# How can a wave have a continuously changing trajectory?

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1. Dec 20, 2014

### JonathanCollins

Consider the release of a single photon or electron into a vacuum. The particle will have an initial trajectory. How is it possible for this event to give rise to a wave that has a continuously changing trajectory?

2. Dec 20, 2014

### Staff: Mentor

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

Last edited: Dec 20, 2014
3. Dec 20, 2014

### JonathanCollins

Does the state permit the particle to be in 2 locations simultaneously?

Thanks
Jonathan

4. Dec 20, 2014

### Staff: Mentor

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

5. Dec 20, 2014

### JonathanCollins

If we then consider an EM wave at its inception (where I assume it would have a specific trajectory as the result of the event that gave rise to it) how is it considered that the wave continues to oscillate? Is an EM wave considered to consist of matter?

Thanks
Jonathan

6. Dec 20, 2014

### Staff: Mentor

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

7. Dec 20, 2014

### Staff: Mentor

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 $v$.

8. Dec 22, 2014

### JonathanCollins

This seems to be something of a chicken and egg scenario. How is it understood that the change in an electric field occurs in order to then cause the change in magnetic fields? If we consider the EM wave or the electric field as consisting of zero mass particles then an individual particle will have a trajectory at a given instant. How can it be explained that such a particle can be influenced by another such particle to alter its trajectory?

Thanks
Jonathan

9. Dec 22, 2014

### Drakkith

Staff Emeritus
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).

10. Dec 22, 2014

### Staff: Mentor

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

11. Dec 22, 2014

### Drakkith

Staff Emeritus
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.

12. Dec 22, 2014

### Staff: Mentor

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.

13. Dec 22, 2014

### Staff: Mentor

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"

14. Dec 22, 2014

### vanhees71

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!