# How fast can light change its direction?

1. Dec 2, 2011

### bmc001

I have a question about measuring the speed of light. As I understand it is done by sending photons from A at time t1 to B. B is at a distance d from A. At B there is a mirror, which sends the photons back to A. At A their arrival time is measured as t2. The velocity then is calculated by (t2 – t1) / 2d.
But is this calculation complete? At B there is a mirror, which changes the direction of the photons. The calculation assumes that the change of direction for the photons takes no time. But is this really the case? At B the photons have to interact with the matter of the mirror for changing their direction. How fast does it happen? I suppose that this time span (if there is any) for light to change its direction is very small compared to the accuracy of the measurement of t1 and t2 and d, or else we would calculate different speeds of light for different distances d between A and B (the longer d, the less important the time necessary for changing the direction).
Are these thoughts correct? Thank you.

2. Dec 2, 2011

### ghwellsjr

Yes, and if it took any time for the photons to change direction, you could measure that turn-around time by changing the distance d or by using the same distance and bouncing the photons many times back and forth between the mirrors.

3. Dec 2, 2011

### bmc001

Thank you for your answer. So the turn-around time is either very small or nonexistent. Are there theoretical reasons to assume it to be zero? The photons have to interact with the atoms on the surface of the mirror. Don’t these atoms form a sort of medium in which the speed of light is smaller than the speed of light in vacuum? What if I don’t use an ordinary mirror, but water to reflect the light?

4. Dec 2, 2011

### ghwellsjr

The photons interact with all the molecules throughout the mirror if it is silvered on the backside like most mirrors (to protect the silver) and so you actually get two visible reflections and if you were firing individual photons and timing them one by one, an almost impossible task, I might add, then there would be ambiguity. Water would have the same problem. That's why front silvered mirrors are always used in optical experiments.

5. Dec 2, 2011

### jewbinson

So you think the mirror absorbs the light, or the light sticks to the mirror before going off in the reflected direction? Okay, so to show the time, t3, that the light sticks to the mirror, is very small, we do two or more experiments.

The first one you do 1m apart. You will measure D1/T1 = c ~ 3 x 10^8 m/s, where D1 is the distance from A to B and back to A, and T1 is the TOTAL time taken (for this experiment). But you will not know how long it was stuck to the mirror for. So we have 3 unknown variables:

t1 - time taken for light to go from A to B
t2 - time taken from B back to A
t3 - time taken stuck to mirror.

To determine the 3 variables, you repeat the experiment either once or twice (I'm not sure yet) at different lengths for each experiment. Our 1st experiment had d = 1m, so for our second one choose d = 10m (why not...).

If t3 in the both experiments is significant (but the same value in both experiments), then the speed of light cannot be constant. If t3 in the first experiment is significant and t3 in the second experiment is 10x that of t3 in the first experiment, then the speed of light can be constant. But then why would the mirror absorption time be 10x more in the 2nd case than in the first, when we used the same mirror? It makes no sense... how can v1(t) and v2(t) (velocity of light in two different experiments) be the same in both experiments, and also t3 be the same for both experiments?

...Unless light accelerates away from a source; however I don't mean it stars at rest from a source... otherwise our everyday observations would be very different. I mean it starts at a high speed and accelerates away from the source.

I am pondering this and the answer will come soon. I imagine it has to do with a 3rd experiment.

6. Dec 2, 2011

### ghwellsjr

I didn't say the mirror absorbs the light (or the photons as the OP was talking about). I said if you used a rear-silvered mirror, then different photons can interact with different molecules resulting in two visible reflections (a bright one and a dim one) if you consider all the photons in a flood of light, but if you are considering them one by one, then you can get a range of times for the reflections and so you wouldn't use a rear-silvered mirror (or water) in an optical experiment. You would use a front silvered mirror to eliminate this problem in which case t3 is zero.

Photons have a length and they "reflect" off a front-silvered mirror identically which means there is no variation in the reflection time. They do not accelerate but it does take time for them to "get going" and to turn around in the sense that the leading edge of the reflected photon starts heading out while the rear end of the original photon is still coming in.

But, like I say, it is virtually impossible to do speed measurements using individual photons for many reasons, not the least of which is that it is almost impossible to know when a photon has left its emission source. Usually, speed measurements are made with very bright flashes of light to make them easier to measure. There are a lot of photons in a visible flash of light.

7. Dec 2, 2011

### jewbinson

Yeah I am ignoring your comment for the moment :).

I am trying to show what would happen if we tried to do experiments to show the speed of light is constant, and what problems of absence o knowledge would arise.

I do not assume outright that the speed of light is c. But I assume that (as in reality) in a measurement, the measured speed of light is c.

But making 1 measurement of the S.O.L. as c does not mean that it is. All you have measured is the total distance between the source and the mirror divided by the total time. You don't know what happens in between.

I am trying to show that you can experimentally verify that the mirror's "absorption time" is minimal (possibly 0), and that it is not significant, even over small distances.

I am not doing this experiment necessarily with a single photon. It is a flash of light if you want... it does not matter. Hopefully now you see the point of my calculations...

8. Dec 2, 2011

### ghwellsjr

Einstein would agree with you completely. Have you read his 1905 paper?

9. Dec 2, 2011

### jewbinson

No... I will probably find it interesting. But it looks quite time consuming

10. Dec 2, 2011

### ghwellsjr

For starters, just read the introduction and the first two sections after that. That part is very simple to understand.