# Speed of light Schmeed of light: things can travel faster

1. Mar 18, 2004

### Namloh2000

okay guys:
i understand relativistic principles but bear with me:

i gots two bodies traveling in opposite directions from a central point in space. both are traveling at .7c

relative to either one of the bodies, isn't the other traveling faster than c?

if there's no absolute rest, everything has to be measured relative to everything else, so this has to be so (even though i know that it may not).

would one body ever see the other while they were moving (would light from one body not be able to "catch up" to the other)?

2. Mar 18, 2004

### Severian596

I'm just a novice at the math behind SR.

It sounds like you've got an incorrect assumption based on your "stationary" observer; that central point in space, C. Just because C observes A moving at 0.7c relative to itself, and B moving at -0.7c relative to itself, that doesn't mean that A and B will observe each other moving at 1.4c. More likely, because A and B do not fall within each other's light cones they'll never observe each other at all.

I'll think on this a bit more until someone else replies.

3. Mar 18, 2004

### Staff: Mentor

As a matter of fact, thats pretty much the funamental postulate of SR.

Namloh2000, you're trying to reconcile Einstein's relativity with classical mechanics. You can't. Put quite simply, Newtonian physics gets less and less accurate as speeds get higher and higher. I know at first read Einstien's relativity is hard to accept, but there is a mountain of emperical evidence supporting it. It really is how mechanics works on a macroscopic level.

4. Mar 18, 2004

### Namloh2000

that's what i don't like... it's mechanics on a macro-scale - if it doesn't apply to everything it's not right...

where's a GUT when ya need one?

5. Mar 18, 2004

### HallsofIvy

Staff Emeritus
"i understand relativistic principles "

No, you don't. If you did then you would know that if two objects are moving directly toward one another, each moving at 0.7 c relative to an object between them, there speed relative to one another is

(0.7c+ 0.7c)/(1+ (0.7c)(0.7c)/c<sup>2</sup>)= 1.4c/1.49= 0.940c, still slightly less than the speed of light.

6. Mar 18, 2004

### Janus

Staff Emeritus
But it does apply to everything. (Relativity that is)

Take your example; two rockets each heading at .7c relative to, and towards point C. Newtonian physics would have you add the velocities like this:

$$u+v=w$$

and get

$$.7c+.7c= 1.4c$$

for the velocity of each rocket to each other as measured by either rocket.

Relativity says you have to use the following formula instead.

$$\frac{u+v}{1+\frac{uv}{c^{2}}}$$

and get an answer of 0.94c

and that this is the correct formula for adding any velocities no matter how small. It is just that when adding small velocities, this formula will give an answer so close to the first formula, tha the difference can be safely ignored.

And since the answers at low velocities differ by so little, and until fairly recently we only had experience with such low velocities, we were fooled into believing that the first formula was the correct one.

7. Mar 18, 2004

### Tom Mattson

Staff Emeritus
The SR velocity addition law does apply to everything.

8. Mar 18, 2004

### Namloh2000

hey guys by opposite directions, i meant away from eachother, not towards...

9. Mar 18, 2004

### Janus

Staff Emeritus
Same difference. It doesn't matter if they are moving away or towards, the same rules apply.

10. Mar 18, 2004

### Staff: Mentor

So its .94C towards each other or .94C away from each other.
It isn't that it doesn't apply to very small things, its just that over small distances, quantum fluctuations have more and more of an effect. An electron (for example) is so small that quantum uncertainty is relatively large compared to its size. By the same token, while there is a very real and finite quantum uncertainty in your position, compared to your size its very small and isn't relevant in most situations.

11. Mar 18, 2004

### Namloh2000

thank you all that posted! as i am naieve in my knowledge of physics, i am nonetheless adept at learning.

as my knowledge partly stems from the questions i ask, and when an apparant inconsistancy or misunderstanding will frustrate me; i am glad i may ask my questions in such a community, proving prompt and knowledgeable answers

12. Jul 23, 2008

### azzkika

me too. i posted another thread enquiring about lights susceptibility to gravity, and if it can vary the speed of light, and if this is so, is there a constant speed as gravity is not constant?

13. Jul 23, 2008

### ZapperZ

Staff Emeritus
You have a faulty logic here. The SPEED of propagation of something isn't the same as the AMPLITUDE of something. I can vary the intensity of light as well. By your logic, I've varied the speed of propagation of light. This isn't correct.

Zz.

14. Jul 31, 2008

### HallsofIvy

Staff Emeritus
Gravity does NOT change the speed of light. Where did you get that impression?