Two objects moving away from eachother at c - Special relativity

In summary, the conversation discusses the concepts of time dilation, the twin paradox, and length contraction in relation to two rockets moving away from each other in space. The question is raised about whether the reference frame of one rocket would see the other rocket moving at a speed greater than the speed of light. It is explained that this is not the case and the actual speed would be 0.9987c. The conversation also touches on the idea that light travels at c in a vacuum and how this applies to the scenario.
  • #1
vorcil
398
0
While I've got all the concepts of time dilation,the twin paradox and length contraction in my head, I still can't get my head around the fact of the following scenario,

Just imagine two rockets in space, moving away from each other in opposite directions at 0.95c or even just c,

in the reference frame of one rocket, wouldn't the other rocket be moving at a speed greater than the speed of light?

what is happening to the opposite moving rocket in one rockets reference frame?
is it getting younger? because of time dilation, wouldn't it turn out to be going back in time? and getting larger instead of contracting(or is it stretching negatively?)

help thanks
 
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  • #2
another thing, light travels at c in a vaccum, so assuming the rockets are traveling in a vacuum also, they won't be able to see each other because in all of the reference frames, they are traveling faster than c"?
 
  • #3
One thing at a time:
vorcil said:
Just imagine two rockets in space, moving away from each other in opposite directions at 0.95c or even just c,

in the reference frame of one rocket, wouldn't the other rocket be moving at a speed greater than the speed of light?
No, it wouldn't, and here's why: first, those .95c speeds you're talking about are measured from a certain reference frame. Let's say that's the Earth's reference frame. But to find the speed of rocket 2 in the reference frame of rocket 1 (which is what you're asking about), you have to "boost" yourself from the Earth's reference frame to the rocket 1 reference frame, and when you do that, the velocity of rocket 2 changes like so:
[tex]v' = \frac{u+v}{1+\frac{uv}{c^2}}[/tex]
It's not just simple addition, like you might think. So .95c + .95c is wrong. When you plug into the proper formula, you get
[tex]v' = \frac{.95c+.95c}{1+\frac{(.95c)(.95c)}{c^2}} = 0.9987c[/tex]
So in the reference frame of rocket 1, rocket 2 is moving at 0.9987c, which is close to but still less than the speed of light.
 
  • #4
diazona said:
One thing at a time:

No, it wouldn't, and here's why: first, those .95c speeds you're talking about are measured from a certain reference frame. Let's say that's the Earth's reference frame. But to find the speed of rocket 2 in the reference frame of rocket 1 (which is what you're asking about), you have to "boost" yourself from the Earth's reference frame to the rocket 1 reference frame, and when you do that, the velocity of rocket 2 changes like so:
[tex]v' = \frac{u+v}{1+\frac{uv}{c^2}}[/tex]
It's not just simple addition, like you might think. So .95c + .95c is wrong. When you plug into the proper formula, you get
[tex]v' = \frac{.95c+.95c}{1+\frac{(.95c)(.95c)}{c^2}} = 0.9987c[/tex]
So in the reference frame of rocket 1, rocket 2 is moving at 0.9987c, which is close to but still less than the speed of light.

Oh,

cheers
 

1. What is the speed of light in special relativity?

In special relativity, the speed of light is considered to be a constant and is denoted by the symbol "c". It is approximately 299,792,458 meters per second in a vacuum.

2. How does special relativity affect the motion of two objects moving away from each other at the speed of light?

In special relativity, the speed of light is considered to be a universal speed limit. This means that two objects moving away from each other at the speed of light would appear to be receding from each other at a speed of "c" for all observers, regardless of their relative motion or position.

3. Can two objects ever actually reach the speed of light in special relativity?

According to special relativity, an object with mass cannot reach the speed of light. As an object approaches the speed of light, its mass increases and it would require an infinite amount of energy to accelerate it to the speed of light. However, light itself is massless and can travel at the speed of light.

4. How does time dilation factor into the motion of two objects in special relativity?

Special relativity states that time is relative and can be affected by an object's speed. As two objects move away from each other at high speeds, time would appear to pass slower for each object from the perspective of the other object. This phenomenon is known as time dilation.

5. Does special relativity only apply to objects moving at the speed of light?

No, special relativity applies to all objects moving at any speed, including objects at rest. However, the effects of special relativity become more noticeable as an object approaches the speed of light.

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