I don’t pretend to understand any of this, but isn’t it all a question of modelling?
I mean, think of a wave of water in the ocean. It’s a wave, right? But it’s all full of particles of water – droplets, molecules, etc. So isn’t the question really just one of modelling – we have these models of reality, and we try to pretend reality fits the models, and we use which ever model gives us the most useful application. Si?
Like somebody said before, the quantum world behaves very much differently than the world we see every day. Pretty much all of quantum mechanics can be derived from Heisenberg’s Uncertainty Principle. This states, essentially, that you can not know the position and momentum of a particle simultaneously. Mathematically, this works out to:
dx * dp >= hbar, where dx is the uncertainty in position, dp is the uncertainty in momentum, and hbar is Planck’s constant divided by 2 * pi. This page will help you visually understand what this means.
The concept of light (or anything in the universe, be it photons, electrons, atoms, or Rush Limbaugh) being a wave or a particle are really only the extreme ends of either spectrum. If you know the position of a particle exactly, then it looks like a particle. (Think when a photon hits a photographic screen). If this is the case, you also know nothing about its momentum.
On the flip side, if you know the momentum of a particle exactly (which, for light means you know its frequency exactly), then it looks like a wave because you have absolutely no idea where the particle is. Its position is only defined by a probability distribution, which is uniform across all space (linear combination of sines & cosines for the nit-pickers).
In reality, most of the particles we encounter are somewhere in the middle of these two extremes. For example, an electron in a hydrogen atom. We have a rough idea where the particle is based on the probability distribution, and we also have a rough idea of the momentum, based on the same distribution. But we don’t know either exactly. There is always some error in theory and measurement. If anybody is really interested in the math behind this, I can try to post it up. It may not be too pretty on here though. This link gives more detailed info and a little bit of math to those so inclined.
Einstein, the person who invented the photon (the quantum, or particle, of light), went to his death still trying to understand the quantum theory of radiation that he conceived. His last words on the subject were written in December of 1951, when he said: ‘All these fifty yeas of brooding have brought me no nearer the answer to the question “What are light quanta?” Nowadays, every Tom, Dick, and Harry thinks he knows it, but he is mistaken.’*
Most physicists discount Einstein’s problem accepting quantum theory, but at the very least, his non-acceptance shows that even one of the greatest geniuses of all time had difficulty with the wave-particle duality.
I’m happy to talk about it, but I don’t really think it adds anything.
The Poynting vector is just the cross product of the E and H field vectors. P = E x H.
It gives the power density in Wm[sup]-2[/sup]. And its direction, obviously, is at right angles to the directions of the E and H field vectors.
All that says is that the power flows (i.e., the wave travels) in a direction at right angles to E and H. Which is what Chronos said.
Instantaneous E and H have to be mutually perpendicular to the direction of propagation. If someone can come up with an instance where they aren’t, then we need to toss out Maxwell’s equations (and probably special relativity as well).
Now, the plane wave thing.
If you’re emitting or observing a wave such that the direction of E and H don’t change over time (in some particular reference frame), what you have is a plane wave. It can be said to be polarised in a particular direction.
If the directions of E and H change over time (in some particular reference frame), you can call it circular or elliptical polarisation, or something else depending on exactly how the directions of E and H change with time.
And with regards to QED, personally, I think that while the concept of force mediation via exchange of virtual photons may be useful in terms of unifying field theories, it’s more trouble than it’s worth when explaining purely electromagnetic phenomena.
You said that each field is confined to a plane. I’m saying that both are present through all space.
user_hostile
No. The E and M orientations rotate in an ellipse, but they do so in tandem, so that at any particular time they are perpendicular to each other (and they aren’t confined to planes). Actually, elliptical polarization is the result of the superposition of two plane waves which are out of phase and have different polorizations.
Desmostylus
Nitpick: if the directions are constant in time and space, you have a plane wave.
That’s a bit naive. It’s like saying the a square wave is actually a superposition of an infinite number of waves having different frequncies and magnitudes. It isn’t actually one or the other. Both are just different representations of the same thing.
I don’t see why the and space should be necessary. Sure, a plane extends across all space. By definition, the wavefront of a plane wave extends across all space. It’s a theoretical construct.
But if you observe that something is parallel to a particular plane, it isn’t necessary to verify that condition holds across all space. And you can’t verify that the condition holds across all time, either. You’ve got something that looks to you like a plane wave, over the time and space that you observed it.
It looks like a duck, it quacks like a duck, and you can treat it like a duck, even if it isn’t the perfect duck described in a textbook.
I thought there was an experiment in which light exhibited both wave-like and particle-like behavior. You send light through a pair of slits as in interference experiments, and behind the slits you set-up a bunch of particle detectors that work via the photoelectric effect. The detectors will register the incoming light as particles, and the detected light will form an interference pattern. Also, you can reduce the intensity of the light so that there is only one photon in the device at a time (as monado mentioned).
The problem, as several others have mentioned, is that particles and waves are classical objects, and light cannot be understood well as a classical phenomenon. Quantum mechanics is necessary to explain it well. Nothing really is a classical phenomenon, but classical particle and wave physics are good approximation of a lot of things, like bowling balls and ocean waves. As other people have mentioned, the wave/particle duality problem is not just a problem of understanding light - electrons have shown the same behavior (interference patterns). Light is just the prototypical case. Quantum mechanics predicts this apparent duality, that any physical object (particle) has a wavelength associated with it. Really understanding what’s going on requires quantum mechanics, and the problem with that is that no one really understands quantum mechanics. But the math works out.
No, I thinks it’s accurate to say that an elliptical wave is actually a superposition of two plane waves. Sure, that’s not the only way to think about it. You can consider elliptical waves to be a separate category if you want. But that’s like saying that four chairs and a dining table aren’t really four chairs and a dining table, because some people call it a dining set, and since there’s disagreement as to what to call it, it isn’t “actually” either. Perhaps you thought that my statement implied that a superposition was the “right” way to think about it, and I suppose that there’s some validity to objecting to that. But I think that it’s important to note that an elliptical wave isn’t a completely separate entity, but rather a special case of planes waves.
Yes, a wavefront of a plane wave extends across all space (in two dimensions). That’s the point; it is doesn’t extend across all space, then it’s not a plane wave.
Sometimes the plane wave model is a good model to work with, even when you know that it isn’t a plane wave, and simply approximates one in the region that you are considering. However, there are situations where other approximations are more useful. For instance, I believe (although I could be mistaken) that another solution to Maxwell’s equations is a cylindrical wave:  
E=a(-yi+xj)/r     or    E=ak/r
H=ak/r                    H=a(yi-xj)/r
S=a(r hat)               S=a(r hat)
a=sin( 2pi(x-ct)/lambda )
If you’re in a region far enough away from the z axis that the singularity there doesn’t matter, but close enough that the curvature does, then this might be a useful model.
OK, The Ryan, I see what you mean now. I meant that the directions of the field vectors are confined to planes, not that their positions are. I’ve still got some egg on my face, though: While it’s true that the directions are confined to a plane, they’re also confined even further, such that they’re all parallel (or antiparallel).
As for the experiment you mention, knock knock: While you do have wavelike and particlelike behaviour showing up in the same experiment, it’s still not really “at the same time”. When the light is going through the slits, it’s behaving like a wave. Then, a little while later when it hits the detectors, it’s behaving like particles. But if you move the detectors up so they’re at the slits, then the interference pattern disappears, since by putting detectors there, you’re forcing it to act like a particle.
OK, The Ryan, I see what you mean now. I meant that the directions of the field vectors are confined to planes, not that their positions are. I’ve still got some egg on my face, though: While it’s true that the directions are confined to a plane, they’re also confined even further, such that they’re all parallel (or antiparallel).
As for the experiment you mention, knock knock: While you do have wavelike and particlelike behaviour showing up in the same experiment, it’s still not really “at the same time”. When the light is going through the slits, it’s behaving like a wave. Then, a little while later when it hits the detectors, it’s behaving like particles. But if you move the detectors up so they’re at the slits, then the interference pattern disappears, since by putting detectors there, you’re forcing it to act like a particle.
Yes, it’s perfectly accurate.
I’m saying that four chairs and a table are simultaneously both four chairs and a table and a dining set. Neither description is truer than the other. Both descriptions are of exactly the same thing.
Yes, I did think that your statement implied that. But you’re again getting back to an argument similar to my earlier analogy. You’re in effect saying that “a square wave isn’t a completely separate entity, but rather a special case of sine waves”. And in doing that, you’re missing the point. Neither description is truer than the other.
No real problem with that, except that it necessitates that time and space are infinite, and we strongly suspect that they aren’t. The real universe as we know it interferes.
Again, no real problem with this, as far as it goes.
If, when presented with something that looked like a plane wave, you were asked whether it actually was a plane wave, you would have to answer “No, because no such thing is possible in the universe as we know it. There is no infinite flat plate radiator. We do not believe that the universe is infinite.”
And you couldn’t defend the cylindrical wave either. You’d be stuck with an infinitely long cylindrical radiator instead of an infinite plate.
Spherical, on the other hand, you could probably get away with.
Now, I guess the real nitpick that you have is with the mere use by Chronos of the term “plane wave”.
And the answer to that is that there are two common usages of the term.
One refers to the theoretical plane wave, which does not exist, and the other refers to things that locally resemble plane waves. I had no difficulty in interpreting Chronos’s sentence as referring to the latter.
user hostile-
I don’t recall whether or not Feynman calls them “virtual photons” in his book but he certainly deals with what physicists have decided to call “virtual photons”. Virtual photons are the photons involved in the force. In a feynman diagram they are the photons that don’t escape. Virtual particles of any kind are the things that bounce around and are “unseen” in any sort of scattering reaction but are crutial in calculating the right answer. With your education and a small amount of extrapolation you can imagine how QED got “cartoonized” and found its way into the cartoon physics book.
One could argue, “Hey that doesn’t explain what virtual photons ARE” in a cocktail philosopher voice that sounds both deep and knowing but the most enlightening part of Feynmen’s QED book IMO is the introduction where he talks about “understanding”.
addressing subtext…
Perhaps some physicists try to propagate the notion that you could Understand all of physics if you could just do all the math or perhaps the people that can’t do the math believe this out of math inferiority complex. Either way this is a myth. At the heart you just have to accept certain things that lie at the foundation of the theory that gives the right answers. No matter how hard you try you can’t get away from the necessity of axioms that may or may not be palatable.
As for historical discrepancies in The Seven Percent Solution, it has also been noted that, when commenting on Freud’s habit of giving nicknames to his patients, Watson mentions “The Wolf Man”. This patient (so named because of a nightmare involving wolves perched in a tree outside his window) was one Freud first met after the period in which the novel is set.
I’ll nitpick myself for a change. I can’t believe I said that quote above. I’ll chide myself for treating Maxwell’s equations and special relativity as separate entities, when they are (sigh) aspects of the same thing.
The fundamental equations are (1) Coulomb’s Law:
F = k q[sub]1[/sub] q[sub]2[/sub] / r[sup]2[/sup]
where
k = 1 / (4 pi e),
and (2) the Lorentz transformations:
x’ = (x - µ t) / (1 - µ[sup]2[/sup] / c[sup]2[/sup])[sup]1/2[/sup],
y’ = y
z’ = z
t’ = (t - µ x / c[sup]2[/sup]) / (1 - µ[sup]2[/sup] / c[sup]2[/sup])[sup]1/2[/sup].
Maxwell’s equations and special relativity can be derived from just the above.
Ref: R. S. Elliott, Relativity and Electricity, IEEE Spectrum, pp 140-152, March 1966.
This whole discussion has neglected to mention the work of de Broglie. All the particles (read: matter) in the universe are all exhibiting wavelike behaivor all the time. It’s not just light that is crazy. Actually, some of you bring it up in around a bout way, but it should be mentioned directly, don’t ya think?
Looking up de Broglie using Google, I found a very nice what explains alot:
http://www.colorado.edu/physics/2000/quantumzone/debroglie.html
To continue that analogy, what if I said that all tables and chairs are in a particular store are wood. Someone then asked “Are the dining sets wood too?” I would probably say something like “Actually, a dining set is just a table and some chairs”. See, the question presumes that the rules that apply to tables and chairs don’t apply to dining sets, as if they were separate things. Similarly, when user_hostile asked whether elliptical polarizations has an oblique (nonright) angle between electrical and magnetic field directions, the question implied that elliptical polarization is somehow separate from plane waves. When thinking of elliptical as being a variation of plane, the question is easier to answer, so I think that that way of thinking about it is more useful in this situation. Sure, that’s not always the case. In fact, I can imagine a situation where it’s actually simpler to think of plane waves as being superpositions of elliptical waves. But in this case, “Elliptical waves are superpositions of plane waves, plane waves have right angles, and superposition doesn’t change the angle” is simpler then actually getting the equations and working it out explicitly.
I’m not clear on what you’re saying. Are you saying that saying that two things are soehow equivalent implies that one is truer?
Hmm, I wonder what for that interference would take. Would the plane wave have to have a wavelength such that the length of the universe is an integer multiple of it?
Would a plane wave be impossible? The curvature of spacetime would require some adjustments, but your objections don’t sound very convincing to me: the universe may be finite, but we don’t know that, and even if it isn’t. that wouldn’t necessarily be a problem. And to say that there is no plane radiator simply begs the questions; if there is a plane wave, then every plane perpendicluar to its propogation would act as a radiator. It certainly would be weird, however, to find an actual plane wave. It’s interesting to contemplate what the implications would be. Isomorphism would be compromised, for one.
Yeah, but I was even less sure about what the equations would look like 
.
It is a bit of nitpick, but then someone who realizes that a plane wave is a theoretical construct used to create a starting point for understanding light probably already knows about Maxwell’s equations, etc.
If the Universe is finite, then any standing wave (of any sort, not just light) must fit into the Universe, which may or may not mean integer resonance (ever deal with hyperspherical harmonic functions? OK, so neither have I, and I’d just as soon keep it that way ;)). I’m not sure if this would also apply to a “perfect” (perpetual, ubitquitous) plane wave as well.
And even if no perfect plane waves exist, by the way, it’s still perfectly possible to discuss perfect plane waves, in a theoretical context. My original discussion of plane waves can be perfectly applied to (theoretical) perfect plane waves, or approximately applied to approximate plane waves. Take your pick, depending on whether you’re an experimentalist or theorist.
One way of the universe being infinite is if its “edges” are identified (if you go out one “edge”, you come in another). In that case, any wave, standing or not, would have to have an integer number of wavelengths across the univese, since f(x)=F(x+d), d=diameter. That’s the only case of a finite universe that I’ve been able to conceptualize; everything else is a theoretical abstraction. If you think you could explain how a wave would work in another type of finite universe, I’m very interested.
Moe said:
Yes, it is stuff that really happens, but it is not like anything that happens on the macroscopic scale, i.e. the scale with we we are familiar. Billiard balls and water tanks happen on the macroscopic scale. We can directly experience the behavior. Thus the English language (and all* other languages) developed on the scale to deal with these macroscopic experiences, and we can relate the words that describe them to the events we can directly witness. But the quantum level involves things that really happen but do not behave like anything we can directly experience. And because we cannot directly experience it, the words do not have a visual analog that we can correlate to. A person blind from birth has no experience of blue. He can be told that color is a wavelength of light, that objects have different colors that make them appear differently. Color could be related to texture in a way. But when told “the sky is blue”, he has no way to understand what that means. Similarly, there is no physical analog we can experience that does the same thing that quantum electrodynamics describes. So you get confusing descriptions that sometimes fall back to analogs we can visualize, namely the particle and wave models. But the particle and wave models are not the whole story, any more than “fuzzy” is a good description of “blue”.
That relates to what dsdtzero is saying at the bottom of his post (is that a quote from Feynman?). The people who can do the math don’t have any better physical analog or understanding of it than the people who can’t do the math, they just can get the numbers to come out correctly, and accept the numbers.
crywalt said:
The explanation is clear. You understand what interference is, and what slits are, and how slits form interference. You’re just thrown by the result of the experiments. How can one electron form an intereference pattern? is not a problem with the explanation, but with the ramifications, because of the concept of the electron as a particle. It doesn’t make sense by not correlating to anything that you can directly experience - particles can’t interfere. The answer is the preposterous notion that electrons aren’t particles. And they aren’t waves.