See Also: FQXi Essay:"How could science have emerged differently?"... 23/04/21
See Also: UQS RE:"Quantum Many Body System"~ FQXi: D. Oriti 11/2021 ... 22/03/18
See Also: UQS Re: "WHY GRAVITY IS NOT A FORCE"~ VERITASIUM 10/9/2020... 21/08/08
See Also: UQS Re:"THIS IS MATH'S FATAL FLAW"~ VERITASIUM 2021... 21/08/08
See Also: FQXi Essay: Undecidability, Uncomputability, and Unpredictability... 20/04/09
See Also: Space-Time Energy As Substance Underlies All Space-Time Energy Phenomena... 19/11/15
See Also: FQXi Essay: What is Fundamental?... 18/01/03
See Also: UQS Analysis: Nassim Haramein... 16/12/05
See Also: UQS Re: Tommaso Bolognesi ... 16/09/16
See Also: UQS Social Media and Forums ... 16/09/16; UPDATE: 18/05/25; UPDATE: 20/05/29; UPDATE: 21/05/01; UPDATE: 21/06/04; UPDATE: 21/06/20; UPDATE: 21/09/03; UPDATE: 22/03/24; UPDATE: 22/05/12; UPDATE: 22/06/18; UPDATE: 22/07/26; UPDATE: 22/08/18; 22/12/05
See Also: UQS Consciousness Investigation ... 16/01/12; UPDATE: 18/05/25; UPDATE: 20/05/29
See Also: UQS Data Bus ... 15/04/09
See Also: UQS Analysis: Wave-Particle Duality ... 14/04/01
See Also: UQS Analysis: S. Lloyd; arxiv.org/abs/1310.3225 ... 13/11/17
See Also: UQS Analysis: Vamivakas/Neukirch Laser Exp. ... 13/08/29
See Also: UQS Analysis: OPERA Neutrino ... 11/09/29
13/06/01 S.Lingo TDA of: 'Quantum-Mechanical Computing'... Seth LloydA Time Displaced Analysis (TDA), of the Oct. 1995 Scientific American Vol. 273 No. 4 pg. 140, with excerpts from article, in bold text.
The Oct. 1995 Scientific American Vol. 273 No. 4 pg. 140, is available at SciAmdigital.com
"... integrated-circuit technology is running up against its limits... where bulk matter reveals itself as a crowd of individual atoms, integrated circuits barely function... the individuals assert their identity, and a single defect can wreak havoc."
In that the physical Universe apparently does function, the "havoc" point may be the result of a theoretical issue rather than a physical issue.
A quantum logic lattice is the geometry coordinate system, unified or otherwise, being used to map the motion we observe in Q-space, and through this lattice lens, we infer Quantum Energy Mechanics.
~ A slight variation in the axioms of the foundation of a theory can result in huge changes at the frontier"... Stanley P. Gudder... Quantum Probability ~
When observing phenomena otherwise unseen, through a virtual logic lens/lattice, even a slight coordinate system variation between the observation lattice lens, and the lattice logic that is in reality dictating the motions of the observed phenomena, will distort the reality of what is being seen.
"... how small can the components of circuits be made?... how much energy must be used...?"
Resolution is an inherent aspect of any quantization... i.e. the smallest attainable theoretical unit of resolution is limited by the ability of the geometry structure utilized as the virtual logic lens/lattice.
To resolve "havoc" at the frontier, the logic lattice must be capable of resolving... i.e. spatially defining ... the mechanics of spherical/symmetrical energy emission from a single point in 3-D space.
At energy emission, the minimum spatial logic/lattice address must be equal to the spatial requirement for distribution of a minimum energy unit ... i.e. spatial definition of minimal energy = the minimum spatial address definition of the information system... i.e. QE = QI.
NOTE: If one's formal logic procedures dictate that the more essential form of energy, within a specified frame of discussion, is designated as E, and the secondary form as E' it would herein be necessary to initiate a decree that E=mc^2 must within the quantum frame be notated as E'=mc^2. However. that would create "havoc", which we are attempting to resolve. Therefor, I have designated the spatial definition of minimal E ... i.e.quantum maxed E... as QE.
To adequately support the notion of energy density, as a per spatial-volume concept, a distinction must be made between the spatial definition of a single minimum unit of QE, and a quantitative value of E... i.e. E being the comparative energy potential of entities of unverifiable spatial definition.
Resolving the choreography of QE emission requires that the quantum information system's minimum address has a spatial definition within the lattice, and contains not only the 2 bit occupied/unoccupied information alternative, but also the 2 bit QE flow direction alternative... i.e. the potential of the individual QE address.
"Choice of the appropriate coordinate system is half of the solution to any field problem."  ~ Walter E. Rogers
"One physical fact of life is that as the components of computer circuits become very small, their description must be given by quantum mechanics."
The Unified Quantization of a Singularity (UQS) coordinate system , is one such description/definition... i.e. a logic lattice in which quantum mechanics can be defined in terms of minimum QE spatial geometry, address pair, singularity, and Base Unit (BU) volume. The UQS virtual quantum simulation of QE emission, currently can co-process two spatially integrated channels, with separate functions... i..e. Inertia events and Radiation events... out to an Inertia Shell Radius=3BU and a Radiation Shell Radius=5BU.
ILLUSTRATION #1 "GROWTH OF A UQS Q-INFORMATION SYSTEM":
To date, the UQS QE emission simulation supports Einstein's notion that the physical reality of space is a spatially defined...i.e. hard wired... logic system/lattice, in which the spatial address entities are defined by 3 sets of 3 independent variables... i.e. a unified field coordinate geometry.
It is the spatial definition of a logic address, that facilitates the location and determination of QE occupied/unoccupied status, of any QE spatial address, for read/write operations, by the information system.
If in a 3-D volume, a 2-D defined address is occupied by a minimum QE unit, there must also be a distinction between the two direction alternatives associated with the QE flow potential.
"In the early 1980s... Paul Benioff... showed that a computer could in principle function in a purely quantum-mechanical fashion."
"Quantum mechanical", in 1980's, being any differentiable state change that could be resolved with limited quantum analysis methods, but the possibilities for "magic" opened a frontier to be explored by the "next" generation, and perhaps applied by the next.
"... began to model quantum-mechanical computers... considered quantum computers in the abstract instead of studying actual physical systems"
Theoretically, as we resolve QE = QI, the distinctions between physical and virtual diminish, and we will need to clarify terminology.
Is a quantum logic lattice and associated QE emission functions/mechanics, running at digitally selectable variable speed, inside a CAD/Sim application, on a conventional digital computer, a physical or virtual device?
I consider it a Virtual Simulation of a Physical Quantum-Mechanical System.
"... suggestion by Richard P. Feynman that quantum computers might be useful for simulating other quantum systems (such as new or unobserved forms of matter)..."
In that Universal QE emission must run in accord with the inherent energy dictates of the geometry in which nothingness fractured, a valid simulation of that fracture will reveal the spatial coordinate dictates/characteristics of the minimum unit of energy (QE) in terms of a single spatially defined address.
Sanskrit literature conceptualizes the "fracture of nothingness" as the differentiation of Mulaprakriti into Prakriti... i.e. investigation of the geometry into which nothingness fractured is an ancient and enduring pursuit. Unfortunately the pursuit has often been derailed onto a quest to "see the face of god".
Planck's "elementary quantum of action", quantized electromagnetic waves in Kg. meters^2/sec. units.
At QE emission... i.e. fracture of nothingness by QE distribution in ALL directions from a single point... Kg. mass does not exist... i.e. inertia channel entities have not yet differentiated... and meters^2 implies a Cartesian logic lattice, which does not support QE=QI, and time in seconds has no reference to the QE emission pulse... i.e. quantization of energy implies pulsed rather than continuous streamed output.
ILLUSTRATION #2 "CLASSICAL LATTICE INFORMATION SYSTEMS... and their limitations:"
Einstein quantized photons, as discrete quanta, which he theorized would be coordinate addressable, within a logic lattice. Although unable to resolve that lattice... i.e. "What is the mathematical character of the universe? ... he was well aware that "rules hold only in respect to certain coordinate systems" , and he correctly predicted that the "coordinate system"  dictating the fundamental choreography of energy, was a "unified field geometry", that would support tensile symmetry.
A point can have location, but it has no inherent spatial volume (2-D or 3-D) definition in the lattice geometry.
That being the case, Einstein utilized Planck's constant and it's relationship to v as frequency.... i.e. wave phenomena... and Planck's constant and it's relationship to v as point to point d/t velocity, to associate energy with time and space. His approach did not yield a volumetric quantization of a spherical QE emission.
"The arrow of time defined by the decoherence process requires a special initial condition for the universal wave function (namely: little or no initial entanglement). Evidently, this must be a physical condition - it cannot just be a condition for initial "human knowledge" or some kind of "information". ~ H. Dieter Zeh 
The difficulty here is that on QE emission, QE must be given spatial definition...i.e. defined by the lattice to which equal pressure in ALL directions fractures nothingness... but the empirical observation that an energy entity of some resolution greater than QE=QI, a photon for example, can apparently be directed along any specified path... i.e. a ray... to any other point in space, seems to favor Ray Emission Models and invalidate Lattice Dictate Emission Models even though they may support energy density functions.
A Unified Field lattice, Cartesian, UQS, etc., has a mutually perpendicular axis of emission. The UQS lattice limits the minimum target angle increment to 90 degs. in 6 directions, from any emission node at QE=QI resolution. This does not support a straight line "Ray" to an address target on a dx=1/dy=2 path, or a dx=1/dz=2 path, or a dx=2/dy=1/dz=1 path, etc.
Perhaps a student of Werner Heisenberg would defend Lattice Dictate Emission theories, by suggesting that intent... i.e. the act of directing the photon... with knowledge of the lattice, would effect the system/field the same as QE, and could act to alter an axis path dictate, to a dx=2/dy=1 path dictate, but I have not attempted to verify that Intent=QI=QE, at UQS QE emission R=3BU.
The UQS QE emission CAD/Sim out to R=3BU does verify that at QE=QI resolution the direction options available to a single QE unit is limited to the minimum angle increments inherent in the lattice geometry, and this would indicate that a photon, although possibly massless (no inertia circuit component), is of a spatially greater scale than a QE Radiation channel unit.
Which means it is possible that current instrumentation and current Q-Theory limitations... i.e. inability to verify photon lattice referent at QE=QI resolution... may be creating the illusion that a photon can be directed along any specified path.
"If no new physics will ever be found to apply somewhere between apparatus and observer, we may have to accept the "many worlds" interpretation.". ~ H. Dieter Zeh 
The object of my work [Addendum] is to demonstrate that an absence of energy density functions/mechanics, is inherent in a quantization made with out deriving a spatial definition of QE=QI at QE emission, and to apply that resolve to the development of the Star Trek Replicator... i.e. a spatially defined minimum unit of QE is required knowledge for emulating minimum physical quantum circuits, such as the Hydrogen Proton.
"This article explains how quantum computers might be assembled and describes some of the astounding things they could do that digital computers cannot."
The potential of Q-logic as perceived by analysis with what coordinate system?... Cartesian?? What physical system?... photons??... which may are may not be the absolute quantum of E????
This article confirms an apparent need for a valid unified field lattice/model that facilitates QE = QI. In the 18 years since this article was published UQS has been developed and it does satisfy the requirement for QE = QI. Has any other lattice model resolved QE = QI ?
ILLUSTRATION: See Oct. 1995 Scientific American Volume 273 No. 4... pg:140
"HYDROGEN ATOMS could be used to store bits of information in a quantum computer."
Hydrogen atoms are a QE choreography in physical space. Bits stored in a physical system require spatial definition... i.e. an address location in 3-D space. To read the smallest address... i.e. minimum QE spatial definition... requires analysis with higher resolution logic than the Cartesian/Polar (combined or separately) coordinate system is capable of. Cartesian logic can not resolve E emission origin without Polar coordinate logic, and combining the two invalidates a unified field. Polar coordinate logic can not volumetrically quantify a unified field.Ref: [ILLUSTRATION#2] Classical Coordinate System, and their limitations
"Atom in it's ground state..."
How much QE in ground state... i.e. QE in terms of physical address space... as opposed to quantitative E in terms of comparative potential... i.e. what is the density of QE in an atom's ground state?
The spatial geometry and QE choreography of a Hydrogen atom needs definition. Without a valid unified field geometry lattice, to accurately referent QE density mechanics, we are "Shooting in the dark at rare birds" ~ A.E.  .
" The atom's bit, 0 or 1, can be flipped to the opposite value using a pulse of laser light. If the photons in the pulse have the same amount of energy as the difference between the electron's ground state and excited state..."
As a result of energy circuit potential?... or energy density??
"... and it's excited state, the electron will jump from one state to the other."
Does energy input increase the spatial volume of the atom's energy choreography influence sphere?...i.e is the electron a surface phenomena at the radius of the influence sphere??
ILLUSTRATION: See Oct. 1995 Scientific American Volume 273 No. 4... pg:141
"READING the bit an atom stores is done... with energy... the difference between the atom's excited state and an even higher... state."
Does energy input reflect in a spatial increase of the atom's sphere of influence, or just energy density?
In the UQS QE emission simulation, the Inertia channel develops QE circuits, and under specific circuit configurations, QE pulse input to the circuit may drain the accumulated circuit QE to the Radiation channel.
"If the atom is in its ground state... no effect."
The energy event occurs outside the atom's energy choreography sphere of influence?
...Cont. article text:
"Niels Bohr... ""Anyone who can contemplate quantum mechanics without getting dizzy has not properly understood it.""
Without an as built/programed virtual navigation model... i.e. valid coordinate system... and a spatial QE direction bit comparative required for tertiary logic gates to function, "havoc" will prevail.
"...quantum mechanics predicts a number of counter intuitive effects..."
Possibly because our intuition has been programed by viewing quantum phenomena through a logic lens of insufficient resolution. An illusion is created if the observed Q-reality is not supported by the geometry model being utilized as the spatial relativistic comparative, which will consequently corrupt Q-Energy motion comparative analysis.
"What we observe is not nature itself, but nature exposed to our methods of questioning."~ Werner Heisenberg Physics and Philosophy.
Predictable, if from emission origin, 2 channels, Inertia and Radiation, are inherent in the geometry coordinate singularity. UQS coordinate system based QE emission simulation, demonstrates 2 spatially integrated channels with differentiated functions, based on the differentials in the lattice geometry.
"... behave under some circumstances like waves and that things we normally describe as waves, such as sound and light, occasionally behave like particles."
Represents intuitive behavior if the coordinate system inherently facilitates QE flow through spatial gates that pass QE from one channel to the other under conditions dictated by logic function development of the pulsed system. Each UQS address pair has a channel specific gate that drains QE accumulation from Inertia channel to the Radiation channel, and vice versa.
Is only valid to the degree that the coordinate system accurately reflects real world quantum spatial characteristics... i.e. the associated QE emission is derived by differentials in the real world lattice, and the lattice resolves at QE=QI resolution.
"... sets forth what kind of waves are associated with what kind of particles and vice versa."
The inherent geometry of UQS Inertia channel addresses, dictates QE particle behavior... i.e. specifies circuit direction... and allows QE to be drained to Radiation channel, where the QE then behaves as dictated by Radiation channel functions, which can dictate that QE be drained back to the Inertia channel. Direction sum dominates the flow mechanics observed.
"... small systems... discrete energy states."
Predictable, if from emission, origin pulsed QE, is choreographed by differentials inherent in a valid lattice geometry, and those differentials inherently establish functions that facilitate unstable address state accumulation and stable state resolve
Albert Einstein considered an energy emission model as the foundation for his Generalized Theory of Gravitation.
"If a light ray in a vacuum starts from a point... in a three-dimensional coordinate system... it spreads as a spherical wave and reaches a neighboring point..."
At this frame of an energy emission simulation... i.e. equivalent to Pulse-1-Open (P-1-O) of the UQS QE emission... he utilizes Polar...i.e. Radian... lattice logic, to spatially "spread" energy. He defines energy in terms of a "point" which can be located in the lattice. He does not define a QE unit in terms of it's spatial characteristics ... i.e. a "point" has no spatial definition only a location relative to the lattice origin by Radian geometry.
This introduces QE density issues in ALL subsequent equations of this genre.... i.e. QE spatial definition is required for QE density functions.
Quantization of a sphere with Polar... i.e. Radian... logic, does not facilitate the option of level two shell encapsulation of an origin singularity, utilizing volume units of the same geometry as the initial sphere quantization... i.e. does not support a unified field quantization. Ref: [ILLUSTRATION#2] Radian Coordinate System @ Origin
At a higher resolution logic, the UQS lattice can facilitate spatial quantization of QE on P-1-O, and facilitates successive volumetric shell enclosures of R=1 BU, utilizing the same volume of unit quantization used to encapsulate the origin ...i.e. achieves a unified field quantized with the UQS Base Unit (BU) of volume. Ref: [ILLUSTRATION#1] UQS Coordinate System @ Origin
"Introducing the velocity of light, c, we write the expression..."
Einstein introduces speed... i.e. c as a constant... and thus references system time to a continuous stream of spatially undefined phenomena?... i.e. the clock is not a pulsed cycle??
The UQS QE emission simulation utilizes a read/write pulsed QE emission cycle, as the clock, and until QE is spatially written into lattice configuration on Pulse-1-Close (P-1-C), no time functions exist... i.e. no speed or distance. The pulse rate, open/close, is the clock, and all time functions are relative to it... i.e. next, next, next...
"... energy in exact amounts, or "chunks" called photons, which might be considered the particles that make up light waves."
QED and QCD do not adequately reveal the photon Q-mechanics required to verify photon spatially as equal to, less than, or greater than the minimum QE spatial unit.
How can one spatially quantify particles in the radiation channel, without knowing the spatial definition of minimum QE?
UQS resolves minimum QE spatial definition as a single address, which suggest it resolves to less than photon spatial resolution... i.e. a UQS address pair is required for Radiation or Inertia channel behavior.
"... quantum-mechanical waves... can be superposed..."
Superposed waves in a 3-D field gets pretty esoteric, and analysis with an incompatible lattice lens, creates illusion. There is no energy 3-D spatial model of wave, frequency, amplitude... i.e. only two spatial components of the analysis can be viewed at one time. We need to verify a valid 3-D quantum lattice.
My work suggest that UQS warrants consideration as a valid quantum lattice, and funding of subsequent lab data analysis from collisions of single photons at specified alignments... i.e. collision cleavage patterns, minimum angle increment constraints, etc.
Are "unity" lasers... i.e. a continuous stream of coherent/individual photons... feasible? If so., are they currently being used for collision alignment experiments??
Are there currently other lattice candidates that resolve QE=QI?
"...waves offer a rough description of a given particle's..."
Particle equals a unified field geometry volume unit?
Relative (with referent) to a unified field coordinate system?
"... waves... combine...the particle's position becomes unclear."
Position can not be resolved with out a valid unified coordinate referent...i.e. lack of clarity as result of lack of resolution in the virtual navigation tool being used. UQS was designed to resolve to minimum QE address in order to eliminate the fuzz.
"Everything is vague to a degree you do not realize until you have tried to make it precise"~ Bertrand Russell... The Philosophy of Logical Atomism
"... both here and there at the same time."
This may be a result of a fuzzy Cartesian/Radian logic lens, or an unstable state inherent in the lattice differentials of the coordinate system being utilized for analysis.
Although UQS facilitates a higher logic resolution than Cartesian/Radian logic, a UQS unstable address pair... i.e. address pair that has accumulated > 2 QE... does not resolve until next QE input.
"...location will remain unknown until some... interaction reveals it to be either here or there but not both."
In the UQS QE emission simulation, if an unstable state results from a QE pulse, the next pulse event, effecting the unstable BU's, must resolve instability utilizing functions derived by growth of the system to current state.
"... two superposed quantum waves..."
If the 3-D spatial characteristics of a valid address lattice are taken into account, what scale, in terms of address configuration, are the separate waves?
"... behave like one wave... coherent..."
Particle position known?
"The process by which two coherent waves regain their individual identities is called decoherence."
In that your current MIT web persona specifies a continued interest in decoherence, you probably have information I would find very helpful in expanding the UQS QE emission simulation. Although I do have entity differentiation, and currently derived QE emission functions predict entities will scale as fractals of initial entity form, I do not have an entity scale function yet.
UQS functions can subtract energy from an unstable state by draining it from one channel to the other. They can also subtract energy from an unstable circuit in the Inertia channel by exciting a larger spatial entity of the Inertia channel.
"For an electron in a superposition of two different energy states (or, roughly, two different positions within an atom), decoherence can take a long time."
Does energy input always resolve the decoherence? ... or is it also possible for energy input to superpose another energy state with the first 2 superposed waves??
"Days can pass before a photon... collide(s) with electron."
Is a photon always assumed coherent?
"... the time it takes for a photon to bounce..."
Can current instrumentation verify that the angle of reflection equals the angle of incidence in accord w/ classical and 1995 quantum theory?... or is it always the same angle??... 90 degs.???
A valid lattice configuration would need to be consistent with this empirical observation, but the observation must be verifiable at QE=QI resolution.
There are cross-roads in the evolution of any theory, and at t = now we are unable to resolve a QE Emission Model which supports both Ray and Density functions.
Apparently the evolution of Q-theory hinges on whether we continue down the Ray Emission Model road, which as far as I know, in more than 100 years ,has not yielded a valid QE spatial definition and associated density functions (and due to mathematical impossibilities is not likely to), or do we investigate the possibility that Lattice Emission Models will verify observations of non-axial path dictates as a resolution/scale issue... i.e. gross measurement issue... which the UQS QE emission CAD/Sim suggest will occur at t = photon scale entity differentiation.
"... too brief for the eye or any instrument to detect."
It has been said that a valid evolution theory would illuminate evolution, and I think it can be said that a valid quantum lattice will illuminate quantum mechanics... i.e. if instrumentation logic were upgraded to higher resolution logic lattice, the instruments will have greater resolution.
"Information comes in discrete chunks..."
Discrete information address chunks require spatial definition... and a clock pulse.
It can be either a physical or virtual definition of space... i.e. it could be an algorithmic space, and algorithmic defined space does not require/imply additional physical dimensions... i.e. 3 dimensions is plenty to locate any address, physical or virtual.
"...as do atomic energy levels..."
Discrete energy levels, can be measured in terms of E comparatives?... but not as spatially defined discrete chunks??
"The quantum of information is the bit."
At QE emission Pulse-1-Open, QE is quantized by the UQS origin singularity... i.e. the spatial minimum address that QE can occupy is defined. QE can now be defined in terms of navigable logic... i.e. information. Ref: [ILLUSTRATION#1] UQS Coordinate System @ Origin
"A bit of information is a simple distinction between two alternatives."
The UQS spatially defined address inherently contains the 2 bit distinction between occupied and unoccupied, and also contains the 2 alternative QE direction flow distinction.
Therefor, in a UQS virtual Q-computer, 2- 2bit distinctions must be written and read at each address
A quantum computer functions by matching the familiar discrete character of digital information to the strange discrete character of quantum mechanics.
"What is the mathematical character of the universe?" ~ A. Einstein.
The character... i.e. address lattice logic... defines the possible mechanics of a system,. If the lattice used to analyze system phenomena and derive mechanics is not in accordance with the actual lattice (mathematical character of the system), weirdness will prevail.
Subsequent UQS pulse cycles, reveal allowable functions inherent in the lattice structure. The UQS Origin Singularity Simulation develops as 24 planar addresses, 2 address/address pair, 4 address pair/Base Unit (BU) volume, 6 Inertia channel BU's with 48 addresses. 8 Radiation channel BU's with 64 address. REF: UQS Differentiation (9sec.) [Youtube] [Win Media IE6]
"...a string of hydrogen atoms can hold bits...
An atom is a highly choreographed QE dance, within a 3-D spatial configuration of minimum QE units of the address lattice.
"... load information...
Interact in a predictable manner with the address lattice gate logic and with the QE choreography? This requires an accurate model of QE dynamics within the lattice... i.e. @ resolution min. QE = address... and it can not be achieved with Cartesian/Radian logic gates, or circuits defined by such. Ref: [ILLUSTRATION#2] Coordinate System Limitations
"... onto the system..."
The address system, could be physical logic... i.e. atoms... or virtual ... i.e. an algorithm running on a conventional digital computer, as a valid 3-D CAD/simulation application.
"... to process that information by way of simple logical manipulations..."
To process either physically, as with atoms, or virtually in an application running on an I-pad, the logic functions available are those inherent in the specified lattice geometry.
Resolving the spatial quantum of information... i.e. minimal address spatial definition... as equal to the quantum of QE... i.e. spatial definition of minimum QE unit... requires a unified field lattice... i.e. all volume units of the 3-D quantization are spatially defined by the same scalable geometry.
A Cartesian... i.e. cubic... lattice is a unified field lattice, but currently has no valid QE emission algorithm, and any attempt to combine Cartesian and Radian (Polar) systems to resolve a spherical emission, invalidates the requirement for a unified field lattice. Ref: [ILLUSTRATION#2] Combined Cartesian/Radian Lattice
"... and to unload it."
This winter I will be working on the code to upload output of the virtual manipulations inherently performed by the pulse/clock cycles of the UQS QE emission simulation to date, to a UQS geometry programed 3-D CAD/Simulation, for output to a conventional digital screen.
"... quantum systems must be capable of reading, writing and arithmetic."
"The UQS emission simulation facilitates functions for logic processing, but the language and geometry are UQS lattice specific."
Content Note: Seth's article describes 1995 state of the physical mechanics of Q-processors. My responses/questions are in terms of an existing valid lattice as discussed above, and will expose me as highly UQS focus blind, revealing my empirical weakness. I am seeking peer review, and I do understand that it is going to take a collaboration of extremist with highly diverse symptoms of a Q-obsession, to achieve the Star Trek Replicator.
"... (given) a hydrogen atom in its ground state... excite the atom... the atom will gradually move from the ground state to the excited state, as its electron absorbs a photon."
Radiation channel QE flow through gates into the Inertia channel within the atom's QE structural configuration and choreography?
A photon (or successive photons) with QE address units equal to number of QE address units in the volumetric shell at radius (in BU's) of ground state... plus one?... or times two??
"If the atom is already in the excited state, the same pulse will cause it to emit a photon and go to the ground state."
What you are describing, suggest to me that QE focused at an overlapped shell BU, creates a Radiation to Inertia drain.
Emission pulse triggered functions/mechanics between Radiation and Inertia channels, are inherent in UQS lattice differentials at pulse 3...i.e. a pulse to Origin Singularity unstable state... triggers a drain to Radiation channel and leaves Origin Singularity empty... i.e. entire system becomes stable.
Need to know if 1 BU volume of the lattice at origin scale equals an electron? If so., and the number of BU volumes in a proton is 1,837, we might expect a proton scale entity to be differentiated at a BU Radius related to this ratio... i.e. if an electron is one Inertia channel BU, there should be some spatial relationship to the ratio between a Hydrogen electron's E and it's proton's E?... i.e. 1/1,837 BU??
Need insight as to whether an electron is equivalent to a channel gate? ... or... a BU in an overlapped shell??... or both under specified conditions???
Knowing this may narrow possible solutions for entity scaling functions/mechanics.
Spatial entity differentiation introduces the requirement for density and scale functions... i.e. density in terms of differentiated entity per unit of defined 3-D space, and scale being relative to some minimum spatially defined geometry form, and/or, QE choreography form.
One can not know the QE density of a quantitative E measurement, without knowing the minimum spatial unit of QE. Current Q-logic lenses, QED and QCD, utilize Planck's constant, which has it's foundation in the Cartesian/Radian lattice.
At current UQS QE emission Simulation: 13/04/31... i.e. P-36-C... the Inertia channel is initialized out to Radius = 3BU, and the first Inertia circuit entities differentiated at P-8-C.
These initial, Inertia circuit entities, map to A. Barzydlo's, Colliding Corpuscular String Theory (CST), wire frame models of the Hydrogen Neutron. No scale can be inferred, but a valid perspective can be obtained, and requirement for 2 quark mass types, up and down can be differentiated.
ILLUSTRATION #3 "CST HYDROGEN NEUTRON MAPPED TO UQS":
Website link to: A. Barzydlo's Hydrogen Neutron Wireframe Model
The Neutron entity differentiates first... i.e. 2 down quarks and 1 up quark... and when subsequent radius expansion facilitates perpendicular input to a singularity, a 2 up quarks and 1 down quark entity will differentiate.
ILLUSTRATION #4 "CST HYDROGEN PROTON MAPPED TO UQS":
Website link to: A. Barzydlo's Hydrogen Proton Wireframe Model
The UQS Radiation channel does not generate entities other than BU's and strings of BUs... i.e. no internal QE choreograph/circuit distinguishes a Radiation channel entity.
Analysis of a UQS QE emission string slice. suggest that when Radiation channel pressure encapsulates the entity, it triggers a channel exchange?
"Each time the oscillating wave comes around it gives the electron a little push."
P-3-C of the UQS QE emission simulation., resolves a configuration consistent with functions/mechanics derived from UQS geometry lattice differentials revealed in the preceding P-1-O to P-2-C valid resolutions ... i.e. a succession of pulses must fill the Origin Singularity Radiation channel addresses before Inertia channel shell expansion.
"When the photons in the field..."
UQS QE emission simulation suggest photon behavior is dictated by Radiation channel functions/mechanics, and that accumulated QE distribution unlocks a Radiation channel to Inertia channel drain, which is inherent in UQS at R= 2BU, as a unstable state to stable state resolve.
Is the electron the Inertia channels interface with the Radiation channel?...i.e. a volumetric shell of R=1BU ... encapsulating the atom??
"... have E= E0 - E1... these pushes..."
By the pulsed Radiation channel?
... coincide with the electron's...
Overlap the atom's Inertia channel shell?... at same spatial scale??
... gradually convert...
A pulsed build of the required distribution configuration, to drain accumulated QE in atom's Inertia channel shell?
This function is inherent in UQS lattice emission at R-2 BU.
... the wave corresponding to the electron...
Is this the same as the atom's ground state wave form?
"...into a superposition of waves having different energies."
A "wave" being a shell configuration encapsulating the atom/proton?
When the photons have the wrong frequency, their pushes are out of sync..".
Sync in terms of spatial scale of influence?... or pulse rate??... or both apply???
Which photon frequency syncs with a Hydrogen atom???
"If the right light is applied for half the time it takes to flip the atom from 0 to 1..."
Can any given fraction of time create a superposition of waves... i.e. 3/4-1/4, 2/3-1/3, etc. infinitely??
"... same amplitudes."
This would reflect energy (E) in terms of potential?... not spatial lattice characteristic??... i.e. has a 3-D spatial model of wavelength, frequency, amplitude, been developed in the interim 18 years?
"...if the atom is in E1, it will be excited to E2 but decay rapidly back to E1 emitting a photon."
The atom's outermost Inertia channel shell only fluctuates one shell radius?... i.e. the outer Inertia channel shell is an interface with the Radiation channel?
Although a fully encapsulated initial Inertia entity has not resolved at R=3BU, the UQS QE emission functions exhibit potential for this behavior at some subsequent entity scale differentiation.
"If it is in the "half-flipped" state, it has an equal chance of emitting a photon..."
Is the flipped state infinitely variable?... i.e. can an event be registered at anything other than full-flipped or "half-flipped" state??
"... linear elements (such as wires, resistors and capacitors)... "
Does "linear" necessarily imply a straight line?...i.e. in quantum functions, may jaggies appear as a straight line if underlying lattice is not resolved??
Nonlinear devices... make the input signals passing through them interact.
Devices that introduce circuit logic level alternative decisions?
The UQS QE emission simulation, utilizes the differentials in the lattice to introduce accumulation driven interaction between the two channels. It is simple math, but requires an Intermittent Calculation State (ICS) on the geometry of the entire Q-system.
ILLUSTRATION #5 "UQS QE-EMISSION SIMULATION":
MECHANIC NOTE: Flow sum, with no fractions of minimum QE, or fraction of minimum address, and no requirement for infinities, is an operative UQS function out to Inertia channel R=3BU and Radiation channel R=5BU, so a UQS digital coded CAD system could be taught to do the ICS very rapidly.
The individual shell volume, and the total system volume, can be calculated in terms of Radius... i.e. the volume in UQS Base Units (BU) of a encapsulating shell of 1BU layer... at any Radius=R, from the Origin.
Inertia Channel Shell Volume in terms of R... [[[2(R-1)-1]^2*48]+30]*8
Radiation Channel Shell Volume in terms of R... [[2(R-1)-1]^2+6]*144
ILLUSTRATION #6 "UQS LATTICE EXPANSION = 5BU":
Don't expect real time simulation to have meaning until QE emission field geometry is casual conversation.
Utilizing quantum physical phenomena as a quantum information system, requires a valid model of the mechanics of the phenomena... i.e. a quantum-maxed resolution of the underlying logic. Logic being the lattice structure and Energy (QE) choreography mechanics inherent it it's differentials.
Given a lattice that resolves the Q of Information's spatial address equal to the Q of Energy's spatial address, which UQS facilitates, Q-mechanics as logic algorithms, will run as a CAD/Sim in a conventional digital computer.
Imagine a Q-logic coded app. resolving the next ICS on a conventional digital computer, with output to an equivalent lattice coded CAD/Sim.
I am currently doing the ICS by hand... i.e. drawing the 3-D geometry circuits... doing the math on standard Scientific digital calculator, and manually inputting the result into the CAD/Sim frame. Ref: [ILLUSTRATION#5] UQS ICS
I have a lattice addressing notation system with codec for input into a Cartesian/Radian CAD/Sim app. Also have developed a shorthand circuit symbol system, which I will test on the P-40-ICS this winter.
Awesome!!... but will it sell cat food?
My first experience with virtual ICS was in 1981, on a dedicated PDP-11 running an x,y, input only CAD system...i..e. no z component input option. I simulated the z component interaction on an HP handheld, then manually altered the x,y screen results frame by frame.
If the ICS results were displayed at 30 frames/sec, the cat food logo did "spin",... UGH!!... but it sold, and by 1986 commercial CAD systems had x,y,z coordinate logic.
I have never built up an "if" from "not", "copy", "and" gates, but there is a standard circuit notation string for the operation and the binary mathematics would not require revision for UQS logic application... i.e. UQS logic will run on conventional digital logic processor. The processor can be based on any physical phenomena that can be digitally coded.
"... particle spins. "
The Q-of Information's spatial address = Q of Energy's spatial address, is not required to resolve particle spin, but have spin mechanics revealed a valid underlying structural lattice and associated path dictates of energy flow in a proton?
"...the orientation of a particle's rotation with respect to some magnetic field - are, like energy levels, quantized."
Quantized in definable spatial shells?... made up of a definable address structure??... or just differentiated as E values???
"... flipping proton and electron spins only part way..."
If entity has a precise spatial definition and E choreography, flipping the circuit flow "part way" would be indicative of E accumulation?... which would suggest flow sum mechanics??... and existence of an underlying Q-of Info address system??... i.e. there can be no fraction of a minimum addressable space.
"... quantum "wires" are hard to build..."
The physical quantum world would be easier to manipulate if a virtual Q-computer could be used to reveal the underlying mechanics of the physical Q-gate phenomena.
"...disassemble atoms... and then reassemble atoms..."
This is the basis of the Star Trek Replicator, and it requires resolve of the Quantum of Energy (QE) spatial address = Quantum of Information (QI) spatial address.
In that Einstein was attempting to solve QE emission, I suspect that if he had had access to a digital CAD system, we would have the Star Trek Replicator by now.
"...without disturbing the particles' spins.
Will require more than a molecular "pizza oven".
"...single photons... ferry bits of information..."
Flow of QE along the lattice logic path dictates, updates the address value... i.e. Q-of info... as dictated by Q-mechanics derived/inherent in the unified field lattice geometry, which we need to know.
I repeat, "What is the mathematical character of the Universe?" ~ A. Einstein.
UQS may not be "the lattice", but after reading this article, I am convinced, it warrants consideration.
"Caltech: ... one photon bit can be flipped partway..."
Implies QE accumulation, and therefore flow sum mechanics... i.e. what we perceive as a photon has an underlying Q-of info address structure, as does the electron?
Can any fraction of "partway" be measured?
"... immune to perturbations..."
If the Q-of Information address = the Q-of Energy address (QI=QE), perturbation is not an element to causality. UQS, unlike QED and QCD, is a non-perturbation system of analysis. For that reason alone Feynman would have given it consideration.
"... length of all optical paths in the system would have to be accurate to within a tiny fraction of a wave length..."
Quantum logic as a virtual application running on a conventional digital processor with CAD visual structural output, can be scaled, rotated, etc., and would aide in the feasibility analysis of proposed Q-physical devices of all kinds, not just computers.
"...isolate qubits in an ion trap..."
What is the current feasibility of applying Moore's law to the physical size of ion trap?
"... transferred to a common register, or "bus"."
On a conventional digital possessor?
"... tens or hundreds of bits..."
UQS QE-emission Run: 13/04/31, @ P-36-C... manipulates between 100K to 150K (initialization density of radiation channel R=5BU shell not yet calculated), at a Q-of Info spatial address = Q of Energy spatial address (QI=QE) resolution, and I am in the process of digitally coding the derived functions/mechanics to run as an application on conventional digital processor.
"As it stands scientists can control quantum logic operations on a few bits..."
In 1995 a few bits was a good direction, to what degree has this been expanded in the intervening 18 years?
"... even with one bit, a quantum computer can do things no classical computer... random bit..."
Perhaps the random bit is a result of utilizing less than quantum-maxed (QI=QE) resolution, but in that Q-mechanics has generated our universe, lack of the random bit, probably will not be a limitation.
"The random-number programs in digital computers actually generate pseudo random numbers, using a function whose output is so irregular that it seems to produce bits by chance."
Likewise if the Q-of Info spatial address = Q of Energy spatial address (QI=QE) resolution is achieved, even virtually, Q-randomness... i.e. weirdness... will be revealed.
ILLUSTRATION: See Oct. 1995 Scientific American Volume 273 No. 4... pg:144
Illustrates a Cartesian lattice logic representation of Q-physical phenomena, is it a valid representation? By 1995 I suspected that there was no valid Cartesian lattice logic representation of quantum mechanics?
Having now developed UQS as a alternative lattice, I have revealed a very simple codec to convert UQS Intermittent Calculation State (ICS) results to be displayed on a Cartesian CAD system, but this does not necessarily imply that the quantum mechanics of the ICS can be resolved with Cartesian/Radian logic. The digital ICS application will have to be UQS coded, then perhaps, if required, a codec could be developed.
LIGHT FLIPS B TO 1 IF A ON ITS LEFT IS 1
This mechanism does not utilize all the available Q-Info in a configuration derived as a result of QE flow. At a resolution of QE=QI there are 3 information bits associated with any 1 Q-info address... i.e. the address location qu-bit, the occupied/unoccupied QE qu-bit, and if occupied, the flow direction qu-bit.
"... same tactics, move the information..."
Illustrates isolated, successive, copy gate logic operations, but no ICS is being done on the entire system. To date, my analysis of Q-logic suggest that at QE=QI resolution, there may be no way to isolate a logic operation from the entire system?
"... a line of atoms to act as a quantum "wire"."
What relational lattice logic is utilized for the quantum "wire" grid?
" ... "double resonance" operations simultaneously in all directions..."
Only in directions facilitated by the quantum wire relational lattice logic grid. If a Cartesian lattice is being utilized, it will not resolve Q-logic at QE=QI resolution.
"... can mimic the dynamics of any system..."
The dynamics of any system that the analog lattice logic supports/resolves... i,e. QE=QI functions/dynamics can not be utilized with a analog lattice that does not support QE=QI resolution.
ILLUSTRATION:Salt Crystal... See Oct. 1995 Scientific American Volume 273 No. 4... pg:144
"... serves as a general-purpose quantum analog computer."
The salt crystal is a lattice whose coordinate address values can be output to a conventional digital CAD application, but there is no reason to assume that the salt crystal is hard wired by nature, with Cartesian lattice logic, and only if the CAD application is programed with the exact same lattice as the analog crystal grid, will the CAD output to screen appear exactly as the Q-information in the crystal.
If the CAD lattice and analog grid lattice are not the same, the CAD output to screen will not accurately describe the crystal, and CAD/Sim energy functions will not emulate the analog functions of the crystal grid. This is why a lattice that resolves QE=QI is necessary to insure illusion is not unintentionally manifest.
Multiparticle Quantum States
"... neither bit is in a definite state..."
Although UQS ability to resolve to QI=QE, eliminates the possibility that an indefinite state is a logic resolution issue, the UQS QE emission model differentiates a stable state... i.e. 1 QE per address... from a unstable state... i.e. > 2 QE per address pair. It is this differential that accumulates and triggers QE flow.Ref: [ILLUSTRATION#5] UQS ICS
"...if you measure one bit, there by putting it in a definite state, the other bit also enters into a definite state.
I have no issue with measurements being altered by E input, but if a bit is "... a simple distinction between two alternatives"... is the alternative state a measurement of one address?... or a measurement of choreographed QE in an entity system?. Without spatial definition of one address, how can the distinction of one bit be made by a digital processor?
"... destroying the coherence between the two..."
Triggers an E flow event? In UQS QE emission simulation, all flow events leave any effected unstable entity stable. The stable state may be an empty entit, if stabilization of flow receptor entity requires all of the available QE. Ref: [ILLUSTRATION#5] UQS ICS
"Even stranger entangled states can be established between three qu-bits."
The mechanics inherent in a UQS QE emission string slice at P-36-ICS, triggers a QE=24 Inertia Channel Emission Node1 drain, to Inertia Channel Emission Node2, and a QE=40 Inertia Channel Emission Node2 drain, to the Radiation channel, all on one Intermittent Calculation State (ICS)... i.e. P-36-O to P-36-C equals 1 system flow event.
... with more bits, a quantum computer could be used to simulate the behavior of any quantum system.
A quantum system IS a quantum computer whose logic address structure is based on the path dictates of a unified field lattice structure... i.e. a 3-D grid.... and it's mechanics/functions are derived from differentials inherent in the geometry of the lattice
At UQS QE emission run 13/04/31: Pulse = 36 Close and System QE = 2,448. The Inertia channel has expanded to R=3BU with 4,608 addresses initialized. The Radiation channel has expanded to R=5BU with between 100K - 150K (approximated because density of initialization of shell R=5 has not yet been calculated) addresses initialized.
"When properly programmed..."
The lattice of the Q-logic must match the lattice of the analog logic, but can be virtual... i.e. running as an application on a classical digital computer.
"... parallel architecture..."
Must be inherent in lattice geometry from QE emission. In nature there is a Radiation channel and an Inertia channel. UQS geometry facilitates differential and integration of 2 simultaneous ICS channels, from QE emission. Each preforms a different function, has channel specific flow gates to and from the other channel, and no fractions of minimums, and no infinities are required. Ref: [ILLUSTRATION#1] UQS Channel Differentiation @ Origin Emission
"... mimic any quantum system in real time...."
Running virtual Q-mechanics as a CAD/Sim application on a conventional digital processor, would facilitate observation at variable speed, and a Q-understanding thus revealed, would facilitate physical Q-computer development required to run real-time Q-logic simulations.
"As Feynman noted, to simulate a quantum system on a classical computer generally requires a number of steps that rises exponentially..."
As a consequence of Q-foam... i.e. infinities inherent in a Cartesian/Radian coordinate integration (Ref: [ILLUSTRATION#2]) ... and an inability to read QE flow direction at a single spatial address.
"What can a quantum computer do with many logical operations on many qubits? "
UQS QE emission Run: 13/04/31 initializes approximately 150K qu-bits, and will grow exponentially with each pulse of the clock, but by P-36-C, I already have derived, from differentials inherent in the lattice, approximately a dozen functions that dictate the set of possible solutions.
The current challenge is to code a UQS logic application, to run on a classical digital processor, and be able to resolve the next ICS on the entire system.
A UQS QE emission starts on Pulse = 1 Open (P-1-O).
"... putting all the input bits in an equal superposition of 0 and 1, each having the same magnitude."
UQS P-1-O distributes 1 quantum of QE = 1 quantum of Information, to 24 spatially defined addresses, on 6 emission axis, as dictated by the UQS lattice. Ref: [ILLUSTRATION#1] UQS Channel Differentiation @ Origin Emission
"The computer then is in an equal superposition of all possible inputs."
On UQS Pulse = 1 Close (P-1-C), 3 components of the lattice address configuration... i.e. the address spatial specification, the QE occupied/unoccupied bit, and if occupied, the direction/flow bit... are registered/written to the UQS programed CAD/Sim application.
"Run this input through a logic circuit that carries out a particular computation."
Visually, in 3-D, observe event results in terms of lattice configuration. On P-1-C the only possible computation = next pulse... i.e. the CLOCK!!!
"The result is a superposition of all the possible outputs of that computation."
Consider configuration possibilities for Pulse = 2 Open (P-2-O), based on the UQS lattice spatially defined address options, in terms of symmetry... i.e. axis, orientation, shared planes, etc.... and in terms of inherent differentials... i.e. divergence/convergence, interior/exterior, etc.
Also consider a need for two integrated channels from emission.
"In some weird quantum sense, the computer performs all possible computations at once."
Intermittent Calculation State (ICS) weirdness is eliminated by knowledge of the lattice geometry dictating the event possibilities.
At emission of QE in a Q-system... i.e. Q-circuit boot... as with booting a conventional digital computer, only hardwired logic is available. In a virtual Q-system, the coded lattice is the only "hard wired logic... i.e. differential options for ICS.
The result of UQS P-2-C, is volume closure... i.e. 4 address pairs comprise UQS volume base unit (BU), 24 address pairs with 1 QE ea. address, comprise the singularity that encapsulate the UQS lattice emission origin. Ref: [ILLUSTRATION#1] Growth of a UQS Q-Info System
UQS facilitates ICS by means of an event sequence... i.e. open/read, ICS, close/write (if stable). However, on pulse open the entire system shares a timeless space in which no time functions (including speed) are operational. This facilitates the ICS as a total system computation, such that on pulse close, the entire system is updated. Anyone viewing the event without QE=QI resolution logic, would not have a clue of the underlying lattice.
This means that how long an ICS takes, can not be determined from inside the system. Now that may promote weirdness!!!
I associate UQS parallelism with two channels, Radiation and Inertia. The computation required for determining the difference in before and after event configuration., I refer to as Intermittent Calculation State (ICS), and due to symmetry I can use a 2-D slice string for the ICS, then can check my event solution in full 3-D CAD model. Ref: [ILLUSTRATION#5] UQS Intermittent Calculation State
"Consider sound waves..."
Although sound waves serve as a 2-D analog... i.e. cacophony does not support differential of a melody on any one instrument... wave form generators utilize Cartesian/Radian logic, and without a valid spatial 3-D frequency, wavelength, and amplitude model, the analogy is inadequate to speculate on Q-mechanical behavior at QE=QI resolution.
"...symphonic effect of quantum parallelism..."
In order to orchestrate output of a superposed wave form, each waveform in the superposed wave form must input a predictable form... i.e. it's mechanics must be understood by the composer.
"... superposition prevails only so long as the environment refrains from somehow revealing the state of the system..."
That is to say E isolation must be sustainable? In the interim 18 years of this temporally superposed discussion, what maximum duration of superposed state has been achieved, under conditions that might facilitate development that will keep pace with Moore's law?
ILLUSTRATION: Ion Trap... See Oct. 1995 Scientific American Volume 273 No. 4... pg:145
"... each ion is in the same state ..."
Have differential ion state strings been achieved?... has ion manipulation/computation been achieved??
"Another problem quantum computers face is error correction."
An issue for physical Q-mechanics, not for a "Virtual Simulation of a Physical Quantum- Mechanical System".
"...noise... can flip bits at random."
If Q-understanding facilitated by QE=QI resolution eliminates "random", that same understanding may reveal inherent physical QE isolation mechanics... i.e. isolation may be achieved by control/design of entity scale configurations.
"So even if quantum computers can be built, they may not be able to perform computations involving many bits over long periods."
This assumes physical stable/unstable state Q-properties must be utilized in the computation, but if the ICS is done by conventional digital computer CAD/Sim application, the physical configuration does not need to be continuous... i.e. it can be read, erased/decoherent, new configuration written. This would verify feasibility of physical analog circuit to emulate Q-system., and obviously it does do so in nature.
"What we observe is not nature itself, but nature exposed to our methods of questioning."...~ Werner Heisenberg... Physics and Philosophy.
"To surpass the factoring ability of current supercomputers, quantum computers might need to follow hundreds of bits over thousands of steps, maintaining quantum coherence all the while."
A UQS QE emission model mechanics sequence, could easily replace factoring as the preferred encryption method. None-the-less, the technique is similar to factoring encryption, in that once the sequence is solved, it is no longer viable as an encryption key.
"To surpass classical simulations of quantum systems, however, would require only tens of bits followed for tens of steps..."
Has this been attained in intervening 18 years?
"And to use quantum logic to create strange, multiparticle quantum states and to explore their properties..."
UQS quantum logic is being used to resolve Q-wierdness by application of QE=QI, which requires QE emission simulation, and derivation of logic mechanics/functions only as a consequence of a valid UQS unified field lattice differentials.
"...is a goal that lies in our current grasp."
Is happening in the UQS virtual lab.
NOTE: In the same 1995 issue of Scientific American in which Seth Lloyd's Q-Computer article is published, there is an article on Thomas Edison, which says his commercial success was in part due to his ability to clarify the object of his work from the onset. In that I am a self-subsidized research project, perhaps I should clarify my object in this work.The object of this work is to:
BIBLIOGRAPHY/REFERENCE:1. Walter E. Rogers; Bell Labs; 'Introduction to Electric Fields... A Vector Analysis Approach'; McGraw-Hill Electrical and Electronic Engineering Series... 1954