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User talk:KSorenson (view source)
Revision as of 05:27, November 13, 2009
, 05:27, November 13, 2009→Action at a distance (let's take a break from the black hole stuff)
So which is it? Can either of you enlighten me? Or fix the article? (By the way, you both write very well.) [[User:PatrickD|PatrickD]] 22:30, 12 November 2009 (EST)
So which is it? Can either of you enlighten me? Or fix the article? (By the way, you both write very well.) [[User:PatrickD|PatrickD]] 22:30, 12 November 2009 (EST)
===Oooh, fun===
"Action at a distance" is a great topic, because it gets to the heart of some of the central concepts of modern physics.
It's important to note that "action at a distance" isn't a technical term in physics; it's a qualitative term. So defining it in a way that's both clear to non-physicists and rigorously accurate might be tricky. The best definition I can come up with right now is, "Interaction between separated bodies with no evident mediator." That's probably too jargony, because both "interaction" and "mediator" are technical terms in physics, but that's a start.
Let's do a thought experiment. Imagine a totally empty universe, with no matter or energy in it at all. (Let's pretend there's no such thing as vacuum energy.) Furthermore, imagine that we're somehow in this universe, but in such a way that we don't interact gravitationally. How? I don't know how, it's just a thought experiment! Point is, we're there, we can observe things, but we don't interact gravitationally at all.
Now imagine that a particle appears, poof, right in the middle, stationary relative to us. This could never happen, obviously, but we're just imagining.
Now imagine that after some significant amount of time, another particle appears at a modest distance from the first particle. For purposes of imagination, let's say these particles or bowling balls or something. They could be stars or even galaxies, but the point is that they're large enough that quantum effects are negligible. Also, let's assume they're uncharged, and finally that when the second one magically appears, it's at a ''reasonable'' distance from the first one. Call it a hundred times the diameter.
Now, gravity exists in this imaginary universe we've constructed. So obviously these two bodies will be accelerated toward each other. But the question is … when? If we plop our second particle in at some time <math>t_0</math>, will they begin accelerating toward each other at that exact same instant? Or will it take some time for the first particle to "become aware," as it were, that there's now a second particle there?
The answer is more interesting than you might guess, if you're not a physicist. The answer is that particle ''two'' will start accelerating instantly, but particle ''one'' won't. Particle one will start accelerating toward particle two at some time <math>t_1</math>, where the time interval <math>t_1 - t_0</math> is equal to the distance between the centers of mass of the two particles divided by the speed of light in a vacuum.
To figure out why, start by remembering that particle one ''already'' existed in the universe when particle two appeared. Remember how we said that "some significant amount of time" would pass before particle two showed up? During that time, the geometry of our imaginary universe distorted in to a non-Minkowski metric. (Minkowski spacetime is to the universe as the Euclidean plane is to the surface of the Earth: an idealized, non-curved approximation. If you want to get technical, the spacetime around particle one would settle into a configuration described by the Schwarzchild metric.) When we wished particle two into existence, it appeared in a spacetime that was already curved. As a result, particle two's inertial path through spacetime was tilted in the direction of particle one from the very first instant, so it began accelerating (as observed from a non-accelerating reference frame).
But the geometry of spacetime does not react instantaneously. The curvature caused by particle two radiated outward from the point where particle two appeared at the speed of light. Until that curvature reached particle one, the geometry in the immediate vicinity of particle one would still be described by the Schwarzchild metric, so it wouldn't accelerate relative to our imaginary frame of reference.
When our (stationary) clock reaches time <math>t_1</math>, particle one begins accelerating toward particle two. Now everything looks like ordinary, Newtonian gravity. As long as our particles aren't too dense, of course. After some amount of time where particles one and two are accelerating toward each other relative to our reference frame … ''clack.'' The bowling balls come into contact with each other.
That's how action at a distance ''doesn't'' happen in real life. The two particles are ''interacting'' gravitationally, but there's a ''mediator'' of that interaction: spacetime itself. Particle two interacts with spacetime via the gravitational interaction, then spacetime interacts with particle one. There's a middleman, if you like.
Let's do another quick thought experiment. Say instead of two bowling balls, we have two electrons. In this experiment, we're going to pretend that gravity does not exist at all (which is not a bad approximation, since electrons have such minute energies). These electrons will accelerate away from each other because they're both negatively charged. Three hundred years ago, we said this acceleration was the result of the Coulomb force, an action-at-a-distance principle. A hundred years ago, we postulated that there was some intangible field surrounding all charged bodies, a field we couldn't directly observe. Pure action-at-a-distance gave way to a vector field theory of electromagnetism.
Today we think there is no electromagnetic field at all, that it was just a mathematical approximation of what's ''really'' going on, which is that charged particles interact through an exchange of photons. The vector field theory gave way to a quantum field theory.
It's important to note that both quantum field theories and metric field theories are ''local.'' What that means is that under either type of theory, objects interact ''only'' with what's directly adjacent to them. They don't "reach out" through space (or spacetime) to interact with distant things. Massive particles interact with spacetime ''where they are,'' then spacetime interacts with other massive particles. Charged particles interact with the quantized electromagnetic field ''where they are,'' and the field interacts with other charged particles.
And that's pretty much where physics stands today. All fundamental interactions are described by either a metric field theory or a quantum field theory. Action at a distance is, at least for the moment, nowhere to be found in theoretical physics.
Does that mean there's no such thing as action at a distance? Not necessarily. It just means that we haven't made any observations that ''can't'' be explained by either a quantum field theory or a metric field theory.
Now, to the second part: "action at a distance," if it exists, does not necessarily occur instantaneously. In fact, it was understood that changes in the electromagnetic field propagate at the speed of light long before the field was quantized and quantum electrodynamics emerged. So the questions of action-at-a-distance and "instantaneousity" (I'm so sorry) are really two separate questions.
Finally, quantum entanglement. Now, I am ''not'' a quantum physicist. My area of focus lies elsewhere. So I can't speak in as much depth about this as I can about gravitation. But I can say that it seems quantum entanglement is one of the most misunderstood aspects of physics.
It all has to do with spin conservation. If a neutral pion decays into an electron and a positron, then the two resulting particles will have opposite spin. The spins have to cancel out, you see, otherwise the universe will suddenly have slightly more up spin than down spin, and that's prohibited under spin conservation. Such a pair of particles is known as a ''singlet.''
But nothing is quite so simple in quantum mechanics. You see, in quantum mechanics it's not quite true to say that the electron has up spin and the positron has down spin, or vice versa. Rather, ''both'' the positron ''and'' the electron are in a state of spin superposition, until you measure one of them. Once you measure the spin of one particle, you know exactly what the spin of the other particle is without having to measure it.
One interpretation of quantum mechanics — called the Copenhagen interpretation — says that when a quantum system is measured, its wave function ''collapses'' into a measurable value. Before it was measured, the system was in a superposition of states, and the outcome of the measurement could only be predicted statistically, not deterministically. Under the Copenhagen interpretation, something ''physical'' happens when a quantum system is measured. An actual change in the system occurs. It's no longer in superposition; it's collapsed.
So imagine letting a neutral pion decay into a positron and an electron in a spin singlet. You capture both particles, and move them ''faaaaaar'' away from each other; say a light-year apart. Then you measure the spin of the electron. The quantum superposition of the electron collapses, ''and simultaneously,'' across the vastness of space, the quantum superposition of the positron also collapses without anything directly interacting with it.
Einstein disliked this possibility, disparagingly calling it "spooky action at a distance" and opining that quantum mechanics wasn't yet a complete theory. It's not hard to see why; singlets are ''weird.''
Part of the theoretical problem is that the Copenhagen interpretation doesn't precisely define just what "wave function collapse" means. It's all rather fuzzy, at least to me, but like I said, that's not my area of focus.
Right now, the question of whether the "spooky action at a distance" is instantaneous, or whether it propagates at some fantastic multiple of the speed of light. My guess? It's instantaneous, and just like the event horizon in the original Schwarzchild solution, it's just a coordinate singularity. But that's just a guess; I'm not an expert.
There's a legitimate question to be asked whether the ''phenomenon'' of quantum entanglement, as observed, constitutes action at a distance. It's got the "at a distance" part, to be sure, but the "action" part is debatable. That's why it's more common to see the whole issue referred to as "non-locality" instead of "action at a distance." Right now, the consensus is that non-local state superposition can't ever actually affect anything, since quantum systems in superposition can't interact with anything without collapsing. So the collapse of a one part of a non-local superposition system can't actually cause anything to occur where the other part of the system is. So "action without a distance" without the action simply becomes "non-locality."
Anyway, like I said. I'm not an expert in quantum mechanics.