Notes & Queries: Apparent Supraluminal Motion

I remember talking about the following question with friends as an undergrad when I saw spotlights moving on the clouds. I think the guideline Avery came up with then was: "if a proposed phenomenon doesn't transmit any info faster than light, then it probably doesn't violate the relativity principles."

The question

From "Notes & Queries", The Guardian, 9 September 1994:

QUESTION: If I were to build a circular wall in space with a circumference of 372,000 miles, and then place a powerful optical laser at the center of the circle, would the speed of the laser's light dot across the wall be twice the speed of light? Or would the concept come to grief on some relativistic frame of reference? Michael Campbell.

My answer

Here is the full text of my email to The Guardian. Passages in italics are what actually appeared in "Notes & Queries", 21 September, 1994.

If one were to observe the movement of this dot of light on the circular wall, one would would in fact see the dot apparently moving at twice the speed of light (assuming the laser rotates once per second). But this does not violate the famous law that nothing can exceed the speed of light. This is because the dot of light is not itself an object, but a series of photons hitting the wall that we interpret as a single entity. No single photon (light particle) is moving along the surface of the wall, so no single photon is travelling the circuit of the wall in one second.

Rather, the situation is more like a cinema marquee with many light bulbs, but with only one lit at any given moment. Turning the bulbs on and off in staggered succession may give the impression of one light moving very quickly across the length of the marquee, but in fact, nothing is moving at all. Similarly, nothing would be moving across the surface of the circular wall in space; there would only be a sucession of photons hitting it, which we would interpret as a pattern of a moving dot. As we do for the question "why do mirrors reverse left/right and not up/down", we find that what appears to be a question about physics is really a question about how our minds interpret the world. Relativity theory need not be invoked, thank goodness.

A reference from Brian Keeley

Date: Thu, 22 Sep 94 17:44 BST
From: ronc (Ron Chrisley)
To: bkeeley@UCSD.EDU, ronc
Subject: Re: [ronc: Answer to N&Q of 9/9/94]

   Date: Thu, 15 Sep 94 18:10:48 -0700
   From: gysin@mugwump.UCSD.EDU (Brian Keeley)

   Ron,

   In reference to your thought experiment, take a look at _Nature_
   (v371,no.6492) [1 Sept 1994].  The cover story is about "Superluminal
   motion in the Galaxy" which discusses apparent superluminal motion of
   the type you discuss (as much as I understand both yours and the
   Nature accounts).  There's a paper (p.46) and a synopsis (p. 18).

OK, I'll take a look.

   Worse than being wrong, you may have been superceded!

Nah, this is just a Q&A section of the paper; it isn't purporting to
be original.

  Brian

Ron

And a good question from Annabel (which Brian also raised)


Date: Fri, 23 Sep 1994 23:28:27 +0100
From: Miss Annabel M Weeden 
To: ronc@cogs.susx.ac.uk
Subject: oh well


      R: The Q was whether the red dot breaks the speed of light.  It does, but
	 that's OK, because it isn't an object, just a series of objects
	 (photons).

     A: Yes, but you can't prove that because you wouldn't be able to actually
        *see* it happening.  Right?

   R: I'm tempted to say: "so I can't *prove* that the light goes off in the
      refrigerator when i shut the door?", but you actually might have a
      point.  Let me think about it.

A: Wow - you mean *I've* sparked off philosophical thought??

I guess the worry is that unlike the refrigerator case, there might be some in-principle reason why, due to relativity, one could never observe the spot to even appear to travel twice the speed of light...

Ron Chrisley