Discussion of 356(3): Electric Component of the Plane Wave

Many thanks, good to hear from Co President Gareth Evans. These patterns of spacetime flow exist also for a static electric field and the acceleration due to gravity. The numerical problem is simultaneous solution of three non linear partial differential equations for chosen boundary conditions in any coordinate system in three dimensions.

To: EMyrone@aol.com
Sent: 27/08/2016 16:18:37 GMT Daylight Time
Subj: Re: 356(3): Electric Component of the Plane Wave

This is very pleasing because it introduces a clear consistency right across physics and a lot of your early research was fluid dynamics at the molecular level. So, almost a full circle and fascinating how the work has evolved. Congratulations as ever!!
Sent from my Samsung device

356(4): Spacetime Velocity Field Induced by a Static Electric Field

In spherical polar coordinates this is found by solving Eqs. (13) to (15) simultaneously. In general, the velocity field has a very interesting structure in three dimensions. The simultaneous numerical solution of Eqs. (13) to (15) also gives the spacetime velocity field set up by a static gravitational field g (the acceleration due to gravity). This entirely original type of velocity field exists in a spacetime defined as a fluid. The spacetime can also be called an “aether”, or “vacuum”. Any boundary conditions can be used. A magnetic and gravitomagnetic field also set up aether velocity fields.

a356thpapernotes4.pdf

Part Two of Discussion of Note 356(1)

These are all good ideas. I just sent over the statement of the problem for spacetime flow set up by any electric field strength E in volts per metre. It needs the simultaneous solution of three non linear partial differential equations in three unknowns, v sub X, v sub Y and v sub Z in cartesian coordinates. Any boundary conditions can be modelled, notably the circuit of UFT311 or the Self Charging Inverter paper by Osamu Ide on www.aias.us. Any coordinate system can be used.

To: EMyrone@aol.com
Sent: 27/08/2016 09:25:32 GMT Daylight Time
Subj: Re: Discussion of Note 356(1)

OK, I already had the idea that the relation of the plane wave potentials

A(1) x A(2) = A(3)*

is identical to the relation of the B’s and therefore they may have the same vector directions. I will try a guess for v(1) and v(2) for the electric field but this might be difficult because of their non-linear relation to E.

Besides this I will set up the term (v dot del) v in cylindrical and and spherical coordinates. Then we can evaluate this term when v is given analytically in such coordinate systems, for example for a coil (note 2).

Horst

Am 27.08.2016 um 10:09 schrieb EMyrone:

OK thanks, yes this is the right result for v(1) and v(2), they play the role of A(1) and A(2) in plane wave electrodynamics, so this is an elegant result and leads to new types of fields as you infer. Your idea of electric and magnetic fields setting up flows of spacetime is very interesting. For the electric component of the plane waves in Eqs. (14) and (15) my notation may have been a bit misleading in that v(1) and v(2) for the electric field case are not meant to be the same as the v(1) and v(2) for the plane wave magnetic field. In general:

E = x (v dot del) v

where x is defined as rho sub m / rho. In general the above is a non linear differential equation for v, given any E. I will explain further in the Note 356(3).

To: EMyrone
Sent: 26/08/2016 19:20:49 GMT Daylight Time
Subj: Re: Discussion of Note 356(1)

The calculation gives that v(1) and v(2) are identical with B(1) and B(2) within a constant factor. Is this plausible? Perhaps there is an error in my calculation.
The E field is zero, except a hypothetical E(3) field. This is plausible because v(1) and v(2) only depend on z, and there is no v_z in both cases, so the derivatives of x and y vanish in the term (v*nabla)v. This differs from your calculation.

For comparison I added the same calculation for a real basis, B(1) = [1, 0, 0] etc.

Horst

Am 26.08.2016 um 14:12 schrieb EMyrone:

The equations are of the format B(1) = curl A(1) and so on, so we know that v(1) and v(2) are plane waves. I think that:

v(1) = (v(0) / root2) (i bold – i j bold) exp (i phi) = v(2)*

where * denotes complex conjugate. This should be checked with computer algebra. Also, the result for a curent loop magnetostatic field, just sent over is analytical.

To: EMyrone
Sent: 26/08/2016 12:45:58 GMT Daylight Time
Subj: Re: Note 356(1): Spacetime Velocity Fields Set up by Electric and Magnetic Fields

Has the factor exp(+/- i phi) to come out from the RHS of eqs.(12,13)? or has it simply to be multiplied to the curl terms at the RHS (a typo)?
In the first case v(1) and v(2) cannot be guessed so easily because there is a Z dependence in the exponential factor.

Horst

Am 25.08.2016 um 13:52 schrieb EMyrone:

The first few examples are idealized plane waves and static electric and magnetic fields. In this case it is not difficult for computer algebra to evaluate the velocity fields in the aether. They will give very interesting graphics. In the next few examples it is possible to consider for example spherical electric and magnetic waves in a material, pulsed electric and magnetic fields, and in general any type of electric or magnetic field in a material or any circuit. These will all general their own pattern of velocity fields in fluid spacetime. The vacuum in this theory is therefore an aether with well defined velocity fields. These are entirely new and original ideas. In the first example, numerical methods are not needed. It is relatively easy to get analytical solutions.

356(3): Electric Component of the Plane Wave

This is the statement of the problem in general. It consists of solving simultaneously three non linear differential equations in three unknowns, v sub X, v sub Y and v sub Z, for any boundary conditions. These are Eqs. (6), (7) and (8). For a plane wave the electric field components are given by Eqs. (9), (10) and (11). I find this line of research to be very interesting, because as suggested by Horst, any electric or magnetic or electromagnetic field in material matter sets up a velocity field in spacetime, defined as a fluid. This is entirely original research based on ECE2 unified field theory. In precise analogy, any gravitational field sets up a fluid flow in spacetime, and any weak or strong nuclear field. This is true form the domain of elementary particles to galactic clusters.

a356thpapernotes3.pdf

Discussion of Note 356(1)

OK thanks, yes this is the right result for v(1) and v(2), they play the role of A(1) and A(2) in plane wave electrodynamics, so this is an elegant result and leads to new types of fields as you infer. Your idea of electric and magnetic fields setting up flows of spacetime is very interesting. For the electric component of the plane waves in Eqs. (14) and (15) my notation may have been a bit misleading in that v(1) and v(2) for the electric field case are not meant to be the same as the v(1) and v(2) for the plane wave magnetic field. In general:

E = x (v dot del) v

where x is defined as rho sub m / rho. In general the above is a non linear differential equation for v, given any E. I will explain further in the Note 356(3).

To: EMyrone@aol.com
Sent: 26/08/2016 19:20:49 GMT Daylight Time
Subj: Re: Discussion of Note 356(1)

The calculation gives that v(1) and v(2) are identical with B(1) and B(2) within a constant factor. Is this plausible? Perhaps there is an error in my calculation.
The E field is zero, except a hypothetical E(3) field. This is plausible because v(1) and v(2) only depend on z, and there is no v_z in both cases, so the derivatives of x and y vanish in the term (v*nabla)v. This differs from your calculation.

For comparison I added the same calculation for a real basis, B(1) = [1, 0, 0] etc.

Horst

Am 26.08.2016 um 14:12 schrieb EMyrone:

The equations are of the format B(1) = curl A(1) and so on, so we know that v(1) and v(2) are plane waves. I think that:

v(1) = (v(0) / root2) (i bold – i j bold) exp (i phi) = v(2)*

where * denotes complex conjugate. This should be checked with computer algebra. Also, the result for a curent loop magnetostatic field, just sent over is analytical.

To: EMyrone
Sent: 26/08/2016 12:45:58 GMT Daylight Time
Subj: Re: Note 356(1): Spacetime Velocity Fields Set up by Electric and Magnetic Fields

Has the factor exp(+/- i phi) to come out from the RHS of eqs.(12,13)? or has it simply to be multiplied to the curl terms at the RHS (a typo)?
In the first case v(1) and v(2) cannot be guessed so easily because there is a Z dependence in the exponential factor.

Horst

Am 25.08.2016 um 13:52 schrieb EMyrone:

The first few examples are idealized plane waves and static electric and magnetic fields. In this case it is not difficult for computer algebra to evaluate the velocity fields in the aether. They will give very interesting graphics. In the next few examples it is possible to consider for example spherical electric and magnetic waves in a material, pulsed electric and magnetic fields, and in general any type of electric or magnetic field in a material or any circuit. These will all general their own pattern of velocity fields in fluid spacetime. The vacuum in this theory is therefore an aether with well defined velocity fields. These are entirely new and original ideas. In the first example, numerical methods are not needed. It is relatively easy to get analytical solutions.

356(1).pdf

Daily Report 25/8/16

The equivalent of 147,316 printed pages was downloaded during the day (537.113 megabytes) from 2,581 downloaded memory files (hits) and 631 distinct visits each averaging 3.1 memory pages and 10 minutes, printed pages to hits ratio for the day of 57.08, main spiders cnsat(China), google, MSN and yahoo. Collected ECE2 1772, Top ten items 1609, Collected Evans / Morris 825, Collected scientometrics 545, F3(Sp) 392, Barddoniaeth / Collected Poetry 381, Evans Equations 347, Eckardt / Lindstrom papers 294, Principles of ECE 293, Autobiography volumes one and two 249, Collected Proofs 242, UFT88 117, Engineering Model 109, UFT311 99, CEFE 76, Self charging inverter 41, UFT321 40, Llais 33, Idaho 27, Three world records by MWE 23, List of prolific authors 19, UFT313 36, UFT314 37, UFT315 44, UFT316 36, UFT317 31, UFT318 50, UFT319 51, UFT320 39, UFT322 54, UFT323 47, UFT324 63, UFT325 55, UFT326 39, UFT327 29, UFT328 42, UFT329 48, UFT330 36, UFT331 45, UFT332 40, UFT333 33, UFT334 34, UFT335 43, UFT336 35, UFT337 30, UFT338 31, UFT339 39, UFT340 36, UFT341 35, UFT342 28, UFT343 29, UFT344 44, UFT345 41, UFT346 48, UFT347 45, UFT348 58, UFT349 64, UFT351 60, UFT352 82, UFT353 66, UFT354 52, UFT355 17 to date in August 2016. Physics University of New South Wales UFT177; City of Winnipeg, publications page extensive; Technical University of Chile Professional Institute Technical Training Center (INACAP) Essay 28 (Spanish); University of Kassel general; University of Florida My CV; Mexican National Polytechnic Institute UFT42; Ateneo de Manila Uaiversity Philippines general; National University of Singapore general; University of Edinburgh UFT139, UFT157. Intense interest all sectors, updated usage file attached for August 2016.

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Discussion of 356(2)

Fully agreed, the graphics will be very interesting!

To: EMyrone@aol.com
Sent: 26/08/2016 14:05:53 GMT Daylight Time
Subj: Re: 356(2): Velocity Field from a Current Loop Magnetic Field

In this case the velocity field v is (within constant factors) the same as the classical vector potential A. Therefore all classical methods computing the A field are directly applicable.
In a magnetostatic case (eq.(20) of note 356(1)) we have

rho_m/rho * nabla x (nabla x v) = mu_0 J

or

nabla x (nabla x A) = mu_0 J.

This is the way in which for example FlexPDE solves magnetostatic problems. The vector potential directly corresponds to the velocity field in case of constant charge densities. In electrical cases this seems to be a bit more difficile because the term

(v*nabla) v

does not appear in classical electrodynamics. However, if v is given analytically, E can be calculated this way. So the above magnetostatic problem seems to generate an inherent electric field, not known in classical electrodynamics.

I will try to compute this E field from v of the notes.

Horst

Am 26.08.2016 um 14:04 schrieb EMyrone:

In this case the result is analytical, Eq. (11), and it can be graphed in three dimensions in spherical polar coordinates.

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