Posted on 04/12/2010 8:40:43 PM PDT by Lorianne
From Wiki:
Speed of gravity
In the context of classical theories of gravitation, the speed of gravity refers to the ultimate speed at which a gravitational field propagates. This is the speed at which a change in the distribution of energy and momentum of matter results in subsequent alteration of the gravitational field which it produces.
The speed of gravity in general theory of relativity is equal to the speed of light in vacuum, c. Within the well-accepted theory of special relativity, the fundamental constant c is not all about light, it is a fundamental ultimate speed for any physical interaction in Nature. Formally, c is a conversion factor for changing the unit of time to the unit of space in a Lorentz transformation of physical laws. However, this makes it the only speed which does not depend either on the motion of observer or a source of light and/or gravity, and equals the speed of gravity and of light, and of any other massless particle.
Newtonian gravitation:
Isaac Newton’s formulation of a gravitational force law requires that each particle with mass respond instantaneously to every other particle with mass irrespective of the distance between them. In modern terms, Newtonian gravitation is described by the Poisson equation, according to which, when the mass distribution of a system changes, its gravitational field instantaneously adjusts. Therefore the theory assumes the speed of gravity to be infinite. This assumption was adequate to account for all phenomena with the observational accuracy of that time. It was not until the 19th century that an anomaly in astronomical observations which could not be reconciled with the Newtonian gravitational model of instantaneous action was noted: the French astronomer Leverier determined in 1847 that the elliptical orbit of Mercury precesses at a significantly different rate than is predicted by Newtonian theory.
http://en.wikipedia.org/wiki/Speed_of_gravity
You are missing the point of what spacetime is. Think of gravity as the shortest path through spacetime, in other words a field.
And yes the field propagates at the speed of light, but the effects inside the field are instantaneous.
I wrote earlier that if the Sun were to suddenly vanish, Earth wouldn't feel the effects for about 8 minutes. Do you disagree with that?
No, because it would take that long for the field to collapse. Both propagation and collapse are at the speed of light.
The more interesting question is if the precise location of the sun as you see it would agree with the Suns actual position?
After we hash this out, we can figure out the ladder in the garage paradox : )
Sorry, second reply.
If the Sun were to vanish that would produce the gravity wave that we are desperately looking for. We could answer a ton of questions if that happened : )
So in an existing gravitational field, the 'bond' between objects is instantaneous? Wouldn't this be apparent, one way or the other, in galaxies where stars orbit a hundred or more thousand light-years from the center? Or do galaxies behave as if they were a rigid solid object?
You are thinking about it wrong : ) Gravity is a force that curves space. That curved space is the field. Objects simply follow the shortest route. The 'tighter' the curvature the higher the gravity.
Nothing is a rigid solid object. Everything is Electromagnetic waves of nothing : )
Getting back to the subject of this thread for a moment. The issue of quasars and “time dilation” has to do with the fact that they are rapidly moving away from us via the expanding universe. They are extremely distant objects and so appear to be rushing away from us faster than anything that is closer.
However, this type of “movement” is not the same as if they were physically moving through space, but rather involves the expansion of the intervening space between them and us. The situation is often described as raisins in a loaf of bread baking in an oven. As the dough bakes, the bread expands and the raisins move apart.
What then is "frame dragging"? Doesn't it involve a time delay of some sort?
By "solid and rigid", I meant galaxies behaving like a spoked wagon wheel, where the rotating stars act as if they were rigidly connected to the center of the spinning galaxy. Ignore local effects for the sake of discussion.
Good post. I doubt the Big Bang stuff. Don’t have an alternative, but I doubt that.
parsy
Cool.
From Discover Magazine...
The Gravity Probe:
If Einstein was right, a spinning planet should twist the fabric of space-time. To see the effect, all we need is a perfect gyroscope. And a perfect telescope. And a perfect vacuum in a perfect chamber in an orbit 400 miles up. After 40 years of planning and half a billion dollars, the test is about to begin. ...”
[much more on the subject at the link]
http://discovermagazine.com/1997/mar/thegravityprobe1075
“You are missing the point of what spacetime is. Think of gravity as the shortest path through spacetime, in other words a field.
And yes the field propagates at the speed of light, but the effects inside the field are instantaneous.”
I think this clears up the confusion very nicely. *Changes* in the field propagate at c whereas the *effects* of the field are instantaneous within the field. The confusion is in confusing the propagation of the field with the effects of the field.
This is looking like a great thread! I’m in a maths tute right now so I’ll catch up with it later tonight.
Frame dragging is taking the whole gravity field along and warping spacetime as the object goes through space. Think of a rolling bowling ball on a trampoline stretching the fabric as it rolls. Notice though that the curvature around the bowling ball always stays the same.
I think that would depend on the speed at which the bowling ball is moving across the trampoline. Because the stretching of the fabric takes time. If the speed of the ball is great enough, a complete field around the ball (symmetrical depression) wouldn't have sufficient time to fully establish itself at every position along the path of the ball. You would have non-concentric "stretching waves" bunching up in front of the ball and loosening up behind. Sort of like sound waves from the horn of a fast moving car (i.e. Doppler Effect).
Then again, since the stretching waves are to be analogous of gravitational waves, the rate at which they propagate would be light speed and constant. And so perhaps a symmetrical depression (gravitational well) would fully establish itself along each point of the ball’s path?
Hmm, I don't know : ) This whole relativistic stuff is not always immediately intuitive. It probably depends on which frame of reference, keeping in mind that the speed of light is a constant, as you well know. Analogies aren't always perfect.
For some odd reason I had always thought that clocks on orbiting satellites ran slower than ours on earth (because they were traveling faster). But it turns out that our gravity well and the acceleration of clocks in that gravity well caused our clocks to run slower.
If light can be bent by gravity, how is it a constant?
Time DOES tick more slowly on satellites due to their high speeds, as compared to stationary clocks on the surface. But gravitational time dilation also occurs mostly strongly near the Earth's surface and would have the opposite effect. I'm pretty sure the high rate of speed wins out. GPS satellites takes these effects into account.
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From Wiki...
Note: I didn't actually read this yet, but will now. Hope it supports what I said! :)
Relativity:
Satellite clocks are slowed by their orbital speed but sped up by their distance out of the Earth's gravitational well.
A number of sources of error exist due to relativistic effects [67] that would render the system useless if uncorrected. Three relativistic effects are the time dilation, gravitational frequency shift, and eccentricity effects. For example, the relativistic time slowing due to the speed of the satellite of about 1 part in 1010, the gravitational time dilation that makes a satellite run about 5 parts in 1010 faster than an Earth based clock, and the Sagnac effect due to rotation relative to receivers on Earth. These topics are examined below, one at a time.
Special and general relativity:
According to the theory of relativity, due to their constant movement and height relative to the Earth-centered, non-rotating approximately inertial reference frame, the clocks on the satellites are affected by their speed. Special relativity predicts that the frequency of the atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by a factor of \frac{v^{2}}{2c^{2}}\approx 10 ^{-10}, or result in a delay of about 7 μs/day, where the orbital velocity is v = 4 km/s, and c = the speed of light. The time dilation effect has been measured and verified using the GPS system.
The effect of gravitational frequency shift on the GPS system due to general relativity is that a clock closer to a massive object will be slower than a clock farther away. Applied to the GPS system, the receivers are much closer to Earth than the satellites, causing the GPS clocks to be faster by a factor of 5×10^(-10), or about 45.9 μs/day. This gravitational frequency shift is also a noticeable effect.
When combining the time dilation and gravitational frequency shift, the discrepancy is about 38 microseconds per day; a difference of 4.465 parts in 1010.[68] Without correction, errors in position determination of roughly 10 km/day would accumulate. In addition, because GPS satellite orbits are not perfectly circular, their elliptical orbits cause the time dilation and gravitational frequency shift effects to vary with time. This eccentricity effect causes the clock rate difference between a GPS satellite and a receiver to increase or decrease depending on the velocity orbital altitude of the satellite.
To account for the discrepancy, the frequency standard on board each satellite is given a rate offset prior to launch, making it run slightly slower than the desired frequency on Earth; specifically, at 10.22999999543 MHz instead of 10.23 MHz.[69] Since the atomic clocks on board the GPS satellites are precisely tuned, it makes the system a practical engineering application of the scientific theory of relativity in a real-world environment.[70] Placing atomic clocks on artificial satellites to test Einstein's general theory was proposed by Friedwardt Winterberg in 1955.[71]
http://en.wikipedia.org/wiki/Global_Positioning_System#Relativity
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