# Speed of Light: Does It Slow Down in a Gravity Field?

In summary, when light bends in a gravitational field due to the effects of general relativity, its speed is slowed down. However, this effect is negligible for objects located far away from a gravitational source.f

Since light bend in gravitational fields in line with the general relativity , does the speed of light slows down? or is it always constant and never change?

Since light bend in gravitational fields in line with the general relativity , does the speed of light slows down? or is it always constant and never change?
Light does not change speed in a vacuum, it just follows the local geodesic, which makes it look bent in terms of Euclidean geometry. A geodesic is a straight line in space-time (Riemann geometry).

Since light bend in gravitational fields in line with the general relativity , does the speed of light slows down? or is it always constant and never change?

As seen locally, the speed of light is always the same everywhere.

However, if you want to describe what happens in a larger region, for example to describe a free-fall path relative to distant stars, you have to choose how to map the locally curved space-time to a convenient Euclidean coordinate system. This is similar to mapping a large area of the curved surface of the Earth, where you have to choose how to project it onto flat paper. Relative to the map, the coordinate speed of light will vary slightly, as if space-time had a sort of "refractive index". Using a typical coordinate chart which matches up with flat space at sufficient distance from the gravitational source, you will find that light apparently bends as it passes the source, and therefore that the speed of light relative to the coordinate system at a lower potential is effectively slightly slower than it is at a higher potential.

the speed of light relative to the coordinate system at a lower potential is effectively slightly slower than it is at a higher potential.
As i understood, that will not affect the fixed speed of light, i wonder what kind of engergy drives light to maintain it's speed?

As i understood, that will not affect the fixed speed of light, i wonder what kind of engergy drives light to maintain it's speed?
Why would it need any energy to maintain speed? What would slow it down?

Since light is a form of energy, and can be measured in energy units (joules, or quanta), therefore what cause , feed, create or drive that energy to maintain a fixed and constant speed, it baffled me

it baffled me

It should. What you wrote down is not correct.

Since light is a form of energy, and can be measured in energy units (joules, or quanta), therefore what cause , feed, create or drive that energy to maintain a fixed and constant speed, it baffled me

As light climbs out of a gravitational potential, it doesn't lose speed, but it does lose energy. This is the gravitational red shift.

While light may not lose speed coming out of a gravity well, does it have a longer path to take than it would otherwise?

I have wondered about the same question...

Observe light's path appears to bend passing by a massive object.

Imagine two lines, one tangent to a point on the path, and another that represents the inward orthogonal component vector of the path's deviation from a straight line.

Which speed of light is the one that is constant?

The one tangent to the light's path?
or
The speed that comprises the vector sum of the tangent and orthagonal components?

If it is the first one, then it seems light should speed up when bent.
If it is the second one, then it seems that the speed of light should slow down when bent.

Another way of asking this is, "Which is the forward direction of light when it is making a bend? The tangent or the inward pointing vector sum?"

While light may not lose speed coming out of a gravity well, does it have a longer path to take than it would otherwise?

This question is a little nuanced in GR. One could roughly say yes, the presence of a gravitational field "increases the path length" taken by the light ray and thereby accounts for the Shapiro delay. Alternatively, one can think of the Shapiro delay in terms of time dilation within the gravitational field. Which view to take is...as far as I know, personal preference. Kip Thorne, for example, takes the former view in his description of Shapiro delay in The Science of Interstellar (I know it's not a physics text or anything, but I think we can trust the great Kip Thorne on this part of GR), but Wikipedia takes the latter view in its description of Shapiro delay. The photon's path is of course null, and the proper length along its world line is 0.

While light may not lose speed coming out of a gravity well, does it have a longer path to take than it would otherwise?

This Quote addresses the heart of my question,
Fig 1 is a straight path of light
Fig 2 is a path of light that is bent by Gravity

the question is will both rays of light reaches from (a) to (b) at the same time?

View attachment 76766

This Quote addresses the heart of my question,
Fig 1 is a straight path of light
Fig 2 is a path of light that is bent by Gravity

the question is will both rays of light reaches from (a) to (b) at the same time?

In GR, where the space is curved, how would you like to define the "straight path of light"? The light will never take that "straight path" as gravitational lensing is a real thing, so the only thing you can compare is "how long would light take to go from A to B if there were no central mass compared with how long would light take to go from A to B with the presence of the central mass?" The answer to that is "without the central mass, the light takes a slightly shorter time to get from A to B, the longer time required in the presence of the central mass is the Shapiro delay". http://en.wikipedia.org/wiki/Shapiro_delay