How can a wave have a continuously changing trajectory?

Will it have an initial trajectory? QM is not like that - you in general cant describe quantum systems that way. It will likely have a well defined momentum, but that has a different meaning than classically.

Unless observed it only has this thing called a state.

States sometimes when expanded in eigenfunctions of position are wave like, but are not a wave in the normal sense used in physics such as a water or EM wave. A single particle in a definite eigenstate of momentum is wave-like in eigenstaes of position.

Thanks
Bill

 

Of course not.

It is only ever observed to be in one place at a time.

What's going on when not observed is however anyone guess - the theory is silent about that.

Thanks
Bill

 

This is not a quantum question - its a classical EM question.

But basically changing electric fields create changing magnetic fields ad infinitum.

Quantum mechanically it consists of photons. Its purely a semantic issue if a photon is matter or not - for me the answer is no - matter has a rest mass - photons do not.

Thanks
Bill

 

There is really only one field - the EM field. A more exact statement is a changing EM field generates a changing EM field.

Again this isn't the forum for this - its purely classical. In fact its relativistic.

Thanks
Bil

 

There's a lot of confusion here. First, as was pointed out before, the electromagnetic-wave thing is entirely classical. It is utterly wrong to say a changing magnetic field is the cause for a electric field and vice versa. There's one electromagnetic field as one entity, and it's described by the 6 components of the field-strength (Faraday) tensor or equivalently by 3 electric and 3 magnetic field components ##\vec{E}## and ##\vec{B}##. Which components you call electric and which magnetic depends on the reference frame anyway, and thus this split in two kinds of fields is not a physical thing but just one of our description with respect to a chosen reference frame. The electromagnetic field is given as the retarded solution of the given evolution of charge and current density. This is an approximation, because it doesn't consider the back reaction of the radiation field to the medium ("radiation damping"), which is a not completely solved problem within classical electromagnetism (at least not for point charges, which are anyway not fitting into a classical field theory).

Another thing is the "photon picture". As a result of more than 100 years of bad didactics, particularly in the popular science literature, many people think quantum theory tells us that the electromagnetic field consists of little massless bullits called photons and taking these bullets as behaving like classical lumps of matter named "particles". This is already wrong for massive particles (even in the nonrelativistic limit), but there at least a classical particle picture exists as a certain limit of single-particle wave mechanics (which works only nonrelativistically fully right), the socalled WKB approximation (named Wentzel, Kramers, Brioullin) of equivalently the stationary-phase/saddlepoint approximation of the path integral for the single-particle propagator.

For photons this is all obsolete. Photon's do not even have a position in the literal sense, let alone a sensible particle limit. A single photon is a one-photon Fock state, i.e., a particular kind of state of the quantized electromagnetic field. A classical field as seen from the point of view of quantum field theory or more specifically quantum electrodynamcis (which is the only consistent quantum theory of electromagnetic phenomena we have today), is a coherent state, which is a superposition of all n-photon Fock states, i.e., the photon number is not determined for such a state. So it's as far from a bullet-like particle picture as a single-photon Fock state either. There's no consistent classical-particle picture of the electromagnetic field!