The Sun, as it is right now, won't have its gravity affect Earth for another 8+ minutes, and the gravity that the Earth feels right now pulling it towards the Sun is actually pulling it towards where the Sun was 8+ minutes ago! (Weird, isn't it?)
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.
I don't think it's incorrect. But for constant velocities it is canceled out because the relative motion causes things to also appear in a different direction. This happens with ordinary light, also. Stars appear in a different place to us because of our relative motion (they appear to be located more "forward" in our direction of motion).
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.)
> And your charge example is not so good. For Galilean invariant theories it's only relative motions that matter.
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).
> 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.
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.
Ah, that's interesting, I never realized the rank was what determined the amount of "prediction" that a field does. That's something that should have been obvious on degrees-of-freedom considerations, but I never thought about it in that way before.
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.
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?
> 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, ....
Well, that's mind blowing. Where could I go to learn more about this?
Other than "graduate textbooks", I'm not really sure. Jackson does cover the E&M case pretty well (EDIT: in chapters 11 and 14, note especially sections 10.11 and 14.1), but I'd combine it with the treatment in Taylor & Wheeler's highly readable _Spacetime Physics_.
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.
Wait, so you are saying we would feel the effects immediately, but the light would not disappear for eight minutes?
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.
No, the sun disappearing would not be constant velocity or constant acceleration motion, so the info would indeed only propagate at the speed of light.
Yes, you are correct. The easiest way to think about it is that while the gravity from the earth moves at the speed of light, while it travels toward the sun, it also moves at the same original speed the earth was traveling at.
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.
This is more or less a correct interpretation (the physics are definitely right). Importantly, the behavior is seen in electromagnetism, which is much easier to think about than general relativity, so people should start there.
(But no one will ever read this comment because the topic is 5 days old.)
Yes you are totally right. Furthermore: In relativity there is no "right now" moment. Two simultaneous events in one reference frame can be one after the other in another reference frame. (see: http://en.wikipedia.org/wiki/Relativity_of_simultaneity) This concept is even true in special relativity and has been tested and a basic principle why GPS is working.
I'm not certain your thought experiment applies. Your use of charges implies that we are discussing EM attraction or repulsion, which we are not.
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.
"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.
Something that puzzles me about "the speed of light in X" discussions is exactly the confusion over whether the speed of light is "different" in a medium. On the one hand, it seems like it isn't, since no actual photons are moving more slowly. On the other, things like Cherenkov radiation seem to indicate that the apparent speed of light matters for things that you'd expect to be based on the constant speed of light in a vacuum. There's a physicist, Ronald Mallett, who has suggested an experiment to see if the constant speed of light or the apparent speed of light is what matters for frame-dragging (!).
But AFAIK Cherenkov radiation occurs in medium, so there isn't any contradiction to the generally accepted limits, and Ronald Mallet is highly unlikely to be trusted, see the wikipedia entry:
I was under the impression that tachyons (should they exist) would be expected to give off Cherenkov radiation in vacuum, but I'm not sure where I got that impression.
I hadn't actually heard anything about Mallett for a few years, and I guess this is why. :)
That would imply that tachyons interact with the electromagnetic force.
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.
Virtual matter can not give off photons - it would violate conservation of momentum (unless it was in pairs, but that would not work with Cherenkov radiation).
There seems to be one paper about Cherenkov radiation in a vacuum [1]. But I have only read the abstract. So you are probably right, that there's no Cherenkov radiation in a vacuum. Or does anyone has any better knowledge?
[1] "Cherenkov radiation in vacuum and plasma-filled microwave sources in the absence of guiding magnetic fields" by GS Nusinovich
As a slightly-related follow-on, see http://en.wikipedia.org/wiki/Cherenkov_radiation for a nice example of what happens in the case of a charged particle moving through a medium more quickly than the speed of light in that medium.
I've always thought what we call 'speed of light' is the indirect observation of a structural property of (this) the universe. A property that has something to do with movement in general and not only the movement of light (the movement of space itself?).
Your intuition is right. Einstein is famous for the theory of relativity not because he was the first discoverer of the relativity equations (they're called the Lorentz transformation for a reason), but because he proposed that the speed of light was encoded in the structure of the universe, and that the universe is not the three-dimensional Euclidean space we think it is.
I'm pretty sure that Einstein intuitively "guessed" that the speed of light would be the fastest possible speed and used that fact to work out the rest of the equations. E = mc^2 was the bizarre discovery that those equations yielded, and it was so weird that he felt like he had made a mistake at first.
That's not quite right. Einstein (and several other physicists of the time) inferred that the speed of light might be invariant in all reference frames from the structure of the Maxwell Equations where the speed of light enters as a true, fundamental physical constant of the universe.
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.
Reminds me of a thought experiment that's always bugged me: if you had an incredibly long see-saw or lever, like the length of the galaxy, would movement at one end instantaneously be matched by movement at the other end? (I think the reason it bugs me is because the object itself is preposterous, but I still want to know)
If it were a physical object (say, a long steel bar), the atoms would communicate at the speed of light, so your object would bend or squish, with a wave travelling along it.
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.
>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...
I'm pretty confident that you're wrong about this, but I don't really understand the scenario you're describing. Could you clarify?
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.
For fun: the moon has a radius of about 1730 km. At full moon we can see about half of the moon, so the distance from one side to the other is about pi * 1730 km. So how fast do you need to move a laser pointer across the moon surface to make the dot attain the speed of light?
Suppose you're on the midpoint of a straight line 6e8 m long, which the dot traverses at uniform velocity.
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.)
I think philh already explained it pretty well. In your question you suppose the laser dot to be 'fairly large', which I think would complicate things (the shape of the dot 'smearing out' as it goes faster). For me, philh's explanation works best if you imagine the laser pointer to be a cannon of photons, emitting one photon after another at a very high rate and in a single direction, with the electrons of the moon's surface always reflecting the photons towards your eye (perhaps a bunch of strategically placed mirrors...).
Actually, the shape of the dot is unchanged by going faster. Since it isn't a real object, it isn't affected by relativistic contraction. If you emit a circle, it'll be a circle.
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.
If the laser emits all photons constituting the dot at the same time, in pulses... I was thinking of the photons that make up the dot arriving at random intervals, but I'm probably making things too complicated.
It seems he is correct. If you imagine a laser pen light being swung on an angle, the further away the screen is, the faster the dot will "move". If the screen is sufficiently far away, the dot will appear to move faster then the speed of light.
Almost. The speed of light is the upper limit on how fast any forces could propagate along the object, in practice they would travel at the speed of sound in the material.
If you move it, you're really moving some of the atoms at one end. They 'bump' into nearby atoms, which 'bump' into more atoms, and so on, and eventually the atoms at the far end get 'bumped', and the far end moves.
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).
Hmm, I'd take your word over mine but this doesn't fee quite right to me. What I'm thinking is, say you reverse the action so that instead of bumping one end of the see-saw, you release your grip on it having been holding it down. So in normal circumstances the other end would fall while the near end rises (of course now an external gravitational field has entered the thought experiment). But if movement is still due to the bumping of atoms , how does it work, where does it start? and if it's something else, then what, and is it still not instantaneous?
Like others have said, any movement will propagate at the speed of sound through the rod. But moreover, as the end of the rod speeds up, it will experience relativistic mass increase from your point of view, so it would still take an infinite amount of energy to accelerate it to c, regardless of how long your lever was. (Though special relativity, dealing with inertial frames, is strictly not applicable to a rotating rod, but you can probably make use of a succession of infinitesimal inertial frames to figure that out.)
Good point. An unobtainium rod as JanezStupar calls it, would be the immovable object, stuck in the universe's gullet gumming up the works. I wonder if God would be able to move it after he created it.
Oh - yes, the unobtainium rod thought experiment :)
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 :)
It would bend or stretch before it snapped. Nearly all, if not absolutely all, materials that you might want to build a see-saw from will deform before they snap. Maybe it won't deform much, but that ok, and is enough to transmit a push from one end of the lever to the other.
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.
I am not a physicist nor an astronomer. I wanted to ask however, when they explain gravity by the analogy of holding a blanket, first the blanket is on earth thus any object that is put on it is being pulled down by earth and the blanket is being held by two people, thus what is pulling the earth and sun down and who is holding the space blanket? Also, seeing some of the images on the site, it is clear that space is something and it is not nothing. Thus, what is space?
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.
It's an analogy, and as such it has limited applicability. Noone is "holding" space, it's infinite. The blanket is two-dimensional and embedded in the three dimensions of our world, hence it has boundaries. Space is, well, space. It's not embedded in anything. This is quite nonintuitive and here's where the blanket analogy hurts more than it helps.
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.
That depends on what you mean by "know", I guess... According to the current best estimates of the cosmological parameters, yes, it is infinite. The basic theory could be wrong, of course, and outside the observable Universe the properties could be different.
That would have been the case if the universe was closed, i.e. if the matter density was above the critical density. However, the matter density is only about 20% of the critical, which means it's infinite. (The remaining 80% of the critical density seem to be the cosmological constant, which means the universe has flat geometry to within experimental error.)
Where was there at shot taken a Newton? AFAICT, he explains how Newton's theory addressed the problem, but there is no shot taken. I've never heard of such a problem as people taking shots at Newton..
Maybe not "taking shots", but I also feel a general "ha, he missed that big one" attitude.
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.)
I don't. Technology had not yet progressed to the point that one could design experiments to test relativity. And such technology depends on insights from other areas of physics.
I hate that curved space graphic. Now you have some mysterious gravity pulling both the sun and earth down. I wish someone would come up with a better example to show gravity as curved space.
But gravity isn't curved space, it's curved spacetime. Think of a graph that shows both space and time, so that it shows constant motion as a straight line (four units of space per one unit of time with the slope constant). Then acceleration is a curved line. Now curve the graph paper - not through some higher dimension, but by stretching it and compressing it in ways that change the shortest distances between two points - so that the Earth orbits the Sun in a straight line. Not a straight line in space, mind you, but a straight line in spacetime: no acceleration. After all, since no one is pushing on the Earth, it should move in a straight line, right? Got it?
This is all well and good, but what the article is talking about is the speed of the propagation of gravity waves. I've never heard anyone who wasn't a crank argue that gravity waves travel at anything other than the speed of light. As the article confirms, observation of pulsars has confirmed the speed of gravity waves to very close to the speed of light.
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.
Yes, in some sense gravitational attraction carries information about the location of the object.
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.
What is the technical definition of "information"? I know what information is in a colloquial sense, and I know something about it's technical definition in the field of computer science, but I don't know what physicists mean when they use the word. Is information the same thing as light? Is it analagous to light? Is it a property of light? Matter?
I guess that information is change of state that is clearly distinguishable from some "random" change of state and caries a "meaning".
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 :)
I just define it for myself as "If it can transmit information, it could also be used given enough technology to send any kind of data, such as a Microsoft word document."
That definition would probably work. Have a look at Feynman's lectures on computer science. He also investigates how much energy has to be used for computing. (Or to be more precise, how much entropy has to be created.)
You don't have to go 'faster than the speed of light' to escape a black hole if you're not affected in the usual manner by gravity. And I'm not aware of any suggestion that gravity itself is affected by gravity.
Gravity absolutely is affected by gravity. The Einstein field equations are non-linear, so gravitational energy is itself a source of gravity. All forms of energy, and momentum, and even stress and pressure are combined into the "stress energy tensor" which determines the local curvature of space-time.
> The Einstein field equations are non-linear, so gravitational energy is itself a source of gravity.
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.
The equations describing a field theory contain terms which are the product the field, the thing it couples to (could be another field) and the strength of the interaction. When a field couples to itself, there are terms non-linear in the field. So the non-linearity of GR indicates that the gravitational field couples to itself, i.e. that gravity gravitates.
The article asks what would happen to gravity if you suddenly "removed" the sun. My question is- is that even possible? How could you instantaneously "disappear" a giant blob of mass/energy? Is this kind of like trying to divide by zero? I'm not being facetious, just wondering if the whole idea is predicated on an impossibility.
Personally I think it's easier to tell people to stop thinking of gravity as a particle or wave - it's not like a beam of light or radio wave.
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.
Ha! But what if it was the opposite and we are simply a cycle down the road of big bang/big crunch/big bang/big crunch/big bang where the speed of light used to be faster but is slowing each cycle because of lost mass/energy.
What if the speed of light was slightly faster or slightly slower, how would it affect the development/entropy of the universe?
Something I wonder about gravity - While it is often mentioned that objects with a large gravitational force can 'bend' light (gravitational lens), can a sufficient amount of light 'pull' objects towards itself?
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.
> can a sufficient amount of light 'pull' objects towards itself?
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.
Mmmm. Okay, but a star puts out a lot of energy, over a long period of time. Is it enough that we calculate the gravitational effect of all those photons, rather than just the mass of star itself when calculating say the acceleration of the pioneer crafts?
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'm not sure I understand your question correctly, but photons have no mass. So light can't pull objects towards itself.
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.
I'd always understood gravity to be a mutual attraction between two masses. So the thing I have difficulty understanding is how light can only be attracted to mass, but itself cannot attract mass, no matter the quantity present.
I think I'm correct in saying that the light isn't attracted to the mass, but the mass bends spacetime around it, so the path of everything traveling through that medium is bent, including the paths of photons.
Hmm, thanks. I did a little more searching and reading about this with my new vocabulary (bending spacetime). It seems like photons also bend spacetime.
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.
It doesn't make any sense to define a gravity field by photons. They're massless, so they don't attract anything, and most of the photons a star has produced over its lifetime are speeding away across the universe billions of light years away from it.
Only things with mass can attract other objects with the gravitational force. Photons aren't in that category.
Your trouble is on focusing on the analogy too much. Instead of, "how can we measure what the effects of gravity would be if matter or energy were created or destroyed?" ask "how can we measure the movement of the curvature of spacetime?"
The speed of gravity is either infinity or millions of times faster than the speed of light. If the speed of gravity was the speed of light, then heavy objects passing near the earth would have more gravity than objects passing away. Less of the gravity beans would be arriving to be measured. Like the red shift in light or the doppler effect with sound.
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.
Wait, what? Did you read the article? The propagation of the curvature of spacetime happens at the speed of light. If it didn't you could use large amounts of energy to propagate information faster than the speed of light, which screws the hell out of causality (using the light cones). If you have a good math background you can solve for it using the equation.
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.
Maybe data could travel faster than light if we find a property of the universe which goes faster than light.
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.
I'm by no means well-versed in the special theory of relativity, but I believe one of its results is that light seems to travel the same speed at you no matter what your own speed may be (since it's all relative anyways, there's no absolute frame of reference for you to really measure your own speed), as a consequence of the Lorentz transformations.
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.
problem because if you had a stable highly elliptical orbit of two bodies, the attraction would be greater during the approaching phase than the departure phase. The equation would not be balanced. Elliptical orbits would degrade due to the pulling being greater on arrival than departure. This is not the case. Maybe it is only a problem as you approach light speed.
No, the article describes something totally different. It talks about cases where an orbit decays because the gravity is felt at a different location from where you expect.
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.