Just trying to understand a bit more about gravity in Relativistic terms: a) If gravity is local curvature of space, then what is gravitational force? Is it correct to say that gravitational force is defined by the depth of the curvature? b) What is the speed of a body travelling the geodesic path of a curvature determined by? c) Is the speed of a body travelling a particular geodesic path the same as the speed of another body travelling the geodesic path of a different curvature? d) What is meant by "gravity well" ? Appreciate any reply. Thanks.
Keep in mind, I'm only trying to help. Be sure and let me know if I'm in the woods on your question or not.
<i>a) If gravity is local curvature of space, then what is gravitational force? Is it correct to say that gravitational force is defined by the depth of the curvature?</i> There is no gravitational force in general relativity. In GR all objects will follow freefall trajectories (geodesics) unless acted on by a force. Hold an apple outside a window. In the GR picture there is only one force on it - your hand preventing it from falling. Now let it go. It now has no forces on it (ignoring air resistance), so it follows a geodesic and falls to earth. <i>b) What is the speed of a body travelling the geodesic path of a curvature determined by?</i> It is determined by the position and motion of an observer watching it. As you watch the apple fall, it gets faster and faster relative to you standing at the window. From your point of view it accelerates towards the ground. However, that is because you are in a non-inertial reference frame (you are prevented from falling along a geodesic by the floor you're standing on). From the apple's point of view, it is you who is accelerating upwards. The apple experiences no forces. <i>c) Is the speed of a body travelling a particular geodesic path the same as the speed of another body travelling the geodesic path of a different curvature?</i> Yes and no. Yes - from each body's point of view, the body is travelling at zero velocity. But their <b>relative</b> velocities may be different. <i>d) What is meant by "gravity well" ?</i> It's a vague region near a mass, within which gravitational effects are "significant". Generally, the term is applied to stars and planets, which have enough mass to bend spacetime considerably.
Fluidity, thanks for the links. James, Is it correct to say a clock resting on top of a mountain and a clock resting at the bottom of the sea (the sea-bed) are both in a non-inertial refence frame? If so, why does the clock at the bottom of the sea ticks slower compared to the one on top of the mountain (I think I read this somewhere)?
<i>Is it correct to say a clock resting on top of a mountain and a clock resting at the bottom of the sea (the sea-bed) are both in a non-inertial refence frame?</i> In the GR picture, yes. <i>If so, why does the clock at the bottom of the sea ticks slower compared to the one on top of the mountain (I think I read this somewhere)?</i> Because they are in <b>different</b> non-inertial frames, according to GR. The clock at the bottom of the sea is lower down in the gravitational "well".
How does time-dilation occur between 2 different non-inertial frames? Is it similiar to time-dilation between 2 different observers (stationary-moving) as in Special Relativity?
Umm...I dunno. Good discussion This is part of the question that is killing me. Two airline pilots took two clocks, very accurate clocks, and flew around the world. The difference in time on the clocks, <i>when they got back</i>, was 59 milliseconds, which corresponds exactly to Einstein's formula for special relativity. It suggests to me, and I am all by my lonesome on this one, that time-dilation is a physical change that takes place in the very mass in transit, due to the relationship of motion through space. Here's why: (Again, I'm all alone here.) I go to point A, a coordinate on Earth, and time dilates 5 minutes on the way there, relative to point B. When I return to point B, my time-dilation is still 5 minutes relative to point B. All in all, time has dilated 10 minutes. (no, not this much in real life) If time-dilation were due to only the relative speed between point A and point B, it would seem logical and explainable if time contracted on the way back, resulting in a net zero time-dilation. This is not the case. According to special relativity, as I percieve it, time-dilation occurs in any direction relative to the position of the origin. If I lose 10 years going out to point B, I lose 10 years coming back. (Lose, meaning: time traveled faster in relation to the origin going both directions.) If time does not <b>contract</b> coming back home, it would seem only logical that time-dilation is relative to speed, not position. If time-dilation is not relative to position, then what is it relative to? Answer: Time-dilation is due to the relative speed of two objects. Paradox: It does not contract when those objects are coming toward one another. It still dilates. Here's a goofy analogy: I'm on a railroad train, I hear the whistle blow the note: F# You hear the whistle blow a clear low C. The whistle actually blows F#. Coming toward you, you hear a high E, but the whistle is actually blowing F#. This is not true of time dilation. You would hear the low C going both ways. This indicates a true paradox. The whistle changes pitch because of its relative speed to you. It dilates going away, and it contracts coming back, all the while blowing a clear F#. My Suggestion: Time-dilation occurs because of my relative speed to the railroad tracks. You hear what the railroad tracks hear in time-dilation. This way, the whistle always blows an F#, but you always hear a low C. Deep in the well of gravity, there's more railroad track around your clock. So, the answer is<b> Yes
Why would it "seem logical and explainable" if time contracted on the way back? On the contrary, it seems to me to be the very essence of illogic and unexplainability to suggest that it would. If you travelled from New York to L.A., a distance of some 3,000 miles, then travelled back, do you think that your total distance travelled would be 0 miles, just because you ended where you began? If not, then you presumably recognize that you have travelled, relative to the Earth, a certain distance; whether you end up in the original starting point or not. If you can see that, then why in the world would you think that "time" should "contract" on the way back? You were still going a positive speed, relative to your starting point, the whole time you were travelling. The only thing that has bearing on the issue of time-dilation is your speed relative to another object-- just as your "time" has only "dilated" relative to that object. Do you not see that the only thing that matters in this question is the fact that you travelled fast enough relative to another object (or place) to cause time-dilation relative to that object (or place)? Do you not see that when you left, you were going a certain speed relative to where you started from; and that, on the way back, you were going the same speed, relative to where you started from? The only way it would be "logical" for time to contract on your return trip is if your speed were the inverse of your speed on the outgoing leg of your trip. What is the inverse of the speed of light? To put it another way, if I go 1,000 mph in a given direction, can I undo having gone that speed by going back the way I came just as fast? Or, alternatively, can you tell me how to go "negative" 1,000 mph? Keep the word "relative" at the front of your mind-- you will find it invaluable in understanding "Relativity"-- however "paradoxical" that may sound...
The "answer" above is on the right track. The "paradox" above-- does not exist. If I am going near the speed of light relative to you, what effect does the direction I'm going have on that relative speed? Does it change the speed in some material way? What if I am not going either directly toward or directly away from you? What if I pick a course exactly between those two? Would time, in your estimation, still dilate, but half as much?
Isarmann The doppler effect is a change in the frequency of sound <b>percieved by an outside observer </b>due to the <b>relative speed </b>of the source of the sound to the observer. The speed of the sound does not change, only the frequency. In relationship to the observer, when the train is moving away, the frequency of sound dilates, causing a drop in pitch. When the train is coming toward the observer, the frequency of sound contracts. Again, this occurs due to the relative speed of two objects in relationship to one another. The distance the train has moved is irrelavent, and of course, a positive distance in both directions. It is the speed at which the train is moving that causes the doppler effect. Away, dilation, toward contraction. Do you not see the paradox between the doppler effect and time-dilation? They are completely different, but we use the same terms to describe them. Things that are the same: 1) The person in the train observes the same frequency at all times. 2) The frequency of sound (time) is viewed differently by an outsided observer. 3) Time (frequency) dilates when the train is moving away from the observer. Things that are different: 1) Time <b>dilates </b>when the train is coming toward us. 2) The frequency of sound <b>contracts</b> when the train is coming toward us.
Re: Isarmann The Doppler effect has nothing to do with special relativistic time dilation. They are independent phenomena. - Warren
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relcon.html#c1 Specifically, http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html#c2 I can also recommend some good books, if you'd like. Let me know if you have q's. - Warren
I would love to read some books that you've read or recommend, Warren. I, too, attend UCB with Astrophysics as my current major. Please Register or Log in to view the hidden image! Any books (textbooks or normal reading) would be a delight to add to my ever-growing collection. When I read that you attend(ed) UCB, I felt better knowing there's a chance I might have a chance at understanding the wealth of information you have with such breadth. Please, recommend away in any subject concerning (astro)Physics. - voltron (What year are you in? I am a 2nd year sophomore.)
The major problem I have is with the use of the rubber sheet analogy -- from this analogy one might infer that we 'sit on top of' a sheet of curved space -- no -- we are IN curved space. As master Yoda says "it surrounds us.... and binds us....". A better analogy might be 'objects' suspended in a jello-mold that was of varying density. There's also the question of the missing mass -- where did all that jello go?
Quick question or 2 for james or warren. This model of curved space isn't a static model is it? Also if you can't have simultanous events then you can't have an instant, is this correct. No static models.
Gundamwing: The rubber sheet picture is an <b>analogy</b>. That means that parts of the picture are useful in visualising the thing the picture is representing. Other parts are completely different. The thing with analogies is not to try to push them beyond their limits. kaduseus: <i>This model of curved space isn't a static model is it?</i> No. The curvature of spacetime varies as the energy and matter within it moves around. <i>Also if you can't have simultanous events then you can't have an instant, is this correct. No static models.</i> You can have simultaneous events. The point of relativity is that when two events are simultaneous from the point of view of one observer, they are not necessarily simultaneous to another observer.
I know James... just adding to the grief pool. Analogies are wonderful things.Please Register or Log in to view the hidden image!
