COULOMB’S LAW ONLY VALID FOR
RELATIVE MOTION RELATIONSHIPS
RELATIVE MOTION RELATIONSHIPS
Our experimental data confirms that elementary charged particles behave according to the expectations of Coulomb’s law when the interacting particles have relative motion with respect to each other, but what about when they don’t have relative motion? For symmetry’s sake if we temporarily accept the notion that same charged particles will behave as if they are attractively interactive when they are overlapping in the same momentum space we might examine the idea that oppositely charged particles which are overlapping in momentum space might behave as if they are repulsively interactive.
I wouldn’t expect anyone to just accept this but rather I am suggesting that such a result can be derived from the re-examination of experimental data and can be arrived at by deductive reasoning using such data and Maxwell’s equations. Quite a few people have wondered why an electron just doesn’t fall right down into the nucleus and tightly bind with a proton. Of course, the typical answer that we get is that the electron must obey the Heisenberg Uncertainty Principle and that as its position becomes more and more localized then its momentum becomes ‘spread’ out.
The more spread out the momentum the higher the kinetic energy. So, the electron can lower its potential energy by moving in closer to the nucleus, but if it was too close then its kinetic energy would go up more than its potential energy goes down. So, it distributes itself at a position of balance, at a happy medium, and that gives the cloud and thus the atom its size. Honest, that’s the answer we get when we ask this sort of question. (If you don’t believe me then do an internet search on Google and use the input argument of ‘Why don’t atoms collapse? or Why don’t electrons spiral into the nucleus? or words to that effect and see what you get.) Raise your hand if you think that this explanation sounds like a load of sophistry.
If the proton can be some place (and it, too, must obey the Heisenberg Uncertainty Principle) then why doesn’t it become distributed in a cloud also? When there is a pair creation event where a high energy photon becomes converted into an electron-positron pair we don’t see any problem with a positron re-acquiring an electron; and it must be that they come to a state that is equivalent to being co-located and being annihilated (together with the electron) and re-converted into photons.
But there’s more to my argument than just to ask you to examine the questions I’ve put before you. Let me introduce a simple intuitive fact or axiom:
1) Quantum particles can only have motion with respect to other quantum particles and not with respect to any arbitrarily contrived coordinate system.
This is the simplest articulation of the universal axiom that all motion is relative. How can you have motion with respect to a fiction? Or how can there be motion relative to a fiction? People can believe in all of the impossible things that they desire but when they are doing that then they are not practicing ‘science’.
Alice laughed: “There’s no use trying,” she said; “one can’t believe impossible things.” “I daresay you haven’t had much practice,” said the Queen. “When I was younger, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.” from Alice in Wonderland by Charles Lutwidge Dodgson.
There may be some who will respond to anger and perhaps a tirade and will perhaps describe me as a crank or kook or quack but doing so is not in keeping with open and honest rational debate but rather is a fear reaction to a challenge to the status quo of their belief system. If not called names then the next reaction is condescension with a friendly but gritted teeth reference to ‘accepted’ texts on the matter as if somehow I must not have been inculcated properly the correct number of times with the reigning dogma. Perhaps they hold to the idea expressed in another Dodgson work:
“What I tell you three times is true.” cf. The Hunting of the Snark.
Now let’s take that axiom above (Quantum motion axiom) and apply it together with Maxwell’s equations and see what pops up. What I’m proposing is that we can logically deduce, using Maxwell’s equations together with principle of the relativity of motion, that elementary charged particles that are at rest with respect to one another will, in fact, behave precisely opposite to the expectations provided by Coulomb’s Law. Bear with me please, while I lay out my reasoning.
When we write Maxwell’s equations in terms of E and H only then we have:
1) ∇ X H = εο ∂H/∂t
2) ∇ X E = -μο ∂H/∂t
3) ∇ ⋅ E = 0
4) ∇ ⋅ H = 0
Equation 1) as applied to a charged particle suggests that if that charged particle should have motion so that there would be a variation in E that then a magnetic field characterized mathematically as a vector field with rotation (∇ X H) should arise around the translational axis of that motion.
Considering the principle that all motion is relative one must reflect that a charged particle cannot move with respect to itself and hence in the rest frame of such particle this predicted vector field could not exist. Instead, such a field could only exist in the rest frame of the particle or observer which had relative motion with respect to the particle.
So, if we had two protons, A and B, which had relative motion, then emanating from B’s location but not local to B (not existing in B’s rest frame) would be a vector field as predicted by equation 1) above. Such a vector field would lie on parallel planes perpendicular to the translational axis of relative motion between A and B. Likewise, because of the relative motion of the two particles, then emanating from A’s location, but not local to A, would also arise a vector field which also would lie on parallel planes perpendicular to the translational axis of relative motion between A and B.
The vector field emanating from A’s location would exist in B’s rest frame (momentum space) and the vector field emanating from B’s location would exist in A’s rest frame (momentum space). Now, for two same charged particles that do not have relative motion with respect to each other one might presume that there would be an electrostatic repulsion between them.
But as I pointed out above, there’s actually no experimental data that has shown this to be the case. Bear in mind that I’m not suggesting that two same charged particles that have relative motion will not repel one another but only that elementary charged particles that don’t have relative motion will not and, in fact, will appear to be attractively interactive. After all, this thesis is the whole point or is produced to establish that point. So, let’s consider two protons, A and B, that are overlapping in momentum space and that are separated by distance d.
In the rest frame of third particle C which has motion with respect to A and B will arise a pair of vector fields: (∇ X H)AC and (∇ X H)BC where AC and BC are subscripts to indicate the vector fields generated by the relative motion of A with respect to C and B with respect to C, respectively.
This pair of vector fields will emanate from A and B respectively but will be nonlocal to both A and B because neither A nor B can move with respect to themselves (as noted above). What I’m proposing here is that for the perpendicular component of the relative velocity of C with respect to a plane coincident with a straight line joining A and B that the two vector fields (∇ X H)AC and (∇ X H)BC will produce magnetic H loops (vector fields) that will interact in such a manner as to produce what appears to be an attractive interaction between A and B.
Those two vector fields will have the same direction of rotation on that plane and hence at the point of intersection the direction of the H flux of (∇ X H)AC will be anti-parallel to the direction of the H flux of (∇ X H)BC. Now, I’m suggesting that at from the point of intersection outward toward each particle is created a null motion gradient. Another axiom-like reference that we can point to are the laws of thermodynamics of which one part we can translate to a vernacular which is: <b>
“All matter and energy moves so as to obtain to the lowest energy state possible.”
</b> Seeing this universal axiom applied together with the axiom of the relative motion of quanta and with one of Maxwell’s equations the end result is that the two particles will begin to ‘fall’ and accelerate toward the intersection point of the two vector fields. Consider that there are very many other particles in the universe which will have relative motion with respect to A and B and that for any component of velocity that each and every other particle may have that is perpendicular to a plane coincident with the line A-B that emerging from the locations of A and B will be generated such vector fields that will also produce what would appear to be an interaction between A and B.
The particles appear to be accelerating toward each other but, in fact, are accelerating in the null gradient field towards the point of intersection of the vector fields. Every one of those vector fields will be nonlocal to the particles A and B and nonlocal to each other so that the total force calculated will be related to the sum of the individual forces produced in each frame and each individual force will be related to the magnitude of the component of the relative motion (velocity) of each and every other particle in the universe that is normal to a plane containing A and B because it is by that velocity that is determined the magnitude of ∂E/∂t in each and every case.
Now for the case of two oppositely charged particles, A and B, that are overlapping in the same momentum space then those two vector fields will have the opposite direction of rotation on that plane and hence at the point of intersection the direction of the H flux of (∇ X H)AC will be parallel to the direction of the H flux of (∇ X H)BC. In this case you have just the opposite of a null point but instead you have a point where the flux density is high and as such is representative of a hill, energy-wise, so that the particles appear to repel one another but, in fact, they are both simultaneously moving to a lower energy state by moving away from the ‘hill’. Quod Erat Demonstrandum.
But, in case you have trouble visualizing the model you can also consider that any two same charged particles that are at rest with respect to one another (overlapping in momentum space) will appear to have parallel velocities with respect to any third particle in the universe that has motion with respect to them.
A charged particle that is in motion is a ‘quantum current element’. Two same charged particles that are overlapping in momentum space are equivalent to a pair of parallel current elements. Laboratory experiments with parallel current carrying wires find an attractive interaction between the wires. Now we know that the force between parallel current carrying conductors is given by:
F=2K*(I1*I2*L)/R
where I1,I2= Current in amps = q/t and L = length of parallel conductors in meters (or v*t for particles), K= 10e-7 nt/amp2 R= distance between the conductors in meters F= newtons If the currents are antiparallel (moving in exact opposite directions) to one another then the force is repulsive. And we know that there is no force between them (other than gravity) when they are not carrying a current so that the implication is that the relative motion of the charges is related to the force between them.
This follows from the idea is that a charge in motion is the simplest definition of a current and that a charged particle in motion is really a microcurrent element. Laboratory experiments with anti-parallel currents (pointing in exact opposite directions) in parallel wires demonstrate a repulsion between the two wires.
Two oppositely charged particles overlapping in the same momentum space will have parallel trajectories but will be anti-parallel current elements. Their flux density vector will point in the same direction at the point of intersection and they will appear to repulsively interact. But the interesting thing here is that as soon as they depart from the same momentum space and have relative motion then they have anti-parallel velocities but are parallel current elements.
So, the result is that they appear to be attractively interactive and will fall towards the same null point. Since that acceleration toward the same null point is mediated by the nonlocal vector fields then they soon come to a point where they are overlapping in the same momentum space and that results in what once again appears to be a repulsive interaction.
Thus a proton and an electron do not bind together because they are in a continuous doh-se-doh dance where they are alternately falling towards the same null point and then falling away from the same high energy hill.
Contrary to popular stellar dynamics theories that posit PP (proton-proton) interactions as the main core energy source for our sun and many other stars, two protons will not ‘stick together’ unless there is a third component to their relationship, something that will continue to keep them overlapping in the same momentum space. That third component is the neutron.
The neutron is a source of a monolithic gravitational ‘field’ that is a time gradient field. A time gradient field is a null motion gradient field and particles in the near region, from the viewpoint of all non-near region particles, will appear to begin to overlap in the same momentum space.
Thus, a neutron, because it produces this null motion gradient field produces the necessary conditions to keep the protons bound closely to it. If two nearby particles of the same charge are in the same rest frame (overlapping in momentum space) and if they both entered that momentum space at the same time then the maximum time that will pass before they can interact is Tmax=Dp/2c but if they did not come into the same momentum space at the same instant then Tmax=(Dp-c(t2-t1))/2c where Dp is the inter-particle distance, t1 is the time that the first particle enters a given momentum space and t2 is time that the second particle enters that same momentum space and c is the speed of light.
If the two particles obtain to a common momentum space at the same instant so that t2=t1 then Tmax=Dp/2c. If c(t2-t1)=Dp then Tmax=0 and the particles will immediately begin to appear to interact. For example, two particles that obtain to a common momentum space at the same instant in time that are on the order of 10 nuclear diameters apart (5e-14 meters) will begin to interact in a maximum time of 8.337e-23 seconds.
This force, which if between nuclei, will appear to be evidence of a strongly attractively interactive force, is a short time scale force, which means that particles that could interact will have to be on the order of a mean free path distance apart from one another and that Tmax has to be on the order of the mean free path flight time. Particles for which Dp> the mean free path will likely be perturbed before the reaction can begin.
So, this force, that is normally interpreted as the nuclear strong force, is not so much a short range force but rather a short time scale availability force and one can see that it is entirely electromagnetic in character. Also, this force is the sum of the forces generated by the number of particles that have motion with respect to A and B so it is a very strong force as well as being a short time scale availability force. In fact, we can see that it really isn’t a ‘force’ at all in the traditional sense because of the nonlocality with respect to the vector fields that emerge as a function of the relative motion of a great number of distant particles with respect to A and B. I used the terms ‘local’ and ‘nonlocal’ in a manner that may be a little nonstandard so please let me explain how I mean them. Definition: nonlocal; adjective, A good definition here is a quote from Nick Herbert’s, Quantum Reality, p. 214, Anchor paperback:
“A nonlocal interaction is, in short, unmediated, unmitigated, and immediate.” Nonlocal interactions do not diminish with distance, “They are as potent at a million miles as at a millimeter.” Nonlocal interactions are not delayed in time. “Nonlocal influences act instantaneously.” Nonlocal interactions are unmediated. “...no amount of interposed matter can shield this interaction.”
He tells us nonlocal interactions are not limited to light speed. Consider two particles A and B that suddenly have relative motion between them. As stated earlier a vector field will emanate from B’s location due to A’s relative motion. Now it doesn’t matter how far away B is from A when they first achieve relative motion. They can be light years apart but as soon as they begin to have relative motion A causes a field to emanate from B’s location and B causes a field to emanate from A’s location. The field emanating from A’s location is non-locally generated per Herbert’s description but it also happens to be an unobservable with respect to A’s vantage point or rest frame simply because A cannot move with respect to itself and hence vary its electric field with respect to itself. So, in this sense it is also not present in A’s frame and hence in this context is also not local to A. In the same context it is local to B because it is in B’s rest frame even though it will take an amount of time that is equal to the distance between A and B divided by the speed of light for it to physically be present at B’s location. <b>
Definition: Overlapping in momentum space or occupying common momentum space -> Two particles that have a common de Broglie wavelength [calculated from a center of momentum frame] that is equal to or greater than the inter-particle distance can be said to be overlapping in momentum space or occupying a common momentum space. This is just a direct manner that one may use to quantify what it means for two particles to be nearly ‘at rest’ with respect to one another, or at least, in the same 'rest frame' without requiring that there be no motion at all. Don't mistake this for saying that they are 'at rest' but not 'at rest' ...because that isn't the intention but only to show that they can be overlapping in the same momentum space and still have some limited motion and with that limited motion will exhibit behavior that is contrary to the expectations of Coulomb's Law.
</b> My goal was to show that using just Maxwell’s equations and the principle that all motion is relative that one can show that elementary charged particles that are overlapping in momentum space will, in fact, act opposite to the expectations of Coulomb’s Law. This means that if two like charged particles are overlapping in momentum space then they’ll appear to be strongly attractively interactive and if two unlike charged particles are overlapping in momentum space then they will be appear to be repulsively interactive.
DHamilton
Last edited by a moderator:
He assured me it was indeed his own.
