On Perceived Positions and Field Directions

G.R.Dixon, 5/23/2006

Fig. 1 depicts a particle at time t=0. The particle has always moved along the negative x-axis with a constant speed of .95c. x_{r} is the retarded position with respect to the indicated observer.

Figure 1

Retarded Particle Position

Now

, (1)

, (2)

, (3)

, (4)

. (5)

Assuming the only particle-emitted photons that can reach the observer at time t=0 are those emitted when the particle is at point x_{r}, x_{r} is where the particle will be __observed__ (i.e. seen) to be at time t=0. But the inertial frame’s clocks (the origin clock in particular) will indicate that the particle is at the __origin__ at time t=0.

These facts lead to an interesting "disconnect." For let us suppose that the particle is __charged__, and that the observer measures the particle’s electric field at time t=0. Since the electric field of a constant-velocity point charge points away/toward the charge at any moment, the electric field vector, at the observer’s position, and at time t=0, will point away/toward the origin … a result consistent with what the origin clock indicates. But the observer __sees__ the particle to the left of the origin! Evidently the adage, "Don’t believe everything you see," applies.

What if the particle also has a large mass and the observer measures its gravitational field at time t=0? One obvious guess would be that the gravitational field would also point toward the origin … a result that would certainly be consistent with the idea that Maxwellian formulas also apply to a particle’s gravitational field (with an "orthogravic" or "gravitomagnetic" field factored in). Of course one should not rule out the possibility that, although the particle’s mass and charge exist at a common point, the gravitational field does __not__ point toward the particle when its velocity is constant.

If the Maxwellian analogies apply to mass-mass interactions, then due caution is suggested in modeling systems of gravitationally interacting bodies. For the gravitational interactions might not always agree with the positions observed through a telescope (for example). The star positions that we observe from an Earth-bound telescope are __retarded__ positions, and the gravitational field centers might be displaced from those positions at any moment in time.