Understanding Relativistic Speeds

A common question I receive revolves around the behavior of starships traveling at light speed: If two spacecraft depart from a shared point and fly in opposite directions at light speed, what would their relative speed be?

First and foremost, it’s essential to note that the speed of light remains unreachable for any object with mass. Hence, these starships cannot travel at light speed. Instead, let's examine a scenario where the ships are moving at a velocity very close to the speed of light, such as 0.9c.

Many of these inquiries stem from a lack of understanding regarding the principles of relativity. In this discussion, I aim to clarify what occurs in the described scenario as simply as possible.

According to relativity, the passage of time is not uniform; it varies for each observer depending on their frame of reference. This means two observers need not have identical clocks to measure the duration between events accurately.

As an object's velocity increases, time appears to slow down for that object when viewed from a stationary reference frame. Therefore, as the speed of the spacecraft increases, time progresses more slowly for it in comparison to the stationary observer's frame of reference. For a more detailed explanation of this phenomenon, please refer to my earlier article.

This principle implies that when two starships move apart from a shared starting point at 0.9c (relative to that point), their relative speed will never exceed the speed of light. But how do we calculate their speed in relation to each other? To determine this, we must use the relativistic velocity addition formula.

By substituting 0.9c for both v1 and v2, we can ascertain that the relative speed of the two spacecraft will be approximately 0.9945c—remarkably close to the speed of light, yet still not exceeding it.

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