Keywords: How can we arrange keywords like numbers 4, 3, 2, 1, 0, -1 and dimension, universe, matter, electric, magnetic, electromagnetic, transmission line, LC circuit, impedance and capacitance, then add a whole different interpretation to each Source? It's not going to be easy. Elaboration on time, space, spacetime and charge is not included here.

Keywords from Each Source and Each Author's Meaning:

• 4
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  ^Ref.taojoe D₄ are the three familiar spatial dimensions, each with vectors orientated 90 degrees from another.

  ^Ref.taojoe The dimensions produced by 2 D 4 and 1 D 2 are the same.

  ^Ref.taojoe D₄ = length, width, height (spatial dimensions).

  ^Ref.taojoe 4 D 2 = 2.

  ^Ref.taojoe D₄ = ordinary matter, always in motion, or always radiating a temperature.

  ^Ref.taojoe It was the attaining the velocity of c that split D₄ into D₂ + D₂; conversely, reducing motion below c would reunite D₂ + D2 into D₄.

  ^Ref.taojoe In words again, we are taking one dimension, say the depth, away from solid matter, to get a plane in motion (once again time as a spatial dimension), but what is a plane in motion? Maybe a tube of some sort. Maybe not. The third option involves negatives. To review: D₄, i⁴ and +1 are all symbols we can use to represent solid matter as we know it.  D₂, i² and -1 are symbols that correlate to electromagnetic waves or photons.

  ^Ref.taojoe In words, this means that we add a new 90 degree vector to our planar electromagnetic wave, producing an abstraction we can refer to as a cubic wave. I don't know about you but I cant visualize that (for a good reason, as you will see). We can also try D₄ - D₁ = D₃.

  ^Ref.taojoe The only difference between D₄ and D₂ is that D₂ = D₄ x c (remind you of something? E = mc², perhaps?). Substituting numerals, -1 = (+1) c, and solving c = -1.  In words, c has the effect of negativizing a phenomenon.

  ^Ref.taojoe D₄ is responsible for what we call ordinary matter, both massive and detectable.

  ^Ref.taojoe Next, consider gravity's far-reaching effects. Not only matter but also even something mass-less like light, is induced to follow the shape of space. So it would be illogical to choose 2 as our denominator, since that excludes the 4 that contain matter.

  ^Ref.taojoe There are only two fractions whose denominator is 4, which would account for the matter, and everything contained in all lower dimensions.  What is it then that reacts with either light or matter, to form space?  What thing plays a role in the effect of gravity; appears in all the gravitational principles and equations? Distance!

  ^Ref.taojoe Therefore the only logical fraction for the dimension of gravity, or the geometry of space in one that points to the interplay of distance (D₁) with each of the dimensions effected by that gravity (D₄). The conclusion:  gravity = D_1/4.

  ***

  ^Ref.sqrtneg1 The square root of -1 is an integer in 5-circle where -1 is 4.

• 3
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  ^Ref.taojoe D₂, D₃, and D₄ are the three familiar spatial dimensions, each with vectors orientated 90 degrees from another.

  ^Ref.taojoe D₂, D₃, D₄ = length, width, height (spatial dimensions).

  ^Ref.taojoe D₃ is 2 spatial dimensions, a solid object.

  ^Ref.taojoe D₃ = before associating phenomena with D₃ some preliminary concepts need to be discussed.

  ^Ref.taojoe D₃ Preliminary Discussion

  ^Ref.taojoe In mathematics, equations are commonly written to describe phenomena in any of the four integral dimensions.

  ^Ref.taojoe The exponent of the variable indicates the degree of dimensionality:

  ^Ref.taojoe First degree equations have one solution and describe straight lines.

  ^Ref.taojoe Second degree equations (with x²) have two solutions and describe planar geometries like circles or parabolas.

  ^Ref.taojoe Third degree equations (3 solutions) describe solid objects.

  ^Ref.taojoe For the fourth dimension, we have a choice:  either write the exponent 2 or write the exponent zero.  Lets do some math and play with a very simple equation.  The equation is x⁴ = 1.  You say x⁴ = 1-  That's dumb.

  ^Ref.taojoe I can think of three ways of getting to D₃ from something we know.  We can take D₂, the photon and kick it up a notch, and do   D₂ + D₁ = D₃.

  ^Ref.taojoe In words, this means that we add a new 90 degree vector to our planar electromagnetic wave, producing an abstraction we can refer to as a cubic wave.

  ^Ref.taojoe We can also try D₄ - D₁ = D₃.

  ^Ref.taojoe In words again, we are taking one dimension, say the depth, away from solid matter, to get a plane in motion (once again time as a spatial dimension), but what is a plane in motion? Maybe a tube of some sort. Maybe not.

  ^Ref.taojoe The third option involves negatives. To review: D₄, i⁴ and +1 are all symbols we can use to represent solid matter as we know it.  D₂, i² and -1 are symbols that correlate to electromagnetic waves or photons.

  ^Ref.taojoe The only difference between D₄ and D₂ is that D₂ = D₄ x c (remind you of something? E = mc², perhaps?). Substituting numerals, -1 = (+1) c, and solving c = -1.  In words, c has the effect of negativizing a phenomenon.

  ^Ref.taojoe If c really does produce an opposite, then i¹or i , becomes its negative, i¹or -i , which is the value of i³, which is, lo and behold, an alternate symbol for D₃.  D₃ then (or i,) is the realm of slower-than-light imaginary points.

  ^Ref.taojoe Since it is sub-light it must have mass, but since it is imaginary, it has no substance.  And this is exactly what our plane in motion is trying to describe, a surface with no thickness and therefore no substance, enclosing on itself trying to form a sphere (or a tube) with no volume. An imaginary figure with mass. Hey, astronomy buffs, what am I describing?  This is dark matter! All that unaccounted-for mass that must exist in the universe but is undetectable.  Its undetectable because its not real.  But because its slowed to sub-light, it has mass. And because these things are negative singularities, similar to the singularity responsible for the big bang and the subsequent universe except hollow inside (like bubbles or macaroni), they are super dense, far more dense even than black holes.

  ^Ref.taojoe D₃ is responsible for the dark matter which is undetectable but comprises most of the mass in the universe.

  ***

  ^Ref.sqrtneg1 The square root of -1 is the integer 3 in 10-circle.

  ^Ref.sqrtneg1 In the counting line of counting circles -1 is a counting line to infinity, -1 is 2 in 3-circle and 3 in 4-circle.

  ^Ref.sqrtneg1 The problem (negative numbers) does not occur in circle math whose counting lines are closed. Positive or add means clockwise in the circle. Negative or subtract means anticlockwise. The confusion vanishes. The math remains. Thus, in 10-circle -1 is 9, which squares to 1, and has 3 and 7 as its roots. The wordiq.com statement (as above) nails the error to the masthead by defining positive numbers as greater than zero, and negative numbers by the illogical expression, "less than zero".

  ^Ref.sqrtneg1 The fact that -1 in 10-circle is 9, whose square root is 3 (and 7) is the touch of death for the mystery sequestered in the square root of -1. This one facet does not explain i, for it is only a fragment of a greater whole, but it is the key. Turn it in the lock and the door will open, for it can be readily understood. Even for those who are far from grasping the pattern of the whole, the illusion of i, the square root of -1 will begin to fade and will continue to melt away until it vanishes.

• 2
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  ^Ref.majka Um = B² / ( 2uo )

  ^Ref.majka where uo is the magnetic permeability of free space. The equation describing the energy density of the particle's electric field, Ue, is:

  ^Ref.majka Ue = eo E²

  ^Ref.majka where eo is the electric permittivity of free space.

  ^Ref.majka The total energy, Ut, of the electric and magnetic field of a particle traveling at some speed, v, is the sum of these two equations. Converting to like terms and combining terms, the total energy equation is:

  ^Ref.majka Ut = ( eo E² / 2) ( 1 + v² /c² )

  ^Ref.majka If we now let V = C, the equation becomes:

  ^Ref.majka Ut = eo E²

  ^Ref.majka (In electrical analysis, since the symbol "i" is used to represent current flow, the symbol "j" is used to represent the square root of -1 and the symbol, w or omega, is used to represent frequency where w = 2 pi f.)

  ^Ref.majka The normalized transfer function, H(jw), of such a circuit is:

  ^Ref.majka H(jw) = 1/( w² - wo²)

• 1
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  ^Ref.taojoe D₁ = time, or change or motion.

  ^Ref.taojoe D₁ is time the first, or primary, or fundamental, or identity dimension, because it acknowledges change without assigning a vector to it.

  ^Ref.taojoe Lets do some math and play with a very simple equation.  The equation is x⁴ = 1.  You say x⁴ = 1?  That's dumb.

  ^Ref.taojoe A fourth degree equation has four solutions, but here, all four solutions are the same.  X can only equal 1, right? Wrong! You are forgetting how to solve an equation like this. Proceed as follows, treating the equation as if it were an ordinary quadratic:

  ^Ref.taojoe 1. Set the equation equal to zero.
  2. Factor the equation into the difference of squares.
  3. Let each factor independently equal zero.
  4. Both these equations are quadratic. The one on the left is again factorable.
  5. Repeat step 3 for this set of equations.
  6. The two solutions for these equations are X = 1 (the answer we already know) or X = -1  (the answer we forgot about but which checks since (-1)⁴ does equal 1.

  ^Ref.taojoe 7. We still must solve the equation on the right side of step 3: X² + 1 = 0.  It is not factorable, so we will need to use the quadratic formula.

  ^Ref.taojoe When ax² + bx + c = 0, then x = 0 +/- Sqrt (b² - 4ac) / 2a

  ^Ref.taojoe 8. Using the formula, where a = 1, b = 0, and c = 1,

  ^Ref.taojoe x = 0 +/- Sqrt ((0)² - 4 (1) (1)) / 2 = +/- Sqrt -4/2

  ^Ref.taojoe 9. Remember that the square roof of -4 is called 2i (right imaginary numbers), so the two solutions for x² + 1 = 0 are i and -i.

  ^Ref.taojoe To check: Is (i)⁴ = 1?  Well, i² = -1, and (-1)² = 1 yes.
  Is (-i)⁴ = 1?  (-i)² = -i² = -1  also yes.

  ^Ref.taojoe Therefore, the four solutions for x⁴ = 1 are +1, -1, i and -i.
  Now for the interesting part.  i is the first imaginary number.  Lets list the first five exponents of i:
  i⁰ = 1 (since anything raised to the zero power is 1)
  i¹ = i (itself)
  i² = -i (by definition)
  i³ = i² x i = -1 x i = -i
  i⁴ = 1

  ^Ref.taojoe Observe that the exponents zero and four give the same result. When we write the imaginary number i, we are really writing i¹.  These two symbols each have cosmological significance:

  ^Ref.taojoe The exponent portion, 1 indicates the first dimension time or motion.  1, the fundamental, imaginary constituent of reality the point. Again, time is going to behave like a spatial dimension, because a point in motion becomes a straight line. Simply by having an imaginary point in motion, we are generating the phenomenon of distance.

• 0
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  ^Ref.taojoe X² + 1 = 0.

  ^Ref.taojoe When ax² + bx + c = 0, then x = 0 +/- Sqrt

  ^Ref.taojoe x = 0 +/- Sqrt ((0)² - 4 (1) (1)) / 2 = +/- Sqrt -4/2

  ^Ref.taojoe Remember that the square root of -4 is called 2i (right imaginary numbers), so the two solutions for x² + 1 = 0 are i and -i.

  ^Ref.taojoe Now for the interesting part.  i is the first imaginary number.  Lets list the first five exponents of i:

  ^Ref.taojoe i⁰ = 1 (since anything raised to the zero power is 1).

  ***

  ^Ref.sqrtneg1 In the counting line of counting circles -1 is a counting line to infinity. Thus it is 0 in 1-circle, because one place anticlockwise from 0 brings us back to 0.

  ^Ref.sqrtneg1 Circle..... -1 in the circle..... Square root of -1

  ^Ref.sqrtneg1 0-circle............ Being without determination, 0-circle has no numerical elements.

  ^Ref.sqrtneg1 1-circle............ 0............... .....0

  ^Ref.sqrtneg1 The rational/ irrational pattern is that, each integral root (0 1 2 3), is followed by double that number of non-integer results:

  ^Ref.sqrtneg1 The. 0. "sq rt. -1". in.. 1-cir. is followed by 0 irrationals, and 0+0=0

  ^Ref.sqrtneg1 We should note that 0 is the identity element for adding and subtracting.

  ^Ref.sqrtneg1 The "internalized counting line", as in the above paragraph, is given in the square roots of 0, 1, 4, 9, 16, 25

  ^Ref.sqrtneg1 Use a horizontal line instead and you have the 0 direction. This gives the answer to combinations that sum to 0.

  ^Ref.sqrtneg1 The truth it is struggling to realize is that the symbol 0 represents the mind, and the mind, as the viewpoint within which number and math exist, is above, and so indifferent to the objects it contemplates. As mentioned, 0 is not a number at all.

  ^Ref.sqrtneg1 Because at the level we teach how to spell CAT we also imply that 0 and 1 are numbers, and at the level we teach "Rover has a ball" we include the thought that zero is a number, "negative" numbers exist, and so on, mathematicians talk about i; science is unable to merge quantum and relativity theory and astronomers talk about the "size" of the universe. We search for the error in the clouds when we should be looking at our feet.

  ^Ref.sqrtneg1 The ancient Greeks pointed out that 0 is not a number because it is nothing.

  ^Ref.sqrtneg1 0 and 1 are functional as the hinge between mind and world. 0 interfaces with the mind, 1 with the world. It is convenient to call 0 and 1 numbers, but strictly speaking they are the agents that, through counting lines and bases, create number, unraveling in the world the order that already exists in the mind.

  ^Ref.sqrtneg1 From this, expanding from the "i", a world in consciousness opens up. 0 and 1 are the active agents in generating this focal relation, and circlemath puts the whole mechanism in place for us to see.

• -1
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  ^Ref.majka In electrical analysis, since the symbol "i" is used to represent current flow, the symbol "j" is used to represent the square root of -1 and the symbol, w or omega, is used to represent frequency where w = 2 pi f.

  ***

  ^Ref.sqrtneg1 The. 0. "sq rt. -1". in.. 1-cir. is followed by 0 irrationals, and 0+0=0
  .... The. 1. "sq rt. -1". in.. 2-cir. is followed by 2 irrationals, and 1+1=2
  .... The. 2. "sq rt. -1". in.. 5-cir. is followed by 4 irrationals, and 2+2=4
  .... The. 3. "sq rt. -1". in 10-cir. is followed by 6 irrationals, and 3+3=6...and so on to infinity. What is happening here?

  ^Ref.sqrtneg1 The answer is that "i", the square root of -1, is switching the whole of mathematics from objectivity into subjectivity, translating the numerical pattern from the external or worldly domain into its internal counterpart, the mental space which we call subjectivity or time.

  ^Ref.sqrtneg1 To multiply by -1 therefore changes only the sign of the result. The "1" in the "square root of -1" is thus a dummy indicator of sign change, whose reality is an internalized counting line to infinity against a background array of fractional results, as shown in the list of -1 roots. Internal here means "in mind" and external means "in world", so that "ordinary" arithmetic, with its straight counting line to infinity belongs to the world. Circle math, with its circles rules and results belongs to the mind.

  ^Ref.sqrtneg1 We work from our knowledge of our ordinary or external math, which is objective to us. The internal circle math of the mind is however the parent and projector of the outer result. The "internalized counting line", as in the above paragraph, is given in the square roots of 0, 1, 4, 9, 16, 25. The "background array of fractional results" that seems to act as a spoiler is the tidy sequence of untidy square roots of 2 3 (two) 5 6 7 8 (four) 10 11 12 13 14 15 (six) in the -1 non-integer circle series, and the whole is the neurological setting from which developed consciousness springs.

  ^Ref.sqrtneg1 The square root problem

  ^Ref.sqrtneg1 In conventional mathematics there is no real number x, such that x^2 = -1

  ^Ref.sqrtneg1 This is because +x times +x comes to a positive result, and -x times -x also comes to a positive result, and there are no other options for x^2.

  ^Ref.sqrtneg1 Unable to assign a value to x satisfying the equation conventional mathematics stipulates that there is such a value, and calls it i for imaginary. It has no idea what "i" is, other than the square root of -1 as expressed in the equation i^2 = -1

  ^Ref.sqrtneg1 Given this, for it an impossible equation, it assigns the "no real number x" to the imagination, calling the square root of -1 "i". It then has a term for this ghost in the mind, supported not by understanding, but the fact that it integrates perfectly into mathematical operations and equations. The cost is that mathematics advances as a ritual of symbolic relations, comprehended only as the formalistic integration of signs and results.

  ^Ref.sqrtneg1 "i", as the square root of -1 is currently a blind spot in our mathematical understanding, walled off and bypassed. The task is to explain it, and in the process turn it from a block to a bond and bridge uniting in-world (linear) and in-mind (circular) math. The imaginary number serves a purpose, making an advance possible, shifting math from its ordinary domain to its higher expression. The further insight needed is to see that this "higher" math is really the internalized circular math we call the mind.

  ^Ref.sqrtneg1 "In Einstein's special theory of relativity there is a Lorentz transformation that leads to Minkowski's four-dimensional space. But the fourth dimension is obtained by replacing time, t, with the imaginary [square root of -1 multiplied by the speed of light, c, and by t itself]. After this, the temporal dimension becomes totally symmetrical with all other three dimensions of space."

  ^Ref.sqrtneg1 "In Quantum Mechanics, the Schrodinger's wave function also involves the same square root of -1 when the spatial locality breaks down and a conscious observer gets involved in the process of measurement."

  ^Ref.sqrtneg1 "This apparent coincidence indicates something extremely significant for understanding the universe and consciousness. It suggests that human consciousness may be a dimension of anti-space that merges into the fourth dimension of negative space so that we cannot see it as spatial any more. It appears as one dimensional time instead."

  ^Ref.sqrtneg1 Therefore, the square root -1 is the Consciousness factor.

  ^Ref.sqrtneg1 Gradually across the years the square root of -1 that divides math and maps to the schism between ideality and reality, has come forward as the kernel of the theoretical problem. Its resolution, whose completion is critical, will mark the turning point between that past and a brighter future. In this realization, the difficulty in the imaginary number, proving itself to be imaginary, will vanish, and people will wonder what it was about.

  ^Ref.sqrtneg1 The one step (switching into the circles) resolves the philosophical ground of math and the "square root of -1", which now falls into place as fully accessible at primary school level.

  ***

  ^Ref.taojoe D₂, i² and -1 are symbols that correlate to electromagnetic waves or photons.

• dimension
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  ^Ref.vogt A hologram is a three-dimensional image produced by coherent light.

  ^Ref.vogt This disclosure relates to a television system that utilizes wave front reconstruction techniques to provide a real time three-dimensional image at the receiving end of the system, with the image changing in perspective as the object and/or observer moves.

  ^Ref.vogt In our existence there are no physical phase or amplitude detectors in this dimension.

  ***

  ^Ref.flandern Moreover (and this is something to note), the size of the universe would be indeterminate, even if our lone particle has "finite" dimensions.

  ^Ref.flandern 1 particle universe- Indeed, it is impossible to say whether the particle has infinite dimensions, finite dimensions, or is infinitesimal (without size), since there is no scale to measure by.

  ^Ref.flandern 2 particle universe- Now, for the first time, we have "scale" in our universe, and can measure the dimensions of the particles themselves as a fraction of the distance between them.

  ^Ref.flandern 2 particle universe- If time is treated like just another dimension (a "fourth dimension" of space), the same remarks might be extended to include the concept of a "minimum possible time unit".

  ^Ref.flandern 2 particle universe- One way to see the resolution of this paradox is by considering time to be another dimension, just like the three dimensions of space (although admittedly not exactly like a space dimension.

  ^Ref.flandern 2 particle universe- Why would they have finite space dimensions, yet infinite dimension in time?

  ^Ref.flandern 2 particle universe- If the substance of bodies always gets denser (more substance per unit volume) at smaller and smaller scales, then in the limit as dimensions approach zero, density approaches infinity and substances approaching each other must make "contact".

  ^Ref.flandern 2 particle universe- By analogy with the proposed resolution of Zeno's paradoxes for space and time, the paradox for mass is resolved, apparently necessarily, by the conclusion that substance must be infinitely divisible, and that it must approach infinite density as size decreases toward zero dimensions.

  ^Ref.flandern 2 particle universe- The upper limits to the structure of substance, the dimensions of the universe, and the extent of time, must all be as unbounded on the high side as they need to be on the small side.

  ^Ref.flandern 2 particle universe- Now introduce a second infinitesimal particle. This gives meaning to orientation, since angles can be measured from the line joining the two particles. It also provides a single measurement of length, the distance between the particles. It does not, as before, provide a scale for the empty universe, since the distance cannot be measured in units of particle diameters, which are still being assumed to have no dimensions.

  ^Ref.flandern 2 particle universe- Of course, for actual particles with finite dimensions, events of coincidence do not occur.

  ^Ref.flandern 2 particle universe- Put another way, a particle reaching one edge of a "vacuum" would skip instantaneously to the opposite edge, just as if the "vacuum" had zero dimensions, because there is no substance to mark the passage of time inside of the"vacuum", and no absolute time without substance.

  ^Ref.flandern 2 particle universe- Conversely, if substance does not start out with density which approaches infinity as dimension approaches zero, it could not assemble itself into such an infinite-density configuration in a finite time.

  ***

  ^Ref.taojoe The operator here is D, a dimensional operator that separates, or divides dimensional combinations by various permutated constituents.

  ^Ref.taojoe D₁ is time the first, or primary, or fundamental, or identity dimension, because it acknowledges change without assigning a vector to it.

  ^Ref.taojoe D₂, D₃, and D₄ are the three familiar spatial dimensions, each with vectors orientated 90 degrees from another.

  ^Ref.taojoe The values in the table are the complete array of dimensions that are generated in this system.

  ^Ref.taojoe Any dimension divided by the identity is equal to itself; but the identity divided by any of the spatial dimensions produces different results.

  ^Ref.taojoe In the case of 2/4, the answer, reduced to lowest terms, becomes 1/2.  This means that the dimensions produced by 2 D 4 and 1 D 2 are the same.

  ^Ref.taojoe There are eleven total distinct dimensions in the system, the same as the number stated by Einstein and others as existing in our universe.

  ^Ref.taojoe This mathematical system may be the most accurate model of how dimensionality is generated in the universe.

  ^Ref.taojoe D₁ = time. Regarding time in the context of this model.
  D₂, D₃, D₄ = length, width, height (spatial dimensions)
  D_1/4, D_1/3, D_1/2, D_2/3, D_3/4, D_4/3, D_3/2 = fractional, composite dimensions.

  ^Ref.taojoe To generate the other 7 dimensions, we will need to divide, and to perform division of dimensions we need to examine the meaning of division as it relates to the physical universe.

  ^Ref.taojoe Now lets take a simple case using dimensions: 4 D 2 = 2. In words, when we extract 2 dimensions from a solid object (in motion, of course), the result is 2 distinct electromagnetic waves (photons), whose amplitudes are perpendicular to each other (intersecting planes).

  ^Ref.taojoe And how do we induce this dimensional split? By accelerating our solid object (already in motion) to the speed of light (c).

  ^Ref.taojoe I think that each of the eleven dimensions represents one basic aspect, one constituent of the universe.

  ^Ref.taojoe In mathematics, equations are commonly written to describe phenomena in any of the four integral dimensions. The exponent of the variable indicates the degree of dimensionality.

  ^Ref.taojoe When we wanted to break our solid object into simpler dimensions, we had to increase its motion to the speed of light.

  ^Ref.taojoe When we step down a dimension, a dimension, we reduce exponents by 1, and to reduce the exponent 2 of i² to 1, to get i¹, we can take the square root (in fact, that is the definition of i is that i equals the square root of negative one).

  ^Ref.taojoe In words again, we are taking one dimension, say the depth, away from solid matter, to get a plane in motion (once again time as a spatial dimension), but what is a plane in motion? Maybe a tube of some sort. Maybe not. The third option involves negatives.

  ^Ref.taojoe Four dimensions, the integral dimensions, have been explained. The seven fractional dimensions remain, and while each is still associated with naturally occurring phenomena in the universe, the job now becomes a lot tougher.

  ^Ref.taojoe It is the geometry of space we are observing, and like other geometries in the universe, it has a dimension associated with it.  But which one?

  ^Ref.taojoe How do we decide which of the seven fractional dimensions is responsible for gravity, or rather, for the geometry of space?

  ^Ref.taojoe What do you notice as you move from D_zero, total nonexistence, up through the dimensions to D₄?  I notice that there is a progression from the least substantive, most abstract manifestation; to the opposite of that the manifestation that is wholly concrete and not an abstraction at all.

  ^Ref.taojoe And if we are lucky, it may additionally be possible to identify elements being utilized by the operator D by deciding which two of the four basic dimensions are interacting to produce the appropriate fraction.  In choosing, we must bear in mind that the seven available fractions all have a value less than 2, and five of them are less than 1.  This means that they all represent significant abstractions.  It is a certainty that none of these dimensions contain massive entities, though it is possible, as with gravity, that their effects are far-reaching enough for us to be aware, or at least suspicious, of their existence.

  ^Ref.taojoe There are only two fractions whose denominator is 4, which would account for the matter, and everything contained in all lower dimensions.  What is it then that reacts with either light or matter, to form space?  What thing plays a role in the effect of gravity; appears in all the gravitational principles and equations? Distance!

  ^Ref.taojoe Distance is created by the first dimension, motion.

  ^Ref.taojoe Therefore the only logical fraction for the dimension of gravity, or the geometry of space in one that points to the interplay of distance (D₁) with each of the dimensions effected by that gravity (D₄).

  ^Ref.taojoe Also, a big problem is that a dimension requires a geometry.

  ***

  ^Ref.taojoe In Einstein's special theory of relativity there is a Lorentz transformation that leads to Minkowski's four-dimensional space.

  ^Ref.taojoe But the fourth dimension is obtained by replacing time, t, with the imaginary [square root of -1 multiplied by the speed of light, c, and by t itself].

  ^Ref.taojoe After this, the temporal dimension becomes totally symmetrical with all other three dimensions of space"

  ^Ref.taojoe "That means that time is itself one more dimension of space but is perceived by our consciousness as different and uniquely temporal.

  ^Ref.taojoe "Surprisingly, in Quantum Mechanics, the Schrodinger's wave function also involves the same square root of -1 when the spatial locality breaks down and a conscious observer gets involved in the process of measurement. This apparent coincidence indicates something extremely significant for understanding the universe and consciousness. It suggests that human consciousness may be a dimension of anti-space that merges into the fourth dimension of negative space so that we cannot see it as spatial any more. It appears as one dimensional time instead."

• universe
  up

  ^Ref.majka we may assume that the universe does not forbid speeds other than the speed of light but would provide an impedance to them.

  ^Ref.majka At light speed, the universe offers no impedance to the propagation of electromagnetic waves.

  ***

  ^Ref.flandern C. The One Particle universe

  ^Ref.flandern In the real universe there is a frame of reference to provide meaning to distance and direction.

  ^Ref.flandern The reference frame is provided both by the presence of distant matter in the universe, as well as by seas of rapidly moving "agents", such as photons and neutrinos.

  ^Ref.flandern The essential point is that the reference frame is provided by the presence of substance in the universe.

  ^Ref.flandern In the absence of other substance in the universe, our lone particle would be incapable of motion,for motion could have no meaning.

  ^Ref.flandern Moreover (and this is something to note), the size of the universe would be indeterminate, even if our lone particle has "finite" dimensions.

  ^Ref.flandern In a 1 particle universe: The number of such particles which can fit into the universe around it is infinite in any case.

  ^Ref.flandern The idea that the presence of distant matter in the universe is the origin of inertial forces is known as "Mach's Principle".

  ^Ref.flandern Our example may start to seem a little less hypothetical if we postulate a finite limit to all of the substance in the real universe, with nothing beyond.

  ^Ref.flandern Under this assumption, (finite limit) the entire substance of the universe would be like our single particle; and all remarks about its size or motion in a larger infinity of space and time would be fully applicable; i.e they would be indeterminate.

  ^Ref.flandern C. The Two Particle universe

  ^Ref.flandern Now, for the first time, we have "scale" in our universe, and can measure the dimensions of the particles themselves as a fraction of the distance between them.

  ^Ref.flandern There is no such thing as "absolute length" in this universe -- we cannot tell if the two particles are "close together" or "far apart".

  ^Ref.flandern Their separation is indeterminate relative to the universe beyond.

  ^Ref.flandern Note that the two particles cannot "see" or influence each other in any way except by collision, since our otherwise empty universe definitely contains no photons or agents to produce forces or actions at a distance, such as electromagnetism or gravitation.

  ^Ref.flandern In the real universe, a suspended pendulum would continue swinging back-and-forth in the same direction in the universe, ignoring the spin of the body.

  ^Ref.flandern But our two-particle universe can have no such properties, because there can be no framework to provide a "remembered" preferred orientation for the pendulum.

  ^Ref.flandern But our two-particle universe can have no such properties, because there can be no framework to provide a "remembered" preferred orientation for the pendulum.

  ^Ref.flandern Indeed, the pendulum could not swing at all, because there is no gravity in this imagined universe.

  ^Ref.flandern Now if the particle on which the pendulum is suspended is imagined to have local gravity only, so that the pendulum can swing; but gravity which does not reach out to influence the second particle, so that no framework is provided to the universe; then clearly the pendulum must keep its orientation with respect to the particle it resides on, since that is the only framework it has.

  ^Ref.flandern But as soon as we imagine a sort of universal gravitation, this immediately provides a framework for the pendulum.

  ^Ref.flandern By these constructions, we begin to see the origins of the what are called inertial forces, and the importance of a frame of reference to the properties of the universe we live in.

  ^Ref.flandern Then a body traveling at a uniform velocity from point A at time 1 to point B at time 2 is traveling on a straight line in this space-time universe.

  ^Ref.flandern In the real universe, the density of matter greatly increases as scale decreases.

  ^Ref.flandern Hence the ratio of mass to volume in electrons is enormously greater(about 1E10 g/cc) than the same ratio for matter in ordinary human experience (of order 1 g/cc), which in turn is enormously greater than the ratio for the entire visible universe (1E-31g/cc).

  ^Ref.flandern From the preceding considerations it seems altogether reasonable, and in a way compelling, to deduce that space, time,and substance are all infinitely divisible; because the consequences of the alternative are logically absurd.

  ^Ref.flandern But if they are infinitely divisible on the smaller scale, what about the larger scale? Recall our earlier argument that the entire visible universe would have undefined scale in space, time, and mass, unless such scale is provided by the presence of other substance in the greater universe beyond.

  ^Ref.flandern The upper limits to the structure of substance, the dimensions of the universe, and the extent of time, must all be as unbounded on the high side as they need to be on the small side

  ^Ref.flandern F. Meaning of Space and Time

  ^Ref.flandern Let us return again to our empty universe which contains no substance, and therefore no frame of reference, except for a single uniform particle of substance.

  ^Ref.flandern But as we have just seen, the particle must itself be composed of an infinitely divisible variety of sub-particles. We could have chosen a single particle at any of an infinite number of sub-levels to be our single particle. To avoid the issue of the arbitrary size of the particle we select, let us conceive of it as having zero radius. Although it does not, this conception will allow us to introduce one scale of distance at a time. As remarked earlier, motion and orientation have no meaning for a single particle in an empty universe.

  ^Ref.flandern Now introduce a second infinitesimal particle. This gives meaning to orientation, since angles can be measured from the line joining the two particles. It also provides a single measurement of length, the distance between the particles.

  ^Ref.flandern It does not, as before, provide a scale for the empty universe, since the distance cannot be measured in units of particle diameters, which are still being assumed to have no dimensions.

  ^Ref.flandern Therefore there is no way yet to determine whether our particles are separated by a microscopic or a macroscopic distance. There is as yet still no meaning to motion in this two particle universe.

  ^Ref.flandern The two particles cannot change direction, since all directions have meaning only relative to the particle-to-particle direction.

  ^Ref.flandern And the two particles cannot change distance, since all distances have meaning only relative to the particle-to-particle distance. In a very real sense, this universe without the possibility of motion or change has no time. Time can have no meaning if there cannot be events or change to mark its progress.

  ^Ref.flandern Put differently, if there were such a thing as an absolute time which existed somehow in addition to our two particles, the lapse of a microsecond or a million years would be just the same and utterly indistinguishable>. But the existence of something with substance, such as an absolute time scale, violates the assumptions of our construction, that nothing exists except our two infinitesimal particles in an empty universe. Remember, we refer to "substance" rather than "matter" to cover ANYTHING which exists.

  ^Ref.flandern An absolute scale of time, just as for a structure or framework in space, would have substance in this broad definition.

  ^Ref.flandern In an empty universe consisting of two elementary units of substance, the ordinary properties of the universe (time, space, matter) do not exist outside of the particles and between events of coincidence.

  ^Ref.flandern It can therefore be said in a logically meaningful way that space and time which are empty of particles and events DO NOT EXIST! This eliminates a logical fallacy we have been skirting around up to now about whether the empty space and time surrounding our particles exist.

  ^Ref.flandern In our construction they do not.

  ^Ref.flandern We are asserting that every point in the perceptible universe is at every moment of time filled with contiguous substance at some infinitesimal level.

  ^Ref.flandern If substance could be imagined to become absent anywhere at any time, time there would cease and the perceptible universe would collapse until the"vacuum" was filled.

  ^Ref.flandern But if there were such regions where matter density is so low that no collisional interactions between units of substance occurred,then all substance on the edge of such regions would instantly dissipate itself into the non-interacting regions, followed by substance slightly further in, and so on.

  ^Ref.flandern All substance in this universe would dissipate instantly into the void.

  ^Ref.flandern Since this does not happen, we conclude that this universe has no such regions where collisional interactions between units of substance do not occur.

  ^Ref.flandern The same reasoning applies to time. A cessation of collisional events would bring a cessation of time; but with matter existing everywhere with sufficient density for collisions, it follows that time continues forever, in both the future and the past.

  ^Ref.flandern The substances whose presence "define" space-time must be infinitesimal compared to the substances in our experience, such as baryons or photons, or even neutrinos.

  ***

  ^Ref.taojoe There are eleven total distinct dimensions in the system.

  ^Ref.taojoe ... as they do in the universe, all these geometries are in motion.

  ^Ref.taojoe I think that each of the eleven dimensions represents one basic aspect, one constituent of the universe.  The attempt by physics to explain phenomena by associating discrete particles with each has gotten out of hand.  It may be more useful and to the point to identify eleven fundamental properties of the universe, each associated with its own dimension.

  ^Ref.taojoe What do you suppose would happen if we slowed this point to a sub-light velocity?  If c really does produce an opposite, then i¹or i , becomes its negative, i¹or -i , which is the value of i³, which is, lo and behold, an alternate symbol for D₃.  D₃ then (or i,) is the realm of slower-than-light imaginary points.  Since it is sub-light it must have mass, but since it is imaginary, it has no substance.  And this is exactly what our plane in motion is trying to describe, a surface with no thickness and therefore no substance, enclosing on itself trying to form a sphere (or a tube) with no volume. An imaginary figure with mass. Hey, astronomy buffs, what am I describing?  This is dark matter! All that unaccounted-for mass that must exist in the universe but is undetectable.  Its undetectable because its not real.  But because its slowed to sub-light, it has mass. And because these things are negative singularities, similar to the singularity responsible for the big bang and the subsequent universe except hollow inside (like bubbles or macaroni), they are super dense, far more dense even than black holes, so it makes sense, as physicists claim, that this dark matter should account for most of the mass in the universe, much more than visible matter. D₃ = dark matter, matter which has been collapsed by one dimension.

  ^Ref.taojoe D₁ D₃ is responsible for the dark matter which is undetectable but comprises most of the mass in the universe.

  ^Ref.taojoe Constancy in the eyes of humans, and constancy in the eyes of the universe, is not the same thing.  (I have already hinted at this.) The speed of light is a kind of threshold for a change of state of various cosmic manifestations.

  ***

  ^Ref.sqrtneg1 (Schrodinger's wave function also involves the same square root of -1 when the spatial locality breaks down and a conscious observer gets involved in the process of measurement.) This apparent coincidence indicates something extremely significant for understanding the universe and consciousness. It suggests that human consciousness may be a dimension of anti-space that merges into the fourth dimension of negative space so that we cannot see it as spatial any more. It appears as one dimensional time instead."

• electric
  up

  ^Ref.majka There is an observer which is at rest with respect to the charged particle.

  ^Ref.majka This observer "sees" the gravitational field and the electric field of this particle.

  ^Ref.majka Let us now add a second observer. The second observer is exactly like the first observer except that it is traveling at some constant speed, v, which is less than the speed of light, with respect to the first observer and the charged particle.

  ^Ref.majka This second observer also "sees" the gravitational field and the electric field of the charged particle. However, this second observer also "sees" a magnetic field surrounding the charged particle.

  ^Ref.majka At the same time, the three observers see the charged particle differently. At a relative speed of zero, the observer "sees" a mass and an electric field.

  ^Ref.majka At a relative speed other than zero but less than that of light, the second observer "sees" a mass, an electric field and a magnetic field.

  ^Ref.majka At a relative speed of light, the third observer "sees" an electromagnetic wave with no gravitational field and no electric field other than that associated with the electromagnetic wave itself.

  ^Ref.majka The hypothesis is that as the relative speed of a charged particle increases from zero to that of light, the particle appears to change to an electromagnetic wave because of the expansion of the magnetic field. This magnetic field combines with some of the static electric field, in proportion to the energy of the magnetic field, to form an electromagnetic wave.

  ^Ref.majka At the speed of light, the electric field is entirely combined with the magnetic field and the particle appears as an electromagnetic wave.

  ^Ref.majka where uo is the magnetic permeability of free space. The equation describing the energy density of the particle's electric field, Ue, is:

  ^Ref.majka Ue = eo E²

  ^Ref.majka where eo is the electric permittivity of free space.

  ^Ref.majka The total energy, Ut, of the electric and magnetic field of a particle traveling at some speed, v, is the sum of these two equations. Converting to like terms and combining terms, the total energy equation is:

  ^Ref.majka Ut = ( eo E² / 2) ( 1 + v² /c² )

  ^Ref.majka That is, when traveling at high speeds, charged particles exhibit particle characteristics and electromagnetic wave characteristics. If, as is hypothesized, the magnetic field combines with a portion of the static electric field to create an electromagnetic wave, duality is expected.

  ^Ref.majka Since the particle is only partially an electromagnetic wave, it should exhibit duality at speeds less than light.

  ^Ref.majka The accepted theory is that mass increases as speed increases. The finding by Bucherer in 1908, that the electric field to mass (e/m) ratio is less for high speed particles, has been accepted as proof of an increase in mass.

  ^Ref.majka The hypothesis proposes that the reason for this finding is not that the mass has increased but rather that the electric field and the mass have decreased.

  ^Ref.majka That part of the electric field which combines with the magnetic field to create an electromagnetic field can not participate in static charge measurements.

  ^Ref.majka The hypothesis states that the apparent mass of the particle decreases with relative speed and that the magnetic field combines with a portion of the electric field to produce an electromagnetic wave.

  ^Ref.majka Transmission lines and space share common parameters. The most notable are the parameters of distributed inductance (or magnetic permeability) in henries per meter, distributed capacitance (or electric permittivity) in farads per meter, characteristic impedance in Ohms and characteristic velocity in meters per second.

  ^Ref.majka We are familiar with speeds less than light. At a zero relative speed, the "stopped" electromagnetic wave appears as a "particle" and exhibits a gravitational field and an electric field.

  ^Ref.majka Similarly, as the speed of a particle increases, the effects of the static electric field are decreased.

  ^Ref.majka At frequencies greater than the resonant frequency, the impedance of the circuit is due primarily to the inductor. We may then assume that, by analogy, at speeds greater than the speed of light, the magnetic field will dominate and will appear to be as constant as the electric field at sub-light speeds.

  ^Ref.majka At these speeds, (greater than the "speed" of light) it may appear that the electric field is a function of the magnetic field.

  ^Ref.majka The impedance offered by the capacitor is analogous to the electric field of a charged particle and the impedance offered by the inductor is analogous to the magnetic field of a charged particle in motion.

  ^Ref.majka Let us assume a series LC circuit, as described above, with no applied signal. The inductor does not have an initial magnetic field nor does the capacitor have an initial electric field.

  ^Ref.majka The electric and magnetic fields of a particle have been associated with the impedances offered by the capacitor and inductor of an analogous series LC circuit.

  ^Ref.majka At speeds greater than light, the hypothesis predicts that the effects of the electric and magnetic fields will be reversed.

  ^Ref.majka At these speeds, it is likely that the magnetic fields will become polar and the electric fields will become circular, that is, a magnetic monopole will result.

  ^Ref.majka At speeds much greater than that of light, the electric field may be expected to collapse.

  ^Ref.majka This collapsed electric field may also pull or twist the fabric of space-time and form a type of field not now known.

  ***

  ^Ref.andersen There the hypothesis (majka) was set forth that the ratio of magnetic-to-electric field "seen" by an observer of a charged particle is a function of the relative motion between the particle and observer.

  ^Ref.andersen Also, that the magnetic permeability of free space and the electric permittivity thereof are analogous to the distributed inductance and capacitance, respectively, of a transmission line.

  ^Ref.andersen Tilton introduces the concept of "super resonance", in which he discusses a dual oscillator system (two pendulums). On page 67 he illustrates a theoretical electrical version of the dual pendulums-- dual LC tank circuits coupled together through back-to- back zener diodes.

• magnetic
  up

  ^Ref.majka This second observer also "sees" the gravitational field and the electric field of the charged particle. However, this second observer also "sees" a magnetic field surrounding the charged particle.

  ^Ref.majka At a relative speed other than zero but less than that of light, the second observer "sees" a mass, an electric field and a magnetic field.

  ^Ref.majka The hypothesis is that as the relative speed of a charged particle increases from zero to that of light, the particle appears to change to an electromagnetic wave because of the expansion of the magnetic field. This magnetic field combines with some of the static electric field, in proportion to the energy of the magnetic field, to form an electromagnetic wave.

  ^Ref.majka At the speed of light, the electric field is entirely combined with the magnetic field and the particle appears as an electromagnetic wave.

  ^Ref.majka At speeds less than that of light, the magnetic field of the electromagnetic wave collapses. The collapsing field distorts or twists space-time which appears to us as a gravitational field.

  ^Ref.majka This hypothesis seems to be justified by equations from classical physics. The equation describing the energy density of the particle's magnetic field, Um, is:

  ^Ref.majka Um = B² / ( 2uo )

  ^Ref.majka where uo is the magnetic permeability of free space. The equation describing the energy density of the particle's electric field, Ue, is:

  ^Ref.majka Ue = eo E²

  ^Ref.majka The total energy, Ut, of the electric and magnetic field of a particle traveling at some speed, v, is the sum of these two equations. Converting to like terms and combining terms, the total energy equation is:

  ^Ref.majka Ut = ( eo E² / 2) ( 1 + v² /c² )

  ^Ref.majka If we now let V = C, the equation becomes:

  ^Ref.majka Ut = eo E²

  ^Ref.majka which is also the energy density equation of an electromagnetic wave. Classical physics equations also show that the direction of the magnetic field of a charged particle, traveling at some speed, is such that the Poynting Vector cross product is satisfied.

  ^Ref.majka ...when traveling at high speeds, charged particles exhibit particle characteristics and electromagnetic wave characteristics. If, as is hypothesized, the magnetic field combines with a portion of the static electric field to create an electromagnetic wave, duality is expected.

  ^Ref.majka Transmission lines and space share common parameters. The most notable are the parameters of distributed inductance (or magnetic permeability) in henries per meter, distributed capacitance (or electric permittivity) in farads per meter, characteristic impedance in Ohms and characteristic velocity in meters per second.

  ^Ref.majka The speed of light is the square root of (1/uoeo) which are the magnetic permeability and electric permittivity of free space.

  ^Ref.majka Therefore, we may assume that the speed of light is the resonant velocity of free space.

  ^Ref.majka Similarly, we may compare the impedance of the inductor to the magnetic field of a particle in relative motion.

  ^Ref.majka At zero Hertz, there is no impedance offered by the inductor and a "particle" at zero relative speed has no magnetic field. As the frequency of the applied signal to the circuit is increased, the impedance provided by the inductor is increased.

  ^Ref.majka As the speed of the particle increases, the effects of the magnetic field are increased.

  ^Ref.majka At speeds less than that of light, the electric field is dominant and the magnetic field is a function of the electric charge.

  ^Ref.majka At frequencies greater than the resonant frequency, the impedance of the circuit is due primarily to the inductor. We may then assume that, by analogy, at speeds greater than the speed of light, the magnetic field will dominate and will appear to be as constant as the electric field at sub-light speeds.

  ^Ref.majka At frequencies greater than the resonant frequency, the impedance of the circuit is due primarily to the inductor. We may then assume that, by analogy, at speeds greater than the speed of light, the magnetic field will dominate and will appear to be as constant as the electric field at sub-light speeds.

  ^Ref.majka At these speeds, it may appear that the electric field is a function of the magnetic field.

  ^Ref.majka The impedance offered by the capacitor is analogous to the electric field of a charged particle and the impedance offered by the inductor is analogous to the magnetic field of a charged particle in motion.

  ^Ref.majka NON-STEADY-STATE CONDITIONS

  ^Ref.majka Let us assume a series LC circuit, as described above, with no applied signal. The inductor does not have an initial magnetic field nor does the capacitor have an initial electric field.

  ^Ref.majka The electric and magnetic fields of a particle have been associated with the impedances offered by the capacitor and inductor of an analogous series LC circuit.

  ^Ref.majka The hypothesis proposes that the mass of a particle is due to the collapse of the magnetic field of the particle.

  ^Ref.majka Mass is not recognized directly but a gravitational field is. A gravitational field is probably not a different form of a magnetic field.

  ^Ref.majka The gravitational field is, most likely, a result of the collapsed magnetic field.

  ^Ref.majka It is possible that the collapsed magnetic field pulls or twists the fabric of space-time in such a way as to form what we call a gravitational field.

  ^Ref.majka As the speed of the charged particle increases, the magnetic field expands and decreases its pull or twist which causes a decrease in the gravitational field.

  ^Ref.majka At speeds greater than light, the hypothesis predicts that the effects of the electric and magnetic fields will be reversed.

  ^Ref.majka At these speeds, it is likely that the magnetic fields will become polar and the electric fields will become circular, that is, a magnetic monopole will result.

• electromagnetic
  up

  ^Ref.majka According to the Theory of Relativity, the third observer must "see" an electromagnetic wave at the location of the charged particle since their relative speed is the speed of light.

  ^Ref.majka At a relative speed of light, the third observer "sees" an electromagnetic wave with no gravitational field and no electric field other than that associated with the electromagnetic wave itself.

  ^Ref.majka The hypothesis is that as the relative speed of a charged particle increases from zero to that of light, the particle appears to change to an electromagnetic wave because of the expansion of the magnetic field. This magnetic field combines with some of the static electric field, in proportion to the energy of the magnetic field, to form an electromagnetic wave.

  ^Ref.majka At the speed of light, the electric field is entirely combined with the magnetic field and the particle appears as an electromagnetic wave.

  ^Ref.majka At speeds less than that of light, the magnetic field of the electromagnetic wave collapses. The collapsing field distorts or twists space-time which appears to us as a gravitational field.

  ^Ref.majka which is also the energy density equation of an electromagnetic wave. Classical physics equations also show that the direction of the magnetic field of a charged particle, traveling at some speed, is such that the Poynting Vector cross product is satisfied.

  ^Ref.majka That is, E x H = I.

  ^Ref.majka The hypothesis is also supported by experiments which have shown that charged particles traveling at a high speed exhibit duality.

  ^Ref.majka That is, when traveling at high speeds, charged particles exhibit particle characteristics and electromagnetic wave characteristics. If, as is hypothesized, the magnetic field combines with a portion of the static electric field to create an electromagnetic wave, duality is expected.

  ^Ref.majka Since the particle is only partially an electromagnetic wave, it should exhibit duality at speeds less than light.

  ^Ref.majka The accepted theory is that mass increases as speed increases. The finding by Bucherer in 1908, that the electric field to mass (e/m) ratio is less for high speed particles, has been accepted as proof of an increase in mass.

  ^Ref.majka The hypothesis proposes that the reason for this finding is not that the mass has increased but rather that the electric field and the mass have decreased.

  ^Ref.majka That part of the electric field which combines with the magnetic field to create an electromagnetic field can not participate in static charge measurements.

  ^Ref.majka Therefore, those experiments measuring e/m will show a lower value for high speed particles than for slower particles.

  ^Ref.majka CHARACTERISTIC VELOCITY OF SPACE

  ^Ref.majka It has been assumed that electromagnetic waves can travel only at the speed of light. The hypothesis proposes that there is an electromagnetic wave which is a characteristic of any charged particle traveling at any relative speed greater than zero and less than the speed of light.

  ^Ref.majka Since electromagnetic waves travel through transmission lines and through space, it is possible to model their propagation through space by a transmission line analogy.

  ^Ref.majka In an "ideal" transmission line, without losses, the resistance is ignored. Since it seems that an electromagnetic wave travels through space without losses, we may assume that the model for an ideal transmission line is adequate for an analysis of free space.

  ^Ref.majka electromagnetic waves, which are characteristic of charged particles, can travel at speeds other than the speed of light.

  ^Ref.majka STEADY-STATE IMPEDANCES

  ^Ref.majka The hypothesis predicts that electromagnetic waves can travel at speeds other than at the speed of light.

  ^Ref.majka At light speed, the universe offers no impedance to the propagation of electromagnetic waves.

  ^Ref.majka We are familiar with speeds less than light. At a zero relative speed, the "stopped" electromagnetic wave appears as a "particle" and exhibits a gravitational field and an electric field.

  ^Ref.majka If we assume the creation of a particle, we would see that this particle causes a disturbance which propagates as an electromagnetic wave.

  ^Ref.majka Now we change the frequency of the applied signal. Again the circuit will respond with an oscillation at it's resonant frequency.

  ^Ref.majka Similarly, if we accelerate a charged particle, an electromagnetic wave is generated. Indeed, any change in the frequency of the applied signal to a series LC circuit will generate transient oscillations just as acceleration of a charged particle will generate electromagnetic waves.

  ***

  ^Ref.vogt "There are direct analogies between this type of invention and our own existence. In Figure 4.10, Object 15 could be analogized as being the information in the diehold. Item 13 and 23 can be considered the tapehead. In this invention it is actually the two parts of the laser beam directed at the object that pick up the information that makes up the image of the object. The microwave oscillator (Item 18) and the optical oscillator (Item 16) can be considered the carrier wave and synchronizing frequencies which we have been talking about. This information is directed to Items 25 (Filter) and 26 (Device functioning as a videocon or image orthocon), which converts the light information to electromagnetic waves. This is similar to what we define as being the second dimension or the transmission dimension.

  ***

  ^Ref.taojoe .....lets take a simple case using dimensions: 4 D 2 = 2. In words, when we extract 2 dimensions from a solid object (in motion, of course), the result is 2 distinct electromagnetic waves (photons), whose amplitudes are perpendicular to each other (intersecting planes).

  ^Ref.taojoe D₂ = wave phenomena, the electromagnetic force, or the photon

  ^Ref.taojoe We can take D₂, the photon and kick it up a notch, and do   D₂ + D₁ = D₃.  In words, this means that we add a new 90 degree vector to our planar electromagnetic wave, producing an abstraction we can refer to as a cubic wave.

  ^Ref.taojoe D₂, i² and -1 are symbols that correlate to electromagnetic waves or photons. The only difference between D₄ and D₂ is that D₂ = D₄ x c (remind you of something? E = mc², perhaps?). Substituting numerals, -1 = (+1) c, and solving c = -1.  In words, c has the effect of negativizing a phenomenon.

  ^Ref.taojoe 1. The speed of light is a misleading term, for while it is the speed of electromagnetic waves.

• transmission line
  up

  ^Ref.majka Since electromagnetic waves travel through transmission lines and through space, it is possible to model their propagation through space by a transmission line analogy.

  ^Ref.majka transmission lines and space share common parameters. The most notable are the parameters of distributed inductance (or magnetic permeability) in henries per meter, distributed capacitance (or electric permittivity) in farads per meter, characteristic impedance in Ohms and characteristic velocity in meters per second.

  ^Ref.majka Models of transmission lines are basic in the study of electricity and electronics. A model circuit diagram describing a typical, real transmission line is shown in Figure 1.

  ^Ref.majka The inductance, L, is in terms of henries per meter. The capacitance, C, is in terms of farads per meter and the resistance, R, is in terms of Ohms per meter.

  ^Ref.majka Note that the circuit diagram basically consists of one RLC circuit repeated for the length of the transmission line. The resistance, R, is responsible for losses in transmission lines.

  ^Ref.majka In an "ideal" transmission line, without losses, the resistance is ignored. Since it seems that an electromagnetic wave travels through space without losses, we may assume that the model for an ideal transmission line is adequate for an analysis of free space.

  ^Ref.majka Also, since the circuit segment is repeated for the length of the transmission line, the analysis of one segment is sufficient.

  ^Ref.majka Figure 2 shows the circuit diagram for an ideal transmission line.

  ^Ref.majka Circuit modeling involves determining the voltages and currents through the circuit. By Ohms Law (E = I x Z), the voltages and currents are related through impedances. (Note: Impedance is mathematically treated as a resistance.

  ^Ref.majka It differs from a resistance in that there are no energy losses through an impedance.)

  ^Ref.majka Figure 3 shows the same circuit with the impedances of the circuit elements.

  ^Ref.majka The values of the impedances are shown in typical electrical analysis notation. Since the impedance of an inductor varies directly with the frequency of the current through it or voltage applied to it, the impedance is in terms of the frequency, jw.

  ^Ref.majka Since the impedance of a capacitor varies inversely with the frequency of the current through it or voltage applied to it, the impedance is in terms of the inverse frequency, 1/jw. (In electrical analysis, since the symbol "i" is used to represent current flow, the symbol "j" is used to represent the square root of -1 and the symbol, w or omega, is used to represent frequency where w = 2 pi f.)

  ^Ref.majka It can be seen that this circuit is also the circuit of a series LC circuit. To go from a transmission line model to a series LC circuit model all we need do is change the terms of the parameters from henries/meter and farads/meter to henries and farads. The normalized transfer function, H(jw), of such a circuit is:

  ^Ref.majka H(jw) = 1/( w² - wo²)

  ^Ref.majka The symbol w represents the frequency of the signal applied to the circuit. The symbol wo represents the resonant frequency of the circuit and it is numerically equal to the square root of (1/LC).

  ^Ref.majka The resonant frequency is the frequency preferred by the circuit.

  ^Ref.majka If a signal was applied to the circuit and it was not at the resonant frequency, the circuit would offer an impedance to the signal.

  ^Ref.majka If a signal at the resonant frequency was applied to the circuit, the circuit would offer no impedance. The reason for this is that the impedance of the inductor (jw) varies directly with the frequency of the applied signal.

  ^Ref.majka The impedance of the capacitor (1/jw) varies inversely with the frequency of the applied signal. At the resonant frequency, the magnitude of the impedance offered by the inductor and the capacitor are equal.

  ^Ref.majka Impedances due to inductors and capacitors are vector quantities. The direction of the inductor's impedance vector varies directly with the frequency of the applied signal in the positive direction.

  ^Ref.majka The direction of the capacitor's impedance vector also varies directly with the frequency of the applied signal but in the negative direction.

  ^Ref.majka At resonance, the magnitudes of the impedances are equal but the vectors are 180 degrees out of phase with each other and thus cancel. At resonance, the circuit offers no impedance.

  ^Ref.majka The values for L and C in a series LC circuit are in terms of henries and farads. The resonant frequency, wo, is equal to the square root of (1/LC).

  ^Ref.majka The resonant frequency, then, is in terms of 1/second or Hertz.

  ^Ref.majka If we were to substitute henries per meter and farads per meter for the values of the circuit elements, then resonance would be in terms of meters per second.

  ^Ref.majka Instead of a resonant frequency we would have a resonant velocity.

  ^Ref.majka Indeed, for transmission lines, the velocity of propagation is the square root of (1/LC).

  ^Ref.majka The speed of light is the square root of (1/uoeo) which are the magnetic permeability and electric permittivity of free space.

  ^Ref.majka Therefore, we may assume that the speed of light is the resonant velocity of free space.

  ***

  ^Ref.andersen Also, that the magnetic permeability of free space and the electric permittivity thereof are analogous to the distributed inductance and capacitance, respectively, of a transmission line.

  ^Ref.andersen This leads to the suggestion that a transmission line's RESONANCE, which depends on its inductance (L) and capacitance (C), corresponds to a RESONANT VELOCITY of free space, that velocity being the speed of light (2.998E8 meters/sec). For the implications of this hypothesis, see the file GRAVITY2.ZIP.

• LC circuit
  up

  ^Ref.majka Transmission lines and space share common parameters. The most notable are the parameters of distributed inductance (or magnetic permeability) in henries per meter, distributed capacitance (or electric permittivity) in farads per meter, characteristic impedance in Ohms and characteristic velocity in meters per second.

  ^Ref.majka Models of transmission lines are basic in the study of electricity and electronics. A model circuit diagram describing a typical, real transmission line is shown in Figure 1.

  ^Ref.majka The inductance, L, is in terms of henries per meter. The capacitance, C, is in terms of farads per meter and the resistance, R, is in terms of Ohms per meter.

  ^Ref.majka Note that the circuit diagram basically consists of one RLC circuit repeated for the length of the transmission line. The resistance, R, is responsible for losses in transmission lines.

  ^Ref.majka It can be seen that this circuit is also the circuit of a series LC circuit. To go from a transmission line model to a series LC circuit model all we need do is change the terms of the parameters from henries/meter and farads/meter to henries and farads. The normalized transfer function, H(jw), of such a circuit is:

  ^Ref.majka H(jw) = 1/( w² - wo²)

  ^Ref.majka The series LC circuit does not forbid frequencies other than the resonant frequency but it does provide an impedance to them.

  ^Ref.majka We should note that the series LC circuit does not prohibit frequencies greater than the resonant frequency.

  ^Ref.majka Since the analogy between series LC circuits and free space has held in other circumstances we may assume that space also does not prohibit speeds greater than resonant speed but will provide an impedance to them.

  ^Ref.majka In the series LC circuit, the impedance encountered by a signal with a frequency of zero Hertz is provided entirely by the capacitance. As the frequency of the signal is increased, the impedance of the capacitor is reduced.

  ^Ref.majka Let us assume a series LC circuit, as described above, with no applied signal. The inductor does not have an initial magnetic field nor does the capacitor have an initial electric field.

  ^Ref.majka Now let us apply a signal of zero Hertz and the circuit will oscillate at its resonant frequency.

  ^Ref.majka In a real circuit, resistances cause the oscillation to dampen. In an ideal circuit, the oscillation does not die out and continues forever.

  ^Ref.majka If we assume the creation of a particle, we would see that this particle causes a disturbance which propagates as an electromagnetic wave.

  ^Ref.majka Now we change the frequency of the applied signal. Again the circuit will respond with an oscillation at it's resonant frequency.

  ^Ref.majka Similarly, if we accelerate a charged particle, an electromagnetic wave is generated. Indeed, any change in the frequency of the applied signal to a series LC circuit will generate transient oscillations just as acceleration of a charged particle will generate electromagnetic waves.

  ^Ref.majka GRAVITY

  ^Ref.majka The electric and magnetic fields of a particle have been associated with the impedances offered by the capacitor and inductor of an analogous series LC circuit.

• impedance
  up

  ^dictionary Symbol Z. A measure of the total opposition to current flow in an alternating current circuit, made up of two components, ohmic resistance and reactance, and usually represented in complex notation as Z = R + iX, where R is the ohmic resistance and X is the reactance.

  ^Ref.majka Transmission lines and space share common parameters. The most notable are the parameters of distributed inductance (or magnetic permeability) in henries per meter, distributed capacitance (or electric permittivity) in farads per meter, characteristic impedance in Ohms and characteristic velocity in meters per second.

  ^Ref.majka Circuit modeling involves determining the voltages and currents through the circuit. By Ohms Law (E = I x Z), the voltages and currents are related through impedances. (Note: impedance is mathematically treated as a resistance.

  ^Ref.majka It differs from a resistance in that there are no energy losses through an impedance.)

  ^Ref.majka Figure 3 shows the same circuit with the impedances of the circuit elements.

  ^Ref.majka The values of the impedances are shown in typical electrical analysis notation. Since the impedance of an inductor varies directly with the frequency of the current through it or voltage applied to it, the impedance is in terms of the frequency, jw.

  ^Ref.majka Since the impedance of a capacitor varies inversely with the frequency of the current through it or voltage applied to it, the impedance is in terms of the inverse frequency, 1/jw. (In electrical analysis, since the symbol "i" is used to represent current flow, the symbol "j" is used to represent the square root of -1 and the symbol, w or omega, is used to represent frequency where w = 2 pi f.)

  ^Ref.majka If a signal was applied to the circuit and it was not at the resonant frequency, the circuit would offer an impedance to the signal.

  ^Ref.majka If a signal at the resonant frequency was applied to the circuit, the circuit would offer no impedance. The reason for this is that the impedance of the inductor (jw) varies directly with the frequency of the applied signal.

  ^Ref.majka The impedance of the capacitor (1/jw) varies inversely with the frequency of the applied signal. At the resonant frequency, the magnitude of the impedance offered by the inductor and the capacitor are equal.

  ^Ref.majka impedances due to inductors and capacitors are vector quantities. The direction of the inductor's impedance vector varies directly with the frequency of the applied signal in the positive direction.

  ^Ref.majka The direction of the capacitor's impedance vector also varies directly with the frequency of the applied signal but in the negative direction.

  ^Ref.majka At resonance, the magnitudes of the impedances are equal but the vectors are 180 degrees out of phase with each other and thus cancel. At resonance, the circuit offers no impedance.

  ^Ref.majka The series LC circuit does not forbid frequencies other than the resonant frequency but it does provide an impedance to them.

  ^Ref.majka Similarly, we may assume that the universe does not forbid speeds other than the speed of light but would provide an impedance to them.

  ^Ref.majka Since the analogy between series LC circuits and free space has held in other circumstances we may assume that space also does not prohibit speeds greater than resonant speed but will provide an impedance to them.

  ^Ref.majka STEADY-STATE impedanceS

  ^Ref.majka The hypothesis predicts that electromagnetic waves can travel at speeds other than at the speed of light.

  ^Ref.majka At light speed, the universe offers no impedance to the propagation of electromagnetic waves.

  ^Ref.majka At other than light speeds, it is expected that the universe will provide an impedance to these waves.

  ^Ref.majka We are familiar with speeds less than light. At a zero relative speed, the "stopped" electromagnetic wave appears as a "particle" and exhibits a gravitational field and an electric field.

  ^Ref.majka In the series LC circuit, the impedance encountered by a signal with a frequency of zero Hertz is provided entirely by the capacitance. As the frequency of the signal is increased, the impedance of the capacitor is reduced.

  ^Ref.majka Similarly, as the speed of a particle increases, the effects of the static electric field are decreased.

  ^Ref.majka Similarly, we may compare the impedance of the inductor to the magnetic field of a particle in relative motion.

  ^Ref.majka At zero Hertz, there is no impedance offered by the inductor and a "particle" at zero relative speed has no magnetic field. As the frequency of the applied signal to the circuit is increased, the impedance provided by the inductor is increased.

  ^Ref.majka As the speed of the particle increases, the effects of the magnetic field are increased.

  ^Ref.majka At frequencies less than the resonant frequency, the impedance of the circuit is due primarily to the capacitor.

  ^Ref.majka At speeds less than that of light, the electric field is dominant and the magnetic field is a function of the electric charge.

  ^Ref.majka At frequencies greater than the resonant frequency, the impedance of the circuit is due primarily to the inductor. We may then assume that, by analogy, at speeds greater than the speed of light, the magnetic field will dominate and will appear to be as constant as the electric field at sub-light speeds.

  ^Ref.majka The impedance offered by the capacitor is analogous to the electric field of a charged particle and the impedance offered by the inductor is analogous to the magnetic field of a charged particle in motion.

  ^Ref.majka GRAVITY

  ^Ref.majka The electric and magnetic fields of a particle have been associated with the impedances offered by the capacitor and inductor of an analogous series LC circuit.

  ***

  ^Ref.andersen An electronic circuit analogy was announced by Schelkunoff in 1938 [footnote 1] in which it was shown that the intrinsic impedance of free space is analogous to the characteristic impedance of a network, and the Q of a lossy medium is analogous to the Q of a network. That analog is in common use today in antenna design.

• capacitance
  up

  ^dictionary 1. Symbol C The ratio of charge to potential on an electrically charged, isolated conductor. 2. Symbol C The ratio of the electric charge transferred from one to the other of a pair of conductors to the resulting potential difference between them. 3.a. The property of a circuit element that permits it to store charge. b. The part of the circuit exhibiting capacitance.

  ^Ref.majka Transmission lines and space share common parameters. The most notable are the parameters of distributed inductance (or magnetic permeability) in henries per meter, distributed capacitance (or electric permittivity) in farads per meter, characteristic impedance in Ohms and characteristic velocity in meters per second.

  ^Ref.majka The inductance, L, is in terms of henries per meter. The capacitance, C, is in terms of farads per meter and the resistance, R, is in terms of Ohms per meter.

  ^Ref.majka In the series LC circuit, the impedance encountered by a signal with a frequency of zero Hertz is provided entirely by the capacitance. As the frequency of the signal is increased, the impedance of the capacitor is reduced.

  ***

  ^Ref.andersen Also, that the magnetic permeability of free space and the electric permittivity thereof are analogous to the distributed inductance and capacitance, respectively, of a transmission line.

  ^Ref.andersen This leads to the suggestion that a transmission line's RESONANCE, which depends on its inductance (L) and capacitance (C), corresponds to a RESONANT VELOCITY of free space, that velocity being the speed of light (2.998E8 meters/sec). For the implications of this hypothesis, see the file GRAVITY2.ZIP.

  ^Ref.andersen That electronic circuit analogy has been developed further by the author [Tilton] in accordance with the ideas that the permittivity and permeability of free space are analogous to the capacitance and inductance, respectively, of a tuned circuit. In this extension of the analogy, the speed of light becomes analogous to the resonant frequency of a tuned circuit.