What is the Speed of Gravity?
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I'm almost positive this statement is incorrect.
Relativistic force laws tend to be forced to contain correction factors that ensure that constant velocity motion is "predicted" and the direction of the force is adjusted accordingly - as long as a body is not accelerating, a purely attractive or repulsive force will be pointing at its current position, not its position 8 mins ago.
To see why this must be the case for a repulsive force, at least, imagine two charges riding on frictionless rails that keep them at a constant, finite distance. Suppose they're both moving with some constant velocity (to start, at least) in the same direction - now the place that the force from the other charge appears to be coming from is behind the charge, so if there was no correction factor, each charge would be getting an extra push forwards. This would lead to a runaway "bootstrap" acceleration, and the particles would accelerate to the speed of light. That's a pretty clear violation of the conservation laws, so...
With attractive forces like gravity, there's still a conservation problem, since the charges would slow down to zero speed eventually, but it's always more convincing to cite the runaway solution as a violation of conservation laws than the run-down one, because while the energy could possibly leak out of the charges into the fields, there's nowhere to pull infinite energy from, so it's pretty clear there's a problem if we'd need to.
And this is somewhat different from the runaway self-action solutions that we grudgingly "accept" in E+M, because those tend to involve some limit to infinitesimal size, whereas this is a completely finite situation that we could theoretically set up in the real world with a couple of charged beads or something like that.
Absolutely correct for E&M. This is because it's a vector field, and the velocity of the source is encoded in how the field moves.
For gravity, it goes one better -- this is a tensor field (hence the notion of gravitons having to be "spin-2" if they were described by a quantum theory), and the acceleration is encoded as well, so you need a non-constant acceleration to notice any difference from the position being instantaneously updated.
Well, that's mind blowing. Where could I go to learn more about this?
For E&M, the standard way to develop this is to explain magnetism as Lorentz-transformed static electrical attraction/repulsion. Take two wires, and run current through them. Transforming to a frame where the electrons are at rest, but the atoms (and hence protons) are moving, length contraction ends up with the density being different, meaning a net charge in this frame. You then get E&M united as tensor field F, but antisymmetric, meaning the spin-2 components are 0, leaving effectively two spin-1 (vector) components. This lets you do relativistic corrections for a propagating field, and the velocity of the original source gets turned into magnetic effects that act the same as if the source were moving at a constant velocity.
Extremely similar things happen with gravity, if you look at weak-field linearized versions of the Einstein field equations. The actual math ... well, it's rather ugly.
That means my bootstrap-runaway argument must be flawed in some way, because a scalar field can't encode any velocity information, and as a classical field equation, it would cause a 1/r^2 force law just like everything else, but aimed at the retarded position.
Suppose we have a scalar field.
For Galilean relativity, a sphere expanding at a given speed will remain so after a boost, but will have a net velocity. Densities will remain the same. A moving source shouldn't matter -- any material will itself will set the rest-frame, and must to have a non-infinite propagation velocity. Whereas, emitting particles, these will have the velocity of the source. Ah! if it's a complex wave equation, you can put a varying phase on everything encoding the velocity. But moving to a complex field is in some sense putting more degrees-of-freedom in.
For Einsteinian relativity, a sphere expanding at light speed remains a sphere in any reference frame, but the density along it changes. A moving source should have that same pattern, so it would seem that local differences (i.e. derivatives) could "point out" the velocity of the source. This behaves the same for particles being emitted. Is there a first-order Lorentz invariant scalar wave-equation, or only second-order, using the d'Alembertian? And that seems to introduce another degree-of-freedom as well.
I'm still really confused. How do pions behave? Is it reasonable to consider them as a fundamental scalar field when they're modeled as pairs of quarks? Particularly when they have excited states that are spin-1?
Te end result is that it appears to travel instantaneously since it ends up at the same place. But this only works for constant velocities - if the earth changes direction suddenly this "correction" will not be correct, since it will still "assume" the earth is still headed in the direction it was heading before.
(But no one will ever read this comment because the topic is 5 days old.)
So let's assume once can cause the sun to vanish instantly somehow. If that's the case, would it then be possible to setup a 'gravitational wave' communication system that travels faster than light?
Ie, I would put a whole bunch of stars together, and then have them disappear at certain intervals. My buddy who sits 100 light-minutes away would then detect the changes and decode the message. TADA: Faster-than-light communication.
I feel safe to say that's not possible.
As as example, assume there is a star directly perpendicular to our motion (and that the Earth moves in a straight line). Due to the vector addition of our motion and the light travel direction, it appears to us that the star is located slightly forward of perpendicular (typically by about 1/100 of a degree) Now assume the star were to disappear. During the light travel time the star would have time to move backwards as seen by us (due to our forward motion) so that at the moment it disappears, it appears to be located perpendicular to us.
In the context of gravity, this effect (it's called aberration) exactly cancels and the net effect is that the gravitational attraction is in a direction different from the actual location of the attractor such that it appears that gravity is instantaneous.
This only works for constant velocities, once you have accelerations it becomes more complicated. And it's not a relativistic effect at all, it's present for all waves with finite propagation speeds. You can do this experiment with boats making waves and get the same result.
Edit: And your charge example is not so good. For Galilean invariant theories it's only relative motions that matter. There is no effect if the two are moving with the same velocity. (Plus, once there are relative motions between the charges, there will be induced magnetic fields which affect the dynamics.)
E&M is Lorentz invariant though, not Galilean.
This causes an issue with your starlight aberration example as well. Velocities do not add linearly (though that is a reasonable approximation for low velocities).
Considering gravity does not have an inverse (a gravitational repulsion) that I am aware of, I'm not certain we can extend your thought experiment to gravity.
Clifford M. Will
"The Confrontation between General Relativity and Experiment" (2001)
http://relativity.livingreviews.org/Articles/lrr-2001-4/
"Gravitational wave damping has been detected in an amount that agrees with general relativity to half a percent using the Hulse-Taylor binary pulsar,"
I also have something to say to the first question in comments there, to which the article author answered that he can't answer. The question was "Is the speed of gravity reduced by the medium through which it travels in a analogous manner to the slowing of the speed of light through various media?"
I was lucky enough to read Feynman Lectures recently, so as far as I understood him, the photons themselves don't really slow down in various media. That is, what we see as the result is the slowdown, but only because it's a new light (new photons) on the other side of the media. The photons on the other side are photons which were pushed out of the atoms of the media, that's why it appears that they come out slower. Inside, between the atoms of the media, photons still move at the speed of light.
I hadn't actually heard anything about Mallett for a few years, and I guess this is why. :)
But if they do we would have detected them long ago.
But it's wrong anyway, it's not the moving particle that gives off the Cherenkov radiation, it's the matter that they move near. And there is no matter in a vacuum.
[1] "Cherenkov radiation in vacuum and plasma-filled microwave sources in the absence of guiding magnetic fields" by GS Nusinovich
Another interisting property is the 0º Kelvin (absolute zero) http://en.wikipedia.org/wiki/Absolute_zero
We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity") to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies.
Further reading: http://en.wikipedia.org/wiki/History_of_special_relativity#E... http://en.wikipedia.org/wiki/Minkowski_space -- the space of special relativity
Well - I guess that when you move an object - you firstly move (push away) - due to electromagnetic force the closest atoms first - which in turn push away the next... etc. until the whole object moves. I guess that what happens is actually an oscillation between atoms.
So you would notice the far end moving in the time a photon would take from one end to other - in best case scenario.
You know that information cannot travel faster than light? Even if you try to send it via wiggling of unobtainium rod :)
Now, let's say you move an ideal laser across an ideal screen some distance away. The further the screen is, the faster the laser dot will move. At some point the dot will move faster than c... But the dot is not an object. If you think in terms of individual photons, no speed limit is being broken.
IANAPhysicist...
I'm pretty confident that you're wrong about this, but I don't really understand the scenario you're describing. Could you clarify?
edit: I eat my words and stand corrected.
Say you have a laser pointer and point it at a screen some distance away. Now, you rotate the pointer such that the tip is moving at, say 1/10th the speed of light. Simple geometry tells you that the spot on the screen will move much faster than the speed of light.
The important point, though, is that no physical object and no informaaation is actually moving faster than light. Each photon moves at exactly c in a straight line from the pointer to the screen.
http://www.google.com/search?q=%28%281730000+*+pi%29+m%29+%2...
A bit less than 2/100 of a second. That seems quite feasible really!
(of course the moon is not a flat screen, but hey, back of the envelope and all that).
If the dot moves at c, you would see nothing for 1s. Then there would be an instant where the first half of the line is entirely illuminated, as light from the dot at each point reaches you simultaneously.
After that, it would look like an ordinary dot moving away from you at c/2: if the dot moves for x seconds, it takes 2x seconds for the light from the dot at that point to reach you. (Note that a dot moving at c/2 would appear to be moving at c/3.)
If it's moving faster than light (say, kc, k>1), then when the dot arrives at you, you'd see a dot appear at your position, then move back to the original position at (k c / (k-1)), and vanish. (k/(k-1) is because you see it reach the start point 1s after it starts moving, and you first see it 1/k s after it starts moving.) If the dot had been stationary at that point before it began moving, you'd still see the dot there until the new one reached it, at which point they would both vanish.
Simultaneously, you'd see a dot move from your position to the end position at (k * c / (k+1)).
I'm not going to try to work out what happens if you're just standing near the path of the dot.
(I'm not sure about this, but it's what I get when I try to work it out. I'm especially not sure that I'm allowed to discount relativistic effects. I think I am because there are no massive bodies undergoing acceleration, but I don't pretend to fully understand relativity.)
It is of course changed by what it gets reflected off of, but that's not special to this situation at all. If you're at the center of an enormous hollow sphere and shine an astronomically-bright laser circle around, it'll always be a circle to you no matter how fast you move it.
Sound waves travel in the same way. So if you move one end, that movement propagates at the speed of sound (in whatever material the lever is made of).
Remember, a lever is just a collection of individual atoms linked together by elecromagnetic forces. You push of the atoms on one end, and they are going electromagnetically push on nearby atoms, and that push is going to propagate as a wave at around the speed of light.
The second thing is that if you carry out the above experiment, the ball would eventually stop. That is because of friction. Why does the earth never stop? What makes it overcome friction?
Someone is probably going to shoot me down for being a complete idiot and knowing nothing, but I am genuinely interested to know the answer or to know if there is no answer.
The best way I know how to think about curved spacetime is by analogy to the Earth. We are effectively two-dimensional on the Earth's surface, as the radius of curvature is much larger than we are. Yet you can imagine drawing straight lines (i.e., great circles) on the ground to make (large) triangles and discovering that the angles don't add to 180 degrees and hence deduce that the surface is curved.
It's sort of the same way with space. Since we are three-dimensional, we can't directly perceive the curvature as we can an embedded two-dimensional object. A straight line would always look straight to us, yet we could measure the curvature by observing that the fundamental theorems of Euclidean geometry don't hold.
The Earth does slowly spiral towards the Sun. There's no "friction" per se, but it loses angular momentum to other stuff, like gravitational waves and the dark matter hslo. It just operates extremely slowly.
Newton was such a great scientist that he made his famous "I don't make hypotheses" statement in regards to the nature of gravity. Knowing the limits of your (current) knowledge is a fundamental trait of being a scientist (and a philosopher, e.g. see Wittgenstein's motto "Whereof one cannot speak, thereof one must be silent." and Socrates' analysis of the Oracle's answer to him.)
Quoting Cecil Adams (http://www.straightdope.com/columns/read/957/was-isaac-newto...),
[He] took six thousand years of disjointed fumbling and made it into a science. Two sciences, actually, physics and to a large extent mathematics.
Feeling any "ha, he" that he missed a development 200 years later loses perspective about what he did.
That graphic is just wrong, and I also hate it.
And gravity isn't the cause of the curvature! It's the effect. The cause is energy (often in the form of mass).
Thank you, Aristotle. Objects not being pushed on continue with constant velocity, they do not stay motionless.
Electrostatic force also causes objects to move. Just making an object move does not make gravity special.
However, I think the larger objection goes something like this:
Gravitational attraction contains information about the location of an object (say, for the purposes of argument, a singularity). Information may not travel faster than the speed of light, by relativity. Information may not escape the event horizon of a black hole, because to do so would require it to travel faster than the speed of light (or to use some funny quantum teleportation that Hawking describes as the mechanism behind Hawking radiation), but which is not described by relativity.
Therefore it follows that the information about the location of a singularity behind the event horizon of a black hole is somehow travelling "faster than light". This is of course impossible if relativity is correct, which leads to a big WTF?
My guess, and I am most emphatically not a physicist, is that you get some funny macroscopic quantum effects near a black hole, which allows Hawking radiation (and therefore also the encoded information about the objects that fell into the black hole) out, and also lets out the information about the location of the singularity itself, so that objects outside the event horizon can be attracted to it.
Perhaps studying black holes in sufficient depth (pardon the pun) will allow us to finally unify QM and relativity.
Eg. If you had an entangled pair of particles on this side of galaxy and another on other side of galaxy. Now you "wiggle" (change its state) one then the other one "wiggles" too - but you didn't send any information - since the other observer cannot know if the particle changed state because of your message - or it changed state "of its own accord". Thus you would still need to notify him of you wiggling the first particle eg. via photon - thus information only moves at the speed of light :)
Bear with my awful analogy - since I really don't know anything about physics :)
Non sequitur? I mean, non-linearity is not the same as feedback. Linear system can exhibit feedback (and still stay linear), and non-linear systems do not have to exhibit feedback.
Still, that's not itself being 'normally' affected by gravity, and I've never seen anything discuss it.
Yes, Information may not escape the event horizon of a black hole, because to do so would require it to travel faster than the speed of light (up to small quantum corrections)
No, it doesn't follow that information about the singularity is getting out of the black hole. The information got out, and stayed out. The horizon prevents updates from getting out, leaving the previous information and attraction "frozen in" to the shape of space-time.
Think of the space/time as the blanket the universe is wrapped in. If that blanket is stretched out like a trampoline, every object on it or moving around on it is causing flexing and ripples. That's gravity.
When a girl bounces off a trampoline, the specific instance of her gravity is gone but the ripples from that instance continue on for some time until everything "settles".
But apparently the goo that is space/time really does not tolerate anything going faster than the speed of light for some reason. Doesn't mean things aren't trying to go faster than that, they just cannot achieve it.
What if the speed of light was slightly faster or slightly slower, how would it affect the development/entropy of the universe?
So I wonder if a star's gravity is mostly the mass of the star itself, but also, in small part, the huge amount of light that surrounds the star on all sides, being densest nearest the star itself.
There's some evidence that gravity may change a little during a solar eclipse http://en.wikipedia.org/wiki/Allais_effect and also the Pioneer anomaly, http://en.wikipedia.org/wiki/Pioneer_anomaly
I am most definitely not a physicist!
In fact it'd to the opposite, which is why solar sails work. Radiation landing on you propels you away from the object emitting the radiation.
The Pioneer anomaly is very interesting. But we don't have sufficient data to determine what it is exactly. We should really send out more probes like that to find out.
This effect causis gravitational lensing: http://en.wikipedia.org/wiki/Gravitational_lens
More info here. All of it contradictory :) http://www.physicsforums.com/showthread.php?t=287888
So I'm still wondering if it is proper to think of a star's gravitational field being caused not just by its matter, but also by all the photons it has pumped out over its lifetime.
Only things with mass can attract other objects with the gravitational force. Photons aren't in that category.
Yup. As the article says, all forms of energy cause gravitational attraction. Even light! But, as you can see from E=m * c^2, it takes an insane amount of energy to make even a little mass-equivalent. C=3 * 10^8 m/s, so c^2 = 9 * 10^16 or 90000000000000000 m^2/s^2. So 1kg of mass at rest is equivalent to 9 * 10^16 joules of energy. It's about equal to a 4.5 megaton hydrogen bomb blast.
so 2.5 * 10^14 kg inside the earth's orbit, or equivalent to 254 cubic kilometers of water - on an astronomical scale, insignificant. Still, bigger than I expected.
I see gravity as more of a property of the universe, every atom in the universe is attached to each other atom in some way.
I see gravity as more of a property of the universe, every atom in the universe is attached to each other atom in some way.
Please don't do science like this. You should use experimentation to differentiate between theories.
I imagine a bowling ball rolling down a blanket stretched tight at half light speed. The bowl shape of the blanket in front of the bowling ball would be very different from the rear. I'm just pointing out that if gravity goes light speed, then something coming toward the earth at half light speed will have a longer delay for us to feel the gravity, and as the object leaves the earth, its gravity will linger longer. Maybe it's true, it boggles my mind.
If gravity is light speed, then an object travelling toward you at light speed will have no gravity until it has touched you. We should be able to detect shock waves like a jet breaking the sound barrier breaking all the windows in a community because the sound builds up. Gravity would build up too.
If something is moving at the speed of light, then light (or gravity) is emitted from it also at the speed of light.
But if you add the two together, it doesn't equal twice the speed of light. Yes, I know it's weird, but that's where the whole time dilation comes in.
I think this was confirmed in an experiment where scientists measure the speed of light from the sun both during sunrise and sunset, since the relative speed between the sun and the measurement devices are different due to earth's rotation (sorry, don't have a link handy for all this, I probably got some details wrong but you get the idea).
I guess the theory of general relativity would extend this to gravity.
This is a problem because...?