If 2 spaceships travel at the speed of light

[Conal]

This is probably a stupid question but why is it that if 2 spaceships pass by each other traveling at the speed of light (assuming that is possible) in opposite directions, they are not traveling 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?

 

[Severian596]

Good questions all. Here's the answer to your first question:
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

You don't add velocities at relativistic speeds (near light speeds) like you do much slower speeds. You must take extra factors into account, and this page explains them succinctly. Google "relativistic velocity addition" for more info.

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 spatial construct (x,y,z coordinates) like in an absolute-space-and-time model.

 

[Conal]

Thanks, that's 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 don't 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 can't add the 2 velocities. Maybe I just need to think about it for a while...

 

[ZapperZ]

Thanks, that's 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 don't 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 can't add the 2 velocities. Maybe I just need to think about it for a while...

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.

 

[jtbell]

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 can't add the 2 velocities.

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?

 

[Severian596]

Thanks, that's helped me comprehend it a bit better...I assume that technically the same formula should apply to 2 cars driving towards each other at 50mph each...

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.

 

[Conal]

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

 

[derz]

This link should get you started:

http://en.wikipedia.org/wiki/History_of_special_relativity

 

[zeusalmighty]

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.

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?

 

[MeJennifer]

What still bothers me is that if I'm going 186000 miles a second, in one second I will cover 186000 miles.

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.

 

[Severian596]

But the gap between us can still close faster than the speed of light, right?

Wow! Frankenstein thread! I wouldn't have ever noticed this if I hadn't received an email notification.

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.

 

[Doc Al]

What still bothers me is that if I'm going 186000 miles a second, in one second I will cover 186000 miles.

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.

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.

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.

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?

Again, as seen by some third party, not as seen by you. In no case is anyone measuring the speed of anybody as being greater than light speed.

 

[zeusalmighty]

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.

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 traveling toward me is traveling 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 traveling 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?

 

[Doc Al]

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)?

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

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 traveling toward me is traveling at 186,000 miles per second, then in one second, should we not have both covered 186,000 miles?

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.