How does light slow in the presence of gravity?

Naty1

I'm interested in some physical interpretations of how light slows in free space in the presence of gravity according to general relativity. I believe the reference frame is therefore distant, essentially infinity....say, as when we observe light moving toward a black hole or passing a star.

For example, in contrast to free space, when light enters a dense optical medium, a nice picture is to view photons being absorbed and new ones being emitted as photons move from atom to atom. The absorption and subsequent emission of a new photon delays the passage of photons hence "slowing" light.

But in free space, what happens? There are no atoms, only gravitons, and I don't think gravitons can absorb and subsequently emit photons, analogous to my example above, so what are some explanations for the electromagnetic (photon or wave ) and gravitational(graviton or field) interaction? It would also be interesting to know if all frequencies slow the same amount. I'm pretty sure they do. Why is this different than a dense optical medium where different frequencies slow different amounts. And is this slowing in free space related to the Shapiro time delay.

George Jones

The physically measure speed of light does not slow in the presence of gravity, only the coordinate speed does. Depending on the coordinates, the coordinate speed of light can be anything, even in special relativity.

Naty1

Well, what I am asking is when a suitable reference frame is chosen to observe a change in speed, what physical phenomena is taking place between the electromagnetic and gravitational entities? There IS some physcial causality! I don't what to choose a reference frame whether there is nothing to observe.

Naty1

Here is an example of wikipedia...if this isn't s change in speed for light what's happening:

http://en.wikipedia.org/wiki/General...ein.27s_theory

Naty1

Here is one source that generated my question:

http://www.physlink.com/Education/AskExperts/ae13.cfm

Naty1

Here is a quote from another post here:

http://www.physicsforums.com/showthread.php?t=144538

The speed of light in a gravitation field:

[quote]If, however, the distance through which the light travelled in the course of measuring its speed was too great, the deviation of the reference frame from being 'flat' would become apparent. That is, gravitational effects would begin to become apparent.

So, it is absolutely true that the speed of light is _not_ constant in a gravitational field [which, by the equivalence principle, applies as well to accelerating (non-inertial) frames of reference]. If this were not so, there would be no bending of light by the gravitational field of stars. One can do a simple Huyghens reconstruction of a wave front, taking into account the different speed of advance of the wavefront at different distances from the star (variation of speed of light), to derive the deflection of the light by the star.

Indeed, this is exactly how Einstein did the calculation....

c' = c0 ( 1 + V / c^2 )*

where V is the gravitational potential relative to the point where the speed of light c0 is measured.

So, the fact that the speed of light changes in a gravitational field was expressed by Einstein himself in 1911 (though he made in this paper an error in the derivation of the bending of light, which he later, luckily for him, corrected before the experiments were made)QUOTE]

* I modified the "C2" term on the post as I believe the correct term is c^2 as shown above.

atyy

The Shapiro time delay is a coordinate time delay. We can choose any coordinates we wish, so there are many viable definitions of the speed of light in General Relativity, and we just have to make it clear which definition is being used. The one definition that is always available is that the speed of light is the same in every local Lorentz frame. Since there is a (different) local Lorentz frame at every point in spacetime, the local speed of light in spacetime is constant in this sense.

This is presumably why the link you provided says: "The reason for the qualification 'properly defined' above is that the speed of light depends upon the vantage point (frame of reference) of the observer. When we say that the speed of light is decreased, we mean from the perspective of an observer fixed relative to the black hole and at an essentially infinite distance. On the contrary, to an observer free falling into the black hole, the speed of light, measured locally, would be unaltered from the standard value of c."

atyy

What you observe is independent of the reference frame. How you describe what you observe is dependent on the reference frame.

atyy

The usual textbook presentation of the Shapiro time delay is that it is the delay compared to what would happen if Newton's law of gravity were correct, and light were not affected by gravity. But when we do the experiment, we only have real light, which we do not yet know obeys General Relativity (since that is what we wish to test), and there is no such thing as Newtonian light against which to compare the experimental result for real light - so how can such a comparison be made?

Here is the quote from Will, Theory and experiment in gravitational physics, CUP 1993:
"Since one does not have access to a "Newtonian" signal against which to compare the round trip travel time of the observed signal, it is necessary to do a differential measurement of the variations in round trip travel times as the target passes through superior conjunction and look for the logarithmic behavior. To achieve this accurately however, one must take into account variations in round trip travel time due to the orbital motion of the target relative to the Earth ... The resulting predicted round trip travel times in terms of the unknown coefficient (1/2)(1+gamma) are then fit to the measured travel times using the method of least squares, and an estimate obtained for (1/2)(1+gamma). [This is an oversimplification of course. The reader is referred to Anderson (1974) for further discussion]"

meopemuk

Shapiro time delay experiment is very simple and straightforward. A radio signal is sent from Earth to Mars, reflects from the Mars surface and returns to the Earth observatory. If Sun is far from the Earth-Mars line then the measured travel time is

T = 2L/c (1)

where L is the Earth-Mars distance. If Sun is close to the Earth-Mars line the measured roundtrip time was found to be greater than (1). There could be only two logical explanations of this time delay.

(a) The Mars-Earth distance L increases when the Sun is between the two planets.

(b) The speed of light (c) decreases when it passes near the Sun.

The explanation (b) seems more reasonable to me.

Note that this slowdown effect can be calculated with a simple Hamiltonian describing the photon-Sun interaction. In the absence of such interaction the Hamiltonian of the 2-body system Sun+photon is

H_0 = Mc^2 + pc

where M is Sun's mass and p is photon's momentum. If the gravitational interaction is turned on, the Hamiltonian is

H = H_0 - 2GMp/(cr) = Mc^2 + p[c - 2GM/(cr)] (2)

where r is the Sun-photon distance and G is the gravitational constant. The term in square brackets can be interpreted as (distance-dependent) reduction of the speed of light. It is not difficult to show (using standard Hamilton's equations of motion) that Hamiltonian (2) yields exactly the measured Shapiro time delay. Note that the speed reduction does not depend on the photon's frequency (momentum). Moreover, the same Hamiltonian explains quantitatively the light deflection by the Sun's gravity.

Naty1

Meopemuk,

Thank's for that reference...I saw it somewhere but could not find it to post here.

In that description it seemed to me maybe the curving (warping) of space by the sun does make the distance traveled by light longer than would be measured as "L" from earth. (If we used a light based measure, we'd be unaware of any change.) So although the path would be the geodesic seen by photons as they travel we would not be aware of such a path observing from earth. Is that a correct interpretation?

Another question: What is "coordinate speed"...I can't find that term anywhere...not Wikipedia, not the popular physics and cosmology texts I use. I'm think I understand that the speed of light is always measured as "c" locally in general relativity, that is, if one sits adjacent to a photon when ones "measures" the speed of light and distances are small relative to curvature they appear flat (Euclidean) and speed is "c".

Is it correct to say when we measure sufficiently large distances for curvature to be a factor, the speed of light is "observed" to vary from c??

atyy:

I don't understand that...sounds like my description is inconsistent!!.....part of my general difficulty in interpretations is that I am unsure what assumptions are attributed to various observers. For example, all earth bound observers are immersed in earth's gravitational field...but an observer in nearly free space experiences far less gravity...so local time measure, for example, is different for each. I believe each therefore measures light speed differently at the others locale, but at c locally...is that the idea?

granpa

http://www.google.com/search?q=%22co...UTF-8&oe=UTF-8

Naty1

Wikipedia provides one possible interpretation:
http://en.wikipedia.org/wiki/Gravity...ntum_mechanics

Naty1

granpa....if you understand any of the google search results a brief interpretation would be appreciated....the first reference says:

But my question(s) pertain to general relativity, that is, in the presence of gravitational fields, while special relativity excludes gravitational effects....the difference between inertial frames (no acceleration) in SR and acceleration in GR prevents me from putting "coordinate" terms in perspective...

atyy

Coordinate speed or coordinate velocity is not such a common term, but it is what people mean when they refer to a velocity that is coordinate-dependent or observer dependent.
http://math.ucr.edu/home/baez/physic..._of_light.html

This can happen even in everyday space. Say you set out cartesian axes x,y,z, and you find there is a cat at x=1. Your friend sets out different cartesian axes which he also calls x,y,z and he finds the same cat at y=99. Is the cat really on the x axis or is it really on the y axis?

Naty1

OK!!....that sounds like a generic term for either SR or GR......any coordinates for observers other than local inertial coordinates for special relativity, and other than free fall for observers for general relativity....all those frames measure local light speed as "c"...

Quoting from a post above:
The reason for the qualification 'properly defined' above is that the speed of light depends upon the vantage point (frame of reference) of the observer. When we say that the speed of light is decreased,(going towards a black hole) we mean from the perspective of an observer fixed relative to the black hole and at an essentially infinite distance. On the contrary, to an observer free falling into the black hole, the speed of light, measured locally, would be unaltered from the standard value of c.

So a single coordinate frame of reference is used in that explanation..and that is ok by me because if I understand that explanation correctly, a difference is observed in the speed of light in free space and the speed of light approaching near a black hole.

So I am now back to my original post: So what's the physcial interaction causing that change? Is there one?...Is it Shapiro time delay an explanation??

atyy

Yes. The key is that in special relativity, spacetime is flat, and an observer can use global Lorentz inertial coordinates that cover all of spacetime. In curved spacetime, all observers have Lorentz inertial coordinates, but only locally. To describe something nonlocal, he must extend his local coordinates to global coordinates, which will be different from the global Lorentz inertial coordinates of flat spacetime.