Possibility of Traveling Faster Than Light?

[OneQuestion]

Hi. I'm a currently 17 years old and a physics student in high school. I am obviously not very educated in the sciences yet but we were discussing black holes in class and something caught my attention. This is mainly a "is this possible" question and I'm sorry if i am breaking any rules... it would just be really nice to slam this in my teachers face. ok so after something passes the 'event horison' of a black hole, then it cannot escape,not even light. well if the gravity of a black hole is stronger than the speed of light then is it not possible for something to theoreticaly be pulled towards the center of the black hole with a higher speed than light? My teacher shut me down and said didnt really give me any feedback. Please give me your thoughts.

 

[Kevin_Axion]

If you were to travel at the half of the speed of light and you turned a flash light on at what speed would that light escape you?

 

[JesseM]

The answer is actually a bit complicated. To define the "speed" of anything, you really need a spacetime coordinate system that can assign position and time coordinates to different points in spacetime, so you can pick two points which lie on the moving object's path and calculate (difference in position coordinate)/(difference in time coordinate) and call that the speed. As it turns out, when physicists say that the speed of light has a constant value (labeled 'c' and equal to 299792458 meters/second), and that massive objects must always travel slower than c, they are only talking about its speed in inertial frames, a set of non-accelerating coordinate systems which play an important role in relativity. In non-inertial coordinate systems this rule no longer applies, massive objects can have a coordinate speed greater than c, and light itself can have a coordinate speed different than c. "Inertial frames" are used in Einstein's theory of "special relativity" where gravity is ignored, but in Einstein's theory of "general relativity" where gravity causes spacetime to become "curved" (see here for some discussion on both versions of relativity), it turns out that no coordinate systems covering large regions of curved spacetime actually qualify as "inertial", but if you zoom in on an arbitrarily small region of curved spacetime the effects of curvature become negligible (similar to how if you zoom in on a small region of a curved surface like the Earth, it looks approximately flat), and so one can define "local" inertial frames in any small region, which according to the equivalence principle will be the local rest frames of observers in free-fall (if you're in free-fall you don't feel the effects of gravity). So in the local neighborhood of an observer free-falling into a black hole, light still moves at c and nothing can move faster c (and if that observer is crossing the event horizon, the horizon seems to be moving outward at c), but in some arbitrary non-inertial coordinate system covering a large region of spacetime both inside and outside the black hole these rules won't necessarily apply (and in general relativity the choice of how to define coordinate systems really is totally arbitrary, see the discussion of 'diffeomorphism invariance' here), not even outside the event horizon (although there is a special type of coordinate system known as Kruskal-Szekeres coordinates where they do). Something similar is true in cosmology, where according to the usual notion of "distance" and "time" used in an expanding universe, galaxies sufficiently far away from us may be moving away with a "speed" greater than c, and light itself may have a "speed" different than c (see the third paragraph here for a discussion), but any freefalling observer in the neighborhood of one of those distant galaxies would measure all massive objects in their local neighborhood moving slower than c and would measure light to still move at c.

 

[Kevin_Axion]

That's what I was going to get at in my question but your answer was a lot better. Here's a very good reference: http://casa.colorado.edu/~ajsh/singularity.html. It all has to do with frame of reference.

 

[yuiop]

Hi. I'm a currently 17 years old and a physics student in high school. I am obviously not very educated in the sciences yet but we were discussing black holes in class and something caught my attention. This is mainly a "is this possible" question and I'm sorry if i am breaking any rules... it would just be really nice to slam this in my teachers face. ok so after something passes the 'event horison' of a black hole, then it cannot escape,not even light. well if the gravity of a black hole is stronger than the speed of light then is it not possible for something to theoreticaly be pulled towards the center of the black hole with a higher speed than light? My teacher shut me down and said didnt really give me any feedback. Please give me your thoughts.

On a small technicality, gravity normally means a force or an acceleration and the speed of light is a velocity, so the units are different and the two quantities can not be directly compared.

As for "is it not possible for something to theoreticaly be pulled towards the center of the black hole with a higher speed than light?", the short answer is no. If your friend jumps into a black hole and falls through the horizon and you jump in after him and shine a torch down towards him, the light from your torch catches up with your friend before you do. Therefore you cannot say you are falling faster than the speed of light.