# Speed of light and relativity: Correct me if I'm wrong
**URL:** https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776
**Category:** Factual Questions
**Created:** [May 7, 2003, 10:41pm UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776 "2003-05-07T22:41:10Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@SPOOFE](https://boards.straightdope.com/u/SPOOFE)
#### Post date: [May 7, 2003, 10:41pm UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776/1 "2003-05-07T22:41:10Z")
Okay, real quick… I just want this confirmed or denied. If you take two rocket ships in space, and sent one off in one direction travelling at 51% of the speed of light, and sent on off in the opposite direction, also travelling at 51% of the speed of light, from the point of view of either ship, would the other appear to be travelling faster than light?
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### Author:  [@Trinopus](https://boards.straightdope.com/u/Trinopus)
#### Post date: [May 7, 2003, 10:56pm UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776/2 "2003-05-07T22:56:44Z")
Nope.
Relativistic speeds don’t add that way.
(They are additive, but not linear.
51% + 51% is about 64%, if memory serves. I left
my calculator in my other brain…)
Trinopus
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### Author:  [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)
#### Post date: [May 7, 2003, 11:06pm UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776/3 "2003-05-07T23:06:05Z")
Here’s a link to doing relativistic velocity addition if you want the math. As **Trinopus** hinted at you can never add velocities in such a way for any observer to view another object as exceeding light speed. If you _do_ see an object exceeding light speed then some trick is at work or the object is not real (e.g. a shadow can be made to exceed light speed but a shadow is a physical thing).
[http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html#c1](http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html#c1)
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### Author:  [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)
#### Post date: [May 7, 2003, 11:13pm UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776/4 "2003-05-07T23:13:48Z")
I’d like to know how you can make a shadow move faster than the speed of light. If you can do that, you can send information FTL, which violates relativity.
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### Author:  [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)
#### Post date: [May 7, 2003, 11:37pm UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776/5 "2003-05-07T23:37:36Z")
> [@](#):
>
> \*Originally posted by Q.E.D. \*
> \*\*I’d like to know how you can make a shadow move faster than the speed of light. If you can do that, you can send information FTL, which violates relativity. \*\*
First off I should correct my earlier post and say a shadow is **not** a physical thing.
As to the question above here is your answer (note that other ‘things’ such as the spot of a laser can manage the same feat).
> [@](#):
>
> Think about how fast a shadow can move. If you project a shadow of your finger using a nearby lamp onto a far away wall and then wag your finger, the shadow will move much faster than your finger. If your finger moves parallel to the wall, the speed will be multiplied by a factor D/d where d is the distance from the lamp to your finger and D is the distance from the lamp to the wall. It can actually be much faster than this if the wall is at some oblique angle. If the wall is very far away the movement of the shadow will be delayed because of the time it takes light to get there but its speed is still amplified by the same ratio. The speed of a shadow is therefore not restricted to be less than the speed of light.
>
> _\_
>
> It is not possible to send information faster than light on a shadow or light spot so FTL communication is not possible in this way. This is not what we mean by faster than light travel although it shows how difficult it is to define what we really do mean by faster than light travel.
>
> SOURCE: [Is Faster Than Light Travel or Communication Possible?](http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#3)
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### Author:  [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)
#### Post date: [May 8, 2003, 1:36am UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776/6 "2003-05-08T01:36:31Z")
The key to this paradox is to note that you, the observer, see the spaceships separating at 1.02c, but neither of them is moving at a speed greater than c relative to you. Thus you never observe any material object moving at a speed greater than c.
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### Author:  [@Ring](https://boards.straightdope.com/u/Ring)
#### Post date: [May 8, 2003, 3:49am UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776/7 "2003-05-08T03:49:47Z")
> [@](#):
>
> \*Originally posted by Q.E.D. \*
> \*\*I’d like to know how you can make a shadow move faster than the speed of light. If you can do that, you can send information FTL, which violates relativity. \*\*
I’ve been trying to envision how you came up with that idea, but for the life of me I can’t do it. How do see a shadow communicating information FTL?
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### Author:  [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)
#### Post date: [May 8, 2003, 3:56am UTC](https://boards.straightdope.com/t/speed-of-light-and-relativity-correct-me-if-im-wrong/173776/8 "2003-05-08T03:56:51Z")
> [@](#):
>
> \*Originally posted by Ring \*
> \*\*I’ve been trying to envision how you came up with that idea, but for the life of me I can’t do it. How do see a shadow communicating information FTL? \*\*
It can’t. That was the whole point. I was trying to get the poster to expand on his/her point, which he/she did.