Okay, so here's the though process that led me to ask this question. We know that the speed of light through a vacuum is constant. Yet if we have a ray of light that passes by earth, or any other large massive object, the light is bent. Gravity pulls on the light, apparently. But how can this be? For this to be so, that curved beam of light must be traveling slower on the end closer to the earth (the more curved portion) and faster on the end away from the earth (the less curved part). General relativity does say that the speed of light decreases near large masses, but is this really so? What if the "bending" of the light had nothing to do with a pulling force of gravity? What if it was simply due to time dilation from the presence of mass? The part of the ray closest to the mass experiences a greater time dilation effect than the portion of the ray further from the mass, and thus time "runs slower" for that part of the light curve. Maybe, the whole ray is still traveling at C, but time differs along the ray. Just some thoughts, have at it.
true Yes - from your point of view. From the light's point of view it's going in a straight line but space is bent. Actually gravity pulls on space Nope A photon is going at the speed of light time runs about as slow as it's possible to run. A photon doesn't experience time passing.
Yes, you're right, I worded that horribly. I didn't mean "experiences" as in from the photon's point of view, I meant what an outside observer sees it experiencing outside the zone of the time dilation. Yes, and the space pushes on us, regardless, gravity exerts of a force on light, be it through pulling on space, etc. This is not important right now. Could you elaborate? I'm trying to understand but according to my brain, a curved light beam has to travel slower on the bottom end and faster on the top end to arrive in one piece.
No one says a beam has to arrive in one piece. Photons on side of a wide beam of light don't know anything about photons on the other side. Light travelling through your camera lens doesn't all arrive at the same time
Okay, I'm not sure I'm understanding. If I were to shine a perfect circle ray of light near earth, it would bend with earth until it passed it, right? If I interrupted its path with a big, white poster (or something) and the light hit it, what shape would we see on the poster?
You have to distinguish between the local speed in a very small patch of spacetime where the effects of curvature are negligible, and the coordinate speed in some coordinate system covering a large region of curved spacetime. In the first case the equivalence principle says you can construct a "local inertial frame" in that patch and that light will always have a speed of c in that local frame, but in the second case your coordinate system cannot qualify as "inertial" so the coordinate speed of light may differ from c (even in special relativity where spacetime is flat, the coordinate speed of light may differ from c if you use a non-inertial frame).
You would probably "observe" the same shape of light....depending on the accuracy of your experimental measurement. But there would be a tiny,tiny difference between the bending of the light nearer earth than farther away.....because space is bent slightly more closer to earth...so the image is actually distorted slightly from its original shape. I think that's what Halls of Ivy meant. "Photons on (one) side of a wide beam of light don't know anything about photons on the other side." Actually, they do. Since all photons have energy there is a tiny gravitational effect between them, but it's dwarfed by the curvature of space from the object causing the beam of light to bend and so can be ignored for practical purposes. "What if it was simply due to time dilation from the presence of mass? The part of the ray closest to the mass experiences a greater time dilation effect than the portion of the ray further from the mass, and thus time "runs slower" for that part of the light curve." In a way you can say that...but the point is curvature of spacetime, gravitational potential, and time dilation all happen concurrently. Einstein's work clearly reflects that space and time are an integrated entity....(even Einstein did not initially realize that) so the change sometimes is due more to one than the other. It's more accurate to say that spacetime is curved,or warped, rather than referring to either space or time as a separate entity.
Probably the most powerful way of thinking of gravity is to think of it as curved space-time. And the philosophical consequence of this point of view is that it doesn't "really" pull on anything. Note that any talk about what "really" happens is philosophical, and that it is generally possible to explain any particular phenomenon in several different ways. So there isn't "really" any single answer to questions about what "really" happens, it's usually possible to provide several, different explanations of what "really" happens, all of which match up perfectly with experiment. As far as science goes, all of these different explanations are "equally good", so there isn't any way to choose among them. It takes a bit of math to fully appreciate how curved space-time leads to the appearance of a force, however. One can actually draw simple pictures that illustrate this, but it's difficult to communicate, as the exacting technical wording in terms of geodesic's appearing to accelerate away from each other tends to be unfamiliar, and every-day attempts to describe the phenomenon are a bit vague due to the imprecision of everyday language. One alternative is to look at the unified whole presented by General Relativity of gravity as curved-space time, and to break it up into pieces. One can think of one particular piece of the unified whole is a "force", and another piece of the whole as "gravitational time dilation", and yet another piece as "curved space". http://www.eftaylor.com/pub/chapter2.pdf has some information about how curvature in General Relativity really works for those that might be interested.
to the op: gravitational time dilation will indeed cause light to curve. in fact, when Dr Einstein first calculated the bending of light near the sun that is all he used. Unfortunately the result was only half of what was actually observed so he went back and included a factor for the stretching of space and that doubled the end result.
Why "through the center of the Earth"? The thought-experiment was just that the initially circular beam was shined "near" the Earth.
Yes, it is really so. The speed of light near a large mass is slower relative to the speed of light further away from the large mass according to the coordinate calculations of a distant observer. I understand what you are getting at here and I understand that you are not talking about the "point of view" of a photon. However, can you justify that light lower down moving slower than light higher up brings about curvature of the light path by itself? For example let us say we two parallel laser beams in a vacuum. One beam has a cube of glass in its path with its incident surface orthogonal to the beam. The beam passing through the glass slows down (due to the refractive index of glass) while the other beam continues at c. The two rays remain parallel to each other at all times. Different velocities do no automatically bring about curvature of the path. Now in high school physics they teach that a beam of light bends as it passes through a prism at an oblique angle to the incident surface, due to the part of the beam that hits the incident surface first slowing down, but personally I think that is a bad explanation. To me, the slowing down is a side effect rather than a cause of bending. One interesting aspect is that the path followed by a ray of light is the fastest possible route between the emitter and the receiver (sometimes called the principle of least action?) and this is might be a more productive avenue to explore?
Johann Georg von Soldner did some calculations in 1801 about light bending, were they very close to Einstein?
I dont know anything about that I can only quote wikipedia http://en.wikipedia.org/wiki/Johann_Georg_von_Soldner
It's fascinating that Soldner calculations came 100 years before Einstein, but he couldn't challenge any astronomer to get some pictures during a solar eclipse...
Newton himself considered light to consist of particles but at that time they could assign a figure to the mass of a photon. However, the downward acceleration of a small particle due to gravity is independent of its mass (Galileo), so anyone could work out how much the bending of light would be due to Newtonian considerations would be without any regard to whether the photon had mass or not. This, I assume is what Soldner did, simply work out the Newtonian downward acceleration of a particle moving at the speed of light and work out how much a light ray would bend as a result. There would have been no strong urge to test Soldner's calculations as at that time no one really thought there were any problems with Newtonian physics. When Einstein predicted that the bending of light ray would be twice what Newtonian physics (or Soldner) predicted at time when there there was still some uncertainty in people's minds as to whether Newtonian physics or Relativity was a better reflection of reality, then there would have a lot of interest. For some reason, vast amounts of research funds are still spent on testing the limits of Relativity predictions, presumably because people are waiting for the next theory to supercede relativity as relativity superseded Newtonian physics. I assume that because I find it hard to believe any serious scientists still think Newtonian physics is more accurate than relativity.