# Vertical speed of light?

1. Feb 29, 2012

### GTOM

How many experiment measured the vertical speed of light?
I wonder, how can gravity affect it?

2. Feb 29, 2012

### sambristol

The speed is not changed but the energy is look up the Pound Rebka experiment in a search engine

3. Feb 29, 2012

### ghwellsjr

Can you propose an experiment?

Keep in mind that you must make a round-trip measurement using a clock at one end, a mirror at the other end, and a rigid mechanical structure holding the two objects a measured distance apart.

We already know that gravity effects the rate at which a clock ticks. Therefore, if you used the same vertical structure to perform two similar measurements at the same time, one with the clock at the bottom (and a mirror at the top) and the other with an identical clock at the top (and another mirror at the bottom), and you assume that the length of the structure is the same (I'll get to that later), then of course you will get two different values for the speed of light.

But now the question is: how do you know what the correct value is for the length of the structure? If you laid the structure out horizontally at the bottom location and measured it and then raised one end, wouldn't you expect it to compress and become shorter? On the other hand, if you laid it out horizontally at the upper location and then measured it and then swung one end down, wouldn't you expect it to stretch and become longer? So wouldn't it be reasonable to assume that from the point of view of the bottom clock, the structure was shorter than from the POV of the upper clock?

Now we know that the clock at the bottom runs slower than the one at the top. I don't know, but it seems possible to me that from the POV of the bottom, with the slower running clock and the shorter distance, the calculated value of the speed of light would be the same as the from the POV at the top, with the faster running clock and the longer distance.

What it really boils down to is determining the measured value of the length of the "rigid" structure.

4. Feb 29, 2012

### nitsuj

does that mean energy of a wave is relative? I wonder if that could be extended to colours are relative.

5. Feb 29, 2012

### sambristol

The energy is affected by the gravitational field - if the light is 'falling down' it ends up with higher energy and if it is 'going up' it arrives with lower energy.
The energy is directly related to the colour - Planck gave us E=h.f where h is called Plancks constant and f is the frequency and the frequency is directly related to the wavelength l (and so the colour) by c= l.f where c is the speed of light so energy is related to wavelength by l= (h . c) / E

6. Feb 29, 2012

### Khashishi

The speed of light using local coordinates is unchanged. On the other hand, the speed of light using coordinates from flat space infinitely far away from the mass, and somehow projecting these coordinates on top of the mass, I think the speed of light would decrease in this case. But that's not really correct procedure.

7. Feb 29, 2012

There is a thought experiment that reveals a surprise to many people. A ray of light travels through empty zero gravity space from one place to another. We measure the distance between the two places and the light’s time of flight (with synchronised clock’s at either end of the journey), and get the usual value of c for the light’s velocity.

Now the experiment is repeated with a large mass, such as a planet, somewhere between the start and the end points. There is a hole right through the centre of the planet, allowing the light to pass through. This time, the amount of time the light takes to get from the start to the end point is greater. So our simple calculation of velocity gives a smaller value than c. This assumes we are still using the clocks stationed at the start and end points.

As pointed out in the previous post, an observer positioned at any point along the light’s flight path would always find the light’s velocity as it passed by to be c.

I remember reading this in a book called Relativity Visualised. It’s low on maths but high on getting across the gist of some very difficult stuff. I lent it to someone years ago and never got it back!

8. Mar 1, 2012

### yuiop

According to the Schwarzschild metric the coordinate vertical speed of light is proportional to $(1-r_s/r)$ while the coordinate horizontal speed of light is proportional to $\sqrt{1-r_s/r}$.

In other words the coordinate speed of light is slower vertically that it is horizontally and slower lower down than higher up. However, as others have pointed out local observers always measure the speed of light as c. If you were to measure a vertical distance using rulers the distance would differ from the distance measured using a two way light travel time method that assumes a constant velocity for the speed of light. These measurements would also differ from the theoretical distance you would obtain from measuring the circumference of two rings and calculated the radial difference using Euclidean methods (which assumes flat space).

9. Mar 5, 2012

### GTOM

I had read about Pound and Rebka, but it was meant to test gravity redshift, as far as i know.

I wondered on the following thing : how can a black hole keep the light beyond the event horizont?
I dont really like the singularity explanation, that requires that something goes infinite, but even a black hole has a finite mass.
If gravity can accelerate light, than inward speed can be 2c, while outward 0.

10. Mar 5, 2012

### pervect

Staff Emeritus
If you measure the speed of light with local clocks and rulers, you'll always get 'c'. This is even true at the event horizon of a black hole - though the only physical observers there will be falling into said black hole.

That said, if you were on a spaceship falling into a black hole, and you measured the speed of some light signal "trapped" at the horizon, it would appear to be moving at the speed of light - it wouldn't appear to be stationary or anything.

Measuring the speed of light in terms of coordinates is tends to be misleading in any physical sense - because coordinates are arbitrary.

An example of measuring the speed in terms of coordinates on a curved surface would be to think about measuring the speed of a naval vessel, by looking at how many degrees of lattitude and how many degrees of longitude it can cover per hour.

One wouldn't seriously belive that the naval vessels "speed up" as they move away from the equator, approaching infinite speed at the poles, because they can move more degrees of longitude per hour. It would be obvious in this case that it's an artifact of the coordinates used. Unfortunately, people don't seem to realize this also applies to black holes. Some can't figure it out even after it's been pointed out...

11. Mar 5, 2012

### GTOM

"One wouldn't seriously belive that the naval vessels "speed up" as they move away from the equator, approaching infinite speed at the poles, because they can move more degrees of longitude per hour."

That analogy still dont explain, why cant light come out, if it dont speed up or slow down...
If it is sucked in by a whirl, so it cant come out, it is speed may not change compared to the water, but change to an outside observer.

12. Mar 5, 2012

### pervect

Staff Emeritus
In the end, it all boils down to the mathematics. The popularizations are just an attempt to "sugar-coat" the math. So, to really understand what's going on and get the correct answers, you need to understand the math. If you're going from just the popularizations, you may or may not get the right answers without the math to guide you, as the popularizations are not always perfect.

That said, there are a number of different approaches one can use. The river model, http://arxiv.org/abs/gr-qc/0411060, may be particularly easy to grasp for non experts.

One thing I don't like about the river model is related to the central idea of space flowing. Any attempt to measure such a flow with instruments is doomed to failure according to special relativity, so it's a bit suspicious that the explanation involves a concept that's not measurable.

That said, it does provide an easy-to-grasp model that explains the prominent features of the horizon in a way that's mathematically correct and hopefully easy to grasp.

Another approach, which is more geometrical, requires a bit of SR to appreciate properly. THis is Marolf's space-time embedding, given in http://arxiv.org/abs/gr-qc/9806123. This shows how one can draw the space-time diagram for the r-t plane of a black hole, a 2 dimensional graph, on a particular 3-dimensional curved surface. It's an embedding diagram for the space-time diagrams - or to put it another way, general relativity can be thought of as drawing the space-time diagrams of special relativity on curved surfaces rather than on "flat" pieces of paper - at least if you don't have any more than one spatial dimension.

To appreciate this model, one does have to understand special relativity enough to know what a space-time diagram is. If one wants to apply it to moving observers, one needs in addition some familiarity with the Lorentz transform.

Around page 11, Marolf discusses the part about light not escaping.

Regions I and II on this diagram are the inside and outside of the black hole. Regions III and IV are white-hole regions. The white hole regions (interior and exterior) an interesting feature that arises from the Schwarzschild geometry which are not necessarily found in a more generic black hole. If you find them confusing, you can ignore regions III and IV if you like, they won't be reachable from our space-time.

13. Mar 7, 2012

### timmdeeg

The dynamic space notion is often used in connection with the Lense-Thirrring effect. Like here:
http://www.nasa.gov/vision/earth/lookingatearth/earth_drag.html
Whether free fall or spiral falling, the thought flow of space coincides with the behaviour of test particles. Said flow isn't measurable. But is the common expanding space interpretation of the cosmological redshift measurable?

I just wonder whether such notions which are in accordance with the observation are nevertheless unphysical because of the lack of measurability.