# What is the speed of light observed?

1. let's say there's a spaceship can accelerate to almost speed of light (0.9999c), and while it keep its speed constant, someone sending a beam of light once it pass through a specific place (which both light and the spaceship goes through almost same speed, at the same starting point, and parallel to each other).

What is the speed of light observed from the person inside the spaceship?

Is it almost stationary since both are almost equidistant as it goes further?

2. Two spaceships approach each other, Spaceship A has a speed of 0.8c, spaceship B has a speed of 0.6c. A passenger on spaceship A aims a laser at spaceship B, how fast does the laser light appear to be moving as observed by a passenger on spaceship B?

on all situation above, does the speed of light observed are $c$?

EDIT: Sorry that I didn't mention, I know there's special relativity but I don't understand the concept and why light observed is always speed of light

If speed is never changed, what property of the light that has changed as you travel almost the speed of light?

• Einstein showed that the speed of light is always measured to be $c\approx3.0\times 10^8$ m/s, regardless of the frame of reference in which the observer is. Does that answer your question? – user77629 Oct 14 '16 at 7:02
• but why, even though a spaceship traveling at almost speed of light? What I thought is like me and my friend riding bike at same speed, my observed speed of my friend is 0 (he seems to be at the same place as my perspective of view) – wuiyang Oct 14 '16 at 7:08
• This seems to be either a do my homework question, which would be off-topic here, or a general question which would require OP to do some research, show their work, and ask about a specific problem or question they face. If it is the latter, it seems to me that either OP knows special relativity exists, in which case they should study it before asking and refer to it in the question, or they don't know, in which case the question should say why they are stuck. – JiK Oct 14 '16 at 8:13
• @Wuiyang, don't worry, when Einstein proposed it, it was a radical idea. But it is true, the speed of light is constant regardless of reference frame. You will learn this when you study some special relativity. – user77629 Oct 14 '16 at 8:55
• When I stand in the middle of the United States facing north, California is to my left. When I stand in the middle of the United States facing south, California is to my right. What property of California has changed as I turn around? – WillO Oct 16 '16 at 14:10

Yes sure, in all cases the speed of light in vacuum is a universal constant. Take the formula from special relativity that tell you how relativistic speeds are seen: $$V=\frac{u-v}{1-\frac{uv}{c^2}}$$ (if the two velocity have the same direction)

If one of the two velocity is c, the final velocity seen from the observer is always c. For example: your spaceship is moving at v=0.9999c and send a beam of light in the same direction. So: $$V=\frac{u-v}{1-\frac{uv}{c^2}}$$ $$V=\frac{c-v}{1-\frac{\not{c}v}{c^{\not{2}}}}$$ $$V=c\frac{c-v}{c-v}$$ $$V=c$$

What is the speed of light observed from the person inside the spaceship?

According to Einstein's special theory of relativity, it's the same.

A passenger on spaceship A aims a laser at spaceship B, how fast does the laser light appear to be moving as observed by a passenger on spaceship B?

As above, the speed is the same.

You are forgetting the consequences of special relativity .

I am copying from wikipedia:

" Special relativity is based on two postulates: a)The laws of physics are invariant (i.e. identical) in all inertial systems (non-accelerating frames of reference). b)The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source."

and :

" Special relativity implies a wide range of consequences, which have been experimentally verified,including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit and relativity of simultaneity."

So the 'price' for the 'absolute' speed of light for all observers ,is the 'relativity' of the properties that these observers can measure ,such as time, lenght etc.

Here is the thought behind the Gr of Einstein, that when you travel in a high speed comparable to light then, the space through which light is travelling and the time taken by the light to reach to you both are changing such a way that the value of space dividing by time became constant, which is nothing but speed of light.hence the speed of light is always c irrespective of the speed of observer.The Gr says in 4 dimensional parameter in lower speed say between two motor cycle or between two car change of time is so small that we can not observe it, hence relative velocity appears.but in the speed of c (as the photon has the such speed) time change is maximum, such that the photon traveled the extra space or lesser space divided by the expanded or compressed time is always became c .As such speed of light is unchanged.