NYT article about the speed of shadow > c

[EnumaElish]

The thought experiment is to glue a "bat" figure on a light source (e.g., lamp). The shadow created by the bat figure is projected into the void, as in Batman. The trick is to rotate the lamp. As the lamp rotates, so does the bat shadow, projected into the space. The trajectory of the shadow is a great circle with the lamp at its center. (Actually, the "circle" itself will be expanding at the speed of light, but the author ignores this aspect, as far as I can tell.)

At a sufficiently large distance from the lamp, the circumference of the circle will have expanded to such a great length that the shadow will be rotating at a speed exceeding the speed of light. At least, that's what I understand the article to be saying. The author does not explain (nor do I remember) the formula tying the speed of the shadow to that of the lamp, but the principle must be similar to the concept of "gear ratio."

The author then goes on to explain how that does not violate relativity.

Comments?

 

[chroot]

If you take a laser pointer and sweep it across the sky from the northern horizon to the southern horizon, the "point" of your laser beam is also moving much faster than c.

This, of course, has nothing to do with relativity, since neither of these phenomena involve the actual motion of any objects. Also, you cannot use either of these phenomena to transmit information. They do not contradict relativity.

- Warren

 

[olgranpappy]

Similarly, if you stand up and spin around quickly one time, then in a reference frame fixed to your body the moon travels around you at a velocity exceeding c.

 

[EnumaElish]

If you take a laser pointer and sweep it across the sky from the northern horizon to the southern horizon, the "point" of your laser beam is also moving much faster than c.

I don't quite understand the mechanics here. If the "point" moves from point A to point B at a faster-than-light speed, how does that not imply that a photon which traveled from the source to point B was traveling faster than light?

Picture 1: point A has light, point B is dark.
Picture 2: point A is dark, point B has light.
It took 0.000...0001 seconds to get from picture 1 to picture 2 (implying point speed > c).
What "shines" at point B is a photon that was emitted during the "split second" between the two pictures.
Doesn't that imply that this photon traveled faster than light?

I guess it doesn't, because arc length > radius.

I might have just answered my question, but if you have a comment please go ahead and post it.

 

[MeJennifer]

Doesn't that imply that this photon traveled faster than light?

It does not.
The photons arriving at A and B come from the laser pointer, they do not travel from A to B.

 

[EnumaElish]

It does not.
The photons arriving at A and B come from the laser pointer, they do not travel from A to B.

They only travel from the source to point B (the radius), which is less than the distance from A to B (the arc). Is this reasoning correct?

 

[EnumaElish]

Similarly, if you stand up and spin around quickly one time, then in a reference frame fixed to your body the moon travels around you at a velocity exceeding c.

This doesn't violate relativity because a reference frame is not a "thing." Is that correct?

 

[olgranpappy]

This doesn't violate relativity because a reference frame is not a "thing." Is that correct?

Well... what's a thing?
...Maybe someone else can field this one since I am at work.

 

[EnumaElish]

Well... what's a thing?
...Maybe someone else can field this one since I am at work.

I meant a physical object.

 

[gabee]

The photon that travels from the source to point A is not the same photon that travels from the source to point B--since the laser beam is a stream of a bunch of different photons, there is no actual physical object that is traveling faster than c.

It's the same in the NYT article--the photons tracing out the edge of the bat's shadow are a bunch of different photons, so there is no real object moving faster than c.

I think olgranpappy's example about spinning around can be explained by the fact that a spinning reference frame is not an inertial reference frame, but that's a little different to what the article is talking about.