It's meaningless to say how fast we're travelling. In our own reference frame we aren't moving. Time hasn't slowed down. All our local clocks stay in synch with each other.
The rest of the universe is moving away from us at an accelerating rate. In a standard choice of coordinate systems, we say that in some remote galaxy time is slowing down. From their point of view our time is slowing down.
Mike W.
(published on 08/05/2015)
