# Question about the speed of light

If the speed of light is 299792458 m / s and the speed of light is the maximum speed an object can travel.

If i have a piece of string with a weight on the end of it and i rotate the string the velocity differers along the length of the string

e.g the end of the string is traveling at a faster speed than a point of the string close to the rotation point.

Now giving the above facts is it not true that there would be a point at which the end of the rotating string would rotate faster than the speed of light given a length of string?

## Answers and Replies

I would say that given the radius of your string, the angular velocity it's limited because w·R < c.

ZapperZ
Staff Emeritus
What type of a force do you think holds the molecules/atoms of the string together? And how fast do you think this force transfers from one end to the other?

Zz.

I'm having a debate on one another forum about something like this too. The question was "if you rotate a laser emitter around it's axis, would the dot projected on the wall (let's say the emitter is in the center of a cylindrical room) move faster than light?".

I thought that the stream of photons would form a hyperbolic spiral when the emitter is spinning fast enough, is that the case? Some other person said that it would move faster and linked me this http://en.wikipedia.org/wiki/Angular_velocity

So then I came here because the people on this forum seem to know a tad more than I.

ZapperZ
Staff Emeritus
You can already get an idea what's going on here simply using water coming out of hose. If you move slow enough, the spot where the water its the ground (or wall), moves at the same speed as how fast you are turning. But try moving faster and faster. You'll see the spot lagging behind more and more. Why? Because it takes time for the water particles to travel from the tip of the hose to the spot on the ground.

The mistake often made in this type of scenario is the explicit assumption that the light from the source instantaneously gets to get to the wall. This is false.

Zz.

You can already get an idea what's going on here simply using water coming out of hose. If you move slow enough, the spot where the water its the ground (or wall), moves at the same speed as how fast you are turning. But try moving faster and faster. You'll see the spot lagging behind more and more. Why? Because it takes time for the water particles to travel from the tip of the hose to the spot on the ground.

The mistake often made in this type of scenario is the explicit assumption that the light from the source instantaneously gets to get to the wall. This is false.

Zz.

So it doesn't move faster than light?

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stewartcs
So it doesn't move faster than light?

Right.

Doc Al
Mentor
spots of light CAN move faster than light speed

I'm having a debate on one another forum about something like this too. The question was "if you rotate a laser emitter around it's axis, would the dot projected on the wall (let's say the emitter is in the center of a cylindrical room) move faster than light?".
You can certainly have a spot on the wall move faster than the speed of light. (If the wall is big enough and far enough away.) The classic example is sweeping a laser beam across the surface of the moon.

Zapper's point about there being a time lag between when you sweep the laser and when the light reaches the target is correct. But when the light finally reaches the target, it will sweep across at the speed with which you swept the beam. Say I set up a sweeping laser beam to sweep across the moon in 1/1000 of a second. The light takes whatever time it takes to get to the moon, then the spot sweeps across the diameter of the moon in 1/1000 of a second.

So it doesn't move faster than light?
It certainly can, but this does not contradict relativity since a spot of light is not a physical object. Further, that moving spot can't be used to send a signal from one side of the moon (or room) to the other.

Even the dot can not move at the speed of light. Then the dot will be not the dot, it's discrete.

stewartcs
For a virtual object (i.e. not physical) that would hold true (referring to Doc Al's comment).

Now giving the above facts is it not true that there would be a point at which the end of the rotating string would rotate faster than the speed of light given a length of string?

However, the OP was asking about a string with some object attached to the end being twirled around, that presumably has mass. I would think in this case that it is impossible for that object to surpass or even get remotely near the speed of light.

Is that not a correct assumption?

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Doc Al
Mentor
However, the OP was asking about a string with some object attached to the end being twirled around, that presumably has mass. I would think in this case that it is impossible for that object to surpass or even get remotely near the speed of light.

Is that not a correct assumption?
Of course: no part of the string will get moving anywhere close to the speed of light.

But Xendance asked a different question. That's what I was answering.

stewartcs
Oh sorry, didn't read what he was quoting!

You can certainly have a spot on the wall move faster than the speed of light. (If the wall is big enough and far enough away.) The classic example is sweeping a laser beam across the surface of the moon.

Zapper's point about there being a time lag between when you sweep the laser and when the light reaches the target is correct. But when the light finally reaches the target, it will sweep across at the speed with which you swept the beam. Say I set up a sweeping laser beam to sweep across the moon in 1/1000 of a second. The light takes whatever time it takes to get to the moon, then the spot sweeps across the diameter of the moon in 1/1000 of a second.

It certainly can, but this does not contradict relativity since a spot of light is not a physical object. Further, that moving spot can't be used to send a signal from one side of the moon (or room) to the other.

I had an interesting thought about this. If the spot traveling faster than the speed of light
hit a sensor causing a chain of events on one side of the moon and then did the same on the other side of the moon, which chain of events would occur first?

Danger
Gold Member
The chain triggered by the first sensor would obviouly happen first. The two events, however, cannot interact with one another at anything greater than c. It would still be faster (essentially simultaneous) to trigger both events with a broad-beam radio.

You can already get an idea what's going on here simply using water coming out of a hose. If you move slow enough, the spot where the water its the ground (or wall), moves at the same speed as how fast you are turning. But try moving faster and faster. You'll see the spot lagging behind more and more. Why? Because it takes time for the water particles to travel from the tip of the hose to the spot on the ground.

The mistake often made in this type of scenario is the explicit assumption that the light from the source instantaneously gets to get to the wall. This is false.

Zz.

I don't think that's quite right. The water spot where it impacts the ground CAN in theory move faster than the speed of light (not just faster than the speed of water through air), even though the water in the stream itself is moving nowhere near the speed of light. And the fact there's some delay if the source is rotating - that's pretty much irrelevant, the spot can still travel extremely fast. So I'm pretty sure it's a flawed argument.

Similarly like when a plane water wave arrives on a beach at an angle. The speed of the point of impact of the crest can move a lot faster than the speed of the water waves themselves. As far as I can tell, there's no logical reason that point of impact can't travel at any speed, even beyond the speed of light. -Since there's no causal link between any two points of impact along the beach (one can't cause the other to happen, nor stop it from happening).

Another example is when you switch a lamp on in a room. The boundary of the rapidly growing bright circle of light cast on a nearby wall will definitely travel faster than the speed light itself...

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russ_watters
Mentor
I don't think that's quite right. The water spot where it impacts the ground CAN in theory move faster than the speed of light (not just faster than the speed of water through air), even though the water in the stream itself is moving nowhere near the speed of light. And the fact there's some delay if the source is rotating - that's pretty much irrelevant, the spot can still travel extremely fast. So I'm pretty sure it's a flawed argument.
ZZ Wasn't saying that the spot can't travel fast. It usually seems that what confuses people is that they envision a straight laser beam tracing out an image on the moon. The laser beam will be bent (in a spiral if you spin fast enough), and the spot on the moon/out in space can move faster than C.
Similarly like when a plane water wave arrives on a beach at an angle. The speed of the point of impact of the crest can move a lot faster than the speed of the water waves themselves. As far as I can tell, there's no logical reason that point of impact can't travel at any speed, even beyond the speed of light. -Since there's no causal link between any two points of impact along the beach (one can't cause the other to happen, nor stop it from happening).
Yes, that's basically the same phenomena.

ZZ Wasn't saying that the spot can't travel fast. It usually seems that what confuses people is that they envision a straight laser beam tracing out an image on the moon. The laser beam will be bent (in a spiral if you spin fast enough), and the spot on the moon/out in space can move faster than C
He said the bending is proof that the spot traced at the tip can't move faster than c.
The (apparent) bending doesn't prove that at all. That's precisely why it's not a good example to use if you're trying to answer the initial question.

Doc Al
Mentor
He said the bending is proof that the spot traced at the tip can't move faster than c.
I addressed this issue of spots of light moving faster than light speed in post #8.