My vision of the universe makes a lot more sense if the earth is shaped like a dinner plate and it sits on the back of a giant tortoise. 
But only if the tortoise is both a wave and a particle, and if it moves at the same speed in all inertial reference frames.
I, um, what is it. Thingy. Starts with “m.”
Oh, yeah: empathize. I empathize with you.
RR
Yep, turtles all the way down! 
I understand the concepts, but I have to say that the article in question is pretty cryptic. Perhaps it could be redone with a straight and to the point answer. The Straight Dope, ya’ know 
Well, originally I’d just intended to make jokes about turtles, but now that I’ve actually gone back and read the article, I don’t exactly care for how certain things were explained – not that I could necessarily do any better. But, silly me, I’m going to try anyway – and I welcome corrections from those of you who understand this stuff better than me.
First, I don’t think it’s necessary to say electromagnetic fields are “one of those Fundamental Mysteries you have to accept.” The idea of “accepting Fundamental Mysteries” bugs me in principle – it seems a little to close to saying “Humans are too dumb to really understand physics so lets quit trying.” But electromagnetic fields are a concept invented by humans – if we can’t even understand that then we’re in bad shape indeed. An electromagnetic field is a vector function that gives the force per charge that a charged particle will experience due to electric forces. If you have a particle with a one Coulomb charge located at certain coordinates, then you can input those coordinates into the function for the electric field, multiply the value of the function at that point by 1 Coulomb, and your result will be the vector representing the electric force acting on the particle. It is not really necessary to consider electric fields to be “real” at all – if one knows the distribution of all other charges in the universe, as well as (this is important) how they were distributed at all previous times, then the electric force acting at any point in space is completely specified. However, the equations are simpler if you express them in terms of the electric field, and there are many times when you might know what the electric field is in a certain region (e.g. by measuring the forces exerted on charged particles in that region) without knowing exactly what charges produced this field.
I suppose some people might be tempted to go the other way . . . i.e. to say that electric fields are real and that charge is an invention – but this makes less since to me. For one thing, even if you know the electric field a particle produces when undergoing a certain motion, you still need to have some concept of charge to know what force that field exerts on other particles. Also, if you are given a charge distribution (and how it changes over time) you can tell what field the distribution produces, but if you only know the field produced in a region of space you can’t necessarily tell what charge distribution produced it. Besides, charges are convenient because every fundamental particle has a fixed charge independent of its motion.
I also think that explaining the wave-particle duality by making an analogy to relatives and their different relationships to different family members is somewhat misleading. The analogy is not a perfect one – your brother is always your brother, but the same observer may see light exhibit wave like properties at one moment and particle like properties at another. Something that seemed to be one thing at one time appears to turn into something totally different the instant one performs a certain measurement on it. It’s more like your brother spontaneously turning into your sister every time you ask him how old he is. (Actually, it’s more like your hermaphroditic sibling suddenly developing a gender whenever you ask him/her whether he/she is a boy or a girl. But I digress.) We shouldn’t pretend that this doesn’t seem weird – it IS weird! But the only reason we find such behavior so odd is that we live on a scale where these effects are not so easily observed. So our intuition has been conditioned to think that everything works they way things a few centimeters or meters long work, when in fact this is not the case. If humans were the size of electrons, I don’t think we’d find quantum mechanical phenomena like the wave/particle duality to be very weird at all.
Since the original question was about the nature of light, and not about electric fields in general, I’d like to add something about that:
I think that the statement “light is a wave” confuses people – really what this means is that the behavior of the electric and magnetic fields that correspond to the phenomenon we call light satisfy a differential equation called the wave equation. This doesn’t mean that light is a wave in the sense of “an oscillating disturbance travelling through a medium”, although such a disturbance can also be described by the wave equation. A light wave and a sound wave are two very different things, despite the fact that the mathematical descriptions of the two are similar.
In fact, I personally find it somewhat misleading to say “light is a distrubance of electromagnetic fields”, because to me that seems to suggest that there is some constant electric field and magnetic field in a region before the light wave passes through it, and then this constant field is restored once the light has left the region. But of course that need not be the case, as light can propagate through a region where there are initially no electromagnetic fields.
I’ve decided that my analogies about siblings changing gender may do more to confuse than to illuminate. Let me try to explain what I meant:
By this I meant that by observing a property of the thing, you change some of its properties.
By this I meant that observing a property of the thing forces that property to assume a definite value when it didn’t have one until the observation was made.
I was referencing the fact that measuring the position (for example) of a photon forces it to assume a definite position, thus making the light “particle-like.”
I think it might actually be misleading to talk about “observing” particles. Particles can’t be seen in the way we watch a pool ball roll across a table. We only know where they are when they collide with something in a way that can be picked up by an instrument.
It’s sort of like “observing” a car by running it into a wall. We know that it used to be a car…
Well, first of all your concept of the electromagnetic field is pretty outdated. Even classical (i.e. non-quantum) physics talks about the Faraday tensor, which is (given a coordinate system) a 4-by-4 antisymmetric matrix. Since space is (as far as we can tell) simply-connected (every loop can be shrunk to a point) and the “derivative” of the field vanishes, this is the “derivative” of a 4-vector, whose components (again, given a coordinate system) are the old scalar and vector potentials. I agree with you to the extent that the numbers are something we use to talk about the field, but the prevailing spirit of physical realism says that the field is really there.
Now the quantum effects: I swear so much of this looks philosophically nicer when you grok quantum field theory. Debating anything in quantum mechanics (other than maybe the measurement problem) is like discussing philosophy of mathematics in terms of Platonism and Formalism. The 4-vector potential in both classical and quantum field theory views obeys a differential equation: the Klein-Gordon equation, whose solutions “propagate”, thus are called “waves”. Basically it’s a spacetime version of the simple harmonic oscillator equation everyone learned about in high school physics. If it helps, think of it just as a 1-dimensional violin string vibrating. I’ll explicitly discuss such “stringons”, but pretty much any quantum field behaves the same way.
Firstly, geometric considerations say that there are only certain kinds of vibrations that can take place. For a violin string the two ends must be fixed, meaning that only sine waves whose wavelength evenly divides twice the length of the string will fit in (and, of course sums of such waves). The different allowed wavelengths are different “states” of a stringon. A stringon in state 1 vibrates as a whole, a stringon in state 2 vibrates in two halves with a node in the center, and so on. The amplitude, though, is arbitrary here. The quantization of this field theory (what some physicists call “second quantization”) says that in addition only multiples of a certain fundamental amplitude are allowed. The whole string vibrating at the fundamental amplitude is a single stringon in state 1. The whole string vibrating at three times the fundamental amplitude is three stringons in state 1. The string vibrating in two halves at twice the fundamental amplitude is two stringons in state 2. Sums of waveforms are just collections of “particles”, each in an appropriate state. That is: a particle in QFT is just a “fundamental” solution to the equations of the theory.
I think this is pretty much accepted. We don’t observe quantum phenomena in daily life because (a) quantum phenomena are scaled by Planck’s constant (b) Planck’s constant is so small that everything averages out on our scale (c) since the effects are so small, there was never any evolutionary pressure to be able to observe quantum phenomena. It doesn’t matter when you’re throwing the spear to hit the mammoth that the mammoth might quantum-tunnel to the other side of the mountain because the chances are so small that effectively it ain’t gonna happen.
Hey, zero is a perfectly good constant. A region with no fields initially does, indeed, have a constant electric field.
alterego, the column started off as straight to the point, but Ed thought it would be easier to understand in the back-and-forth format. Are there any particular points which you think need clarifying? Unfortunately, it’s not too constructive to just say “the article is cryptic”.
And Mathochist, a minor nitpick, but I wouldn’t say that Planck’s constant is small. Rather, I would say that the actions and angular momenta we typically encounter and measure are very large. And while I do agree with you that once you’ve got a handle on QFT things become easier to understand, I’m not entirely sure that you can give enough of a handle on it in a message board post to be helpful. A little learning can be a dangerous thing, and I think that at this level of detail, QFT is probably just confusing the issue.
Good point. I take back my objection to the phrase “disturbance of electromagnetic fields.”
In fact, thinking of the situation before the wave enters the region as “a constant field whose value is zero” instead of thinking of it as “no field” actually makes the whole thing seem a little clearer to me for some reason. (Maybe that says something about me, since “no field” and “zero field” mean exactly the same thing.)
Well, that’s kind of a matter of semantics, isn’t it? I mean, if we’re comparing to what we consider normal from our ordinary experience, then Planck’s constant is small. If we’re comparing to the fundamental constants of the universe, then the angular momenta we typically encounter are large. But the words “large” and “small” don’t really mean anything without some agreed upon standard of comparison.
OK, but at least at the introductory level I think colleges still teach the inverse sqaure law for the electric force first, and then define the electric field as the force per charge. But I guess real physicists prefer to start with potentials or the Faraday tensor or whatever and define fields based on that. I suppose this is another case of the tendency of physics professors to say “Here’s how we’ll explain it until you’re ready to understand how things are really done.” Which isn’t a teaching philosohpy I really care for, but I can’t really think of a better alternative.
If the field is considered a real thing, then I can accept that. I wouldn’t want to be the only one calling it an invention if everyone else calls it real. To me it just seems more natural to think of particles and their interactions as real, and everything else as sort of a man-made framework for describing these interactions. I can imagine that an alien species might develop a formulation for electrodynamics that doesn’t have an exact equivalent for what we call fields and potentials, but that still gives the same values for the forces that the particles exert on each other. But maybe I’m wrong about this, and fields and potentials really are the only way to go.
I guess it boils down to what it means for something to be “real.” Are all the mathematical objects (tensors, vector fields, etc.) used in physics equally real, or is there something specific about electromagnetic fields that lets you say they’re “really there”?
I bet if Dave Barry read this board, he’d declare Quantum-Tunneling Mammoths to be an excellent name for a rock band.
Sorry, just had to throw that in there.
Well, for one thing, you can store energy in electric and magnetic fields. In fact, if you have a collection of charges with some electric potential energy, the fields are where all the energy is stored. If you measured where the energy is (which, in princple, can be done gravitationally), you’ll find that it’s spread through space whereever the field is.
As for the other various vectors, tensors, etc., it depends. Some of them are definitely “real” (at least in the same sense that anything can be “real”), and some of them are definitely just abstractions. The stress-energy tensor, for instance, is real: Basically, it’s “stuff”. It’s just a more sophisticated way to describe energy densities (including mass). And on the other end, the h tensor field used to describe gravitational waves is not “real”. It’s an approximation, that roughly tells us how the actual curvature of space differs from flat space. But the true metric tensor there is the “real” tensor. There are also cases where it’s not clear what’s “real”, as with, for instance, the electric potential four-vector. There are many different possible electric potential four-vectors to generate any arrangement of electric and magnetic fields (this is referred to as “gauge freedom”). Is the potential “really” one particular one of those? Does it really “exist” at all? It’s certainly a useful mathematical tool, but is it anything more than that? One can reasonably argue either side, here.
The question of what is “real” or not in physics is much deeper than the OP, although, many of the issues were brought to the fore by quantum mechanics.
Einstein considered (well, I paraphrase) that there were two kinds of physical theories: real ones and unreal ones. Specifically, a physical theory was “realistic” (I’m defining it here. don’t think it means “reasonable”) if to every element of a theory there corresponded an “element of physical reality”. Now, this seems a bit circular, but we’re talking philosophy now, not physics. Quantum mechanics, in Einstein’s view could not be realistic. In fact, the EPR paper was supposed to be a reductio for quantum realism. That is, since things like wavefunctions being real contradicted “obvious” things like locality, they must not be the final story. Quantum mechanics is a very good calculating scheme, but it’s not “real”, and something will be along later that does describe “what’s really happening”.
Oh, and tim314, if you’re still thinking particle in terms of little chunk of something, you’re way behind the epistemic edge. Try “representation of SO(3,1)xSU(3)xSU(2)xU(1)”. Even I balked the first few times I head that a particle was a representation of a symmetry group.
But that’s not really true, right? John Bell proved that reality really is non-local. So the real world works in a way that’s not “realistic” by Einstein’s standards. And even if there is some underlying theory that explains quantum mechanics, non-locality must be a characteristic of such a theory. So does that mean quantum mechanics is “real”, at least as much as anything else?
No, that’s just the point. The collection of philosophical statements in the EPR paper (including “quantum mechanics is a realistic theory” and “Locality is true”) is inconsistent. This means that for the set of statements {p[sub]i[/sub]}, the statement p[sub]1[/sub] AND p[sup]2[/sub] AND … AND p[sub]n[/sub] is provably false. For this to be the case (assuming the law of the excluded middle is true), at least one of the p[sub]i[/sub] must be false. Since all the other statements in the set were taken by EPR to be obviously true (including locality), “quantum mechanics is realistic” must be false. This is what it means for an argument to be a reductio (ad absurduum).
Now, what they were really doing wasn’t taking “quantum mechanics is realistic” in there, but rather “quantum mechanics doesn’t overlie a hidden-variables theory”. Now, if there were an underlying hidden-variables theory, then quantum mechanics couldn’t be realistic (the wavefunction would be a useful tool, but not what’s “really there”). The real conclusion of the paper was that there was a hidden-variables theory underlying the calculational theory of quantum mechanics.
What Bell’s setup (actually performed, IIRC, by Aspect) showed is that there isn’t a hidden-variables theory underlying quantum mechanics, but the EPR argument was still valid, meaning another assumption had to be false. The consensus is that locality had to go.
I’d love to see this explained in more detail. I have read that particles are invariant under U(1), SU(2), and SU(3) transformations, and that these correspond to the electromagnetic force, the weak nuclear force, and the strong nuclear force, respectively. (I am simplifying here – the text I’m looking at has the U(1) invariance giving rise to a boson B, and the SU(2) invariance giving rise to bosons W1, W2, W3. The photon and the Z boson are then linear combinations of B and W3, whereas W+ and W- are combinations of W1 and W2.)
I didn’t know what SO(3,1) was, but I did a search and found that it’s the Lorentz group – i.e. the group generated by rotations and Lorentz boosts.
I’m not quite making the mental connection to see why a particle is a representation of the direct product of these groups. As I said, I’d love to see an explanation of this.
This is getting into deep waters, but: as I understand it, in every measurement we make, we see a particle. (Evidence of things like interference come from the statistics from measuring large numbers of particles.) If that’s the case, shouldn’t the particles be considered more “real” than the waves? They’re the only thing we can see.
Every particle-style measurement we make “sees” a particle, yes. Particles, for instance, are not polarized. Every time you put on a pair of sunglasses you “experiment” and filter out photons (minimal excitations (waveforms) of the photon field) that aren’t polarized in a particular direction. This is “seeing” waves.