Is time slowing down or is it just taking a longer amount time?

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The faster you travel the slower time travels. But instead could we be thinking in terms of it taking longer for things to occur? A particle traveling near the speed of light will take longer to decay then at rest. A person traveling close to the speed of light will take longer to age, and the clock being worn will take longer to mark off time then if at rest.
 
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parkerren said:
But instead could we be thinking in terms of it taking longer for things to occur?
That's what time 'slowing down' means. (No need for the 'instead'.)
 
Since you have to measure time with events (e.g. the ticking of a clock hand, the swing of a pendulum, the vibrations of a cesium atom, etc), there is no difference between "time slowing down" and "things take longer to occur".
 
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