In the Matthew McConaughey movie “Insterstellar”, 1 scientist stays in the orbiter ship while the others go to the water planet. The orbitor ages years while the planetary travlors age days/hours. Would not that be backwards?
Nope, they got it right. The planetary explorers were deeper in a gravitational well, so less time passes for them.
Here is an article that discusses the phenomenon.
Chronos got it but without explanation.
Remember that the speed of light is measured as the same for ALL observers.
No matter how you are moving (right/left/up/down/diagonal/sitting still/zooming in a rocket/etc) you will ALWAYS measure the speed of light the same as anyone else (e.g. all reference frames will come up with the same answer).
So, you are in a gravity well (be it planet or black hole). The deeper you are in the gravity well the “slower” light will go. It is harder for it to get away.
BUT…we always measure light at the same speed. Something has got to give and that is your clock.
Speed is distance/time (e.g. miles per hour).
So, if you do the math (which in this case is simple) then since the light cannot travel as far in a given time-slice in a gravity well than it can away from one the only thing you can do to balance the equation is adjust how fast your clock ticks.
As it happens this is exactly how it works and has been validated by numerous experiments. The implications of that starts making things weird but this is how the universe works.
Relevant literature:
Probable-Possible, my black hen,
She lays eggs in the Relative When.
She doesn’t lay eggs in the Positive Now
Because she’s unable to Postulate How.[indent]-- The Space Child’s Mother Goose, Frederick Winsor[/indent]
Does this mean that light “goes slower” when it is going up-hill, but not when it is going horizontally or down-hill in a gravity well? If I’m at some specific depth in the well, does time go at different speeds depending on which direction I’m looking? Does it go at one speed up-hill and a different speed (faster?) down-hill?
There was a young lady named Bright,
Whose speed was much faster than light.
She set out one day,
In a relative way,
And returned the previous night.
I’m not sure that that explanation is particularly useful, since it explains something that’s true by appealing to things that aren’t true (or, at best, are “true”). You’d be much better served explaining it in terms of blueshift… but then you’d just need to explain why light is blueshifted deep in a gravitational well.
My favorite college bathroom graffiti (or is it “graffito” ?) …
“Interested in time travel? Meet me here last Tuesday”.
No, and that’s why – as Chronos says – the explanation given isn’t really accurate. A gravity well is best characterized as redshifting light when observed from a higher gravitational potential (i.e.- farther away, or “uphill”, from a massive object) due to time dilation within the stronger gravity well (from a higher gravitational potential you observe time passing more slowly there, therefore light having a lower frequency and a longer wavelength, regardless of which direction it’s moving). The most intuitive rationalization for why light can’t escape at all from within a black hole is that at the event horizon it’s redshifted to infinite wavelength.
BTW, in the spirit of giving credit where credit is due, I think the reference to “the Matthew McConaughey movie Insterstellar” is unfair. It should be “the Christopher Nolan movie Insterstellar which Matthew McConaughey and a bunch of other folks were lucky enough to be hired to act in.” 
Relative Time
Here; at this moment it is 3:45 PM 3:45 PM
Relative Time
Here; at this moment it is 3:45 PM 10/24/2015
at this moment in New York it’s t is 4:45 PM 10/24/2015
What time/date is it where you are?
at this moment in time
From that article:He confirmed that when we walk up a flight of stairs, time is at war with itself. Being farther from the pull of Earth’s gravity causes our clock to tick faster, but moving counteracts this effect.
Ignoring the “at war” nonsense, it means that “moving” is just another gravity, ie, a locally “obeyed” acceleration.
Right?
No. “Moving” (relative motion) in special relativity is specifically the absence of acceleration.
And the “at war” reference isn’t really nonsense as it does describe opposing effects exactly as observed in spacecraft. Indeed GPS systems, which depend on extremely accurate measurement of time, would be practically useless if we didn’t compensate for the satellite clocks tending to run faster than clocks on earth because of the effect of lessened gravity and slower than clocks on earth because of their relative motion. We have to adjust to a net factor that reflects both.
bold added
OK, I see the situation. I still think “at war” is an unfortunate choice of words.
I’ve always understood the definition as the opposite. Same meaning, ultimately.
Correct me if I’m wrong, but isn’t it also accurate to say that those distant galaxies that we see which are receding from us faster than the speed of light have their arrow of time reversed relative to our frame of reference and that they will eventually fade from our view when they cross the point of being “born” and emitting light? Because…that’s pretty cool. 
Check. I’ve loved that book since I was a kid. It’s still somewhere around.
Someone can correct me if I’m wrong, but I don’t think any such galaxies are believed to exist because the universe is still too young and too small. I think the general idea is that eventually this will happen for the most distant galaxies as space continues to expand, at which point they will just disappear from our view. But it has nothing to do with a reversal of the arrow of time, just with the photons no longer able to reach us. And of course nothing is really moving faster than light, it’s just that the cumulative expansion of space will (eventually) be carrying the most distant galaxies away from us at apparently faster than light.
It looks like the jury is still out (pdf) on that question.
But, if we do observe faster than light recession of galaxies, it appears to me that we would literally be seeing something that is going backward in time.
The “cool” part would be if we could observe this effect in detail: either through exceedingly great telescopic resolution, or if the distant galaxy star systems are really, really…really big—with planets big enough to harbor aliens a million light years tall (they’d be first draft picks in the NBA for sure). We’d see those guys making baskets before throwing the ball.
OK - but if a star was receding faster than light; surely we wouldn’t see it. We may detect some disturbance caused by it but that’s like tracking an elephant through the long grass.
I still find it astonishing that we can look up into the sky and observe something that happened thousands of years ago.