This has always baffled me. There is no absolute speed as I understand(or is there)? Speed is a relationship between two objects. So how can you calculate how much time slows down for an object based on its speed without specifying which other object you are relating it to? Also, since the selection of the object you are relating it to is totally arbitrary how can the answer have any meaning at all?
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You're right, there is no absolute speed. That is the key insight of relativity. Really, however, this comes from a broader principle: there is no absolute space or time. By that I mean your coordinates are not my coordinates, your time is not my time. So let me ask you a counter-question, which I hope to convince you cancels your questions out: what is time slowing down relative to? Alice's time is just as valid as Bob's, and neither of them have some Great Universal Clock to appeal to. Instead, all we can is that Alice's clock goes at a certain rate relative to Bob's. And now you'll see that we do have a way to define speed: it's the speed relative to whatever clock we're using as a baseline.
You might say, well, Charlie is here as well, and he also has a clock--what makes Bob's clock/reference frame better to calculate Alice's time change? Nothing. All we can do is talk about what an individual will observe. Bob will observe Alice as having a time dilation with her velocity relative to him; Charlie observes Alice as having a time dilation with her velocity relative to him. They don't agree, but then, nobody said they had to.
zeldredge
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