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

[parkerren]

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.

 

[Doc Al]

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'.)

 

[Matterwave]

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".