# Speed of Light

1. Oct 4, 2004

### Roy_06

In a black hole, since light cannot escape are the photons slowed down or changed in direction?

2. Oct 4, 2004

### pervect

Staff Emeritus
The speed of the photon will always be 'c' according to measurements made by a local observer, using the local clocks & rulers of said observer.

The rate of change of the space coordinate with respect to the time coordinate of the photon will not in general be constant, and can even be zero, the latter occurs for instance on the event horizon of a Schwarzschild black hole when Schwarzschild coordinates are used.

Coordinate speeds (the rate of change of a position coordinate with respect to a time coordinate) don't in general have a lot of physical significance, as they depend greatly on the coordinate system adopted, which can be arbitrary.

When people talk about the speed of light being constant, they are talking about the measurements of the speed of light by observers using their own, local, clocks & rulers.

3. Oct 5, 2004

### Roy_06

So using e=mc^2 is the c based on the local speed of light? If something had a certain mass and hypothetically was right next to a black hole, would the energy of that object be 0 if the speed of light in that area was 0?

4. Oct 5, 2004

Staff Emeritus
The speed of light near a black hole is c.

5. Oct 5, 2004

### soeren

sorry, i wasn't very weak, when i wrote this.. so it's better i delete it ;-)

Greets
Soeren

Last edited: Oct 5, 2004
6. Oct 5, 2004

### pervect

Staff Emeritus
A local observer is just that - a local observer. Someone performing experiments near the event horizon of a black hole would measure the same value for the speed of light (using his clocks and his rulers) as would someone anywhere else. He'd also get the usual result for E=mc^2, if for instance he fused some deuterium-tritium and measured the energy produced.

An observer could do these experiments and come up with the same values even while falling through the event horizon of a black hole. (He couldn't stay stationary at the event horizon though, at least not without an infinite acceleration as measured by his clocks, rulers, and the seat of his pants.)

7. Oct 5, 2004

### Roy_06

Hopefully you all can understand how I could get confused about a topic such as this.

Question 1.

If I was observing the speed of light at the event horizon of a black hole, and wasn't moving myself, if the light was not moving to an outside observer (wasn't escaping the black hole), it just seems hard for me to imagine that I would view the light as moving at all - either away from the black hole or towards it or whatever the theory is, without time changing for me.

Edit: I guess the space-TIME is changed by the gravity not just space. However 0 x infinity is still 0 for the speed of light.

Question 2.

If a light bulb was turned on (a very very bright one), and I was one light-year away when the light was first turned on, and was moving away from the light bulb at the speed of light, would I see the light from the lightbulb in exactly one year (according to my clock).

Last edited: Oct 5, 2004
8. Oct 5, 2004

Staff Emeritus
Your question 1. Your error is in assuming that because the light inside the horizon never gets to an outside observer, therefore the light immediately outside the horizon is not moving. This does not follow logically, and is in fact not true. Compare this example from terrestrial physics. A certain rocket doesn't have enough speed to go into orbit. Does this mean that another rocket, which is in orbit, has no speed?

Your question 2. Under the assumptions, you would never see the light bulb, because the light from it would be chasing you at the same speed you were going, so it could never make up the initial gap between you and the light bulb.

9. Oct 5, 2004

### pervect

Staff Emeritus
The assumption that you can do this is incorrect. If you're at the event horizon of a BH, and you have a rest mass, you are moving.
The problem is with your initial assumption, you can't be at the event horizon and not moving in Schwarzschild coordinates unless you are massless

You can't do that either. Since you have rest mass, you can't move at light speed. There are a few interesting things you can do, but I hesitate to mention them, because it would probably just confuse you more :-(.

10. Oct 5, 2004

### franznietzsche

First realize that in relativity light moves between points with a null spacetime seperation. From one point on the event horizon to another point on the even horizon there is a null spacetime interval--meaning it is seperated by the speed of light. Between a point on the event horizon and a point outside it, there is a positive spacetime interval--meaning it would require faster-than-light travel. Note: Whenever i speak of spacetime interval, i've assumed that the time interval is positive (moving forward in time) as measured by the local observer.

11. Oct 5, 2004

### Roy_06

Ok what I attempted to post were hypothetical situations. I'll try to rephrase.

For question 1:
If I hypothetically was not moving within the even horizon -- somehow I could see but had no mass/energy -- why would the speed of the light that I observed not be 0?

For question 2:
Scenario 1
If I was one light-year away from a light bulb hypothetically (maybe I had 0 mass) moving at the speed of light away from the light bulb, when it was turned on would I never see the light from it.

Scenario 2
If I was hypothetically traveling at the speed of light -1, and was 1 light-year away from the light bulb moving away from the light bulb, when the light reached me would it appear to be moving beside me at the speed of light according to my clocks and rulers.

12. Oct 5, 2004

### pervect

Staff Emeritus
Hypothesizing impossibilities is always dangerous. The classic example is the old saw by Lewis Carroll, a perfectly valid and completely rigorous proof of the fact that if 2+2=5, I am the King of England.

I'd like to add the usual URL

to my previous response.

The problems with having a reference frame move at 'c' are legion and well-known (to people who have studied relativity) - I can see where the problems involved might not be as clear to someone who hasn't been through the same ground dozens of times. Hopefully, the above URL will illustrate some of the problems, and if that fails, at least communicate the idea that it _really isn't_ a good idea to spend a lot of time thinking about the answers to impossible questions. As the above URL also mentions, Einstein got away with it, but probably one of the key breakthroughs he made (IMO) was when he realized that it was a silly question.

Last edited: Oct 6, 2004
13. Oct 6, 2004

### chronon

Yes.

But there are a few things which need clarification. The assumption is that the light bulb was turned on at a certain time when it was 1 light year away, but you need to specify whose reference frames the time and distance are being measured relative to. I assume that it's your reference frame. However, all movement is relative, so you may as well say that you are stationary and that the light bulb is moving away from you at nearly the speed of light when it lights up, in which case it isn't that hard to believe once the light has left the bulb it doesn't matter what the bulb is doing, the light will take one year to reach you and be travelling at c when it passes you.

From the lightbulb's point of view things are different. You aren't 1 light year away when it flashes. However, you are moving away so fast that in the bulb's frame it takes many years for the light to catch up with you.

14. Oct 6, 2004

### chifos

the light is coverd by the strong radation made from the black hole it not that the light is sucked in it just gets blocked

15. Oct 7, 2004

### PatPwnt

Your question 2. Under the assumptions, you would never see the light bulb, because the light from it would be chasing you at the same speed you were going, so it could never make up the initial gap between you and the light bulb.[/QUOTE]

How so? I thought light traveled at C no matter how fast you were going. But, I guess it would take infinite time for the light to reach you relative to a person standing still. But, to the person that is moving, it would only take a year.