# Does gravitational differences affect the distance light travels? (a thought experiment)

My question is: How is light passing through different gravitational densities affected?

The value of "c" is constant in a vacuum. I'm curious about if various time frames have any effect.

This is the thought experiment that occurs to me.

Suppose we are doing a test in two different regions of the universe. In the first region, we have an observer in a place in between two galaxies. This is a region that should have the least amount of gravitational influence, being many thousands or millions of light years between centers of mass.

The second region is a place of high mass, thus high gravitational density. Suppose, for the sake of argument, that our second observer is in the middle of a Sol-sized star. Additionally, this star is transparent so we can shine light through it and it can come out the other side. Also, our observer is sufficiently protected so as not to be cooked and turned into heavier elements via nucleosynthesis.

The passage of time in each region will be different, where the observer inside the star will experience time moving slower relative to the observer in between the galaxies. Higher gravity, slower time passage.

To setup the model of the thought experiment:

We would measure the distance of a laser beamed between points A and B, where it passes through the exact center of the two spatial regions previously described.

The distance between points A and B is exactly one light second, or 299,792,458 meters.

Visually, it would look something like this:

A -------> CENTER -------> B


In the low-gravity region, it is expected that a laser pulse fired from point A will arrive at point B in exactly one light second, as expected.

In the high-gravity region, will a laser pulse passing through the center of the star arrive at point B in exactly one light second, or will it be delayed by passing through a region of space that has high gravity?

As I am thinking through this scenario, it occurs to me that there are at least a few ways of thinking about this in terms of perspective.

In the low-gravity location, I place points A and B in the same gravity as the center. However, in the high-gravity location A and B can exist in the same gravity as the center, or A and B might be points outside of the gravity region of the star's center.

There are also questions about where the passage of the laser is being observed from. In the low-gravity location, I put the observer in the same low gravitational field. However, in the high-gravity context the observer could be within the same high-gravity environment or could be observer the experiment from the low-gravity perspective. The high-gravity observer would see the experiment from the context of their time frame and might get different results than the observer from outside in the low-gravity time frame.

I am unsure how to reconcile these scenarios.

• A light-second is 299792458 meters, not kilometers, and also: how exactly is the distance between points A and B being measured? Is this one light-second along the path that the light ray travels between the points, or do you have some other definition? – David Z Nov 17 '11 at 5:48
• precisely, the length measuring device itself will succumb to the nasty space time curvature generated by the gravitation pull. So, effectively you would get your light pulse in 1 sec in both case... – Vineet Menon Nov 17 '11 at 6:12
• Thanks David for noticing that. I corrected the typo. It might have been lost in the length of the text, but I was careful to define the use of a laser versus a general light source. My understanding may be off, but I intended to present a scenario where a single point of light traveling in a confined direction would be used to avoid problems of gravitational lensing, etc. The basic answer to how you would measure the distance would be to set up points A and B at exactly one light-seconds distance from each other. In the low-grav region, A, B, and center are not influenced by external gravity. – Geuis Nov 17 '11 at 7:36

If you are asking whether gravity can slow down light passing from A to B, the answer is yes. You don't have to go to all the trouble you describe--- just make points A and B very far apart, and a then there are a whole host of nearly parallel paths of nearly exactly the same length between A and B, that light can travel on. In the absence of gravity, light will take an equal amount of time to travel along all these paths.

If you place a star in the middle, between A and B, it can focus some of these parallel paths to a point, which means that two parallel light rays collide. If two initially parallel light rays L and M collide, you can catch up to L by running alongside M, and swerving to hit L right before the point of collision. Since the first light rays that go to B from A are the first thing that reaches B from A, the focused light is not part of the forward front anymore, it has been slowed down by gravity.

Light is generically slowed down by passing through any region with a gravitational potential.

• Thats very interesting. In my scenario I intended the use of a laser to only test a single beam of light to avoid complicating the idea with parallel paths. Would it be measurable, then, that in the high-gravity region that the laser passing through the star would take 1.00001 seconds (or whatever fractional amount of time longer) to arrive at B than in the low-gravity region? – Geuis Nov 17 '11 at 7:41
• These downvotes are tiresome--- there is nothing wrong with this answer, and it is well known stuff. – Ron Maimon Nov 17 '11 at 14:41
• @Geuis: the problem is that the notion of time in gravity is local, so that when you put a star there, how do you synchronize the clocks? The reason for parallel rays is that when they focus, you get an objective way to say that light has slowed down, without needing distant synchronization, which is impossible in a general gravitational field. – Ron Maimon Nov 17 '11 at 14:42
• Ahh, thanks Ron. I think I understand. A light source generates photons which travel as waves and move along all possible paths. The light source is point A. I am at point B. There is a high-gravity region exactly centered between us. Light traveling close to the star is bent towards it before reaching me. If I measure both the focused and unfocused light when it reaches me, the unfocused light will reach me slightly before the light that was influenced by the star. Is that more or less right? – Geuis Nov 17 '11 at 20:00
• @Geius: that is not more or less right, it is precisely right. – Ron Maimon Nov 17 '11 at 23:38

The speed of light is only locally invarient. For example if you stand well away from a black hole and shine your laser at it you'll find you see the light slow down as it approaches the event horizon.