Does an observer on a carousel see a horizon?

**heinz** · Jun19-09, 08:30 AM

Special relativity shows that any accelerated observer
sees an event horizon. In fact, if an observer is accelerated
by a, the horizon is at distance l=c^2/a in the direction
opposite to a.

If an observer is on a carousel or merry-go-round,
he is accelerated inwards. Does he then see a horizon
on the outside?

If so, does a horizon also appear for an observer in orbit,
thus when circling the earth or the sun?

Hz

**George Jones** · Jun19-09, 08:40 AM

No.

For an observer with constant 4-acceleration, there is a region of spacetime from which no signal reaches the accelerated observer. The boundary of this region is the horizon.

For the observer on a carousel, there is no such region of spacetime, and thus no horizon (boundary). A spacetime diagram that has two space dimensions and one time dimension shows this clearly.

**heinz** · Jun20-09, 02:43 AM

Originally Posted by George Jones

No. For the observer on a carousel, there is no such region of spacetime, and thus no horizon (boundary). A spacetime diagram that has two space dimensions and one time dimension shows this clearly.

Thank you! Can I read this somewhere, maybe with a picture of the diagram?

Hz

**MeJennifer** · Jun20-09, 03:42 AM

Originally Posted by heinz

If so, does a horizon also appear for an observer in orbit,
thus when circling the earth or the sun?

An observer in orbit does not accelerate. Such an observer would travel on a "straight line".

**George Jones** · Jun21-09, 06:21 AM

Originally Posted by heinz

Thank you! Can I read this somewhere, maybe with a picture of the diagram?

Hz

I haven't tried to find this anywhere.

Suppose that the centre of the carousel is in an inertial reference frame, that the plane of the carousel is the x-y plane, and that a person on the edge of the carousel moves with constant speed 1/2 (c=1).

Then, the coordinates of the person on the edge are $LaTeX Code: x = \\cos \\left( t/2 \\right)$ and $LaTeX Code: y = \\sin \\left( t/2 \\right)$ . Plotting this worldline on a t-x-y spacetime diagram gives a helix about the t-axis (worldline of the centre).

Now pick an arbitrary event in spacetime. The attached spacetime diagram shows that there is a lightlike path from the event to the worldline of the person on the edge of the carousel.