Harry, I see your objection and I certainly would agree that two electrons moving in parallel to each other would not see any relative motion. The question that we need to address is how does a randomly moving observer make a determination that a magnetic field would influence the forces appearing between the electrons? For the stationary electrons there is no magnetic field but instead coulomb repulsion.
If we now assume that we occupy a new frame that is moving relative to the two electrons then what should we measure? First, the movement of the first electron should result in the generation of a magnetic field along with the electric field that is normally expected. This magnetic field will have a component that appears in the location of the second electron from our point of view. I assume that we are in agreement about this issue. Also, we observe that the second electron is moving through the magnetic field component that is a result of the motion of the first electron. I can think of no reason that we would not be able to calculate the force experienced by the second electron due to the field. This is how I approached the problem. One of the expectations for this line of reasoning is that there should be an infinite number of values for the force encountered by the second electron depending upon the relative movement of the observer. When I plugged in the force generated by this process when the observer is moving at the speed of light, I obtained a magnetic force that is exactly equal to the coulomb force but opposite in direction. This seemed to be quite a coincidence. A bit of reflection suggested that this calculation might well be an indication that electrons moving at approximately the speed of light relative to an observer are indeed frozen in position due to infinite time dilation and not repelled apart. Using opposite charges also yields the same result. I suppose that I tend to think of particles moving within an accelerator at nearly the speed of light as being similar to the case I am describing. They should experience time dilation due to the movement and should tend to remain grouped together instead of springing apart as you might expect from like charges. Perhaps this line of reasoning is interesting to further pursue. Dave -----Original Message----- From: H Veeder <hveeder...@gmail.com> To: vortex-l <vortex-l@eskimo.com> Sent: Tue, Feb 18, 2014 5:51 pm Subject: Re: [Vo]:Velocity dependent model of Coulomb's law Dave, John is saying is that the Biot Savart law for a point charge only makes sense if the velocity refers to the relative motion between the point charge and another charge. Since there is no relative motion between the charges in your example there should be no magnetic force. However, I have been looking at a few presentations of the law and they all make it appear as if the velocity can be taken relative to an independent reference frame. If these presentations are logically correct than it should be possible for an observer to increase or decrease the magnetic force between point charges by simply choosing to move relative the charges at speeds much less than c. Since this does not happen, these presentations of the Biot Savart are misleading. Therefore, it also seems to me that the Biot Savart law cannot provide a logically consistent explanation of the phenomena of relativistic electron bean confinement described by Jones. Harry On Mon, Feb 17, 2014 at 8:58 AM, David Roberson <dlrober...@aol.com> wrote: You are describing the case of zero electron motion when you use the observation frame that is synchronized to the electron motion. That is just one of an infinite series of view points. In that frame only the coulomb effect is seen. Time dilation is determined by what an observer believes is happening to objects that he measures and in this case it is the moving pair of electrons. In that observers world both are moving at a velocity through his instrumentation so he measures the field of one of them first at the location of the second one. The effect of that field then can be calculated as it modifies the movement of the other electron. This is similar to us looking at two electrons that are in motion within an accelerator. Dave -----Original Message----- From: John Berry <berry.joh...@gmail.com> To: vortex-l <vortex-l@eskimo.com> Sent: Mon, Feb 17, 2014 3:13 am Subject: Re: [Vo]:Velocity dependent model of Coulomb's law David, if the electrons do not see that in their world view, then the second one is hardly exposed to something that does not exist for it. Every electrically charged object has in other reference frames various magnetic fields, the axis and direction of the magnetic field is decided by the relative motion of the observer. Since radiation of various forms exists moving in every possible direction towards every charged object, that we can propose that every charged object has multiple magnetic fields with every possible magnitude, direction and axis in different reference frames that are being regularly observed in those frames. Of course none of this is true if SR is incorrect, and if the motion in question is relative to an aether providing an unknown frame of reference... On Mon, Feb 17, 2014 at 8:52 PM, David Roberson <dlrober...@aol.com> wrote: We observe two moving electrons in my calculation. The first one generates a magnetic field that the second one is exposed to. The electrons do not see this effect in their world view. This is equivalent to what we might see if we look at two parallel beams of charged particles. Speed them up to nearly the speed of light and my calculation is that they do not attract or repel each other. Dave -----Original Message----- From: H Veeder <hveeder...@gmail.com> To: vortex-l <vortex-l@eskimo.com> Sent: Sun, Feb 16, 2014 11:41 pm Subject: Re: [Vo]:Velocity dependent model of Coulomb's law What is the source of the magnetism? Harry On Sun, Feb 16, 2014 at 6:24 PM, David Roberson <dlrober...@aol.com> wrote: Sorry, I realize that my wording was flawed. I mean that the two particles are moving in parallel at the same velocity. Dave -----Original Message----- From: H Veeder <hveeder...@gmail.com> To: vortex-l <vortex-l@eskimo.com> Sent: Sun, Feb 16, 2014 3:20 pm Subject: Re: [Vo]:Velocity dependent model of Coulomb's law On Sat, Feb 15, 2014 at 9:44 AM, David Roberson <dlrober...@aol.com> wrote: Once I made a calculation of the attraction between two charged particles that are moving together at a constant velocity relative to my frame of reference. I was pleasantly surprised to find that as the velocity of the two charges approached the speed of light, a perfect balance between the electric force and the magnetic force was achieved. This implied that there would be precisely zero electromagnetic force between the two and hence no acceleration either together or apart at the speed of light. This matches the special theory of relativity since at light speed the time dilation reaches infinity for the objects being viewed. Since their time was slowed down to zero, they should not be seen as accelerating towards or away from each other. Dave Dave, what do you mean by "moving together"? Moving on parallel paths at constant velocity or moving off in different directions at constant velocity? Harry
