When we say something travels close to the speed of light, what is its speed rel

Question

When we say something travels close to the speed of light, what is its speed relative to?

For example, we have 4 highly advanced spacecraft at rest beside each other, labelled A, B, C and D.
We leave A at rest and accelerate B, C and D to .8c.
We can now consider B, C and D to be at rest and that A is retreating from them at .8c. Considering B, C and D to be at rest we can now accelerate C and D to .8c relative to B.

Can we then consider C and D to be at rest and further accelerate D to .8c with respect to C and continue doing so ad infinitum with an endless array of spacecraft?

Explanation / Answer

Left unspecified, it is generally understood that the speed is relative to the frame of reference in which one is at rest. However, it's better to explicitly specify the reference frame with respect to which some object has a relative speed.

For example, one might write "twin A observes twin B to have a speed of 0.8c" or better, "twin A & twin B have a relative speed of 0.8c".

In the case of 4 spacecraft, there is a relative speed between spacecrafts A & B, A & C, A & D, B & C, B & D, and C & D. Indeed, each spacecraft has a speed relative to an infinity of inertial reference frames.

So, unless the context is clear, it's best to explicitly identify with respect to what a speed is relative to.

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