How to measure speed of light?

[homer5439]

Thought experiment.

Let's imagine I'm on my spaceship moving in the void. For this example, I'm assuming my flight started on the Earth, where I could see the ground and landscape and thus I was able to tell that I was moving; however, without accelerating or decelerating, I progressively got further from the Earth, and at some point I entered the void, which is where I am now. There is nothing around my ship to see, and so as expected I'm effectively unable to tell my speed (but I know that I'm not still - or don't I?).

Now, let's imagine that, from time to time, I turn on some special engine and accelerate a bit, then again turn the engine off and go back to uniform motion (but with a greater speed than before). During the acceleration phase, I can tell that I'm accelerating.

At any time, I don't know my speed, except that after each acceleration my speed is greater than before. (I hope things are plausible up to here).

Now, is there something that prevents me from eventually reaching the speed of light or even exceeding it? If that is not possible, then I suppose at some point I should be able to detect that I cannot accelerate anymore, and thus infer that I'm moving at or near the speed of light.

But what's the meaning of "speed" and "moving" when you are in the void, if there's a meaning at all?

 

[Dale]

At any time, I don't know my speed, except that after each acceleration my speed is greater than before.

Not in all frames. In some reference frames each time you activate your engine your speed is reduced.

 

[DrGreg]

Whatever speed you are traveling at, the speed of light is always 299,792,458 m/s faster, from your point of view, so there's nothing to stop you accelerating and going even faster.

In relativity, velocities don't add together as you expect.

If you are going at 99% of the speed of light relative to your starting point, and then go at 2% of the speed of light faster relative to your current speed, you end up traveling not at 101% of the speed of light but at

$$\frac{0.99 + 0.02}{1 + 0.99 \times 0.02} \, c = 0.99039 \, c$$​