So how come in this case, it isn't the reference frame of us sitting on the particle moving more slowly than the scientist observing the particle? I just keep envisioning the particle as a spacecraft instead (just because it's slightly easier to grasp) and isn't it normally the other way around? i.e. the thing that is moving has time travelling more slowly and the thing in the external frame of reference has the 'faster' time? Ah sorry Jamon
Okay let's spaceship it! So the spaceship is travelling at speed, and let's say we are watching a clock tick inside the spaceship (as a substitute for measuring the lifespan). So, we measure the clock on the spaceship from our frame of reference. Remember, there is no absolute reference frame for time, so we have to just compare it to our own. The clock on the ship will be
slower than ours. Why? Because time slows down at speed. So when we look at the spaceships clock, it has slowed down, because it is moving at relativistic speed.
Keep in mind that
on the spaceship, we could watch a clock on earth. If we are in the spaceship,
the clock on Earth will be slower than our clock on the ship. What the hell is that about, it's backwards to what we just said?
That's relativity. Because in our frame of reference, the spaceship is moving at speed. In the spaceships frame of reference, the spaceship isn't moving at all, the Earth is! And thus, we see the clock moving at speed and thus, the clock moving slower.
So we will
always view a moving reference frame as having slower time than ours, because the frame of reference we are in is always considered as stationary, and we compare to it.
So when the spaceship comes back to earth, its clock is no longer moving slower. So, it will tick through a minute faster, and so the
lifetime (as equivalent) will be shorter.
I kind of feel like you understand this Neutron! Because the expression:
i.e. the thing that is moving has time travelling more slowly and the thing in the external frame of reference has the 'faster' time? That is correct, the thing we observe has time travelling more slowly. So you get this. I think there is some subtle thing that's throwing you off (which is common with relativity). Read this a few times, does it help? I'm waiting for the "aha" moment