Special relativity - with no absolute motion how can we approach the speed of light?

If there is no absolute motion and light is a constant how can we ever say that an object is approaching the speed of light. In the typical train cited to explain time dilation in which the train is approaching the speed of light, surely from the train perspective the platform is also approaching 'c' in the other direction? So what distinguishes the two scenarios?Special relativity - with no absolute motion how can we approach the speed of light?Good observation! All speed is relative, so when we say something's approaching "c", we must specify some reference frame against which that speed is being measured. You're correct in observing that the train is approaching "c" from the platform's frame, while the platform is approaching "c" from the train's frame.



And, as Lola pointed out, each observer finds that the "moving" clock (the clock in the other frame) is running slowly. This at first seems like a contradiction -- how can each clock be slower than the other? -- but in fact it works out that way. It only seems like a contradiction because we're accustomed to thinking in terms of an "absolute" time reference against which all clocks' rates can be measured -- but in fact no such reference exists.



It's instructive to go through an exercise in which two observers actually measure each others' clocks. Imagine two spaceships, "A" and "B", that separate from each other at 1/2 lightspeed. At the instant of their separation, the synchronize their clocks so that each clock reads, "12:00 Noon".



By a prior agreement, Captain "A" waits until his clock reads "1:00 PM", and then sends a laser signal (which of course travels at "c") toward ship "B".



When Captain "B" receives the signal, he notes the time (on his OWN clock), and writes it down in his ship's log.



The question is, "What does Captain 'B' write down?" If you know the formula for time dilation, I encourage you to work out the answer. Try it first from the reference frame of Ship "A" (assume ship "B" is moving), and then from the reference frame of Ship "B" (assume ship "A" is moving). You'll see that the note in the ship's log is the same either way, but ONLY if the "moving" clock is running slower than the "stationary" clock (regardless of which one you choose as "moving" or "stationary").Special relativity - with no absolute motion how can we approach the speed of light?Nothing distinguishes the two scenarios.



Time dilation happens when an object approaches c relative to an observer.



The observer on the platform observes the train traveling at nearly c, and the train passenger observes the platform traveling at nearly c. Each observes the other's clock to run slow.