Relativistic Doppler shift
in [Relativity]
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From: Dono. on 25 Jul 2010 22:52 On Jul 25, 2:05 pm, "I.N. Galidakis" <morph...(a)olympus.mons> wrote: > > Btw, this expression seems to give a "blue-shift" for a fast-rotating green > laser (since I find that the 532nm reduces towards the blue to 520nm for my > case), but I understand that the term "redshift" may be used generically for > both cases, blue-shift and red-shift. > "red-shift" is meant to mean "observed frequency < emitted frequency"
From: Tony M on 26 Jul 2010 15:11 I was also thinking about the relativistic Doppler shift lately. Two observers A and B are heading towards each other at relative speed c/2. Observer A shoots a laser beam of frequency fA (as measured by A) towards observer B where it is received at frequency fB (as measured by B). What fB does B measure? What should fB be from observer As perspective? Will the two observers agree on the value of fB? The way I see it: From As perspective B is heading towards him at c/2 so fA is Doppler blue-shifted. Bs clock is slower so theres an additional relativistic blue-shift. B should measure fB = fA x 2 x gamma. From Bs perspective A is heading towards him at c/2. As clock is slower so fA first gets a relativistic red-shift then a Doppler blue- shift. B should measure fB = fA x 2 / gamma. So A and B would disagree on the value of fB, if Im analyzing the problem right.
From: Androcles on 26 Jul 2010 16:31 "Tony M" <marcuac(a)gmail.com> wrote in message news:902294a8-81ff-4a2d-86c2-b6b46f721dce(a)z10g2000yqb.googlegroups.com... I was also thinking about the relativistic Doppler shift lately. Two observers A and B are heading towards each other at relative speed c/2. Observer A shoots a laser beam of frequency fA (as measured by A) towards observer B where it is received at frequency fB (as measured by B). What fB does B measure? What should fB be from observer A�s perspective? Will the two observers agree on the value of fB? The way I see it: From A�s perspective B is heading towards him at c/2 so fA is Doppler blue-shifted. B�s clock is slower so there�s an additional relativistic blue-shift. B should measure fB = fA x 2 x gamma. From B�s perspective A is heading towards him at c/2. A�s clock is slower so fA first gets a relativistic red-shift then a Doppler blue- shift. B should measure fB = fA x 2 / gamma. So A and B would disagree on the value of fB, if I�m analyzing the problem right. =================================================== http://www.fourmilab.ch/etexts/einstein/specrel/www/ � 4. Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks "For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity." -- Einstein. You forgot to play the part, physically, of an infinitely stupid relativistic clown.
From: dlzc on 26 Jul 2010 16:39 Dear Tony M: On Jul 26, 12:11 pm, Tony M <marc...(a)gmail.com> wrote: > I was also thinking about the relativistic > Doppler shift lately. Two observers A and B > are heading towards each other at relative > speed c/2. Observer A shoots a laser beam of > frequency fA (as measured by A) towards > observer B where it is received at frequency > fB (as measured by B). What fB does B measure? > What should fB be from observer As > perspective? Will the two observers agree on > the value of fB? > The way I see it: > From As perspective B is heading towards him > at c/2 so fA is Doppler blue-shifted. Bs clock > is slower so theres an additional relativistic > blue-shift. *red* shift. > B should measure fB = fA x 2 x gamma. No, probably not. > From Bs perspective A is heading towards him > at c/2. As clock is slower so fA first gets a > relativistic red-shift then a Doppler blue- > shift. B should measure fB = fA x 2 / gamma. > So A and B would disagree on the value of fB, > if Im analyzing the problem right. Just in case you are intersted, Stephen Speicher did a nice little derivation / analysis you might find helpful to your cogitations... http://groups.google.com/group/sci.physics.relativity/msg/d0bcbd1d158a4a16 David A. Smith
From: harald on 27 Jul 2010 06:25
On Jul 26, 9:11 pm, Tony M <marc...(a)gmail.com> wrote: > I was also thinking about the relativistic Doppler shift lately. > Two observers A and B are heading towards each other at > relative speed c/2. That's a bit ambiguous; I'll assume you to mean that they measure each other's speed as c/2. > Observer A shoots a laser beam of frequency fA (as measured by A) > towards observer B where it is received at frequency fB (as > measured by B). What fB does B measure? > What should fB be from observer As perspective? http://www.fourmilab.ch/etexts/einstein/specrel/www/ Section 7: f'/f = gamma*(1 - v/c) or f'/f = sqr[(1-v/c)/(1+v/c)] With v apparently taken positive for receding. Or, with v taken positive for approaching (more standard): fB/fA = sqr[(1+v/c)/(1-v/c)] This is composed of time dilation and true (classical) Doppler. Sanity check: 1. Doppler: fB/fA = 1+v/c for A in rest. Ok. 2. time dilation: fB/fA = gamma for A in rest. Ok. > Will the two observers agree on the value of fB? Of course - the value fB is a fact of measurement. > The way I see it: I can't follow your reasoning at all. With B taken "in rest": 1. Doppler: fB/fA = 1/(1-v/c) 2. Time dilation: fB/fA = 1/gamma = sqr(1-v^2/c^2) Combined effect: fB/fA = sqr(1-v^2/c^2) / (1-v/c) fB/fA = sqr[(1-v/c)(1+v/c)]/ (1-v/c) or, fB/fA = sqr[(1+v/c)/1-v/c)] That is the same - as it should be. Harald > From As perspective B is heading towards him at c/2 so fA is Doppler > blue-shifted. Bs clock is slower so theres an additional > relativistic blue-shift. B should measure fB = fA x 2 x gamma. > From Bs perspective A is heading towards him at c/2. As clock is > slower so fA first gets a relativistic red-shift then a Doppler blue- > shift. B should measure fB = fA x 2 / gamma. > So A and B would disagree on the value of fB, if Im analyzing the > problem right. |