# Dumb Question

This is probably a dumb question, but if Einstein proposes that nothing can travel faster than light via Special Relativity, then what is the speed at which light gets sucked into a blackhole?

cristo
Staff Emeritus
The speed of light. What makes you think it is anything different?

Once again, I apologize if its a stupid question... i'm just trying to understand Special Relativity. But wouldn't gravity have to be attracting light at a greater speed to change its direction? Say, light is travelling by a blackhole, and gets pulled in. Would that mean that light is then traveling at the speed to which gravity attracts it towards the blackhole?

cristo
Staff Emeritus
Special relativity does not describe black holes; for this you need general relativity. In general relativity, gravity is not described as a force, but is a result of the curvature of space-time, and so light does not get pulled into a black hole.

There's no need to worry about black holes until you start studying general relativity.

DaveC426913
Gold Member
Once again, I apologize if its a stupid question... i'm just trying to understand Special Relativity. But wouldn't gravity have to be attracting light at a greater speed to change its direction? Say, light is travelling by a blackhole, and gets pulled in. Would that mean that light is then traveling at the speed to which gravity attracts it towards the blackhole?

Light is not a particle that is attracted by gravity. Gravity is the curvature of spacetime such that light follows the shortest distance between two points. Near a black hole, the curvature is such that the light's path will lead into - and never out of - the black hole.

pervect
Staff Emeritus
This is probably a dumb question, but if Einstein proposes that nothing can travel faster than light via Special Relativity, then what is the speed at which light gets sucked into a blackhole?

Using local clocks and rulers, the speed of light in a vacuum is always equal to 'c', even in GR.

However, the coordinate speed of light is not necessarily equal to 'c'.

One has to be very precise as to how the 'speed' is being measured.

Thus if you carry a clock, ruler, and a light source with you, and jump into a black hole, you will always measure the speed of the light from your light source (or from any external source, for that matter) to be equal to 'c', even when you fall into a black hole.

Is it not possible for light to have orbits in the Schwarzschild geometry ?

This is probably a dumb question, but if Einstein proposes that nothing can travel faster than light via Special Relativity, then what is the speed at which light gets sucked into a blackhole?
That rule belongs to special relativity. In general relativity the speed of light may have different values. From an observer at rest outside the black hole he will reckon that a light beam falling radially in towards a black hole will eventually slows down, i.e. the speed approaches zero as the light proceeds toward the event horizon. The light never passes through the event horizon from the external observer's point of view, so it never gets "sucked into" the black hole. The frequency of light diminishes to such a low value that it eventually becomes invisible to any instrument of finite precision.

Pete

Using local clocks and rulers, the speed of light in a vacuum is always equal to 'c', even in GR.

However, the coordinate speed of light is not necessarily equal to 'c'.

One has to be very precise as to how the 'speed' is being measured.

.

Pervect - can you give some examples - e.g., do you consider the one way sagnac correction used in GPS to be an example of a non "c" coordinate light speed?

pervect
Staff Emeritus
Pervect - can you give some examples - e.g., do you consider the one way sagnac correction used in GPS to be an example of a non "c" coordinate light speed?

That's one example, I suppose. Another example would be the use of clocks and rulers "at infinity" in the Schwarzschild coordinate system, i.e. using schwarzschild r and t coordinates to measure 'speed'. It turns out that the 'speed' of light (or any other object falling into a black hole) is zero at the event horizon using this particular definition.

The point is that coordinate speeds vary all over the place in GR - only when you use local clocks and rulers is the speed of light constant.

To even talk about measuring the speed of light, one has to use a somewhat outdated notion of distance (basically, using a replica of the standard meter bar in Paris as the definition of distance). But if one does use this outdated definition of distance, and caries around a meter bar and a clock, relativity predicts that the measured speed of light is constant wherever one goes, including falling into a black hole.

In your examples, either gravity or acceleration exists .. can you extend this to the coordinate (one way) speed as between two objects in uniform relative motion, e.g., the coordinate speed of a photon traveling between two objects separating at velocity v.

Thanks

Yogi

This would seem to indicate a possible conflict with SR

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DaveC426913
Gold Member
Um. Point of order:

Is this helping the OP get his answer? Side discussions are one thing, but do you think discussions about the "sagnac correction" (which *I*'ve never even heard of) will help the OP?

Pervect already gave an answer to the initial inquiry - that answer was two fold; the part dealing with the measurement of the coordinate speed of light evokes further questions.

pervect
Staff Emeritus
If I mention that in order to measure the sort of velocity I'm talking about that one needs two clocks (rather than just one), a ruler, and a method of synchronizing the two clocks (the Einstein convention), will everyone be happy?

To measure the velocity of an object, one needs to mark out a course of known length (with the ruler), have one clock (at the start of the course), and another clock at the end of the course (the finish line). One synchronizes the two clocks at the instance the object whose velocity one is measuring crosses the starting line, and reads out the duration of the trip on the second clock at the finish line.

If one is timing anything other than light, one can make a similar measurement with an "onboard" clock, using only one clock. This sort of measurement will not give a velocity less than 'c', it will give a number known as a 'rapidity' that can be arbitrarily high. Rapidity and velocity can be thought of as two different ways of measuring the same abstract idea, "speed", but they are numerically different.

Note that we've talked about all of this before, too :-).

There's a little more to be said about "fair" methods of clock synchroization, the general idea as presented in Einstein's original paper is "isotropy". One way of describing isotropy is to say that the relation between the one-clock method of measuring rapidity and the two-clock method of measuring velocity must not depend on the direction in which one traverses the course. This is a "fair" method of synchronizing clocks. For an example of an "unfair" method of synchronizing clocks, imagine that one defined clocks to be synchronized on the Earth whenever the sun was directly overhead. Note that taking this idea seriously will break Newton's laws, among a number of other non-features.

At this point, we've probably confused the OP, and yogi has heard all this before, I think.

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