Now, to explain all this, note that the gradient of a function at a given point is oriented in the direction of maximum rate of change and is a vector field. Think of standing on a hill and looking down at the ground locally to determine which portion of the proximate hill-side is the steepest. The divergence of a function is a measure of how the function diverges. For example, consider a water sprayer that converts an obviously collimated straight line or curvilinear line flow of water. The water upon passing through the spray nozzle then fans out as typical of a gentle spray used to water seedlings in a home garden. The divergence of the water as it flows through a differential element of hose length is substantially equal to zero while the water that is fan-sprayed has non-zero, positive divergence. Divergence can be positive, negative, or zero. A magnifying glass that focuses light to a small focal point produces refracted light having negative divergence as it travels to form a hot spot. The hot spot can burn your skin so admonish young children not to play dangerously with magnifying glasses in the broad sunlight. The Laplacian as the divergence of a gradient is simply a measure of how all of the vectors in a field of gradients diverge. Now, the higgs field is generally at a macroscopic level, and even ordinary quantum scale levels, of substantially zero divergence. This is the reason why the hggs field is referred to as a scalar field, because the field generally has no net direction of change and thus no gradients. This is why the higgs field may act as a kind of “molasses” to imbue massive particles with non-zero invariant mass, while at the same time producing a drag-like effect on the particles to thereby slow the particles below the velocity of light. Since there is no bias or gradient in the higgs field as is generally the case in natural settings for which the scale of distance is on the order of ordinary quantum distances or greater; at these scales and larger scales, there is no potential energy of higgs field form for massive particles. However, at ultra-microscopic distances on the scale of the Planck Length and associated Planck Time, the higgs field theoretically behaves as a kind of roiling bubbly froth with arcs, bridges, bubbles, and tunnels, of effectively more or less random size and temporal duration. Every so often, the roiling randomly varying gradient of the higgs field at or near the Planck length and distance scales by chance line up to an extent to which a non-trivially large gradient in the field forms. According to a major class of big bang theories and versions thereof, if the gradient is large enough and/or of sufficient temporal duration, the resulting potential energy is converted to positive energy, thus resulting in an explosive big bang event. Such big bangs should be happening just about everywhere just about all of the time in our universe. Some of these big bangs inflate in a permanently runaway manner, whereas other big bangs will initially experience one or more rapid periods of expansion but then slow to a modest rate of expansion, while other universes simply collapse almost immediately after they are born. Regardless of the nature of the universes thus born, the universes theoretically would at least almost always become decoupled from the parent universe which gives birth to the off-spring universes. The progeny universes lasting long enough will produce their own progeny, and these latter universes like-wise in some cases produce their own progeny. The multiverse thus formed may continue to forever grow like an infinite fractal. The reason why we do not observe this baby universes forming all of the time to continually trash our universe is that these universes decouple from our universe on a scale of time about equal to the Planck Time Unit or less. The Planck Time Unit is very tiny indeed at about [5.39 x ( 0 EXP -44)] second. This is 0.0000000000000000000000000000000000000000000539 second or about a billionth of a trillionth of a trillionth of a trillionth of a second. It is possible the number of ancestor universes in a given lineage extends infinite numbers of generations backward in sequence from the latest generation which for us, here and now, is our own universe. A whole topologically related group of such fractal-verses is referred to as a forest, and a whole group of forests as such, is referred to as a biosphere. Like-wise, a whole related group of biospheres is referred to as a solar system and a whole related group of solar systems is referred to as a galaxy. The number of hierarchies may plausibly be infinite to any arbitrary level. The generative mechanisms for these extended levels are conjectured to be more general, more primitive, and broader levels higgs-like fields more commonly also referred to as scalar fields. What might be possible if we were able to produce a gradient in the higgs field in the space or near the space occupied by a starship? What would be possible if we could produce a higgs gradient vector field with positive or negative divergence? What would be possible if we could produce a vector field from the natural higgs field with extremely large curls? I will explain all of these ramifications in greater detail in my forthcoming books on the subject and how such imbalanced might be produced. For most of the day today, Ive been working on my first book to address these scenarios.
Posted on: Thu, 01 Jan 2015 03:53:29 +0000
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