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

 

A wave cannot have a specific trajectory because it is spread out in space. Just like a wave in the surface of water, it can be more intense in some areas than others, but you cannot pick a single point and say the "the wave is here and only here at this moment" - and that means no trajectory, because a trajectory is nothing more than a series of such statements.

An EM wave does not consist of matter. It's the electrical and magnetic field that is waving back and forth. Write down an equation saying that the strength of the electric field at point ##x## and time ##t## is ##sin(x-vt)## where ##v## is a constant and you've described a (very simple) wave propagating in the ##+x## direction at speed ##v##.

 

It's not "one causes the other which then causes the first". It's that both occur at the same time. Neither one came before the other, a changing electric field was created at the same time as the changing magnetic field.

You can't consider an EM wave as consisting of zero mass particles. Photons are not particles in any sense that you've ever heard of. They are the quantized interaction of the wave with matter, which is something entirely different than what you see in classical physics and something that only quantum physics explains (specifically quantum electrodynamics).

 

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

 

No, the wave doesn't have a specific trajectory. If we consider a "perfect" emitter then the wave is emitted in all directions, regardless of how much energy the wave has. What I mean is that you can't say that the wave consists of only one photon and then attempt to trace the trajectory from emission to absorption. If you were to emit a great many of these single-photon EM waves, one at a time, and then record where the photon was absorbed you would find that the photon from each one is found equally in any direction on average.

You may also not be aware that the oscillation of an EM wave typically refers to the classical electric and magnetic field vectors, which vary in magnitude and direction over time. These vectors represent the strength of the fields and the direction of the force they exert on charged particles and, as far as I understand, have nothing to do with where the photon is located.

 

All waves (water waves, sound waves, any system whose behavior is described by the wave equation - google for "wave equation") have this chicken and egg problem. The answer to this chicken/egg question is also the same for all of them: there has to be some initial disturbance to start things going. In the case of an electromagnetic wave, the wave starts when a charged particle is accelerated; this causes a change in the electric field nearby, which causes a change in the magnetic field a bit further away, which causes a change in the electric field a bit further away... And we have a wave. If you can get hold of Purcell's E&M textbook you'll find a good explanation, less mathematically demanding than most, of how this happens.

It can't be explained, but all that proves is that you cannot think of an electrical field as consisting of zero mass particles. That's just not what it is, and the massless photons and other particles that appear in quantum field theories do not act anything like the classical particles that you're thinking of.

 

You should also be aware that Bhobba had it right back in #6 when he said that the questions you're asking about wave behavior are purely classical not quantum mechanical. Try googling for "Huygens wavelet"... a lot of this was worked out hundreds of years before QM. For a much more modern application of this thinking, try "phase-steered array radar"