An overview of the description of E-M wave phenomena
Warning, this is super long.
jtbell said:
The photons in a magnetic or electric field that doesn't transport energy from one place to another are virtual photons, not real ones. Some people consider virtual photons to be simply a name for a mathematical construct that pops up in calculations in quantum electrodynamics. Others consider them to have some degree of "reality" but not as much as real photons.
And even real photons are pretty strange things. Don't think of them as little tiny balls flying around!
Ok, to clarify. Electromagnetic phenomena occur in different distance scales, namely the classical and the quantum. Magnetic fields do not exist in isolation from electric fields because there exist no magnetic monopoles (point sources of magnetism) observable in today's universe, as stated by Maxwell's equation div(
B)=0. Classically, a moving electric charge will produce a changing electric field, thereby inducing a magnetic field because a time-varying electric field creates a magnetic field: curl(
E)=-1/c d
B/dt , curl(
B)= 1/c d
E/dt +4Pi
J /c [
E=electric field,
B=magnetic field,
J=current density, c=speed of light, all this in vacuum with Gaussian units]. A charge moving at constant velocity will produce a constant
B field, because curl(
B) is directly proportional to the first derivative of
E (gradient); so if that first derivative is constant
B is constant. Now if the charge is accelerating, the d
E/dt will not be constant, and
B will change. This means that as the disturbance caused by an accelerated charge on the electric field travels through space in time, there is a corresponding disturbance in the magnetic field that will accompany it. This is what is called an *electromagnetic wave.*
What, you might ask, are these fields exactly, and therefore what is this wave I speak of? An electric field is simply a description of what will happen to a charged particle if I place it inside that field. A magnetic field similarly describes what force arises if I have a moving charge (remember magnetic fields come into play classically only with *changing* electric fields). Ok, fine. But if these fields are only descriptions, then how can an E-M wave be a physical entity when it is a propagating disturbance in a 'description' of something I measure?
The answer relies on a closer look at the phenomenology. We are only measuring interactions between particles. E-M fields are defined by what we measure to happen on charged particles: how other charges cause them to move through space in time. A disturbance in these fields, namely an E-M wave, will exist in that it will change the effect we measure on charged particles. But how exactly do fields and their disturbances affect said particles? Classically, the fields exert forces, or accelerations on the particles that can be measured via the time-dependence of their spatial location. This is why charge is defined by the action it effects as can be measured in space and time. But on small scales, there are other strange effects. Enter quantum theory.
When we deal with really tiny distance scales, quantum effects alter how physics behaves. I don't want to get into the heart of it, but quantum mechanics is based on the fact that on tiny scales (larger scales too, but not noticeably) particles of matter are also to some degree waves (matter waves!). de Broglie showed that each particle has an associated wavelength indicated by lambda=h/p [lambda=wavelength, h=Planck's constant, p=particle's momentum]. Associated with this property is Heisenberg's Uncertainty principle, which means that if you measure a particle, the product of the uncertainty in its position by that in its momentum must always be greater than a particular constant. In other words, you can never measure exactly both where it is and where (and how fast) it is traveling. Exactly equivalently but in a different form, the same result holds for the energy of the system and its location in time (more abstract, but will describe soon). You cannot measure its energy exactly without being uncertain about when the hell that energy state existed, and if you know exactly when a particle passed a certain place you can't be sure of how much energy it was carrying.
Because of particle/wave duality, this means that with a particle you have a choice of how to measure it: you can figure out where it is or where it is going, at what time it passed or how much energy it was carrying. If you measure location very precisely, you will be measuring the system as a single unit of information about location (a particle). If you measure momentum very precisely, you will be measuring how it travels but not exactly where it is (a wave). For an overly simplified analogy, think of a rope that is suspended in midair. If you give it one jerk, there will be a pulse traveling on the rope and you can say, "hey, my 'thing' is right there, I can see its location"; but can you determine the wavelength from one pulse? It's not so well-defined to say what its wavelength is because it's not measured to be undulating (and remember that wavelength is directly related to momentum via de Broglie's formula). Conversely, if you start moving the end of the rope up and down you'll get a regular wave pattern, but you can't ask where your 'thing' is anymore, it's all along the rope. You can say, "my 'thing' has a wavelength that looks to be lambda, say, but it's kind of everywhere, it's not located at anyone point."
Ok. That was a little much, but we understand conceptually what the uncertainty principle means between wave-like and particle-like behavior. But now we are talking about the E-M waves. How do we measure *them*? We measure them by their effect on charged particles, but this means that they are subject to the
Rules of Quantum Mechanics (quantum electrodynamics, to be precise)! E-M waves can be measured as either pointlike or wavelike depending on how we measure them. If we use atomic transitions to measure them, they are particles. If we use crystals and slits and things they appear to behave like waves. The electron is most familiar as a particle, but it also has an associated wave. *It is not one or the other.* Likewise with E-M waves, they are both particles and waves, depending on what scale of interactions you are looking at. Light is a particular example of an electromagnetic wave, and generally the energy determines how it will
act; a highly energetic gamma ray will act like a particle because it has such a high energy that it will allow a large uncertainty in the momentum and thus a small uncertainty in the position, whereas low-energy radio waves are always dealt with and measured as waves, or undulating E-M forces on antennae and such (actually undulations acting on the quantum fields of the constituent atoms, causing resonances). Einstein showed that Energy=hf=hc/lambda. Light 'particles' are called *photons*.
But when we get down to it, most of the matter we are concerned with are electrons, nuclei, and atoms, and we are interested in how light affects them. These are quantum mechanical systems involving tiny constituents. Electrons can certainly affect one another, because they are both electrically charged. If one accelerates, it will generate a changing E-M field and thus a photon/EM-wave, which will then move in space as time increases and then affect the other one by causing an acceleration. This is an *electromagnetic interaction,* one where one electron emitted light and the other one absorbed it (more or less, this is not very precise language). The acceleration in one caused an acceleration of another, or also the change in momentum of one caused the change of momentum in the other (Newton's 3rd law). But since energy is conserved here (can you find any energy loss in the process?), what happened to the energy after the electron emitted the E-M disturbance but before the other electron received it? The energy was carried by the E-M disturbance itself! This is one way (potential theory is another) to argue that the E-M field itself carries energy. Also, look at the conservation of momentum--the first accelerated electron has changed its momentum but the other one hasn't been affected yet. The photon/E-M wave carried that momentum! [Note, this is why lasers can actually suspend small spheres of quartz by pushing light on them against the force of gravity!] This is a most remarkable property of the E-M field and its disturbances.
Ok, now remember the Heisenberg Uncertainty Principle, that because a photon is a physical entity (it carries energy and momentum!) it is subject to uncertainty based on its momentum (or equivalently energy). If two electrons are close enough, the light will take very very little time to travel from one to the other (it *is* traveling at the speed of light, after all). This means that the time frame involved is tiny, and thus we can have a very large uncertainty of the energy. Actually, the conservation of energy can be violated for very small time windows: a 'virtual' photon can be emitted by one and received by the other and not even preserve energy--the photon energy plus the electron energies can be greater than the total initial energy--so long as it occurs for a really really short time. For a quaint analogy, this like a magician saying, "Ok, now don't blink... Did you notice anything? I just created a rabbit out of thin air and then made it disappear, but it was so fast that you couldn't see it." The argument is that energy will be transmitted from one system to another system by a virtual particle that for a very short time can have more energy than both systems combined, provided that the time is short enough for it not to be directly measurable (observable by
any other system). This means that it doesn't actually exist on its own, and thus it doesn't actually carry energy around with it as do 'real' particles.
Thus, photons on the most fundamental level are what causes charges to interact (exchange force). But there is a difference between real and virtual photons; 'real' photons can be seen (and philosophically thence they exist) *on their own,* whereas virtual photons do not exist by themselves. But here is where the philosophy of science becomes unclear, because then we have all these photons and what exactly are they but quantizations of some action? The modern viewpoint is what I said, that light is really made of particles that on large time scales can be measured as waves; the Coulomb force and Lorentz force are described by E-M fields, which are quantized to interact by virtual photons (not able to be seen individually), and E-M field disturbances are energy described by photons/E-M waves.
So, that is it. I am sure I missed some subtleties here and there, but that is the best way I can see to introduce a beginner to the idea of light. Some very good introductory texts from which I have borrowed some examples include
Electricity and Magnetism by Edward M. Purcell,
Optics by Eugene Hecht, and
Quantum Mechanics by David J. Griffiths.
. It's all about falsifiability, really.
