# If 2 spaceships travel at the speed of light

1. Mar 1, 2006

### Conal

This is probably a stupid question but why is it that if 2 spaceships pass by each other travelling at the speed of light (assuming that is possible) in opposite directions, they are not travelling at 2 times the speed of light from each others perspective. How can there be any speed limit at all if there is no point in space that is stationary? Is it because time is warped at such speeds?

2. Mar 1, 2006

### Severian596

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

The "speed limit" does not require a stationary point in space. Since all moving bodies will measure the same speed for light in a vacuum (postulate #1 of the Theory of Special Relativity), THAT is what makes it the speed limit. You don't need to be stationary; you can be moving and you will still measure the same speed of light, so that fact is the thing that all moving objects have in common. Not a rigid spacial construct (x,y,z coordinates) like in an absolute-space-and-time model.

3. Mar 1, 2006

### Conal

Thanks, thats helped me comprehend it a bit better. I can accept that using einstein's velocity addition formula no object can exceed a speed of c from another's point of view. But I still dont know why. I assume that technically the same formula should apply to 2 cars driving towards each other at 50mph each - i just don't see why you cant add the 2 velocities. Maybe I just need to think about it for a while...

4. Mar 1, 2006

### ZapperZ

Staff Emeritus
This is because when you use the term "velocity", you have implicitly assume the nature of the "space" and "time" that is used to measure and define those two quantities (recall that velocity depends on the time rate of displacement). Under normal circumstances, these are your Euclidean space and time that assume the instantaneous motion of light. At slow speeds, this assumption is valid since c is such a large value.

However, at larger speeds, when v is comparable to c, then our idea of defining "space" and "time" is no longer the same. This means that what we term as "velocity" also needs to follow a new set of rules. How a velocity, a length, and a time are measured/defined now becomes significant.

Zz.

5. Mar 1, 2006

### Staff: Mentor

Try calculating what the relativistic velocity-addition formula actually gives you for two cars driving towards each other at 50 mph (or 50 m/s which makes the arithmetic easier). How much different is this result from ordinary velocity addition, and how easy do you think it would be to detect the difference?

6. Mar 1, 2006

### Severian596

You're welcome! Glad to help. ZapperZ (as always) has provided a very concise and informative answer to your next question or why we can't straight-up add velocities together. I just popped on to say that you can use the relativistic velocity addition method at normal speeds. the factors that use c just become insignificant.

In fact...General Relativity equations act this way with all Newtonian calculation methods (as far as I know). GR equations perform "equal to or better than" their Newtonian counterparts because at low speeds the relativistic components drop out, and at high speeds they yield correct results where Newtonian equations break down.

7. Mar 2, 2006

### Conal

Are there any good links about what led einstein to his theory?

8. Mar 2, 2006

### derz

9. Sep 11, 2008

### zeusalmighty

What still bothers me is that if I'm going 186000 miles a second, in one second I will cover 186000 miles. So if I am 372,000 miles away from another speed of light traveler facing me and we both are going the speed of light toward each other, then I will cover 186,000 miles in a second and the other traveler will cover 186,000 miles in a second, so the gap between us will have gone from 372,000 miles to 0 in 1 second - twice the speed of light.

The links that you have pointed to describe the relative velocity with respect to an external viewer or either me or the other traveler. But the gap between us can still close faster than the speed of light, right?

10. Sep 11, 2008

### MeJennifer

What do you think when you write 'cover'?

Remember that you are always going at a certain speed with respect to something else, there is no such thing as an absolute speed, all speed is relative.

11. Sep 11, 2008

### Severian596

Yes, the distance between two objects (relative to a 3rd perspective in this case) can change at faster-than-light speeds. The distance between two objects is a massless piece of information.

12. Sep 11, 2008

### Staff: Mentor

If you are moving at that speed with respect to a third party (Earth, for example), then you will cover 186,000 miles as measured by you in one of your seconds. If you happen to be 186,000 miles away from Earth as measured by Earth observers, then in one Earth second you will reach Earth.
Only as measured by a third party. Your speed with respect to each other will still be a bit less than light speed. So if you are 372,000 miles from each other according to your measurements, then it will take about 2 seconds for you to meet.

If you are both 372,000 miles apart as measured by some third party (Earth, say), then according to the third party's measurements you will meet in 1 second.
Again, as seen by some third party, not as seen by you. In no case is anyone measuring the speed of any body as being greater than light speed.

13. Sep 11, 2008

### zeusalmighty

If speed is relative, does that mean that the speed of light is also relative? If so, then why is 'c' a constant? Isn't 'c' 186,000 miles per second (about 300,000 km/s)?

So relative to a fixed point in a vacuum with no large gravitational bodies nearby (so a basically flat space-time??), if I travel 186,000 miles in a second, and the guy travelling toward me is travelling at 186,000 miles per second, then in one second, should we not have both covered 186,000 miles? Going toward each other doesn't change our speed, does it? If we are travelling side by side, we would be exactly even the entire way with respect to any fixed point, right? Let's define my point on the line (x), the midway point (y) between my starting point (x) and the other traveler's starting point (z). If me and the other traveler can travel identical speeds, but we perform this test separately, I can travel from x to y just as fast as he can travel from z to y, right? So what changes when we are both simultaneously performing this test?

14. Sep 11, 2008

### Staff: Mentor

All speeds are relative to something, else meaningless. Light is interesting as its speed is always c with respect to any observer.

Again, to have a speed you must have a speed with respect to something. "A fixed point in a vacuum" means nothing. Reread my earlier post and see if that clears anything up.