1

So we've all heard of the concept of time dilation and length contraction (from both general and special relativity). Suppose we work with a metric of a black hole, and person A is far, far away and Person B is just outside the Schwarzschild radius. If Person B sends a series of signals separated by what he perceives to be a second, person A will measure that gap as much, much longer. In other words, Interstellar. The same phenomenon happens for a man accelerating away in a rocket and returning home. The person who is accelerating/in highly curved spacetime will age slower than the guy at rest.

I'm wondering if there is some sort of space-time geometry that makes the opposite effect possible, that is, pulse lengths are quickened instead of shortened. I suspect that there is some simple theorem that forbids this, but I can't think of it.

Aurey
  • 275
  • You fly towards the source or you look up into the sky of your Interstellar black hole planet. Time dilation and length contraction are totally different from these red/blue shifts, though. – CuriousOne Jul 15 '16 at 05:33

2 Answers2

2

Yes, there is a principle related to this, but we need to be precise in stating it.

Suppose we take two points in spacetime $A$ and $B$. For example in the twin paradox point $A$ could be when the twins part and point $B$ could be the point when the twins return. There are an infinite number of possible paths linking the two points. For example the twin who stays on Earth gets from $A$ to $B$ by staying still while the other twin gets from $A$ to $B$ by racing around in a rocket.

For every path there is an associated path length called the proper time, which is calculated using the metric. If you're interested in the details, I talk about how to calculate this path in What is time dilation really?.

The principle of least action tells us that the path taken by a freely falling observer will be the path that has the highest value for the proper time. That is, an inertial observer measures the most elapsed time between $A$ and $B$ and all other observers must measure a shorter time. Put another way, all other observers have their time dilated with respect to the freely falling observer.

This only applies to observers who, like the twins, start and finish at the same point so it doesn't immediately apply to separated twins e.g. one near a black hole and one far from a black hole. However to compare their clocks there must be a point where the twins can see both clocks, so a loop is always involved.

Community
  • 1
John Rennie
  • 355,118
1

It is shown in movie "The contact" where it passes just a second or so on earth, but during the same time, the astronaut records many hours of static. What people on earth saw was that the space ship crashed before even taking off, but astronaut experienced having made a journey to other words. As far as I remember, the concept is not clearly described in the movie, you may try watching it. What I am suspecting is - We know gravity slows down time. The space ship must have created anti gravity (or negative gravity) that would have given the opposite effect, i.e. sped up the time. Therefore stretching a second of earth time to many hours in that environment inside the ship. So, the geometry should be that of anti gravity - inverted curving.

kpv
  • 4,509