Magnetic Vector Potential [M.V.P.] and Electric Scalar Potential [E.S.P.]

[kmarinas86]

What is momentum?

It is the change of the mass moment with respect to time.

What is mass moment?

It is simply the product of mass and a vector denoting the distance from an arbitrary point.

The mass moments of particles of a system can used to calculate the point which is the center of mass.

You can replace the arbitrary point with the center of mass.

Now what is:

q A

It is the product of the charge [q] and vector potential [A].

It has units of momentum.

What is A?

It comes from a moving "source" charge.

A_s = (μ₀/4π)q_sv_s/|d_r,s|

Which is the magnetic vector potential of a source charge [q_s]. Where the magnetic constant [μ0] is divided by 4 pi [4π], multiplied by the product of the source charge [q_s] and velocity [v_s], and divided by the norm of the distance vector [|d_r,s|].

The product of a receiver charge [q_r] and the vector potential [A_s] gives us:

q_rA_s = (μ₀/4π)q_rq_sv_s/|d_s,r|

Which is recognized as the field momentum.

See: http://www.worldsci.org/pdf/abstracts/abstracts_730.pdf
On "hidden momentum" of magnetic dipoles

An alternate theory, suggested by Harold (Hal) E. Puthoff suggests that static fields, like the static magnetic field and charge in the above article, do not convey momentum.

http://arxiv.org/pdf/0904.1617.pdf

Note however, the key statement he makes is that:
"As alluded to earlier, the Poynting vector definition leads to a possible (mistaken) inference that momentum transfer accompanying power flux can be associated with crossed static electric and magnetic fields, even though there are no observable consequences of such (and, worse, the drawing of faulty conclusions that such momentum transfer can lead to, say, propulsive mechanisms). Though once fully integrated over boundary surfaces the two approaches, the potentials-based approach and the fields-based approach, lead to identical results, it is the point-by-point distributions that differ, with the (A,φ) approach being more in harmony with our ordinary intuitions concerning the relationship between causal charge/current sources and field effects."

Therefore, it follows from this statement that if you integrate the field momentum for a static system all over space, in both approaches, you should get zero field momentum, although in the old approach only the local momentum is non-zero where there exists crossed magnetic and electric fields. In Puthoff's approach, static magnetic and electric fields do not produce momentum at any point.

However, a REAL "static magnetic dipole" consists of a rotating system of charges, like that described in Randell Mills' model of subatomic particles, which correctly predicts the magnetic moment of many subatomic particles, atoms, and even molecules. If you look at Mr. Puthoff's definition of field momentum, the component based on the time and spatial derivatives of the scalar potential, as well as those of the vector potential, you can see that for a moving charge, there will be a net momentum distributed all over space in a direction dependent on the movement of the charge. If you sum these for the "chargelets" which make up a charged particle as in Mills' model, you should also obtain an angular momentum for the electromagnetic field of static magnetic and electric fields which consists of equal numbers of negative and positive chargelets in relative cyclic motion.

Therefore, despite Puthoff's theory being probably more accurate in regards to the actual flow of power in EM systems (when compared to the Poynting vector model used by EH and cross-field antenna engineers, as well as the QM model suggested by Tom Bearden), I would wager that there is field momentum that exists which, though based on Puthoff's math, is different than how he applies it.

The electric potential energy between the receiver charge and the source charge is:

q_rφ_s = (1/4πε₀)q_rq_s/|d_s,r|

Now, notice that before, we found that the product of a receiver charge q_r and the vector potential gives us:

q_rA_s = (μ₀/4π)q_rq_sv_s/|d_s,r|

Which is recognized as the field momentum.

The field momentum can therefore be in a sense derived from the electric potential by multiplied by v_sε₀μ₀ or v_s/c^2.

The factor (μ₀/4π)q_rq_s/|d_r,s| (i.e. the electric potential divided by c^2) can be thought of as the "field mass", which when, multiplied by v_s gives the field momentum. It only exists because there is more than one charge q, and there is relative motion of at least one charge in the frame specified.

The energy stored in the field due to relative motion of charge is based on the dot product of q_rA_s and the velocity of the receiving charge [v_r]. The result is:

q_rA_sv_rcos(θ) = (μ₀/4π) * q_rq_sv_rv_scos(θ)/|d_s,r|

Where v_r and v_s are measured in the center of momentum frame of the interacting masses. In Mills' model of subatomic particles, both mass and charge emerge from the discontinuity formed by electric field lines terminating on a surface, which he says is also responsible for the Lorentz contraction of space-time itself. The result is that charge and mass are distributed, even on a neutron surface, where the sum of positive and negative chargelets is zero. Conversely, in Mills' model, photons do not curve space-time, as it has no terminating electric fields, and instead they are loops when observed in the photon's frame of reference.

However, what about field moment, whose time derivative is the field momentum? Could there be a way to control the "mass moment" and by extension the "center of mass", by controlling the "field moment" counterpart?

Since the time integral of "kinetic" momentum [mv] is mass moment [md], then the time integral of the vector potential [A_s] at some charge [q_r] should give a value that is equivalent to a "field mass" moment. If we say that the canonical momentum [mv + qA] is conserved, this results in a net displacement of some mass. If we wish to maximize this displacement, we merely have to maximize the function.

Taking the time integral of a function usually requires adding an arbitrary constant. In this case, it is not arbitrary, as long as we decide on a preferred reference point, which in this case is the source charge. So, let's consider the frame of reference where the receiving charge is stationary and the source charge is moving.

The expression of the time integral of qA becomes:

(μ₀/4)q_rq_sd_s/|d_s,r|

And because we chose the frame of reference where the receiving charge is stationary:

|d_s|=|d_s,r|

So the time integral of qA (i.e. the "field mass" moment) becomes:

(μ₀/4)q_rq_sdhat_s,r

Where dhat_s,r is the unit vector from q_s to q_r. The result of this is quite interesting. This seems to imply that our ability to displace a mass via such effect is limited only by our ability to sort charge. It does not depend on the distance with which we separate the charges, as one might reason by analogy between the momentum and the mass moment, but rather only the accuracy and intensity in which we sort the charge need apply, so as to maximize the sum of the above expression for all pairs of charges. If done with sufficient accuracy and intensity, the result should be a relative displacement with respect to surrounding charges. This, theoretically, should manifest as an increased range of the forces between masses. In typical environments, electromagnetic repulsive forces overshadow gravitational ones at distances on the order of nanometers. What I suggest is that one can possibly increase this distance by introducing qA field effects, which I suspect is the true mechanism behind the EM drive. I'm sure that this can resolve the issue with the EM drive supposedly violating the law of conservation of momentum.

A rough calculation suggests a possible connection with subatomic physics and chemistry:

(μ₀/4π)q^2 * Avogadro's number / 1 gram = 1.54586545 * 10^-18 meters

https://www.google.com/search?q=magnetic+constant+%2F+(4*pi)+*+elementary+charge^2+*+avogadro's+number+%2F+1+gram

Using Google, this value is within 1 percent of the classical proton radius (albeit the result is circular, and should be exact if you remove the electron mass from the equation).

Now, assuming that net charge per electric dipole varied in direct proportion to mass, as opposed to the square root of mass, the maximum qA effect of 1 mole of charge, based on the square of net charge per dipole, would be the generation of a mass moment of:

(μ₀/4π)q^2 * Avogadro's number^2 = 930.942015 m kg

If only transporting itself (i.e. just the 1 mole / 1 gram mass), the maximum possible displacement would be as high as:

(μ₀/4π)q^2 * Avogadro's number^2 / 1 gram = 930.942015 kilometers

If one were to maximize the effect of one mole of charge to displace a mass of one metric ton, the maximum displacement would be on the order of one meter.

So significant displacements through this qA effect should be possible with reasonable amounts of mass.

So, instead of trying to maximize qA, per se, which requires a very strong presence of charge as well as strong magnetic fields (or fast moving particles), or a potentially dangerous High-Q microwave cavity, such as one the EM drive uses, perhaps designing a system that maximizes its time integral is what we need to get at to obtain maximum effect. This would only require us to polarize material, but somehow prevent its induced electric field from being screened by surrounding dielectric, similar to the effect described in the book "Secrets to Antigravity" by Paul A. LaViolette, which is based on capacitors having a very large dielectric relaxation period, in contrast to the tendency of commercial industry, especially in microelectronics, to minimize this value.

https://keychests.com/item.php?v=jxmqzrgwwdc

Note that when a magnetic field rotates on its axis, it too generates a difference in charge, as determined from the Lorentz force (approximation). If you could make it rotate fast enough, it would prevent it from being screened. At macroscopic scales, this is totally impractical. However, at smaller scales, they should become feasible. Randell Mills' "hyperbolic electron" (now coined "psuedoelectron") is essentially one that spins faster (approaching the speed of light) at its north and south poles as a result of strong collision with a neutral atom, which at some level must be changing qA of the electron, which to Mills looks like "negatively curved space" as opposed to a qA effect. Perhaps another way to prevent screening of the electric field would be to heat the outside, or to induce some "non-thermal" disturbance (i.e. one deviating from statistics of the Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein types).

It would be interesting to see if it were at all possible to accomplish significant qA effects with a mere electromagnetic oscillator of a specific configuration, instead of having to deal with microwaves, electron guns, and the like.

[gmanqqq]

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