Time is a concept relative to the viewer. Einstein, in his theory of relativity showed that time can be altered. That real time depends upon ones relative position in space with respect to that which is being timed. Time is not always the same for different viewers.
Time is a concept. Time is not absolute and it may not be real. For example, is time real to one who is dead or, to one who has not yet been born or, to one who will never be born. Time is dependent upon the ability to realize it.
Assuming the ability to realize time, then the concept of time can be broken into three parts; the past, present, and future. The past is what has occurred, the future is what will occur and the present is now. All humans who are alive today are in the state now. At birth humans begin to realize time. People from birth begin to develop the concept of time. Science has defined time but is bewildered as to "How it got started" and "When will it end?"
Because events relative to time are important to humans, humans strove to developed a means of measuring time. The measurement techniques have become very technical since man first came on this planet. Almost all animals have a concept of time. Man's most primitive concept of time is knowing the difference between night and day.
As society progressed people needed to break the day up into increments which had some sort of consistency. To measure time, all one needs is a uniform rate of occurrence. Very early time measurement devices were burning rope, twigs and logs. Then came the concept of the month which was determined by the moon. It didn't take primitive humans much measuring techniques to watch the moon go from full to waning, then waxing back to full. Early, it became easy to tell relatively long periods of time.
As agriculture progressed, people needed to know what period was the best time to grow their crops. Advanced devices as stone hinge appeared. Eventually needed was accurate ways to break up the day so people could get to work on time and watch for favorable positions of stars. Increasingly accurate measurement devices as the sundial, hour glass, and water tower came along. All these devices worked for thousands of years. Such devices however, were subject to errors, but they measured time sufficiently well for their time period.
Then came the study of time for times sake. It is said that the modern day concept of accurate time measurement came around 1600 with Galileo's work with the pendulum as a device to increment time. Galileo found that the period of a pendulum swing is uniform in time. However, the pendulum acquired friction problems so ways to add energy to the pendulum were devised and humans now had a fairly accurate clocking device. The pendulum device then allowed Galileo to accurately track the movements of heavenly bodies. Time took on a new importance in the tracking of the havens.
The pendulum was an accurate device but it also had its limits of ability to increment time. For example, the pendulum vibrational increment of time ranged from tenths of seconds to several seconds. The differences in time of hundredths of seconds could not be detected. However, for normal human references a spring and pendulum worked great, but the quest for better time pieces kept going on.
The advent of electricity brought a more stable force than gravity drawn weights and springs. Therefore, more accurate time pieces were developed.
One of the first electrical time devices which came into being was the synchronous motor. This electric clock was fairly accurate and broke the second into hundredths of seconds.
Still humans wanted more accurate time for time sake and science. The quest of time continues. Two indirect advancements of time occurred in the modern era. One was the ability to record events. This had the effect of passing on occurrences far beyond the relatively limited story telling about the event. The other advancement was the ability to date rocks and other objects by scientific means. These two advancements took the mysticism out of explaining past events.
The time of reality dawns. All through history religion has been detrimental to the advancement of science. In the new world religion and state were somewhat separated, allowing a greater freedom of thought. Religions, typically create the fear of the unknown. The phrase "Fear of God." for example. Religious people, from a scientific standpoint are the blind leading the blind. There are still people who believe the Earth was created in six days and seventh day God rested. In fact, just recently, the pope acknowledged the Earth was not the center of the universe.
Soon vibrating electrical waves were discovered, and the measurement of time became vastly more accurate. It became possible to create an oscillating wave within the megacycle region. This is one complete cycle of an electric wave in one millionth of a second. Very accurate devices came into being. One such device was the crystal controlled oscillator. The crystal itself was a small easy to handle device, and it was relatively easy to power the crystal. Also, the crystal's environment was more easily controlled for such errors as gravity, barometric pressure and temperature.
During this period, the concept of a day being constant fell. Although clocks were not very accurate still, they were however, accurate enough for a person named N. Stoyko. In 1936, Stoyko showed that the Earth took different times to rotate one complete turn. What a disturbing situation. A day is no longer a day.
During this period it became evident that one could not yet keep accurate time.
Just after World War II, another clock was invented which could keep track of time to within 23,870 million parts per second. This was known as the Atomic Clock. It was called atomic because it kept track to the atomic vibrations of the ammonia molecule. The device monitored a crystal oscillator by absorbing a spectral line of the proper frequency, when the oscillator varied from the fundamental frequency a feedback system corrected the crystal oscillator. The ammonia atomic clock was accurate to about three parts per billion. But science was not satisfied.
The next generation of Atomic Clocks were real atomic clocks because they measured the vibrations of the atom itself.
The next clock was made from cesium metal. It involved monitoring the precession axis of the outer electrons of the atom. This allowed a clock to vibrate at 9,192,631,770 cycles per second, with an accuracy of variation to less than one part per ten billion. This is the new definition of a second because times involving the Earth were no longer accurate enough.
Using the new clock it was possible to very accurately determine that the Earth was not rotating at a constant rate, and that it was actually oscillating in its rotation. In 1969 a R.A.Chandler showed that not only was Earth changing in its average rotation rate annually, but also cyclic with the year.
Time has gone from the rotation of the Earth to defining the Earths rotation in terms of electron precession. It is a matter of viewpoint. Now, time has moved from reality to relative. Time is a matter of viewpoint and along came someone who asked the question "Who's viewpoint?" A simple scenario was set up, and it was shown that time depends upon where one is when they are measuring time. The simple scenario was taking two boats in a river. One boat travels up current a particular distance turns around and comes back to the starting point. On the same river, another boats starts perpendicular to the current, goes out the same distance turns around and comes back. The question; "how long did each trip take?" Or; "what are the instantaneous affects of the occurrence directed at the observer, opposed to the same action directed perpendicular to the observer, in a medium moving in some direction relitive to the both the action and observer?"
Enter Einstein's Special Theory of Relativity:
Einstein and Lorentz redefined time. Time no longer goes tic...tic...tic. Time itself changes as an object approaches the speed of light. The theory states that the change of time for observer A is different than the change of time for observer B by: c is the speed of light

According to this equation, as observer B approaches the speed of light, observer B's time decreases toward zero. Also, according to this equation, traveling at the speed of light, time does not exist. Traveling faster than the speed of light is only imaginary.
The square root of minus one is imaginary. For those who like number games, evaluate the square root of minus one.
The truth of the matter is that the limit of the speed of light was consider impossible to exceed, was due to this equation being meaningless at v = c. I personally do not believe the speed of light can not be exceeded. One simply has to ask the question "Does all light travel at the same speed?" It has been demonstrated, light of various colors travel at ever so slightly different speeds. It's my personal opinion, the speed limit of an electromagnetic wave is limited by the media which the wave is propagated in, and not by physical limitations of force.
Time has three discrete parts; the past, now, and the future. For those who believe in destiny, what has happened can not be altered, and what is destine to happen can not be altered either. An individual may believe they can change destiny, but the mere fact that it occurred means that it was destine to occur, and they were destine to make the change. Thus, the future is simply a reflection of the past about now. So much for philosophy. In both physics and astrophysics time becomes very important. What makes time important is not the change in time but what happens in that change of time.
I could have called this section Calculus, but I want the reader to keep thinking time while reading this section, and keep thinking vectors. I believe the type of person who reads this book should know Calculus already. I include this to refresh anyone who may have forgot Calculus. Also, this is a very limited rendition.
Basically, Calculus is dealing with changes. As such, Calculus has a specific symbol delta denotes change.

Just having a change of time does no one any good. Then it follows that something has to change in a change of time. Typically, most people are aware of velocity. This is a function of distance in time. If s is some distance then:

It makes no difference to the term s/ t if an object is moving at 10 feet in 10 seconds or 1 foot in 1 second. The velocity is 1 foot per second in either case. However, what happens if the time interval approaches zero? In Calculus, this condition is called a derivative, and it's symbol is ds/dt. Such that:

The is usually called the first derivative, but it depends upon where one starts. Many times it is called the function prime which is what the tic stands for. Suppose the object is changing speed. Thus:

This is called the second derivative. In the above equations this is a term for acceleration.
There is a lot of rules to this. It is not my intention to write a Calculus book but only to jog the readers mind. However, I will include four rules or theorems since one should have an idea about this. These rules or theorems can be found in all the Calculus books as they are very common.
The first theorem is the derivative of a constant is zero:

The second theorem is if n is positive and c is a constant, then:

The third theorem is the derivative of the sum of an finite number of differentiable functions is the sum of the derivatives of the functions:

The chain rule:

The second great power function of Calculus is called the integral. The integral is simply the inverse of differentiation. The symbol for integration is . Due to the nature of an integral there are two types. There is the indefinite integral and the definite. The indefinite integral is an integral without limits and the definite integral has limits.
Indefinite integral: If F'(s) = f(s) then:

Definite integral: If F'(s) = f(s), and f(s) is positive within the limits a s b then:

C is a constant and in the definite integral it is canceled out.
Integrals are use extensively in physics to sum up various occurrences. For example, suppose one wants to find the length of a curve between two points. the formula for this is:

Suppose there is a curve with the equation of y = 2 * x^3/2 and the points of interest are x = 1/2 and x = 5/2, then:

As I said, the object isn't to teach Calculus, but only to demonstrate the math system which is being used to support this theory. So what was the object? The object here is to connect Calculus to Vectors to Supersymetry to Time to a Magnetic Field.
Basically, Calculus is a mathematical way of handling occurrences at an instant. Calculus either sums a group of instants ,or brakes thing down to a group of instants.
Velocity is a vectored quantity. That is an object is traveling at change in distance per change in time in a particular direction. Suppose that the supersymetery theory is correct and that time is a dimension. All space seems to have three physical dimensions. But all space seems to have a quality of electromagnetic cohesion too. Thus, supposing there is an element of space which is again as small as the difference in size as the Sun is to an atom.
Now, further supposing, that space electromagnetically reacts to change exactly like Isaac Newton's laws of force and motion. Applying Einstein's theory of relativity to an electric charge in motion, the affects of the charge to a position directly in front or behind the direction of motion, would be different than the affect of the charge to the sides of the motion by the relativistic value.
Several relationships exist with the motion of Q. A magnetic field is the reaction of space to a charge in motion. Therefore, the charge must be moving at some velocity in a particular direction. The distance from one point Q to the next point S is ds. The velocity vector is ds/dt. At all points L, perpendicular to the direction of motion of the electric field E are going to be equal to k q / dl^2. If dl is large compared to ds then dà is very small. At all points away from Q the electric intensity of E is changing.
Space at point L, reacts to the displacement of q, yielding a reaction vector
directed at Q. At point L, the direction of displacement is going to be in the direction of ds, and proportional to the velocity. This poses the problem of what happens if another Q immediately replaces the old Q. The second part of this theory is that Q is unique in space and that time travels outward as a vector from
. It's not instantaneous. It takes time for the affect of Q-S to reach L-Ls. A reaction to the displacement in q is traveling towards L for any point beyond Q. Then the reaction of L, would be toward Q, as being negative the affects of time traveling away from Q as
. This could be termed a rip in space traveling dl/dt spherically outward causing a reaction vector at L instant in time. These vectors would yield a cross product H proportional to the
field vector
and
according to the cross product of
crossed into
, and proportional to cos
. The trigonometric acceleration of all angles is proportional to functions of ds/dt in vector form.
Any element with a moment would have a torque provided by vectors 1 & 2. (1 & 2 being in the plane of velocity and not H.)
The cross product magnitude of the vector
not perpendicular to Q-S would be proportional to the sin of the angle between the point and the velocity direction of q in a 360 degree circumference about the line of velocity. Since the migration speed and number of charges would sum in space along a line of length l the Biot-Savart law can be used to calculate H at any distance from the line. Choosing the proportionality constant to equal 1.257 x 10^-6 w/a-m and the velocity of time travel toward L as c, then all the rest of the formulas work too. This idea of time having a speed is a problem but can be overcome by semantics. That is the velocity of time equals the propagation constant of electro-tonic elasticity of space to a change in charge at any point with respect to any other point.
Time in motion is the problem and this why I left this discussion in Time. The action vector in time is dependent upon the direction of action, but the perpendicular affect is proportional to Einstein's relavistic time constraints, and the affect can be a vector.
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