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"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
- Albert Einstein
The concept of a field is "magical". Humans with their limited senses can not feel or experience a field. We can only feel FORCE or ENERGY. We can not even measure a magnetic or electrical field directly. But we can measure the field with such things as voltage and force, and deduce a fields "measure". A field shows itself in many other ways as well.

CARTOONVANGO.JPG, 60 kB Cartoon The concept of a field is paramount, and all other "evident" parameters derive from it. The concept of the field is profoundly real and essential, although hidden.

In addition, intrinsically - fields involve waves and other dimensions. If anything is real, it is Waves. They are the building blocks of all corpuscular "matter" that we personally experience. We have a biological obsession with material "things", and not their constituent waves.

Our limited - intuitive - world is not real. What is very real is the world that we can not see. Such a world derives all "things". For all devices inherently are physical, and utterly fail in measuring a "profound and intrinsic" bigger world. I wonder if our consciousness can encompass a field. Millions of years of evolution have hardwired our brains for a different world. Silly us, we are hardwired for particles and things - not waves and fields.
"Also He has put eternity into man's mind,
Yet so, that he can not find out what God has done from the beginning to the end." Ecclesiastes 3:10

I believe that this can be paraphrased as a Law:
As science discovers a truth or solves one question, a multitude of additional questions arise. Discovery can never encompass - instead, the gap only widens. With our humble instruments and are pitiful brains, it is utterly impossible to look towards the Face of God. Foolish ones look for an equation for everything. They only indicate their arrogance, and a lack of mature scientific understanding.

"Any relationships between numbers, functions, and operations become transparent,
generally applicable, and fully productive
only after they have been isolated from their particular objects
and been formulated as universally valid concepts"

- Emmy Noether
Emmy knew the difference between pure and glorious thoughts, and reality.

BANAST15.gif The Great Ones

The Electrostatic fields and the Magnetic fields are intimately related. They are both fields of charges. There is only one difference between the two. A magnetic field is produced by a MOVING charge. An electrostatic field is produced by a NON moving charge.

GALAXY.JPG, 10 kB There are modern day consequences to the concept of the field. One concerns Black Holes. Sense fields can not be directly detected or measured, fields have to produce something to be measured. In the case of this example, it is "Force". Instruments can measure force. But what if a black hole produces a field - a very REAL field - which does NOT produce Force, or voltage, or energy, or anything else that we are accustomed to measure. What if it produces Matter, for example? No laws are broken. The field still exists, we just can not detect it. What if this new field produces quarks, mesons, leptons, or something? Perhaps this new matter could be measured by increased gravity in the fields immediate area. These would be radial bands. Perhaps this new matter would produce gravity waves emanating from these bands, and radiating outward.

OK, I will get back to the fields that I know something about. I just wanted to make a very important point about the mysterious nature of fields: they are DERIVED, but very REAL. They are hidden, constantly behind the scenes, and create our personal physical reality.


BBALLBLU.GIF, 0 kB Field strength: ACCELERATION g ...Definition

GRAVSUN.JPG, 51 kB A Gravity Field
(Vectors point inward for gravity.)

Defining measurements were made timing the fall of objects on this planet's surface for acceleration.
Equating inertial mass to gravitational mass.
And measuring the attraction of two suspended masses or torsion balances. Force=mg

The field can not be measured directly - only "materilized-effects" such as force. By convention, field lines were arbitrary set as pointing toward the gravity source.
The gravitational acceleration varies all over the earths surface due to surface features and subterranean densities. Such anomalies make underwater and underground gravitational navigation possible; also drill mapping.

GRAVITYEARTHM.JPG, 65 kB A Gravity Field
(Vectors point inward for gravity.)
Shown in yellow are equal attractive points between the earth and the moon.
The locus is a hyperbola. ( two dimensions, with asymtotes)
There is a defined infinitesimal point where there is zero field strength. It is at the apex of the hyperbola.
(I put a dot there.) In special circumstances, the field density can be extraordinarily strong NEAR this point. If we add two one-dimensional vectors
Eqn1.gif, 1 kB
with the conditions that
a=-b, and a>>0
Eqn2.gif, 0 kB
You can see from an engineering standpoint, the "balancing spot" can be precarious - at best.

There is another zero point: at the center of the earth.
There is another point: near the center of the moon.
These spots are not necessarily symetrical, or neat singular areas.

All fields, not just gravity, have one, and only one, vector representation in space.



EqE.gif, 0 kB

ELECTROSTATIC.JPG, 52 kB Electrostatic Field
Negative charge, Vectors point toward source.
ELECTROSTATIC2F.jpg, 45 kB Electrostatic Field

BBALLBLU.GIF, 0 kB Field strength: Force/q ...Definition

One dyne of force; produced by one statcoulomb to another one statcoulomb charge; one cm away. ...Definition

Electrostatic fields - and All fields - are a measure of line density through an orthogonal surface space.
Defining measurements were performed:
Using torsion balance threads for force,
And also suspension of oil drops against gravity.

General free space equation is inverse square law due to purely Geometrical considerations. (The Strong and Week fields are not Geometrical fields.)
It involves only charge and geometry, and later, by a charge-media, known as a dielectric. EqER2.gif, 9 kB
BBALLBLU.GIF, 0 kB Field strength: in statvolts/cm ...Definition
Measurements of statvolts with voltmeters.
With the first CGS equation being the defining equation. The CGS equation is the birth - and native - expression. It requires no constant: as it is constitutional by definition.
Later, the universal SI system (MKS) dominated, with complete equivalency.

VBImage1.gif, 67 kB
My program...
Two like charges...
I wrote this program to visualize fields.
In later pages you will see more. But for now, I just wanted to show you what a computer can do for you with precision and great detail. Color graduations represent field strength, and the choise of color can be very dramatic. The green is quite striking. But I can place dramatic colors to represent contours at any location. The red (low intensity) is smooth and plain. However, when I made the transition to green, the inverse square law really becomes evident. One can inhance graduations with color at any chosen location of interest.

I told my program to place vectors at random locations to represent Direction of field. And, for ease of viewing, vector density does NOT represent true density. The white dots on the ends of vectors represent heads, and with this convention, all vectors point outward.

One can see a location between the charges where the vector field is zero. The field immediately surrounding the area quickly escalates in intensity.

Contour1.gif, 33 kB
VBImage2.gif, 57 kB
Two UNlike charges.

In this field, the charge on the right is positive, and the charge on the left is negative. Also, notice the shapes of the fields: ovals - or in three dimensions - ellipsoids.


Charges in Motion

GREENELECT.gif, 284 kB

Electrons may not literally "spin" on their axis but mathematically, with angular momentum - they DO). What IS real is the magnetic field!
"Spinning" (on their axis) electrons in valence orbits give ferromagnetics their field strength.
While standing-wave electrons in "orbits" around a nucleus give diamagnetics their field strength. What is important here is motion-of-charge.
Originally, a magnetic field was observed with loadstone: a permanent magnet. Originally, the magnetic field strength was defined as a field strength from permanent magnets that would produce one dyne of force one cm away per area (in square cm). But the real defining moment came from a definition of moving charges - as current in wires.

Remember - we can not measure the field directly; only a quality produced by the field. In this case "force". A subtle fact, exposed by the definition.

BANAST15.gif More about MAGNETIC Fields

RULERMAR.GIF, 1 kB It may be interesting to compare the electrostatic field force to the gravitational field force...
...after all, the electrostatic and the gravitational fields are the most alike.

Eqnforcee.gif, 1 kB
Let q be one unit electrostatic charge, ether positive of negative:
q=1.6021764874...E-19 (Defined)

EqnforceM.gif, 1 kB
Let G = 6.6735337996E-11
(I will later derive this value using the neutron.)
EqnforceRATm.gif, 2 kB
You may arbitrarily choose any one-unit charged particles of mass m that you wish...

EqnforceRATe.gif, 2 kB
Two electrons...

EqnforceRATp.gif, 2 kB
One electron and one proton...

1942Mom.JPG, 14 kB Mom 1942
Mom's name was Wanda.

And my mother asked me, just days before she passed away, if she would come back-to-life (reincarnation). She protested, as if she already knew the answer, that she did not want to come back as a man. Still preoccupied with the question, she showed a disgusting expression at the thought. Appearing before me was a great moment in which to share my thoughts on fields, and waves, and God. I received A's in physics, and knew very well of electrostatic fields, magnetic fields, and gravity fields, and their waves. And with pride, if I could comfort mom, I would do it, for, after all, I was her son. I told her that I did not know. But I did know what it was LIKE...

I began: It is like each of our lives is a wave. Each wave is born from a common sea. On this ocean, you can observe a wave; in fact, you can SEE a wave; you can point at it; and in your mind, you separate it from the water. And you can ascribe an identity to it, that separates it from all other waves. But microscopically - and in the final analysis - when you precisely count the molecules and measure such things, you exactly measure nothing but the sea itself! You can not separate this bunch of water over here from that water over there.
It is a mysterious thing: It lives. And that life exists in, and on, a MEDIUM.

The waves are an energy that manifests itself in a form, which is what we see with our eyes. Our bodies - that you do see - are not really "us". We are glorious-effects in a common medium (or sea). The medium does not have to be water. The medium may be DNA. The medium may even, in the end, be mere DIRT. In any case, we are a "ripple". A medium can be all kinds of stuff, but is never hidden and always forms our reality; You can feel it, touch it, smell it, and intimately measure it in every way. One the other hand, the underlying causes of the waves are a little more difficult and hidden - just as all fields are directly hidden from science. Only the EFFECTS of fields are known to science.

My mom knew of my love of science. I felt pride for her to come to me and I would do my best.

I continued... For example, in analogy to people, the measure of the height of a wave could be a measure of some kind of stature compared to the other waves, perhaps your pretty hair, mom. Mom had thick healthy hair, with a touch of silver.

I told my mother that the waves can exist in the water, and the waves have "identity". Not so with the water: There is no identity there. Science knows that on a molecular-level, there is no difference between one water molecule and any other. The waves, therefore, transcend the water - and, as a mysterious form, live forever. Or, at least can live anywhere at any time.
I told my mom not to worry; Something is making the waves. That is the secret! In addition, in the analogy, the beautiful wave equations that produce the beautiful "forms" are really, when applied to people - "spiritual" equations that are quite transportable. And, just as in the analogy, do not depend on any specific physical medium.
We are immortal. Perhaps we existed before.

Such was my scientific corollary to my mom. In good faith, I considered it only an academic exercise, but mom embraced it as gospel. There is no such thing as "cerebral" between a mother and son. I could see in her loving eyes that mom did not work that way; even going back when I was a young kid. She placed my words on a high shelf in her mind as of something precious. No way; should they be there. I could never reach that high.

My mom then shortly passed away, leaving me with my fancy words of rationality that, now, seemed so utterly hollow. I did not intend for her to go forward with any authority from the likes of me. Coming from me, it would not have mattered what I told her, she would have held it to heart.

If only, perhaps, I could change my mind and rewrite an equation. If only, I could scribble on a piece of paper, and easily erase a line and draw another. Despite the hopeful physics, on a personal level, I could not argue away the finality. Mom was really gone. ...Seemingly chiseled in stone. The emptied halls of my science were deadend with silence.