Do gravitational waves propagate backwards in time? Gravitational waves are spacetime waves, which stretch and squeeze both space and time. Since relativity puts space and time (almost) on an equal footing, it seems to me that since gravitational waves propagate in all directions in space (from their source), they should also propagate in both directions in time. This seems to me to be also a major plot point in the movie 'Interstellar', wherein Kip Thorne played an important role as scientific advisor. In particular, I mean the scene where gravitational waves are propagated back in time to make a watch tick.
My question is, are there any caveats to this, if it is true? Wouldn't we able to detect gravitational waves from the future as well, if so?
 A: I was laying awake last night thinking about this very question, there may be a way to test this by looking for a specific type of signal in something like the LIGO. This type of signal would precede the actual event that created the signal (a binary merging event 2ly away would arrive 2 years prior to the actual event occurring) and the data should be "reversed". Specifically, the peak gravitational wave intensity, produced as the binary system merges, would show up first AND from the opposite direction from where the signal originated. You would see a "reversed" signal, starting with a peak and tapering off that would seem to travel in the opposite direction from where the event took place (due to the wave travelling backwards through time). If gravitational waves acted in this manner, this "pre-event" signal would be followed by a "post-event" signal that started small and ended with a peak, traveling in the direction from where the event took place, due to this signal traveling in a direction of time that we are more accustomed to experiencing. For the example used above, the "post-event" signal would arrive 4 years after the "pre-event" signal (2ly away, takes two years to travel to the Earth going both backwards AND forwards in time, thus a 4 year separation between signals). Just some thoughts, I would be interested in hearing other people's opinions and to see what other types of signals LIGO and other detectors will uncover in the near future!
A: Gravitational waves are on the same footing as electromagnetic waves - they are lightlike processes, propagating with speed of light c.
For all fundamental problems concerning time, we may not forget to have a look at the corresponding proper time. The proper time of lightlike processes is zero, their spacetime interval is empty. Observers are synchronizing the (zero) proper time of the observed process with the proper time of their own clock, and they get coordinate time. All lightlike processes are measured by observers to happen with velocity c, or more precisely, with velocity +c.
We don't know yet about processes which are moving backwards in time (that means which are moving against the direction of our own time arrow). The ideal candidates for processes moving backwards in time would be antiparticles, but it seems that such a presumption cannot be confirmed by experiment.
However, if we imagine that such an "antimatter observer" moving backwards in time would exist, this observer would measure lightlike processes as happening with a velocity of +c from his point of view (according to the second postulate of special relativity), that means -c from our point of view (opposite to the direction of our time arrow).
As a result we can say that light is interacting with matter in our direction, and if it would interact with some antimatter moving back in time, it could do so only in the opposite direction. However, as I said, no processes moving backwards in time are currently known.
A: The Einstein equations which describe general relativity do not make a difference between waves propagating forward in time and waves propagating backwards in time. Just as the Maxwell equations, which describe electromagnetism, allow both solutions for waves propagating forward in time as well as for waves propagating backwards in time. 
However, for an observer, it is impossible to distinguish a forward traveling photon from a backwards traveling photon. A photon is just the electromagnetic field having different values at different positions in space and time. A forward traveling photon and a backwards traveling photon can cause the same field distribution in space-time and are thus indistinguishable. We say that the photon is its own antiparticle. 
The same holds for gravitons. They represent a deformation of spacetime, which can be described by either a forward traveling graviton or by a backwards traveling graviton. Gravitons are also their own antiparticles.
Because almost all of physics is time reversal invariant (the same laws apply if you think of time flowing in the opposite direction), it is actually not so trivial to state in which time-direction things are flowing.
The one thing which does not seem time invariant is entropy, since it always seems to increase in one time-direction. Most discussions concerning the direction of time therefore use the direction of increasing entropy as the positive time direction.
By convention, in order to conserve causality, we describe all waves and particles as traveling forward in time, with the definition of forward based on entropy. 
