Lightspeed.

[Aquatain]

I have a question : Can gravity accelerate light to go faster than the speed of light?

[Grandmaster Jogurt]

I have a question : Can gravity accelerate light to go faster than the speed of light?

No. Light can only change speed by changing its medium (it travels slower through air or glass than vacuum), not by gravitational acceleration. Gravity can redshift or blueshift the light, though; light being "pulled forward" by gravity would not change velocity, but rather would blueshift to a higher energy wave to compensate for the loss of gravitational potential energy.

[Aquatain]

Thanks for the quick reply Grandmaster Jogurt.

[CaptainZoidberg]

I've always wondered how the speed of light can be constant if light can be trapped in a black hole (where presumably it either has to move in a circle around the black hole or slow down).

[Napoleon the Clown]

The light essentially comes to a crawl so slow that it isn't moving detectably. This is because it hits matter with density beyond imagination. Or so I would think.

[Singular Intellect]

I've always wondered how the speed of light can be constant if light can be trapped in a black hole (where presumably it either has to move in a circle around the black hole or slow down).

You're misunderstanding General Relativity theory...it doesn't say the speed of light cannot be altered to lower values, it asserts that the speed of light will not be affected by different frames of reference.

To put it simply: If you stand still and throw a baseball forward, assume it will reach a speed of C (speed of light). If you run forward at speed X, you would normally expect to throw he ball the exact same way with the resulting speed being C + X...that is not the case with light. The speed is always C, it does not matter how fast or what direction you are running in.

[Feil]

Technically, light doesn't slow down, ever. Passing through a medium, a photon hits one side of an molecule, and there's a delay before it is emitted from the other side. Where a photon exists, it travels at c; it's the delay between absorption and emission that gives light a lower effective speed in a medium.

From the reference frame of the photon, the photon never reaches the black hole, so the issue of whether it bounces off or loops around or passes through dense stuff doesn't seem to me to be an issue. If a singularity has zero volume and a light beam always travels at c, though, it would make sense for it to look around forever. But I don't think singularities work that way. Somebody who knows more can answer this properly.

[Lancer]

I've always wondered how the speed of light can be constant if light can be trapped in a black hole (where presumably it either has to move in a circle around the black hole or slow down).

You're misunderstanding General Relativity theory...it doesn't say the speed of light cannot be altered to lower values, it asserts that the speed of light will not be affected by different frames of reference.

To put it simply: If you stand still and throw a baseball forward, assume it will reach a speed of C (speed of light). If you run forward at speed X, you would normally expect to throw he ball the exact same way with the resulting speed being C + X...that is not the case with light. The speed is always C, it does not matter how fast or what direction you are running in.

That's actually Special Relativity. General Relativity deals with how gravitation deforms spacetime, which is more relavant. Light doesn't come out of a black hole because there isn't any path from within the event horizon that doesn't curve back into the black hole, not because it gets "frozen".

[Sriad]

I have a question : Can gravity accelerate light to go faster than the speed of light?

Instead of accelerating or decelerating, light traveling through a gravitational field will be blue-shifted as it travels down a gravity well and gains energy, or red-shifted as it travels up a gravity well and loses energy.

This is the same effect you'd see in a spaceship traveling at relativistic speeds (our friend relativity yet again) seeing the stars bluer in front of you and redder behind.

[Fingolfin_Noldor]

Gravity is more likely to make a photon appear to be very slow, but in truth, in the frame of reference which is accelerating, it is traveling at the same speed. Bearing in mind, that we are dealing with an accelerating frame of reference. Depending on the magnitude of acceleration and direction, the doppler effect will result in blue shifts and red shifts.

Instead of accelerating or decelerating, light traveling through a gravitational field will be blue-shifted as it travels down a gravity well and gains energy, or red-shifted as it travels up a gravity well and loses energy.

This is the same effect you'd see in a spaceship traveling at relativistic speeds (our friend relativity yet again) seeing the stars bluer in front of you and redder behind.

I'm not so sure as to call it a "gain in energy" or a "loss of energy" especially when it implies that the energy "lost" or "gained" has to come from somewhere. I would rather think the wave got stretched or compressed.

[Wyrm]

Instead of accelerating or decelerating, light traveling through a gravitational field will be blue-shifted as it travels down a gravity well and gains energy, or red-shifted as it travels up a gravity well and loses energy.

This is the same effect you'd see in a spaceship traveling at relativistic speeds (our friend relativity yet again) seeing the stars bluer in front of you and redder behind.

I'm not so sure as to call it a "gain in energy" or a "loss of energy" especially when it implies that the energy "lost" or "gained" has to come from somewhere. I would rather think the wave got stretched or compressed.

Potential energy is energy of configuration. Gravity fields give different particle configurations different energies (since you have to do work to move them around). When you rearrange the particles in the system, obviously the potential energies will differ. This is where the energy comes from that the photon gains when gravitationally blueshifted, and where it goes when it is redshifted.

To say that the wave is stretched or compressed doesn't help: the wave is still at a different frequency, and different energy, begging the question of where the energy came from or has gone to.

[Twoyboy]

Technically, light doesn't slow down, ever. Passing through a medium, a photon hits one side of an molecule, and there's a delay before it is emitted from the other side. Where a photon exists, it travels at c; it's the delay between absorption and emission that gives light a lower effective speed in a medium.

From the reference frame of the photon, the photon never reaches the black hole, so the issue of whether it bounces off or loops around or passes through dense stuff doesn't seem to me to be an issue. If a singularity has zero volume and a light beam always travels at c, though, it would make sense for it to look around forever. But I don't think singularities work that way. Somebody who knows more can answer this properly.

Forgive me if I'm wrong, but I vaguely recall a news story from the past year or so about an experiment which "trapped" light somehow, to it still existed as photons, but they were stationary. Unfortunately I can't remember enough details to Google it. Anyone know anymore about this?

[Darth Wong]

I have a question : Can gravity accelerate light to go faster than the speed of light?

You've been watching Star Trek 4?

[Paolo]

I have a question : Can gravity accelerate light to go faster than the speed of light?

No. Gravity does not accelerate light. From any perspective, light propagates at a constant speed.

[Starglider]

Technically, light doesn't slow down, ever. Passing through a medium, a photon hits one side of an molecule, and there's a delay before it is emitted from the other side.

I'm pretty sure that isn't correct. Refraction is a result of an interaction between the incident electromagnetic wave and the electrical field of the atoms in the material. I don't understand the exact mechanism, but I can't see how photons could be constantly absorbed and reemitted (by electrons) as they pass through material without scattering randomly.

[starslayer]

I'm pretty sure that isn't correct. Refraction is a result of an interaction between the incident electromagnetic wave and the electrical field of the atoms in the material. I don't understand the exact mechanism, but I can't see how photons could be constantly absorbed and reemitted (by electrons) as they pass through material without scattering randomly.

They are scattered randomly. However, they are not all of the same phase. We see a ray of light going in a certain direction simply becuase the photons scattered in that direction are generally in phase; the ones scattered in all other directions tend to be out of phase and destructively interfere, at least in dense homogenous media. This is not true in air and similarly tenuous media, as evidenced by the blue color of the sky.

[Ted C]

I have to wonder if this is technically correct.

Since gravity can change the direction of a ray of light, it technically changes the velocity of the ray of light, since velocity is a vector.

Since the ray's velocity has changed, it has undergone acceleration.

Therefore, gravity can accelerate light.

It can not, to my knowledge, change the magnitude of the vector; in a given medium, light travels at the same speed regardless of its direction.

A black hole keeps bending "turning" the vector back toward the the center (much as the Earth's gravity keeps turning the Moon's vector back to the center), so it seems that -- in a sense -- light and radiation trapped by a black whole is "orbiting" inside the event horizon.

That actually stand up to scientific scrutiny?

[Feil]

I have to wonder if this is technically correct.

Since gravity can change the direction of a ray of light, it technically changes the velocity of the ray of light, since velocity is a vector.

Since the ray's velocity has changed, it has undergone acceleration.

Therefore, gravity can accelerate light.

It can not, to my knowledge, change the magnitude of the vector; in a given medium, light travels at the same speed regardless of its direction.

This much is correct. The rest looks right, but I don't know for sure.

[Kuroneko]

In GTR, there cannot be any local measurement that has light in vacuum at anything other than its usual speed. If your space is expanding in certain ways, then it is possible for you to see objects that have an superluminal comoving speed relative to you (the Hubble sphere, denoting luminal recession velocity, can itself expand faster than the light outside of it, making such objects observable), so you could say some of the light emitted by those objects is likewise superluminal relative to you.

As for acceleration of light, no so fast. The force four-vector vanishes along any geodesic; both light and massive objects follow straight paths in the absence of non-gravitational effects. In spacetime, gravity doesn't change the direction of anything, but rather can be said to define "straight" in the first place. For example, viewing a falling apple's trajectory as bent (parabolic in (t,x)-coordinates) is a Newtonian prejudice; in GTR, it's straight and you're the one that is accelerated (you feel your weight whereas objects in freefall do not feel theirs). It's similar for light.

[Feil]

As for acceleration of light, no so fast. The force four-vector vanishes along any geodesic; both light and massive objects follow straight paths in the absence of non-gravitational effects. In spacetime, gravity doesn't change the direction of anything, but rather can be said to define "straight" in the first place. For example, viewing a falling apple's trajectory as bent (parabolic in (t,x)-coordinates) is a Newtonian prejudice; in GTR, it's straight and you're the one that is accelerated (you feel your weight whereas objects in freefall do not feel theirs). It's similar for light.

Very true. So what? Light traveling on straight paths through curved spacetime may make the math prettier, but given that this discussion is about understanding the observed effects, it's a whole lot more useful to describe things in terms that make physical sense. Unless I'm missing something that you're not.

[Paolo]

Very true. So what? Light traveling on straight paths through curved spacetime may make the math prettier, but given that this discussion is about understanding the observed effects, it's a whole lot more useful to describe things in terms that make physical sense. Unless I'm missing something that you're not.

Without recognizing what the math implies physically, you're missing a lot. The rate of comoving expansion, for example, doesn't even have units of distance over time, so "superluminal separation" doesn't even mean anything physically. A measurement of one object's instant velocity in the comoving frame of the other will still bear out special relativity; the point being you can always choose an inertial frame. Defining metrics on curved spacetimes is necessary to reconcile this very real, physical behavior with accelerating frames.

[Kuroneko]

Very true. So what? Light traveling on straight paths through curved spacetime may make the math prettier, but given that this discussion is about understanding the observed effects, it's a whole lot more useful to describe things in terms that make physical sense. Unless I'm missing something that you're not.

You're aren't going to understand a lick about GTR if you don't understand the equivalence principle, i.e., the relative existence of the gravitational field itself: while you are in freefall, you experience no gravitational forces, and so it is the freefalling frame that should be considered inertial.

Saying that gravity makes light accelerate is thus no different from saying that otherwise inertial objects are observed to accelerate when you view them from a rotating frame (e.g., centrifugal and Coriolis forces). It is true, but it is not fundamental--why that frame and not another? We call these kinds of forces 'fictitious' precisely because they're purely an artifact of the reference frame rather than any physical interaction. On the other hand, the force four-vector is what is actually fundamental, because that is what the particle itself experiences, and that is independent of any observer. Mathematically, it is the curvature of the particle's trajectory in spacetime, which is why we say that paths of vanishing four-force are 'straight'. But it is not something just to "make the math prettier", but a physical, measurable quantity.

Conversely, if you understand the equivalence principle, you'll go a long way to at least qualitatively understanding the various phenomena of GTR, including the observed bending of light-rays. For example, suppose that you are in deep space and you see a light ray intersecting an accelerated transparent rocket.
Conclusion: By EP, an observer standing on a gravitating body will see light curve.
Now suppose that in the rocket, on top and bottom, there are two scientists sending light signals to each other at regular intervals of their personal, very precise clocks. The rocket is accelerating upwards, so the bottom-directed light signal travels a lesser distance compared to the upward-directed light signal. But, from EM, the speed of light should be constant.
Conclusion: By EP, an observer on a gravitating body is time-dilated relative to an observer higher up.


You are still missing a lot if you dismiss the mathematics, but if you also dismiss the equivalence principle, you're missing everything. None of the above predictions make any physical sense if we don't treat the freefalling frames as inertial and the stationary ones as accelerated, but with that interpretation, the above qualitative effects fall out of the theory will hardly any work at all.

Without recognizing what the math implies physically, you're missing a lot. The rate of comoving expansion, for example, doesn't even have units of distance over time, so "superluminal separation" doesn't even mean anything physically.

Er... in the comoving frame (i.e., comoving with the bulk of the matter of the universe), r' = Hr, where H is the (time-dependent) Hubble parameter, which has units of 1/time, so the separation velocity r' does have units of distance over time. It's true that as a matter of practical observation, this involves some hand-waving, but in theory we've no such difficulty, since we can still talk about a hypothetical distant galaxy such that the instantaneous rate of increase of the proper distance between and its current position, v_r, plus its local peculiar velocity v, can be superluminal. The quantity v_r has some meaning in that a light signal directed toward us in the region of v_r>c is actually moving away from us. This is physically meaningful.

Though in practical astronomy, that isn't how things are done at all because distance measurements in general aren't directly accessible in so neat a manner, but nevertheless in theory (in which we know the metric, particularly in the FRW approximations), it's just a matter of number-crunching.

[Paolo]

Er... in the comoving frame (i.e., comoving with the bulk of the matter of the universe), r' = Hr, where H is the (time-dependent) Hubble parameter, which has units of 1/time, so the separation velocity r' does have units of distance over time.

The Hubble constant the expansion rate, as I understand it. At least that's how MTW treats it. Yes, recesslional velocity does have units of distance over time, more on this in a sec.

It's true that as a matter of practical observation, this involves some hand-waving, but in theory we've no such difficulty, since we can still talk about a hypothetical distant galaxy such that the instantaneous rate of increase of the proper distance between and its current position, v_r, plus its local peculiar velocity v, can be superluminal. The quantity v_r has some meaning in that a light signal directed toward us in the region of v_r>c is actually moving away from us. This is physically meaningful.

I just finished reading Davis and Lineweaver on this matter, and I guess they're talking about me and my textbooks, but my understanding is that we only arrive at superluminal velocities by dividing proper distance today by cosmological time, even though proper and comoving distance differ in the past. And considering we are detecting redshifts high enough to compute superluminal recessional velocities, the result of simply crunching H_0*D doesn't appear to me as physically meaningful on its own. Then again, I've only looked at the Davis and Lineweaver paper and tried out Baez's exercise; I still don't follow D&L's argument that recession velocitieis mean something when it comes to cosmological redshift.

[Kanastrous]

Is it correct to say that all orbiting bodies are traveling in straight lines, through curved space?

[Paolo]

Is it correct to say that all orbiting bodies are traveling in straight lines, through curved space?

Absolutely.