 63,894,749 120,539,581 Cash and bank accounts 1,491,851 256,861 Account receivables 79,277,097 86,833,983 < EN-Administration SPAN mso-fareast-font-family: FONT-FAMILY: black; COLOR: 11pt; FONT-SIZE:>Equity - Total, out of which - - Public Equity - - Provisions for risks and expenses 39,064,867 46,044,157 Debts Total 446,815,120 836,638,329 Profit and Loss Indicators Turnover 774,723,654 989,998,690 Total revenue 876,154,828 1,034,609,637 Total expenditures 668,827,774 895,703,995 Gross profit of the financial period 207,327,054 138,905,642 Gross loss of the financial period - - Net profit of the financial period 174,943,055 114,553,963 Net loss of the financial period - -


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# inside

1. ### Magnetic field inside

What happens to the magnetic field inside this solenoid, if you double the number of revolutions, simultaneously stretching the solenoid twice as much as the original length? Suppose that the applied voltage was kept constant, and the additional wire length for additional turns of the coil did...
2. ### Why is the electric field inside the dielectric cancelling?

So, I was studying force between the plates of a capacitor when a dielectric is inserted. Here is my question https://ibb.co/cenvXk Shouldn't it be like this picture below https://ibb.co/kOUsCk So, why is my teacher saying that the electric field inside the dielectric cancelling...
3. ### Kinematics: moving car with person inside

https://postimg.org/image/aff9jx8mz/ At the time $t_0 = 0$ a train starts to accelerate from rest and person starts to walk inside the train from point A to point B (distance d). The acceleration of the train is given as a function of the distance covered: \$a_T(s) =...
4. ### charge inside the conductor

what does it exactly mean " charge enclosed by conductor" ? Whereas we know that charges only resides on the surface of the sphere.
5. ### Does Fermat principle explain refraction inside water?

A light ray is the fastest route between two points P and Q,but what if Q is at the bottom of the sea so that light cannot reach it?
6. ### Gravitational force inside the earth

I read the proof that for a thin spherical shell with mass M, the potential energy U for a point mass m inside the shell is constant (depending only on the radius R of the shell) and thus the gravitational force on m is 0 at any point inside the shell. Then they talk about a point mass inside...
7. ### Pressure inside a bladder when subjected to an outside liquid pressure

I have an elastic bladder that is charged with 300 psi gage pressure of a nitrogen gas inside the bladder, at atmospheric pressure outside the bladder. This is being used as a pulsation dampner for a liquid dye pulsing pump. If I subject that bladder to a liquid dye pressure of 25 psi gage...
8. ### Electric field inside non-uniform shells

Consider a spherical shell where the charge is distributed only on the outer surface of the shell but the charge is not uniformly distributed. Is the electric field zero everywhere inside the shell? explain why. Sky
9. ### Pressure inside a tank

A rigid tank of volume 83 m3 contains 100 kg of H2O at 100oC. The tank is heated until the temperature inside reaches 120oC. Determine the pressure inside the tank at (a) the beginning and (b) the end of the heating process.
10. ### Calculation of pressure inside cylindrical vessel

Hi I need to know the pressure inside a sealed cylindrical vessel which has following parameters a) thickness of wall and bases = p b) dia of base = d c) height of cylinder = h d) height of liquid filled inside cylinder = g e) surrounding temp = T f) thermal conductivity of cylinder material =...
11. ### electric field inside a conducting sphere

Greetings everyone!! electric field intensity inside a conducting sphere set by an external source is 0. (I guess first there will be a charge distribution on the surface of the sphere due to induction. the electric field set up by these induced charges will cancel the electric field due to...
12. ### Why electrons can't remain inside the nucleus?

I am trying to solve this question," Why electrons can't remain inside the nucleus?"I am trying to mention three points here- 1.Nuclear size 2.Nuclear spin 3.Nuclear magnetic moment For the third part,I think I am pretty clear about it since the magnetic moment of electron is 1836 times greater...
13. ### Force Inside a Solenoind

Hello I'm working on a personal project which involves a solenoid. I'm trying derive an equation for the Force(N) that an object would experience due to the flux density inside the coil. The flux density can be calculated relatively easily by the fallowing equation. Given the material...


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## Calculus 8th Edition

$-2.5$
From table, we observe that the function $f(x,y)$ approaches to $-2.5$ ,as the $(x,y)$ approaches to $(0,0)$. Our guess can be proved by taking the help of substitution method as follows: $\lim\limits_{(x,y) \to(0,0)}f(x,y)=\lim\limits_{(x,y) \to(0,0)}f(x,y)\frac{x^{2}y^{3}+x^{3}y^{2}-5}{2-xy}$ $=\frac{-5}{2}=-2.5$


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# Why does going faster than the speed of light require infinite energy?

1. Jun 8, 2012

### Reptile202

I honestly can't make any sense of this. I've been told traveling even one time faster the speed of light, the mass becomes infinite; therefore, infinite energy is required.

However, traveling just one time above speed of light isn't an infinite speed. The object isn't constantly increasing in speed, rather it's maintaining a certain speed.

If one was constantly picking up speed, and had no intentions of stopping, I could see why infinite energy would be required.

To make short, does traveling faster than the speed of light actually require infinite energy? Or is the supply just some much, we call it infinite...Perhaps because not even our universe altogether has the needed supply?

2. Jun 8, 2012

Traveling faster than the speed of light does not require infinite energy!
What requires infinite energy is to accelerate a massive body from a subluminal speed to the speed of light. You can approach the speed of light but you will never quite make it, because for each unit of energy you put into body the speed change is less and less than before.
And yes the energy required is infinite, not just a really large number, but true infinity. Physically that means that no matter how much you put in you will never make it.

Now the topic of traveling faster than the speed of light is even worse since only bodies with imaginary mass can travel faster than light. For them, the situation would be opposite. They can travel as fast as they want but they cannot slow down to the speed of light. But of course that's largely irrelevant 'cause, you know, imaginary mass.

3. Jun 8, 2012

### Reptile202

Technically, wouldn't that mean the speed of light, even with infinite energy, is impossible? Because even if you have infinite energy, the more you put into the object, the speed change is going to be less and less regardless of a unlimited supply?

4. Jun 8, 2012

### nitsuj

Yes, oddly that's a better understanding than the first post.

Don't forget that infinite is an undefined quantity, imo better said as; it's a concept. In particular when used in this context.

I am sure you understand the concept of infinity.

There are other variables that you could correctly use, such as you can go the speed of light, but it would require an infinite amount of time / distance / energy. And again back to the point of infinity not being a specific quantity.

One last note, and touching on your last post. It's not specifically a lack of distance, energy or time that "makes it impossible" for a massive object to go c. It's the "mechanics" of the motion of electrodynamic bodies.....

I'm not one to recommend using math to better understand something. But play with an equation that can be used to calculate gamma or whatever, but in this case it would help reduce the idea of "limiting speed" to what it "really" is, and not what particular scenario you can imagine (infinite energy ect).

Last edited: Jun 8, 2012
5. Jun 8, 2012

### Nabeshin

The use of infinity in such statements as 'it requires an infinite amount of energy to accelerate a massive body to c' is simply sloppy language. Most people will sort of intuitively understand what is meant, but that doesn't make it technically correct. The correct statement would be something like, 'the energy required to accelerate a massive object arbitrarily close to c is unbounded.'

6. Jun 8, 2012

### Reptile202

So in actuality, not even infinite energy will make an object go beyond the speed of light? Basically, infinite is just a term used to describe the impossibility?

7. Jun 8, 2012

### nitsuj

But there is no such thing as "infinite" energy. I should still say yes to answer though. For the last question, no it's not.

Infinite in this case describes the "diminishing return" (i have a finance background) of energy input to a "motion" output. You can put in more and more energy into an object, as it gets towards the speed of c you (who is measuring the speed) will notice the object take on different characteristics other than acceleration (and infinitely so), despite efforts to accelerate the object.

Though this isn't a very good train of thought to better understand this concept. If you are interested and can put effort into this, look into calculating gamma via pythagorean theorem.

It's a small exercise for a big improvement in understanding in this fascinating regime.

8. Jun 8, 2012

### Naty1

You likely learned early on that everyone observes 'c' when they measure the local speed of light. A better way to think about the issue is that no matter how fast you go, light always passes you a speed 'c'. You can speed up as much as you like, expend as much energy as you wish accelerating, no matter how fast you peddle your bike nor press down on the accelerator, light will still blaze by you at the same old 'c'.

But exactly why that is the case, why electromagnetic waves travel at 'c' is not at all clear. We have no set of first principles from we can derive the speed of light, the charge of the electron and so forth. For now, they are what we observe.

9. Jun 8, 2012

### Reptile202

Thanks.

I believe I'm starting to make some sense of all of this.

"As the body's speed approaches c, light speed, the mass becomes huge and approaches infinity."

The above is something I found; however, it didn't go into the details I'd like to know. Basically, the mass would start increasing and never stop, which would require infinite energy? That is to say even if you maintained an exact speed around that level, the mass would still increase regardless?

10. Jun 8, 2012

### nitsuj

Yes that's generally correct (the part in quotes) Note there is a difference between the two "masses" here.

"rest mass" & "relativistic mass". With "rest mass" being typical (what's weighed by a scale), and the other what you had referred to above. Someone may mention a more popular term for "relativistic mass".

Your last question the answer is no. And Im not sure what is asked in the first. But maybe a good time to consider the idea that energy doesn't "disappear". If the body is near c and more and more energy is applied to the object it must "go somewhere". In this case an increase in "relativistic mass"/kinetic energy. ( i maybe wrong on the last part regarding increased kinetic energy, just seems right from concepts)

Last edited: Jun 8, 2012
11. Jun 8, 2012

### Reptile202

Sorry for the confusion.

Well, it said the mass would approach infinity; therefore, wouldn't the mass of the object have to start increasing with no end since it's infinite?

12. Jun 8, 2012

### nitsuj

yea for sure but as a result of increased energy input. Again appreciate that this is not Mass in the "at rest" sense, but in the kinetic sense. ( again I'm pretty sure that's right).

13. Jun 8, 2012

### Reptile202

So, even if an object maintained a speed, neither increasing or decreasing, the mass will continue to increase and increase with no end? And in order to keep the object moving, nothing less than unlimited energy will be needed?

14. Jun 8, 2012

### nitsuj

Shoot, that's what I was trying to steer you away from, you hinted this idea in post #9.

if the object moving near c relative to you is inertial (not accelerating) than it's "relativistic mass"/kinetic energy will also remain the same.

If you apply energy in hopes of accelerating the object, you would notice it mostly just gets harder to accelerate (because of increased "relativistic mass"/kinetic energy).

Keep in mind the "law" that something in motion stays in motion.

And for kicks to throw in a "loop", motion is relative. To someone else that object you have moving near the speed of light maybe going pretty slow. A cure for that, is to consider all of this we are discussing is about measurements that take place "across" spacetime.

Last edited: Jun 8, 2012
15. Jun 8, 2012

### Staff: Mentor

If the object maintains its speed, neither increasing nor decreasing, it will maintain the same mass. If you add more energy, it will speed up some and gain some more mass. But it will always get at least a little bit more speed with each increase in energy - you can't turn all the added energy into speed. This may be easier if you actually look at the equations (which are ONLY VALID for speeds below that of light!):

$m=m_{0}/\sqrt{1-(v/c)^{2}}$
$E=mc^{2}$

Where $m_{0}$ is the mass that will be measured when at rest relative to the observer doing the measuring, and v is the velocity of the object when moving. Plug some numbers in, and you'll see that you can't change m without also changing v, and no matter how large you make E and m, you can't get v to come out above c.

16. Jun 8, 2012

### Reptile202

:)

So it's impossible to go faster than light because too much of the energy would be used as mass?

17. Jun 8, 2012

### Staff: Mentor

To be very precise, it is impossible to take an object that has non-zero mass and is travelling at less than the speed of light, and accelerate to a speed equal to or greater than the speed of light.
The more energy you pour into it (push it, strap giant huge rockets to it, or whatever) the more of the added energy will go into increased mass and the less will go into increased velocity. Although it can get arbitrarily close to the speed of light (try plugging v=.999c, or v=.9999c, or v=.99999c into the equations above), it will never quite get there.

There's a different set of equations that govern the behavior of massless particles such as photons. They can ONLY travel at the speed of light, and there's no way of slowing them down.

18. Jun 8, 2012

### DrGreg

In Newtonian physics, when you accelerate an object it gains kinetic energy which is given by$$E = \tfrac{1}{2}m_0 v^2 \mbox{ ..................................(Newton)}$$But this is only an approximation to the true relativistic kinetic energy$$E = m_0 c^2 \left( \frac{1}{\sqrt{1-v^2/c^2}} - 1 \right)\mbox{ .........(Einstein)}$$This value "diverges to infinity", i.e. keeps on increasing without limit, as v gets closer to c. If it were possible for an object (with non-zero rest mass) to reach the speed of light it would have infinite kinetic energy. Where would that come from?

A simpler argument, without mentioning energy, is to note that all observers measure the same value for the speed of light. So if you have reached 90% of the speed of light relative to your starting point, according to you the speed of light is still 299,792,458 m/s, not 29,979,245.8 m/s, as you might expect. In other words you are no nearer your target and still going 299,792,458 m/s too slow. And you remain going 299,792,458 m/s too slow, from your own point of view, no matter how long you accelerate.

19. Jun 8, 2012

### nitsuj

I'd agree with that, seems well said given the context.
(as in the energy "put into" the object in order to try and accelerate it would be measured "more and more so" as an increase in mass as calculated above)

20. Jun 8, 2012

### Reptile202

Ah, thanks!

So the reason for not being able to travel at certain speeds is because the energy is being converted into mass? So really...infinite energy is irrelevant, because it too will be converted into mass as well?


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1. ## another integral

I understand how the book solved the integral but don't get how they got an answer of infinity.

$\int_{0}^{\pi/2} tan x~dx=\lim_{b\to(\pi/2)^-}ln |secx|(from~0~to~b)=\infty$. I get an answer of 0. $\lim_{b\to(\pi/2)^-}[ln|secb|-ln|sec0|]=0-0=0$

What am I doing wrong?

2. Originally Posted by Possible actuary
I understand how the book solved the integral but don't get how they got an answer of infinity.

$\int_{0}^{\pi/2} tan x~dx=\lim_{b\to(\pi/2)^-}ln |secx|(from~0~to~b)=\infty$. I get an answer of 0. $\lim_{b\to(\pi/2)^-}[ln|secb|-ln|sec0|]=0-0=0$

What am I doing wrong?
$sec \left ( \frac{\pi}{2} \right ) = \frac{1}{cos \left ( \frac{\pi}{2} \right ) } \to \frac{1}{0}$
which most people take to be infinite.

-Dan