AntiGravity v2

8/13/2019 AntiGravity v2

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ON A GENERALIZED LORENTZ FORCE

LUCIAN M. IONESCU

Abstract. The generalized Lorentz force is investigated as a possible avenue to countergravity.

Contents

1. Introduction 12. Two-body Systems 32.1. Coriolis and Centripetal Forces 4

2.2. Electric and Magnetic Forces 42.3. Gyromagnetic Forces 52.4. Gravitational Forces 52.5. Gravito-Magnetic Forces 53. Experimental Evidence and Conclusions 64. Annex 6References 7

1. Introduction

Electromagnetism is a framework for dynamicsDiff erential Equations: ma=F, Geometry: F =FTangential+ FNormal,

with a cobordims flavor due to a tangential (work related) and normal (curvature related) de-composition, generalzing Newtons framework for mechanics by including in the constitutiveequation defining the forces:

Constitutive Equations: FT =eE+ mG, FN=ev B.

A dipolar charge electric force intensity E is included besides the monopolar chargegravitational force intensity G , together with magnetic force intensity B . While E and Gare responsible for local work, allowing for the definition of a potential energy, B modelslocal curvature, a geometric force which does not produce work locally.

Now the correct linear momentum is the

Canonical momentum: P =mv+ eA

where A is the vector potential (in alternative EM units: P =mv + e/c A ).

Date: May 25, 2011.Key words and phrases. Quantum information dynamics, antigravity, Lorentz force.

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When interpreting the formalism from the background space-time independent point ofview of Quantum Information Dynamics, velocity can be interpreted as a external gaugefield, as in general relativity, dual to the internal gauge field A for the interaction underconsideration (see Annex).

Since the resulting physics contains aspects attributed to the existence of an ether, similar

to the reduced mass and normalized charge concepts, we will use the term etherto indicatea reference to this framework (Embedding the intrinsic dynamics into a space-time; mathtools: adjunction and as internal Hom ).

We consider the Lorentz Force FLorentz together with the Coulomb force FCoulomb = eEthe prototype of a constitutive law in the context ofNewtons Law, called electromagnetic

force:

mv

t =F, F =FCoulomb+ FLorentz,

FCoulomb=eE, E= e/r2, FLorentz=v eB, B= j

/r2.

Here we preferred a discrete (quantum) formulation using a magnetic charge j (fluxon) to

state a discrete version of Bio-Savart law (a related version using a moving electric chargecan be found for comparison at [2]), in addition to the undisputed electric charge e usedto formulate Coulomb law for the electric force (The field versions are B = A andE= ).

The term representing Coriolis acceleration aC (force FC ), present in the general casewhen we do not impose the inertial frame Galilean gaugecondition, is:

mv

t =v m= FC, = v.

Thecentripetal acceleration(force Fc ) is:

vt =v = aC, = v.

It is a mechanical force term with no EM analog so far (fictitious vs. material is adebatable classification, since mechanical rotations are the analog of magnetic vortices;also electric charges, as sinks and sources, can be replaced by wormholes - see Wheeler andMisner - so, to be real or fictitious is a hamletian question, really!).

The mechanical analog of the electric force is the gravitational force:

FG= mG, G= kN m/r2.

Note that we cannot normalize the equation by rescaling the charge, as in the case of theCoulomb force.

In compact form it is written as:

mv

t =v P.

For reasons of symmetry, FNormal needs additional terms:

FTangential= eE+ mG FNormal= ev B + ... .

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Heretangentialand respectivelynormalcomponents refer to the direction of motion, whichbinds to the time variable in the 2 + 2 1 + 3 hermitian correspondence (Hodge relativedecomposition for cobordism model of dynamics, i.e. time [6]).

It is natural to symmetrize and define the generalized Lorentz forceto include the twoterms representing the ether reactions, and representing a way to compensate the use of

a rigid metric when embedding (material) systems in fictitious ambient space-times:

eA

t =A P,

eA

t =A m= FPK, e

A

t =A eB = FS.

The term e A/t is usually interpreted as amotional electric force(motional electric field;E=A/t ), not due to free electric charges.

Altogether, the generalized Lorentz Force FN , normal to the direction of motion, is ofthe type:

P , = P,where is a generalized vorticity fieldincluding centripetal/Coriolis and magnetic forces.A closer inspection:

P = (mv+ eA)(mv+ eA)...

reveals the presence of coefficients involving strange products of coupling constants: m2, e2, meThe proper analysis requires the use of quternions, or spinors, with its shadow, special rela-tivity (see [6], hermitian model 2 + 2 1 + 3 ), and the collaboration of a physicist!

The generalized Lorentz force entails the following additional terms (replacing . . . above),which involve vorticity = v as the analog of megnetic force intensity B = A :

FN=FL+ FC+ FPK+ FS,

Lorentz Force: FL= v eB, Centrifugal F orce: FC=mv ,

de PalmaKozirev Force: FPK=A m, Searl F orce: FS=A eB.

Note that there may be additional quantum effects, i.e. due to non-simply conectednessand associated geometric/Berry/Aharonov-Bohm phase, in the case offorce-free configura-tions, i.e. when B = A= 0 and/or = v= 0 (see also Beltrami force-free fields). Wewill not consider such effects at this stage.

2. Two-body Systems

The main two-body system of interest in this article is the system Earth-Spinor, wherebyspinorwe mean a rotating body possessing a magnetic field, e.g. Searl Effect generator(SEG / flying disk) or a Kerr blackhole.

The local vorticity and magnetic fields are denoted as follows:

Earth: E, BE, Spinor: , B.

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Special cases of such an object are: 1) a gyroscope, used in experiments of Bruce de Palmaand Kozirev [4]; 2) homopolar generator (Faraday etc.).

The interactions between two such bodies involve both bodies masses and charges, togetherwith the corresponding vorticity and magnetic fields.

2.1. Coriolis and Centripetal Forces. These are the analog of magnetic force and electricforce (e.g. homopolar generator):

Coriolis acceleration:aC=v ,

Centripetal acceleration: ac= v .1

As a typical example, for Earth and a point-wise object, the Coriolis (first term) and cen-tripetal excess acceleration (second term) which acts vertically as a correction for gravita-tional acceleration, is [1]:

aCC= 2+ (v2

+ v2

)/R,

where measures the latitude and measures longitude.

The importance of Coriolis force is given by the Coriolis parameter and Rossby numberf= 2 sin , Ro=

v

f L, fE 10

4s1, Ro /E.

For a gyroscope, the torque due to Coriolis force corresponds to Rossby number Ro= 104 ;if = 100s1 then Ro= 106 and the Coriolis force can be neglected.

These forces can be thought off as corresponding to a linear momentum / angular mo-mentum coupling between the two mechanical descriptions of the two objects.

2.2. Electric and Magnetic Forces. The equivalence of linear momentum implied by thecanonical momentum P =mv+ eA can be extended to canonical angular momentum. Forsimplicity we will refer to P = m +eB , instead of using Euler equation d/dt= as

a rigid body analog of Newtons Law dp/dt= F.Then, the Homopolar Generator can be qualitatively analyzed by analogy: magnetic field

B corresponds to angular momentum (vorticity):

aL= v B aC= 2v ,

and electric field E corresponds to centripetal acceleration:

A

t =aE=v B ac= v .

Since Coriolis acceleration is perpendicular to velocity, by the mechanical-EM analogy,there should be a perpendicular component of the field intensity, interpretable therefore asamotional electric force:

aC= v/t aMemf=A/t.

It should be compared with the claims of Hoover a.a. [4].Can this etherical centripetal acceleration be so strong as to yield the purported ioniza-

tion of the Searl disk?

1A queternionic formulation should allow the unification of the two forces.

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2.3. Gyromagnetic Forces. The new aspects of the above generalization is the couplingbetween mechanic and EM phenomena. The latter include gravity as a deformation in thedirection of the speed of light Einsteins constant (even though the constitutive equationsof EM, i.e. the metric or the associated Hodge structure, form a tensor, so that there arefour speeds of light in the continuum ambient space-time formalism of EM).

So, what is the order of magnitude of the term E A ? More precisely, what is theimpact of a solution of:

eA

t =EA.

as a correction to the main terms?

2.4. Gravitational Forces. Gravity seems to be a deformation of EM [7]. Can this bemodeled as an effective force by averaging AB ?

Recall that the other well-known terms v , v B require by symmetry a term ofthe form A , representing the gyro-magnetic force probably notices by de Palma andKozirev in their experiments of falling / weighting gyroscopes, and a term of the formA B , representing the EM analog of the Coriolis force, conceivably responsible for theanti-gravitational force present in the Searl Effect.

Is Bifield-Brown effect due to the A v term, or to the disparity between the negativeand positive charge?

Remark 2.1. To emphasize the role of the vector potential A , which should be interpretedas an ether flowwhenever comparing the modern theory with the historical statementsabout ether, we will call fictitious forces of the type A asetheral / etheric forces.

These are geometric in nature, present whenever assuming a rigid ambient space-time asthe world-stage for dynamics, special relativistic or not.

Assuming that gravity involves such etheral forces, the combinations between the theseetheral forces of earths and a spinning body, will be referred to as gravito-magnetic forces.

2.5. Gravito-Magnetic Forces. Although anti-gravity might not be a question justabout forces, since a multi-valued potential could yield effects similar to those of a gen-uine force defined as a gradient, we will discuss the local aspects: potentials which locallydefine forces.

The terms coupling Earths magnetic and vorticity fields to the angular momentum of arotating magnetic field could provide levitation forces against gravity.

Remark 2.2. 1) Is the magnetic field due to a vector potential AEarth compensating for theEarths rotation?

PE= 0, PE=mvE+ eAE= 0.

2) The Hall effect lines of magnetic force show the presence of two complementary vortices(see [5]). Is this structure compatible with the aurora borealis phenomenon?

The term left to be investigate experimentally are the etheral forces ABE (Searl) andA E (Faraday). They are proportional to the net electric charge.

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3. Experimental Evidence and Conclusions

There is plenty of experimental evidence that Lorentz force, i.e. classical EM, cannotexplain phenomena observed by Tesla, de Palma, Kozyrev, Biefield-Brown, Searl, etc., notto mention more exotic evidence that reality is much more complex then the Newton-

Maxwell local picture (non-local phenomena are not included here, since they belong toquantum theory and cybernetics).There is a need for a careful classification of the reported evidence in raport with the

possible terms of the generalized Lorentz force presented above.On the other hand the theory of EM has been generalized from an U(1)-gauge theory to a

SO(3) -gauge theory (or SU(2) to include spin and quantum phenomena as well: QID). Thehermitean correspondence 3+ 1 = 2+ 2 would provide an alternative formulation expressiblein terms of Pauli matrices / Dirac spinors, via quaternions; but this is not desirable at thisstage, since it would hide the practical meaning.

Regarding the main-stream research picture, the electroweak theory provides alreadyworked-out theoretical material. It should be understood though that in reality symmetry

is NOT broken (from SU(2) to U(1) ), but only in theory, in order to build a bridge withMaxwell-Heaviside theory, which in fact is just a Hertzian approximation of the full EM(QID), as countless researchers have pointed out during the last two centuries.

Our intension is not to convince the reader, but to raise a doubt, for him/her to startlooking outside the academic-box.

Meanwhile we will enjoy the corresponding practical incarnations as free-energy and anti-gravity devices, not in a single instance like Teslas case was, but, due to the web, in mostcountries simultaneously.

4. Annex

The new physics is based on an intrinsic theory, background space-time independent.Compare with intrinsic vs. extrinsic geometry (metric, curvature etc.).

Briefly, a system is modeled intrinsically as a flow of qubits on a graph. Graphs form adg-coalgebra; they form graph extensions, and a graph can be factored in many ways as anextension (compare with Hopf ring: divisibility of integers done using coalgebra structure).This framework is that of Hopf algebra approach to renormalization (see Connes-Kreimer),generalized by the author to include Kontsevich homology differental, in order to formulatethe theory of Feynman Path Integrals in homological algebra terms (see Ionescu [8]).

Such a collection of graphs with divisibility and differential leads to a Quantum FieldTheory, where the number of loops/particles, is not a constant.

Now, consider such representations of graphs Q

Net

Hom(, G), G= SU(2) (QuatumNet) embedded into a space-time Space Time= M3,1 :

Embedding: Quantum Net Space Time.

This is a generalized singular homology, with standard models graphs, rather then thesimplices which are total graphs.

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In a similar way, there is an adjunction (see the brieffing on Grothendiecks approach inYu Manins and S. Gelfand book on homological algebra):

Hom(Hom(, G), M)< > Hom(, GM)< > Hom(Riemann Surface, CallabiY a

providing the correspondence with String Theory approach (viewing the IDOFs and EDOFs

together in the 11D-manifold, the landscape), via some ribbon graphs - Riemann surfacescorrespondence.

The dynamics of the Hodge structure from the intrinsic model is perceived as the ethercontribution in the right side, due to the assumption of a fixed background space-time. Thesolution to the question Which landscape is the right one is none.

The proof that the intrinsic side can model at least what the right side does, is in theFormality Theorem of Kontsevich.

References

[1] en.wikipedia.org/wiki/Coriolis effect (see also Etvos effect)[2] en.wikipedia.org/wiki/Biot-savart#Point charge at constant velocity

[3] L.M. Ionescu, On some points of math-physics from a computer science viewpoint.[4] see Rex Research: de Palma, Kozyrev, Hoover etc.[5] Howard Johnson, The Secret World Of Magnets - Magnetic Energy - Magnetic Vortex Spin.pdf[6] L.M. Ionescu, On some points of mathematical-physics from a computer perspective.[7] L.M. Ionescu, On Quantum Gravity: an essay.[8] L.M. Ionescu, works on arXiv.org and www.virequest.com (Research; Grant proposals).

Department of Mathematics, Illinois State University, IL 61790-4520

E-mail address: [email protected]

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AntiGravity v2