Time Dilation: Away or Toward Observer?

[Involute]

I thought the answer was no. I.e. the traveler's proper time always passes more slowly than a stationary observer's clock regardless of the traveler's direction with respect to the observer. I was watching Brian Greene's NOVA episode on time, however, and, at 23:15, he has a demonstration involving an alien 10 billion lightyears from Earth riding a bicycle away from, and then towards, us. When he's riding away, time slows down for him (with respect to us). When he's riding towards, it speeds up. This seems contradictory, but maybe I'm missing a detail, or misunderstood SR to begin with (or both). Thanks for any tips.

 

[PeroK]

I thought the answer was no. I.e. the traveler's proper time always passes more slowly than a stationary observer's clock regardless of the traveler's direction with respect to the observer. I was watching Brian Greene's NOVA episode on time, however, and, at 23:15, he has a demonstration involving an alien 10 billion lightyears from Earth riding a bicycle away from, and then towards, us. When he's riding away, time slows down for him (with respect to us). When he's riding towards, it speeds up. This seems contradictory, but maybe I'm missing a detail, or misunderstood SR to begin with (or both). Thanks for any tips.

That all makes no sense. I notice the title of the video is:
The Fabric of the Cosmos: The Illusion of Time

I doubt you can learn any serious science from a video like that. It's not surprising you got some nonsense about an alien on a bicycle!

 

[Nugatory]

@Involute If A and B are moving relative to one another and watching each other’s clocks through telescopes... if they are moving towards one another they will both see the other’s clock running fast, and if they are moving away from one another they will both see the other’s clock running slow. This has nothing to do with relativity and time dilation; it’s just the Doppler effect, caused by the light travel time changing as the distance between them changes.

However, when they allow for the light travel time - that is, the light they see in their telescopes was emitted earlier and spent some time getting to them - and calculate the clock rates that would produce what they actually see then they both calculate that the other’s clock is running slower than their own. That is relativistic time dilation, and it is best understood as a manifestation of the relativity of simultaneity, not as “time slowing down”.

 

[FactChecker]

You are misinterpreting that part of the video. The difference between the two cases of the alien going away versus toward Earth is not about how fast the clock ticks. It is about how the clocks at different positions are synchronized to define simultaneous time ("now") in the reference frame of the alien as he goes away versus as he goes toward the earth.