Trying to Understand Time Dilaton

[RJ Emery]

Neil DeGrasse Tyson has written a book, Death by Black Hole and Other Cosmic Quandaries (2007, W.W. Norton), which by and large is a collection of articles he wrote for the American Museum of Natural History’s monthly magazine, Natural History. Chapter 39 is entitled “Hollywood Nights,” about how movie makers distort scientific fact under the auspices of creative license. Following is an excerpt from pp. 327-328:

At the end of the 1977 Disney film Black Hole, which sits on many people’s 10 worst movies list (including mine), an H. G. Wellsian spaceship loses control of its engines and plunges into a black hole. What more could special-effects artists ask for? Let’s see how well they did. Was the craft and its crew ripped apart by the ever-increasing tidal forces of gravity—something a real black hole would do to them? No. Was there any attempt to portray relativistic time dilation, as predicted by Einstein, where the universe around the doomed crew evolves rapidly over billions of years while they, themselves, age only a few ticks of their wristwatches? No. The scene did portray a swirling disk of accreted gas around the black hole. Good. Black holes do this sort of thing with gas that falls toward them. But did elongated jets of matter and energy spew forth from each side of the accretion disk? No. Did the ship travel through the black hole and get spit out into another time? another part of the universe? or in another universe altogether? No. Instead of capturing these cinematically fertile and scientifically informed ideas, the storytellers depicted the black hole’s innards as a dank cave, with fiery stalagmites and stalactites, as though we were touring Carlsbad Cavern’s hot and smoky basement.

My questions are on time dilation, a topic I do not easily fathom. To me, time is time. If the universe is at t=x in its present age, that is the time at any given moment throughout the entire universe and at every location, whether we are here on Earth or about to be sucked into a black hole, should one be nearby, or off in a distant galaxy or even in a part of the universe beyond our visual horizon.

If t=x, is that not true everywhere at the same instant?

Do not all observers here and everywhere see the age of the universe as the same?

Tyson seems to imply that time depends on location, that time just outside (or presumably even within) a black hole's event horizon is very different from time a megaparsec distant, not only the actual time but the rate by which time advances.

Ignore for the moment the crew’s atomic demise under the gravitational and tidal forces of a black hole.

In the scenario above, if portrayed with time dilation in mind, the doomed crew would have had time slowed while the universe aged onwards normally. Their clock would tick slower, while the clock for the rest of the universe would tick inexorably onwards at its customary rate. Thus the rate of the ticks, and the absolute value of time itself, seems to be location dependent.

If the crew were able to determine the age of the universe before coming under the influence of the black hole, and then measure the age again just prior to crossing the event horizon (or even afterwards), they would see a universe accelerating in age as measured by their clock, would they not?

This observed acceleration of the universe by the ship's crew would give the effect of an accelerating universe, that is, the universe would appear to be expanding if not evolving at a faster rate than otherwise observed.

Let us now switch to our present day on Earth with the results of two supernova surveys that point also to an accelerating expansion of the universe.

Does this supernova result, among other explanations, indicate we may be moving towards an unseen black hole?

 

[pervect]

My questions are on time dilation, a topic I do not easily fathom. To me, time is time. If the universe is at t=x in its present age, that is the time at any given moment throughout the entire universe and at every location, whether we are here on Earth or about to be sucked into a black hole, should one be nearby, or off in a distant galaxy or even in a part of the universe beyond our visual horizon.

If t=x, is that not true everywhere at the same instant?

In special relativity, there is no universal definition of what "at the same time" means.

For a discussion of the relativity of simultaneity, see for instance the wikipedia article or Einstein's original treatment

Do not all observers here and everywhere see the age of the universe as the same?

In cosmology, because of the big bang, there is a way to assign a specific time coordinate to every event. This assignment is, however, incompatible with the assignment of special relativity done by any particular inertial observer. So if you try to do special relativity with this sort of cosmological time assignment, you'll run into severe problems. You can get a taste of the sort of problems that you'd run into here on Earth, by assuming that daylight savings time was the "correct" way to synchronize clocks at distant locations. This would imply that identical planes flying east or west have significantly differing velocities, among other problems. Other problems would include flights taking 8 hours in the lab frame, while only taking 4 or 5 by the onboard clocks, even at very low (non-relativistic) velocities, and colliding identical planes with equal "veolcities" not having zero total momentum.

So in short, the existence of a cosmological time does not disprove the relativity of simultaneity any more than the existence of daylight savings time does. Both give us a way to synchronize distant clocks (though the later only works on the Earth's surface).

Tyson seems to imply that time depends on location, that time just outside (or presumably even within) a black hole's event horizon is very different from time a megaparsec distant, not only the actual time but the rate by which time advances.

Falling into a black hole is an interesting topic in its own right. Falling into a Schwarzschild black hole, one would not see the sort of effect that Tyson writes about - one would not see the future of the universe play out in a blinding flash. Some models of rotating black holes may have this characteristic, but the details of a realistic rotating black hole collapse are still being worked out, so the best answer is that it is not entirely clear what the inner structure of such a black hole is, and thus it is not clear what one would see. While the movie is not to be taken seriously, at best Tyson assumes we know more than we do.

Let us now switch to our present day on Earth with the results of two supernova surveys that point also to an accelerating expansion of the universe.

Does this supernova result, among other explanations, indicate we may be moving towards an unseen black hole?

No. There isn't any really clear way to tell from local measurements whether one is crossing the event horizon (at least none that I can think of quickly), but if we were falling towards a black hole, from a global perspective one would expect everyone else would be too. This would show up as an observed convergence or contraction of the paths of these observers. We don't see any such global contraction - on the largest scales, the universe is expanding, not contracting.

 

[Chronos]

Time, like politics, is always local. There is no way of escaping this aspect of reality, as pervect noted.