graner@ut-ngp.UUCP (Nicolas Graner) (05/10/85)
I find it sad that people interested in physics (at least enough to
read net.physics) don't have *some* basic ideas about relativity,
as shown by the recent discussion about speed of light. Sigh.
Anyway, here is the puzzle:
I have a laser on a turntable in such a way that the beam falls on
the moon during each revolution. If my laser rotates at omega
rad/s and the moon is at distance D, the spot moves on the moon
at speed V = omega*D. Since I can make omega as big as I want,
V can be made very big, and certainly much more than C. (e.g.
with D ~ 300,000km and omega = 10rad/s, a very gentle speed,
V = 3,000,000km/s = 10*C)
How can anything move at 10*C without violating relativity ?
(I know the beam between earth and moon will be curved, but this is irrelevant)
Nic. {ihnp4,seismo,...}!ut-ngp!graner
*If Murphy's law can go wrong, it won't*gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (05/10/85)
> How can anything move at 10*C without violating relativity ?
It can't.dxm@lanl.ARPA (05/10/85)
> I find it sad that people interested in physics (at least enough to > read net.physics) don't have *some* basic ideas about relativity, > as shown by the recent discussion about speed of light. Sigh. > > Anyway, here is the puzzle: > > I have a laser on a turntable in such a way that the beam falls on > the moon during each revolution. If my laser rotates at omega > rad/s and the moon is at distance D, the spot moves on the moon > at speed V = omega*D. Since I can make omega as big as I want, > V can be made very big, and certainly much more than C. (e.g. > with D ~ 300,000km and omega = 10rad/s, a very gentle speed, > V = 3,000,000km/s = 10*C) > > How can anything move at 10*C without violating relativity ? I suppose somebody should answer this "puzzle" for the sake of completeness in the universe. Nothing is moving faster than c here. As anyone who took PHY 353 at UT Austin will tell you, the spot on the moon can go as fast as it likes because it is not an entity except in your mind. The spot that exists over Tycho crater, say, is not the same spot ( and here I mean same energy or aggregate of photons ) as the spot several kilometers away a few seconds later. Since there is no actual motion involved here (except for the light going from laser to moon), relativity isn't destroyed which is a great relief to us all. :-) And now, a counter-puzzle: replace the above laser with a long ( *very* long) rod. It is easy to move it at the 10 rad/s speed mentioned above; how fast is the rod moving out near the moon ? Pseudo-hint: rigid body mechanics ain't gonna help you here. Make any assumptions you like about the rod (mass distribution, moment of inertia, rigidity, etc), just don't replace it with a string (in which case the problem becomes "how long does it take to roll up a very long string ?"). Doug Miller currently at dxm@lanl ....!ihnp4!lanl!dxm Los Alamos National Laboratory, P.O.B 1663 MS J960, Los Alamos, NM 87545 but soon to be at ...ihnp4!ut-ngp!bomber bomber@ut-ngp.arpa -------------------------------------------------------------------------------
karsh@geowhiz.UUCP (Bruce Karsh) (05/11/85)
> > I have a laser on a turntable in such a way that the beam falls on > the moon during each revolution. If my laser rotates at omega > rad/s and the moon is at distance D, the spot moves on the moon > at speed V = omega*D. Since I can make omega as big as I want, > V can be made very big, and certainly much more than C. (e.g. > with D ~ 300,000km and omega = 10rad/s, a very gentle speed, > V = 3,000,000km/s = 10*C) > > How can anything move at 10*C without violating relativity ? No particle is moving faster than C. This is the difference between group velocity and phase velocity. -- Bruce Karsh | U. Wisc. Dept. Geology and Geophysics | 1215 W Dayton, Madison, WI 53706 | This space for rent. (608) 262-1697 | {ihnp4,seismo}!uwvax!geowhiz!karsh |
brooks@lll-crg.ARPA (Eugene D. Brooks III) (05/11/85)
> I find it sad that people interested in physics (at least enough to > read net.physics) don't have *some* basic ideas about relativity, > as shown by the recent discussion about speed of light. Sigh. > > Anyway, here is the puzzle: > > I have a laser on a turntable in such a way that the beam falls on > the moon during each revolution. If my laser rotates at omega > rad/s and the moon is at distance D, the spot moves on the moon > at speed V = omega*D. Since I can make omega as big as I want, > V can be made very big, and certainly much more than C. (e.g. > with D ~ 300,000km and omega = 10rad/s, a very gentle speed, > V = 3,000,000km/s = 10*C) > > How can anything move at 10*C without violating relativity ? > > (I know the beam between earth and moon will be curved, but this is irrelevant) > > Nic. {ihnp4,seismo,...}!ut-ngp!graner > > *If Murphy's law can go wrong, it won't* Actually there is a more real world example of this pseudo puzzle. Consider the movement of a spot on a high speed oscilloscope. The answer to the puzzle is that only the geometric intersection of the beam and the moon is moving at a speed greater than c. No mass is moving that fast and no information is being transmitted that fast. An article discussing this paradox appeared in Scientific American a few years ago.
matt@oddjob.UUCP (Matt Crawford) (05/12/85)
Pardon me while I repeat the question from graner@ut-ngp (Nicolas Graner): >I have a laser on a turntable in such a way that the beam falls on >the moon during each revolution. If my laser rotates at omega >rad/s and the moon is at distance D, the spot moves on the moon >at speed V = omega*D. Since I can make omega as big as I want, >V can be made very big, and certainly much more than C. (e.g. >with D ~ 300,000km and omega = 10rad/s, a very gentle speed, >V = 3,000,000km/s = 10*C) > >How can anything move at 10*C without violating relativity ? > >(I know the beam between earth and moon will be curved, >but this is irrelevant) There is no object or particle in this situation which is moving faster than the speed of light, only the point defined by the intersection of the beam with the surface of the moon is doing so. To contradict any of the accepted physical laws you would have to demonstrate a way of using this system to communicate some information faster than light. That the beam is curved is not irrelevant but instead points up the fact that any decision you may make about changing the motion of the beam at the source will not reach the moon at any speed faster than c. _____________________________________________________ Matt University crawford@anl-mcs.arpa Crawford of Chicago ihnp4!oddjob!matt
js2j@mhuxt.UUCP (sonntag) (05/13/85)
> I have a laser on a turntable in such a way that the beam falls on > the moon during each revolution. If my laser rotates at omega > rad/s and the moon is at distance D, the spot moves on the moon > at speed V = omega*D. Since I can make omega as big as I want, > V can be made very big, and certainly much more than C. (e.g. > with D ~ 300,000km and omega = 10rad/s, a very gentle speed, > V = 3,000,000km/s = 10*C) > > How can anything move at 10*C without violating relativity ? > Nic. {ihnp4,seismo,...}!ut-ngp!graner This one's pretty old. In a more familiar example, the spot on the CRT of some very high-speed oscilloscopes can move faster than the speed of light. This doesn't violate relativity, as no actual object is moving FTL, only the place where the electron beam is currently hitting the phosphor. Since 'a place' doesn't really have any mass, the position of the place can change faster than any physical object's position is allowed to change. -- Jeff Sonntag ihnp4!mhuxt!js2j "I said, 'Doc, a world war passed through my brain.' He said, 'Nurse, grab your pad, the boy's insane.'"-Dylan
ethan@utastro.UUCP (Ethan Vishniac) (05/13/85)
> I find it sad that people interested in physics (at least enough to > read net.physics) don't have *some* basic ideas about relativity, > as shown by the recent discussion about speed of light. Sigh. > > Anyway, here is the puzzle: > > I have a laser on a turntable in such a way that the beam falls on > the moon during each revolution. If my laser rotates at omega > rad/s and the moon is at distance D, the spot moves on the moon > at speed V = omega*D. Since I can make omega as big as I want, > V can be made very big, and certainly much more than C. (e.g. > with D ~ 300,000km and omega = 10rad/s, a very gentle speed, > V = 3,000,000km/s = 10*C) > > How can anything move at 10*C without violating relativity ? > Hmmm... This one is pretty old. Nothing travels from the beam end at one time to the beam end at another time.
josh@topaz.ARPA (J Storrs Hall) (05/15/85)
> I have a laser on a turntable in such a way that the beam falls on > the moon during each revolution. ... > How can anything move at 10*C without violating relativity ? Enough already! It's time to launch a reductio ad adsurdum: Let's talk about the sun. It's big. It's hot. Now consider Alpha Centauri. It too is big and hot. But wait! The SUBJECT OF CONVERSATION has moved more than 4 lightyears in less than a second, a velocity in excess of 100 million times C. How can this be?!?!?!?!? --JoSH
fred@mnetor.UUCP (Fred Williams) (05/15/85)
In article <1720@ut-ngp.UUCP> graner@ut-ngp.UUCP (Nicolas Graner) writes: > >I have a laser on a turntable in such a way that the beam falls on >the moon during each revolution. If my laser rotates at omega >rad/s and the moon is at distance D, the spot moves on the moon >at speed V = omega*D. Since I can make omega as big as I want, >V can be made very big, and certainly much more than C. (e.g. >with D ~ 300,000km and omega = 10rad/s, a very gentle speed, >V = 3,000,000km/s = 10*C) > >How can anything move at 10*C without violating relativity ? The 'thing' that is moving is not a mass object. It is not even an energy object, (ie a photon). It is only an image and hence not bound by the restriction of the maximum speed of 'c'. Cheers, Fred Williams. PS. By the way, if you want another relativistic puzzle, consider the following,(I'll post the answer in a few days after I've had a chuckle): If the speed of light is constant in all reference frames, how come we can see doppler shifts? This is a good exercise in learning how to apply laws such as the conservation of energy.
jeff@heurikon.UUCP (Jeffrey Mattox) (05/16/85)
Another "real world" example:
Consider the point of intersection of the blades of a scissors.
Picture a BIG scissors - mile long blades. As you close the
scissors, the point of intersection could move faster than the
speed of light even though the blades are moving "slowly".
--
/"""\ Jeffrey Mattox, Heurikon Corp, Madison, WI
|O.O| {harpo, hao, philabs}!seismo!uwvax!heurikon!jeff (news & mail)
\_=_/ ihnp4!heurikon!jeff (mail - best)karsh@geowhiz.UUCP (Bruce Karsh) (05/18/85)
>Another "real world" example: >Consider the point of intersection of the blades of a scissors. >Picture a BIG scissors - mile long blades. As you close the >scissors, the point of intersection could move faster than the >speed of light even though the blades are moving "slowly". Consider a paper punch!! Every point on the circle is being cut at the same time!! So the "cut point" must go around the circle at infinite velocity. And since it's going around a circle, it's accelerated!! Wow!! Einstein was wrong!! Well, I'm off to Switzerland to collect my Nobel Prize. See ya all later!! :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) (I bet you can't wait till I disprove Quantum Mechanics too!!) :-) -- Bruce Karsh | U. Wisc. Dept. Geology and Geophysics | 1215 W Dayton, Madison, WI 53706 | This space for rent. (608) 262-1697 | {ihnp4,seismo}!uwvax!geowhiz!karsh |
stekas@hou2g.UUCP (J.STEKAS) (05/20/85)
> Consider the point of intersection of the blades of a scissors. > Picture a BIG scissors - mile long blades. As you close the > scissors, the point of intersection could move faster than the > speed of light even though the blades are moving "slowly". This isn't true. The blades of the scissors are held together by E&M forces between the atoms. When the handle is squeezed, the E&M force won't be transmitted to the far end of the blades any faster than C. The result is that the blades will "bend". The point of intersection of the blades will propigate no faster the "bend" - the speed of light. Jim
goran@erix.UUCP (Goeran Baage) (05/21/85)
In article <186@geowhiz.UUCP> karsh@geowhiz.UUCP (Bruce Karsh) writes: > ..... >Well, I'm off to Switzerland to collect my Nobel Prize. See >ya all later!! > ..... Switzerland is not where you collect it, that's where you bring the the money to avoid taxes (a numbered bank account perhaps). :-) :-) Goeran Baage
lwall@sdcrdcf.UUCP (Larry Wall) (05/22/85)
In article <471@hou2g.UUCP> stekas@hou2g.UUCP (J.STEKAS) writes: >> Consider the point of intersection of the blades of a scissors.... > >This isn't true. The blades of the scissors are held together >by E&M forces between the atoms. When the handle is squeezed, >the E&M force won't be transmitted to the far end of the blades >any faster than C. The result is that the blades will "bend". >The point of intersection of the blades will propigate no faster >the "bend" - the speed of light. Who says anyone has to squeeze the handle to have the scissors closing? Ever heard of velocity? Larry Wall {allegra,burdvax,cbosgd,hplabs,ihnp4,sdcsvax}!sdcrdcf!lwall
emh@bonnie.UUCP (Edward M. Hummel) (05/27/85)
>> Consider the point of intersection of the blades of a scissors. >> Picture a BIG scissors - mile long blades. As you close the >> scissors, the point of intersection could move faster than the >> speed of light even though the blades are moving "slowly". >This isn't true. The blades of the scissors are held together >by E&M forces between the atoms. When the handle is squeezed, >the E&M force won't be transmitted to the far end of the blades >any faster than C. The result is that the blades will "bend". >The point of intersection of the blades will propigate no faster >the "bend" - the speed of light. Sorry, Jim, but it is true. The propagation of "motion" along a rigid body is indeed limited by the "forces between the atoms". A push on one end of an object takes a while to propagate to the other end of the object (the speed of sound gives a first order estimate). But once the motion has been obtained the point of intersection of a large pair of scissors indeed can travel faster than c. Ed Hummel ...!ihnp4!clyde!bonnie!emh
rosalia@tekig4.UUCP (Mark Galassi) (06/04/85)
In article <186@geowhiz.UUCP> karsh@geowhiz.UUCP (Bruce Karsh) writes: >Well, I'm off to Switzerland to collect my Nobel Prize. See >ya all later!! >:-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) :-) Sweden, not Switzerland. Be careful not to miss you prize because you got the country wrong! Mark Galassi