Bob_for_short

I always say that charges are "long-handed". One can consider them as overlapping. Point-likeness of a charge means a simple dependence of the force from distance. But the force is a long-range one. Charges are quite different from neutral atoms that need close contact to interact. Charges are long-handed and sticky.

In order to explain it to you, I have to know what you understand, what does not cause questions to you. A magnetic field is a quantitative notion. It stands in the charge motion equations and determines the force on a moving charge. It also stands in the magnetic dipole motion equations and determines the external magnetic force. Magnetic fields are created with magnets and currents. You may safely understand it as an interaction of moving but rather neurtalized charges so the Coulomb interaction is not the main part of the charge interaction.

I like the organization in http://www.physicsforums.com/.

This derivation determines the radial part of the total acceleration. The tangent part is determined with a tangent part of an external force.

DH answer is absolutely right. Acceleration is a vector and may have not only a radial but also a tangent component even with constant r. Its absolute value may be different from v^2/r.

Then we can use a dimensional analysis. Time is about r/v and velocity is v so the acceleration is v/t = v^2/r.

What A. Einstein obtained was ∆E = ∆m c^2, i.e., change in energy leads to change in mass of a body. c-squared is here because it was derived for light emission/absorption that carry some energy-momentum expressed with help of c. The true meaning of the formula E = m c^2 was established after discovery of antiparticles. Then the total mass of a particle-antiparticle system can be transformed into the energy of photons and vice versa. If you know, kinetic energy is also expressed as a product mv^2/2 so it has the same dimension - joules, ergs, or electron-volts, depending on the unit system chosen.

If a photon travels directly towards your black hole, it cannot miss it.

H. Poincaré also arrived at this relationship and A. Einstein mentions it. See http://en.wikipedia.org/wiki/Henri_Poincar%C3%A9 and http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence "Although the merely formal considerations, which we will need for the proof, are already mostly contained in a work by H. Poincaré (1900), for the sake of clarity I will not rely on that work."

It is not possible to obtain a "deterministic evolution" of the wave function like "collapse" into one specific state. A wave function describes the probability amplitude of different outcomes, and this is very good! This is what we need. What to do with a theory capable of describing only one of possible outcomes?

There is no empty space. There are objects with different coordinates whose motion we observe. It is useless and wrong to speak of some space coordinates without a body at it, in my opinion. Also, gravity is apparently an always classical thing, like an antenna of a powerful radio transmitter. No quantum effects in such conditions are observed and needed, actually. What we need is a better physical theory of classical gravity rather than quantization of GR.

All electrodynamics (without gravity) lives well in the flat Minkowski space-time.

You can safely think of gravity in the Newtonian sense because the GR effects are very weak in the Solar system.

If we speak of a transparent medium, glass, for example, two photons (waves) of different frequencies ω1 and ω2 may propagate with different velocities due to n(ω) < 1. The light velocity in vacuum c is the maximum possible for a wave. In a tarnsparent medium with a variable n(r,ω) the wave may accelerate and decelerate - its wavelength λ(r,ω) may vary with r. This is well known in the optical waveguides.

Yes, it is, at least in CED. As you porobably know, the radiation is a part of the total electromagnetic field created by a charge. This part is relatively small at short distances (1/R < 1/R^2, R < 1) but becomes the only carrying away the field energy-momentum at remote distances (1/R >> 1/R^2, R >> 1). Concerning the radiative friction term in the particle equation, the only reasonable expression in CED is that of jerk in the perturbation theory. Your reasoning about acceletarion is wrong. An additional acceleration term in the particle equation changes the particle mass. With a heavier mass the actual particle acceleration becomes smaller. But this approach fails: it does not fit experiments. See http://arxiv.org/abs/0811.4416.

A photon, as a wave, is created with its source (like with an antenna). It is a particular process in the source that determines the photon direction, in my opinion.

Correct. But even with c = infinity (classical mechanics) the past makes sense as a "memory" of series of "present" (instant) events. It's the clock running that distinguishes different moments of time and ranges them in a series.

I cannot see myself in the past because there is no delay or retardation between me and me. On the other hand, I can look in the mirror and see me in the past and at some distance, if you like.

Yes, to a great extent yes.

Yes, we can. With help of our memory, movies, and other means to store the recorded data.

Yes, we have to observe our clock and other objects. Such an observation occurs via collecting many photons. Everything we observe is compound, complex, non redusible to one "pixel" so we need reliable frame images of our "film". Each "frame" has some minimum exposition time. As to future, we may extrapolate/calculate future events if we have a good theory and good initial data.

I agree about the past and the present with the following reservation: Any instant of time t is in fact a short interval sufficient to collect a reasonable picture from bits of information observed as a flow (flux) of finite density. Like a photo - it needs some time interval to be of good quality. I disagree about future. We cannot find our future inside ourselves but only with waiting for it. Reducing the observer decreases the retardation to zero but nothing permits to attain the future, in my opinion.

When delta-potential is different from zero, it is f'' of f itself that compensate the potential term in the equation. So the plane wave cannot be a wave equation solution everywhere. "Inside" potential barrier the wave function is specific, zero, for example.

The original equation makes sense only if delta is a constant which is not the case. For any other function you have a contradiction: (T-1)delta = k. A constant cannot be variable so the original equation has the only solution: T=1 if k = 0.

When we write the field E(r,t) at a given t, is it an ensemble of instant or differently retarded values?