MadSci Network: Physics

Re: How can blackholes move at all?

Date: Sun May 10 21:47:53 2009
Posted By: Vladimir Escalante-Ramirez, Faculty
Area of science: Physics
ID: 1240728629.Ph

This is a question of reference frames. Time is a relative quantity, says Einstein. According to relativity theory, time depends on the observer in much the same way that position depends on the observer and there is not an absolute observer that can say his or her positions and times are absolute. In practice this means that if an observer moves with respect to another observer, they see different things. Each observer defines a reference frame, which is nothing more than a set of positions and time. Every phenomenon is described in terms of positions and time, but since positions and time are different in different reference frames, we must always specify the reference frame where the phenomenon is being observed.

Suppose that we have two observers, and one observer moves with respect to the other. If each observer carries a clock, they both see their clocks run as time goes on at the same pace. However when one of the observers compares his/her clock with the other clock, that other clock appears to run slow. This takes us to a number of paradoxes, the most celebrated one being the twin paradox. If a twin makes a long trip, leaving behind the other twin, the traveling twin will be younger than the twin left behind because time ran slow in his frame of reference. This may sound odd, but the effect has been proven. Muons are particles produced in the upper atmosphere by cosmic rays. They travel at 98% the speed of light. A muon lives for 2.2 microseconds. At that speed most muons produced at the top of a mountain, cannot travel more than a mile before they disintegrate. Yet a large quantity of muons are seen at the base of the mountain, some 2 miles below. The explanation is that a muon traveling at 98% of the speed of light is seen to age slower, that is, the muon clock appears to tick slower when we see it in our reference frame. See a description of this experiment in "A Compact Apparatus for Muon Lifetime Measurement and Time Dilation Demonstration in the Undergraduate Laboratory" by Thomas Coan, Tiankuan Liu, Jingbo Ye.

Notice that in the muon experiment, the observer on Earth sees his/her clock ticking at a normal pace while the muon clock is ticking at a slower pace. We say that there is a time dilation predicted by the special theory of relativity. One interesting thing is that an observer traveling with the muon sees the muon clock ticking at a normal pace while s/he sees the clock of the observer on Earth running slow. This is because an observer moving with the muon is at rest relative to the muon clock, while s/he sees the observer on Earth moving.

In the general theory of relativity, gravitation is treated as an acceleration, and time is also dilated for an accelerated observer. As you say, at the edge of a black hole, usually called the event horizon, time dilation becomes infinite. That means that the clock of an observer falling into the black hole, appears to slow down and eventually stops from the point of view of a distant observer safely hovering over the black hole. However this does not stop the distant observer's clock. Time continues as usual for the distant observer. The distant observer sees the falling observer moving ever more slowly until it freezes in time or disappears depending on the acceleration of the fall because the time for the falling observer becomes infintely dilated as seen by the distant observer. The black hole as seen in the reference frame of a distant observer continues to move and spin as usual.

Vladimir Escalante Ram�rez
Center for Radio Astronomy and Astrophysics
UNAM Campus Morelia

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