# Question's About the Speed of Light

1. Oct 15, 2004

### Gecko

ok, im new to SR and had a couple questions about the speed of light. The first is, i recently read that if 2 beems of light where going towards each other at the speed of light, the distance between them would close only at 1 c instead of 2c. how is it possible that the distance between only closes in at the speed of light? shouldnt it be 2x the speed of light?

the second actually pertains to light traveling faster than 300,000 km/s. there is a site HERE that says that they have recorded light traveling waaaay faster than the speed of light. wouldn't this really screw up SR and GR? also, is this true, or, how would this be worked out in SR and GR?

thanks.

2. Oct 15, 2004

### mijoon

That is incorrect.

I should be and is.

The end of the article says;

William Happer, a physicist at Princeton University argued that several specific problems exist with the experiment, including the fact that pulses get distorted when passed through any media other than a vacuum, or empty space.
In addition, he said Wang and his colleagues performed the experiment in a way that doesn’t tell the whole story, and that it can be interpreted incorrectly. "This is anything but dramatic," said Happer. "If you look at the data, there’s essentially no evidence that [the beam] is going faster than the speed of light."

3. Oct 15, 2004

### Staff: Mentor

Here's an example that may clarify things. Say we have two flashlights 2 lightyears apart (as measured by us on earth; pretend the flashlights are on space stations at rest with respect to the earth). If we turn on the flashlights, how long does the light take to cover the distance and meet in the middle? One year, of course, since each beam travels at the speed of light = 1 lightyear/year. So, in a sense, the relative "separation rate" of the two light beams is 2c, since they get 2 lightyears closer in one year. But note that each light beam always travels at the same speed c with respect to any observer (in this case, us on the earth).

This is no different than having two runners who can run a 4 minute mile sprint towards each other. If they start a mile apart, they will meet in 2 minutes. Does that mean they can run a two-minute mile? Of course not.

What the original statement was probably referring to is this: Say two high-speed rockets are traveling directly towards each other, each moving at 0.99c with respect to the earth. If they are initially about 2 lightyears apart (according to our earth measurements) then they will crash in about one year (again, according to our earth measurements). But what would the pilot of one rocket measure as the speed of the oncoming rocket with respect to him? Special Relativity tells us that the relative speed of Rocket 2 as measured by Rocket 1 is:
$$v = \frac{0.99c + 0.99c}{1 + 0.99 \times 0.99} = 0.99995 c$$
So the relative speed of the oncoming rocket approaches, but never quite reaches, the speed of light. (Of course, for this to make sense, other relativistic effects must also be considered, such as "length contraction".)

4. Oct 15, 2004

### Gecko

yeah, thats the formula i saw. thanks for clearing that up. and i only read about half that article so i never saw the ending -.-' so does the formula you used only work for objects that have mass? which means they couldnt travel faster than light, or that formula only works for speeds less than light.

also, why is it that the speed of rocket 2 relative to rocket one is .99995c instead of almost 2c? arent they both feeling accelerations which would mean that neither could claim to be at rest so they would both have to be traveling at .99c and close in at 1.98c. and judging from your last sentance, this could probably be answered if i where to take into account "length contraction" which judging be the name means that the distance between the 2 ships would be half as long relative to one of the ships, so they would close in at half the speed but have to travel half the distance as well. thats what im guessing anyway ^.^'

5. Oct 15, 2004

### CJames

From any given reference point, it is impossible for anything to travel faster than the speed of light. If we watch these two rockets from Earth, they will both be traveling near the speed of light, and as he said the "separation rate" would be close to 2c. However, from the point of view of the rockets, the other rocket must be traveling slower than the speed of light. And yes, this is due to length contraction or time dilation, depending on whose point of view you take.

6. Oct 15, 2004

### Gecko

ooohhhh, ok i got it now. thanks alot you guys. last question (i think) does what you (CJames) posted also apply to light? like if the referance was from one beam of light that was heading towards another, the beam of light that was coming would only be traveling at c with respect to the other beam of light? but to someone observeing the 2 beams of light, the distance would be closing at a speed of 2c?

7. Oct 15, 2004

### Severian596

Good thought, Gecko, but unfortunately light beams do not have reference frames. It's impossible to define a frame of reference where a light beam (or a photon, for that matter) is at rest. If you attempt it, the photon's spacial axes x, y, and z, and its time axis t, begin merging (during the Lorentz Transformation to velocity v=c). Eventually the photon's "frame of reference" would only have one dimension, time, and one unit of measurement on this axis would be infinitely long.

In summary, things that apply to matter don't apply equally to photons or light beams.

(ps You guys can correct the nuances of my statement. I performed something like this a while ago and got a huge distortion of t' and x', where x' shrunk indefinitely, and t' expanded indefinitely...it looked like an infinity/zero problem, so that's why I assumed it was undefined. Someone else confirmed this at the time, and I believe this fits with current accepted theory)

8. Jul 8, 2009

### Guesser7

This question is irrelevant as the observer is stationary. It is like the relevance of a pedestrian crossing a road with two cars approaching from oposite directions at other at 30mph, the cars are not doing 60mph and he would no have to cross the road any faster.

On the other hand if you could be sitting on one of the beams of light it would also be irrelevant as for you time would stand still and nothing would be observed to move.

As far as two beams of photons where some collide they would convert to mass. However we would have an almost incalculably small amount M=E/C2