Can gravity bend the path of light?

[Chaos' lil bro Order]

Hey, considering light refracts when entering denser or sparser mediums from that which it came, I was wondering if the same is true for gravity.

Can gravity refract?

 

[daveb]

What refracts is the propagating wave when moving from one material to another. I suppose that if gravity waves were shown to exist, then they would also experience refraction, as well as reflection. the question then becomes what kind of material could reflect gravity?

 

[DaveC426913]

Correct me if I'm wrong, but isn't that how they determined the validity of General Relativity? via the Sun's gravitational lensing* of Mercury's apparent position?

(*lensing = refraction)

Einstein's GR predicted that Mercury's appearance from behind the Sun would have a time discrepancy that Newton couldn't explain. Mercury indeed appeared at exactly the time that GR predicted.


[Edit: Oops. you don't mean "does gravity refract light?", you mean "do gravitational waves themsleves get refracted by the media they pass through?" Scratch this post.]

 

[pervect]

I would expect that gravitational radiation could refract under the right circumstances. Note that gravitational radiation is different from gravity itself.

"Gravity" (gravitational attraction) is analogous to the electrostatic columb force between two charges, while gravitational radiation is analogous to electromagnetic radiation.

Electromagnetic radiation refracts, but I can't think of any sense in which it's meaningful to say that the electrostatic columb force "refracts".

The most important numerical factor in refraction is undoubtedly dielectric permittivity - for a definition of this term, if needed see:

http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/dielec.html

The speed of light is $1/\sqrt{\mu \epsilon}$, where $\epsilon$ is the permittivity of the media, so it can be seen that the permittivity is important to the speed of electromagnetic radiation.

The fact that matter is made out of electric dipoles is important to the details of electric permittivity. Gravitational dipoles do not exist (because there is no equivalent to a "negative charge"). I have not seen any calculations or papers on the topic, but I strongly suspect that there is not any direct equivalent of electrostatic permittivity for gravity in everyday matter.

Other mechanisms do exist for refracting light, however. We know that light can be refracted by gravitational lensing, and this mechanism of refraction should also refract gravity waves.

Of course, since we have not yet even detected gravity waves, we don't have any experimental data on whether or not they refract, only experimental predictions.

 

[Intuitive]

Does Gravity have a Wave Length, if so, then what is its full Wave length?

 

[rbj]

Does Gravity have a Wave Length, if so, then what is its full Wave length?

depends on the frequency of the wave. like light, most physicists believe the speed of gravity is $c$ and for any wave:

$$c = \lambda f$$ .

 

[Intuitive]

depends on the frequency of the wave. like light, most physicists believe the speed of gravity is $c$ and for any wave:

$$c = \lambda f$$ .

1. Does Gravity have a Wave length longer than a 1Hz EM Wave Length?

2. If so, Would this be why Gravity Waves can penatrate so easly through Materials?

 

[pervect]

1. Does Gravity have a Wave length longer than a 1Hz EM Wave Length?

Gravitational radiation could have a frequency higher or lower than 1hz. The wavelength would then be shorter or longer, respectively, than the 3e8 meter wavelength of a 1hz E&M wave.

2. If so, Would this be why Gravity Waves can penatrate so easly through Materials?

No.

 

[Chaos' lil bro Order]

"Gravity" (gravitational attraction) is analogous to the electrostatic columb force between two charges, while gravitational radiation is analogous to electromagnetic radiation.



Other mechanisms do exist for refracting light, however. We know that light can be refracted by gravitational lensing, and this mechanism of refraction should also refract gravity waves.

Not true. Coloumb force is attractive between two 'opposite' charges and repulsive for two 'alike' charges. In addition, gravity has no charge, so this analogy seems very poor to this reader.
I don't understand what you mean by gravity vs. gravitational radiation. If a body like the moon emits 'gravitational radiation', the radiation is the 'attractive' force that acts upon the Earth. Why are you
saying Gravitational attraction is separate from Gravitational radiation? The first is the effect, the second the cause, together its one phenomenon called gravity. You are puzzling me.


Why do you think a gravitational field should refract gravitational radiation that glances by it? Just because Eddington saw light refracted as it glanced by the sun, why should gravity from the same source as the light also be refracted in this manner as it glances the sun?
Maybe I'm wrong, but I thought there has never been any evidence that gravity interacts with other gravity.

 

[pervect]

Not true. Coloumb force is attractive between two 'opposite' charges and repulsive for two 'alike' charges. In addition, gravity has no charge, so this analogy seems very poor to this reader.

I don't understand what you mean by gravity vs. gravitational radiation. If a body like the moon emits 'gravitational radiation', the radiation is the 'attractive' force that acts upon the Earth.

No, gravitational radiation is absolutely not the same thing as the attractive force between two bodies.

Gravitational radiation is the equivalent of electromagnetic radiation. You might try for instance the sci.physics.faq on gravitational radiation for a little background information.

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html"

Gravitational radiation is what experiments such as LIGO are trying to detect in the laboratory - currently, we only have indirect astronomical arguments to support its existence as mentioned in the above FAQ (the pulsar orbital decay observations).

The analogy between electromagnetism and gravity starts with drawing the analogy between the inverse-square law attraction of charges (the coloumb force) and the inverse square law attraction of gravity - the analogy that you found "not convincing" (?!). Unfortunately if you don't accept basic stuff like this, it's going to be very difficult to talk with you.

There are some important differences - gravity is not electromagnetism, after all, the analogy is only an analogy. The sign of the relation is different. The analogy works surprisingly well, though - one can even find a gravitational version of Maxwell's equations for the weak field, though there are important differences in the magnitude of some constants.

See for instance

http://www.rwc.uc.edu/koehler/biophys/4a.html

The notion of mass as gravitational charge is perhaps the best "theoretical" notion of mass we have. Note that this idea of mass is qualitatively different from the idea of "inertial mass": that quantity which makes it difficult to change the velocity of an object. That these two quantities, gravitational charge and inertial mass, are equal, is another of the fundamental mysteries of physics.

http://musr.physics.ubc.ca/~jess/hr/skept/E_M/node2.html

This force law, also known as the COULOMB FORCE,17.1 has almost the same qualitative earmarks as the force of gravity: the force is ``central'' - i.e. it acts along the line joining the centres of the charges - and drops off as the inverse square of the distance between them; it is also proportional to each of the charges involved. [We could think of mass as a sort of ``gravitational charge'' in this context.]

So what are the ``minor differences?'' Well, the first one is in the sign. Both ``coupling constants'' (G and kE) are defined to be positive; therefore the - sign in the first equation tells us that the gravitational force on mass #2 is in the opposite direction from the unit vector pointing form #1 to #2 -- i.e. the force is attractive, back toward the other body. All masses attract all other masses gravitationally; there are (so far as we know) no repulsive forces in gravity.

http://en.wikipedia.org/wiki/Gravitoelectromagnetism

(This may be too technical for you unless you know vector calculus, but extends the analogy between weak-field gravity and electromagnetism to include all of Maxwell's equations. IT also points out some of the important limitations of this analogy .
)

Why do you think a gravitational field should refract gravitational radiation that glances by it?

According to general relativity, gravitational radiation travels at the speed of light. This is enough information to know that according to GR for empty space and for weak fields, both sorts of radiation will follow the same path, technically known as a null geodesic.

This is a prediction specific to GR, where gravitational radiation does travel at the speed of light, and where bodies that are not acted on by other forces follow geodesics in space-time.

 

[Chaos' lil bro Order]

I'm having trouble with your statement, 'Note that gravitational radiation is different from gravity itself.'

Does this really need to be said? The radiation is simply the messenger particles (gravitons) spreading out through space, while the 'gravity' is simply the field that result from the aggregation of these particle.








'The analogy between electromagnetism and gravity starts with drawing the analogy between the inverse-square law attraction of charges (the coloumb force) and the inverse square law attraction of gravity - the analogy that you found "not convincing" (?!). Unfortunately if you don't accept basic stuff like this, it's going to be very difficult to talk with you.
'
Ok the analogy starts there, but doesn't get much further does it. The analogy certainly doesn't assure me that gravity refracts because light does. Even your GR argument leads to inductive conclusions that have no concrete scientific merit. I'd say we don't know if it refracts, unless you have some gem of a fact to prove this wrong perhaps?

 

[SpaceTiger]

The radiation is simply the messenger particles (gravitons) spreading out through space, while the 'gravity' is simply the field that result from the aggregation of these particle.

I think, in this case, radiation refers to the classical wave behavior, not the theoretical quantum carriers of the force. An electromagnetic wave (or electromagnetic radiation) is made up of many photons, just as a gravitational wave would be made of many gravitons. A single graviton wouldn't constitute "gravitational radiation" in the sense that we mean it here.

The force of gravity exists independently of the wave behavior that it can theoretically exhibit.

I'd say we don't know if it refracts, unless you have some gem of a fact to prove this wrong perhaps?

Observationally, we don't even have proof that gravitational waves exist. I think pervect's point is just that, if they did (and we really expect them to), then there's no reason they shouldn't be able to refract like any other kind of wave.

 

[SpaceTiger]

1. Does Gravity have a Wave length longer than a 1Hz EM Wave Length?

There are many astrophysical sources that exhibit gravitational radiation at frequencies much less than this. For example, a pair of orbiting neutron stars (PSR 1913+16) have an orbital period of ~8 hours and thus emit gravitational radiation with frequencies around 30 microhertz.

 

[pervect]

I'm having trouble with your statement, 'Note that gravitational radiation is different from gravity itself.'

Does this really need to be said? The radiation is simply the messenger particles (gravitons) spreading out through space, while the 'gravity' is simply the field that result from the aggregation of these particle.

It really needs to be said. Take the electromagnetic analogy. The force between electric charges is not due to the exchange of real photons, though it can be thought of as the exchange of virtual photons.

Similarly, the attractive force of gravity is due to the exchange of virtual (not real!) gravitions.

It is actually quite difficult to explain attractive forces due to virtual particles. It is obviously necessary, though - in electrostatics, a positive charge can attract a negative charge, and gravity is always attractive.

See for instance

http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

The most obvious problem with a simple, classical picture of virtual particles is that this sort of behavior can't possibly result in attractive forces. If I throw a ball at you, the recoil pushes me back; when you catch the ball, you are pushed away from me. How can this attract us to each other? The answer lies in Heisenberg's uncertainty principle.

Suppose that we are trying to calculate the probability (or, actually, the probability amplitude) that some amount of momentum, p, gets transferred between a couple of particles that are fairly well- localized. The uncertainty principle says that definite momentum is associated with a huge uncertainty in position. A virtual particle with momentum p corresponds to a plane wave filling all of space, with no definite position at all. It doesn't matter which way the momentum points; that just determines how the wavefronts are oriented. Since the wave is everywhere, the photon can be created by one particle and absorbed by the other, no matter where they are. If the momentum transferred by the wave points in the direction from the receiving particle to the emitting one, the effect is that of an attractive force.

The moral is that the lines in a Feynman diagram are not to be interpreted literally as the paths of classical particles. Usually, in fact, this interpretation applies to an even lesser extent than in my example, since in most Feynman diagrams the incoming and outgoing particles are not very well localized; they're supposed to be plane waves too.

Look closely at the moral of the story - virtual particles are not to be interpreted literally as the paths of classical particles. This is why we do not talk about or observe the coulomb force as "refracting", and why we also should do (or not do) the same for "gravitational force".

Ok the analogy starts there, but doesn't get much further does it. The analogy certainly doesn't assure me that gravity refracts because light does. Even your GR argument leads to inductive conclusions that have no concrete scientific merit. I'd say we don't know if it refracts, unless you have some gem of a fact to prove this wrong perhaps?

A bit snippy, aren't we, Mr. Chaos? Consider my original quote.

According to general relativity, gravitational radiation travels at the speed of light. This is enough information to know that according to GR for empty space and for weak fields, both sorts of radiation will follow the same path, technically known as a null geodesic.

--->Note the boldface type in "according to GR". <---

Therefore when (if) we are able to actually observe gravitational radiation experimentally, if it does not refract in the same manner as light in a vacuum, we will have falsified GR. This is something that is useful to know for anyone interested in science.

One should not have to emphasize that one is talking about GR when one is talking in the GR forum. When one does emphasize that one IS talking specifically about GR, in the GR forum, it seems like that should get the point across to any reasonable reader.

Also, it's rather dismissive of GR to say that its theoretical predictions are "of no scientific merit" - GR being not only the topic of the forum, but the current leading theory of gravity.

 

[Chaos' lil bro Order]

According to general relativity, gravitational radiation travels at the speed of light. This is enough information to know that according to GR for empty space and for weak fields, both sorts of radiation will follow the same path, technically known as a null geodesic.


How is it enough information to know that gravity will refract simply because it travels at the speed of light? GR really predicts this, how so?

Yes, I like to be snippy with you and ZapperZ because you are combatative and very curt in many posts I find, so I feel I need to defend myself and point out your inconsistencies when you don't fully explain something, even if I agree with you. Notice that SpaceTiger gets respect because he gives it (plus he's the biggest genius on PF).

Still I like you Pervect

 

[pervect]

Well, we definitely agree about Space Tiger :-) - and BTW congratulations to ST for his recent promotion.

As far as gravitons go, one of my textbooks (MTW's Gravitation) actually has a chapter titlte which is "Orbit of a Photon, neutrino, or graviton in the Schwarzschild geometry".

Now this particular book was written in the days before the neutrino was known to have mass, but the point of the chapter title is that in GR, any massless particle will follow the same orbit as any other massless particle. (And the graviton is even mentioned by name).

Let's see if I can explain why

Suppose we throw a ball on the Earth, and look at its trajectory. As long as the ball is a test particle (one that is light enough that it does not disturb the motion of the Earth appreciably) the path of the ball is independent of its mass. The path of the ball depends only on how fast and in what direction we throw it - i.e. its velocity.

This is true for any value of velocity including zero initial velocity - i.e. if we have several balls at rest (massive balls) and we drop them, we expect all balls to fall at the same rate, and to follow the same path.

In Newtonian theory, this happens only because the gravitational mass of the various balls are equal to their inertial masses. There is no explanation in Newtonian theory for why the two masses should be the same.

In GR, the equivalence of gravitational and inertial masses is part of the theory - the principle of equivalence. Therfore, the assumption that all balls will fall at the same rate is built into the theory.

If we go through the details of how we calculate the path of a ball or test particle in GR, we find that it satisfies a particular equation, called the geodesic equation. (Actually we do need to assume that the particle doesn't have any appreciable angular momentum or spin to apply this reasoning in general.)

The nature of the geodesic equation is that a geodesic can be specified by a single point, and a velocity at that point. All objects will follow the same orbit if they start at the same point moving at the same velocity, this is a consequence of geodesic motion. The mass of the object doesn't matter, just as the mass of the ball doesn't matter as to how fast it falls.

This even includes "objects" which are massless particles moving at the speed of light. This logic also implies that if we have a neutron moving at slightly under 'c', it will follow almost the same path as a light beam that moves exactly at 'c'.

So we expect gravitational radiation to follow basically the same path as light, because both of them will follow geodesics, and a geodesic can be specified by a single point and a velocity at that point.

Potential sources of differences between light & gravitational radiation

light interacts with dipoles in the interstellar media (slowing the light down and not affecting the gravitational radiation).

Very very tiny effects in a very very strong gravitomagnetic field due to the Papapetrou equations (if the light and/or gravitational radiation are circularly polarized so that they have angular momentum).

[add]
There's another way to approach the question that I thought of - again, the key is the principle of equivalence.

Suppose we have an accelerating rocketship. In this rocketship, we have a beam of light, and a beam of gravitational radiation which "fall" along some path. I'm thinking of a path at right angles to the acceleration of the spaceship, but actually the orientation of the path doesn't matter.

The acceleration of the rocketship can be construed, by the principle of equivalence, to be the same as a uniform gravitational field for an observer moving with the rocketship. As long as we know that the beam of gravitons and the beam of light both move at 'c' in an inertial frame that they must appear to "fall" identically in the uniform "gravitational field" of the observer moving with the rocketship.

 

[Chaos' lil bro Order]

Excellent post Pervect, brilliant in its simplicity and insight, well done!

I am trying to summarize it in my head and have come to this notion, please tell me if its fair to say that:

Consider the case where the Sun refracted incident light very slightly (re: Eddington). Since it is the Sun's gravitational field that slightly warps space, and as you pointed out gravitons and photons will both take the geodesic path, it goes to say that both photons and gravitons would be refracted (have their paths slightly skewed inwards towards the sun) while glancing the Sun's gravitational field.

Thanks again for the great post!