Experiment to test mutual time dilation
in [Relativity]
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From: Paul B. Andersen on 5 Aug 2010 15:26 On 05.08.2010 01:16, Koobee Wublee wrote: > On Aug 3, 9:27 am, harald wrote: > >> BTW this is an old topic but with a slightly different presentation: >> http://www.natscience.com/Uwe/Forum.aspx/physics/18921/Testing-mutual-time-dilation > > The second post by Professor Roberts has a wrong conclusion on > relativistic Doppler effect. The Lorentz transform actually leads to > a reverse Doppler effect. Where have the self-styled physicist been > in the past 100 years? See the following recent posts by yours truly > at: > > http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en > > http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en > > <shrug> So can you please point out the error in the following derivation? A wave propagating in the positive x direction in the unprimed frame can be written: E cos(phi(t,x)) where phi(t,x) = wt - (w/c)x Let the primed frame be moving at v along the positive x-axis. The same wave transformed to the primed frame can be written: E' cos(phi'(t',x')) where phi'(t',x') = w't' - (w'/c)x' Applying the LT transform: t = g(t' + vx'/c^2) x = g(x' + vt') g = 1/sqrt(1-v^2/c^2) yields: wt - (w/c)x = wg((t' + vx'/c^2) - (w/c)g(x' + vt') = wg(1-v/c)t' - (w/c)g(1-v/c)x' = w't' - (w'/c)x' Thus: w' = wg(1-v/c) = w sqrt((1-v/c)/(1+v/c)) The wave is red shifted in the primed frame. -- Paul http://home.c2i.net/pb_andersen/
From: Koobee Wublee on 6 Aug 2010 02:48 On Aug 5, 12:26 pm, "Paul B. Andersen" wrote: > On 05.08.2010 01:16, Koobee Wublee wrote: > > The second post by Professor Roberts has a wrong conclusion on > > relativistic Doppler effect. The Lorentz transform actually leads to > > a reverse Doppler effect. Where have the self-styled physicist been > > in the past 100 years? See the following recent posts by yours truly > > at: > > > http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en > > > http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en > > So can you please point out the error in the following derivation? > > A wave propagating in the positive x direction > in the unprimed frame can be written: > E cos(phi(t,x)) where phi(t,x) = wt - (w/c)x > > Let the primed frame be moving at v along the positive x-axis. > > The same wave transformed to the primed frame can be written: > E' cos(phi'(t',x')) where phi'(t',x') = w't' - (w'/c)x' > > Applying the LT transform: > t = g(t' + vx'/c^2) > x = g(x' + vt') > g = 1/sqrt(1-v^2/c^2) > yields: > wt - (w/c)x = wg((t' + vx'/c^2) - (w/c)g(x' + vt') > = wg(1-v/c)t' - (w/c)g(1-v/c)x' > = w't' - (w'/c)x' > > Thus: > w' = wg(1-v/c) = w sqrt((1-v/c)/(1+v/c)) > > The wave is red shifted in the primed frame. First, you are stating the following which stands on no ground. ** w (t - x / c) = w' (t' - x' /c) Secondly, you can easily write the result as the following instead, ** w = w' sqrt(1 + v / c) / sqrt(1 - v / c) Where ** v = Speed of w' relative to w And proudly claim w-w' moving away (v > 0) as Doppler blue shift. Notice the classical Doppler effect for sound cannot be derived using your method. This should be an alarm ringing in your head on your part. Once again, your mistake is in the application of the Lorentz transform. The time transformation can generally be written as follows. You must pay very close and crucial attention to the directions of these vectors. The self-styled physicists have been hand-waving and spoon- feeding this nonsense to their brain-washed pupils in the past 100 years. ** dt' = (dt - [v] * d[s] / c) / sqrt(1 - v^2 / c^2) Where ** [v] = Velocity of dt' as observed by dt ** d[s]/dt = [c] = Velocity of light ** d[s]/dt * d[s]/dt = c^2 Since you are making the same mistake again, I shall not count this one as a score of mine. Please study my posts below more carefully. It is not that hard. <shrug> http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en Since you have brought up the wave equations for light, solutions to Maxwell's equation in free space are: SUM_n[[E_n] exp(a_n (w_n t + b_n [k_n] * [s]) + c_n)] Where ** a_n = +/- 1 or +/- sqrt(-1) ** b_n = +/- 1 ** [E_n] = Constant vector ** [k_n] = Direction vector ** [s] = Position vector ** k_n^2 = w_n^2 / c^2 ** * = Dot product of two vectors Filtering out solutions that do not allow propagation of waves, what is left is the following representing one particular frequency of interest. E cos(w t - [k] * [s] + theta) Where ** theta = Phase You understand k^2 as 1 / wavelength^2. <shrug> Should the Lorentz transform be applied to [k] and w?
From: Paul B. Andersen on 6 Aug 2010 17:16 On 06.08.2010 08:48, Koobee Wublee wrote: > On Aug 5, 12:26 pm, "Paul B. Andersen" wrote: >> On 05.08.2010 01:16, Koobee Wublee wrote: > >>> The second post by Professor Roberts has a wrong conclusion on >>> relativistic Doppler effect. The Lorentz transform actually leads to >>> a reverse Doppler effect. Where have the self-styled physicist been >>> in the past 100 years? See the following recent posts by yours truly >>> at: >> >>> http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en >> >>> http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en >> >> So can you please point out the error in the following derivation? >> >> A wave propagating in the positive x direction >> in the unprimed frame can be written: >> E cos(phi(t,x)) where phi(t,x) = wt - (w/c)x >> >> Let the primed frame be moving at v along the positive x-axis. >> >> The same wave transformed to the primed frame can be written: >> E' cos(phi'(t',x')) where phi'(t',x') = w't' - (w'/c)x' >> >> Applying the LT transform: >> t = g(t' + vx'/c^2) >> x = g(x' + vt') >> g = 1/sqrt(1-v^2/c^2) >> yields: >> wt - (w/c)x = wg((t' + vx'/c^2) - (w/c)g(x' + vt') >> = wg(1-v/c)t' - (w/c)g(1-v/c)x' >> = w't' - (w'/c)x' >> >> Thus: >> w' = wg(1-v/c) = w sqrt((1-v/c)/(1+v/c)) >> >> The wave is red shifted in the primed frame. > > First, you are stating the following which stands on no ground. > > ** w (t - x / c) = w' (t' - x' /c) It should be clear from the context that the event with coordinates (t,x) in the unprimed frame has the coordinates (t',x') in the primed frame. The phase of the wave at a specific event is the same in all frames of reference. That is, phi(t,x) = phi'(t',x') where (t,x) and (t',x') are the coordinates of the _same_ event. You do know that the LT transforms the coordinates of an event, don't you? Or don't you? :-) > > Secondly, you can easily write the result as the following instead, > > ** w = w' sqrt(1 + v / c) / sqrt(1 - v / c) Sure. If the frequency of the wave in the primed frame is lower than its frequency in the unprimed frame, then the frequency of the wave in the unprimed frame is higher than its frequency in the primed frame. Do you find this obvious triviality remarkable? :-) > > Where > > ** v = Speed of w' relative to w > > And proudly claim w-w' moving away (v> 0) as Doppler blue shift. Sure, what's wrong with that? The wave is propagating in the positive x-direction! ------> wave |----> x' ->v |----> x If the wave has the frequency w' in the primed frame, an observer in the unprimed frame will measure the frequency w = w' sqrt(1 + v / c) / sqrt(1 - v / c) which is a blue shifted compared to w'. > Notice the classical Doppler effect for sound cannot be derived using > your method. Why not? "Classical Doppler" -> Galilean transform. An acoustic wave propagating in the positive x direction in the unprimed rest frame of the medium can be written: A cos(phi(t,x)) where phi(t,x) = wt - (w/c)x where c is the speed of the wave in the medium. Let the primed frame be moving at v along the positive x-axis. The same wave transformed to the primed frame can be written: A' cos(phi'(t',x')) where phi'(t',x') = w't' - (w'/(c-v))x' (The speed of sound in the prined frame is c-v) Applying the Galilean transform: t = t' x = x' + vt' yields: wt - (w/c)x = wt' - (w/c)(x' + vt') = w(1-v/c)t' - (w/c)x' = w't' - (w/c)x' Thus: w' = w(1-v/c) The wave is red shifted in the primed frame. Note that k' = w/c = k k' = k and thus lambda' = lambda The wavelength is the same in all frames. > This should be an alarm ringing in your head on your > part. Once again, your mistake is in the application of the Lorentz > transform. There is no mistake. You seem very confused about what Doppler shift is. Try again to find an error? :-) > The time transformation can generally be written as follows. You must > pay very close and crucial attention to the directions of these > vectors. The self-styled physicists have been hand-waving and spoon- > feeding this nonsense to their brain-washed pupils in the past 100 > years. > > ** dt' = (dt - [v] * d[s] / c) / sqrt(1 - v^2 / c^2) > > Where > > ** [v] = Velocity of dt' as observed by dt > ** d[s]/dt = [c] = Velocity of light > ** d[s]/dt * d[s]/dt = c^2 > > Since you are making the same mistake again, I shall not count this > one as a score of mine. Please study my posts below more carefully. > It is not that hard.<shrug> > > http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en > > http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en > > Since you have brought up the wave equations for light, solutions to > Maxwell's equation in free space are: > > SUM_n[[E_n] exp(a_n (w_n t + b_n [k_n] * [s]) + c_n)] > > Where > > ** a_n = +/- 1 or +/- sqrt(-1) > ** b_n = +/- 1 > ** [E_n] = Constant vector > ** [k_n] = Direction vector > ** [s] = Position vector > ** k_n^2 = w_n^2 / c^2 > ** * = Dot product of two vectors > > Filtering out solutions that do not allow propagation of waves, what > is left is the following representing one particular frequency of > interest. > > E cos(w t - [k] * [s] + theta) > > Where > > ** theta = Phase > > You understand k^2 as 1 / wavelength^2.<shrug> No. k^2 = 4*pi^2/wavelength^2 = w^2/c^2 for a non-dispersive wave EM-waves in free space are non-dispersive. And so are audible acoustic waves in air. <shrug> So setting the arbitrary constant theta = 0, and letting the wave vector be parallel to the x-axis, we are back to my equation above. E cos(phi(t,x)) where phi(t,x) = wt - (w/c)x or E cos(wt - (w/c)x) <shrug> I took for granted that you knew that this is a solution of Maxwell's wave equation. (Or any wave equation, for that matter). <shrug> > > Should the Lorentz transform be applied to [k] and w? If you want to transform the wave to a different frame, of course. <shrug> You can see above how k = w/c and w are transformed. Note that k' = (w/c)sqrt((1-v/c)/(1+v/c)) That means that lambda' = lambda ((1+v/c)/(1-v/c)) <shrug> -- Paul http://home.c2i.net/pb_andersen/
From: BURT on 7 Aug 2010 00:50 On Aug 6, 9:46 pm, artful <artful...(a)hotmail.com> wrote: > > > > > What does time do if not slow down from a fastest point? > > > > What a stupid question from a stupid person. > > > There are Two Times that can slow down. One is from gravity. The other > > is from mass in motion. > > Now you're just spouting nonsense. Yours is a typical response from a > troll .. can't say anything relevant and meaningful, so pout some > nonsense assertion and try to divert the topic. One time comes from Einstein's theory of gravity and the second comes from his theory of motion. These are the Two times. Mitch Raemsch
From: artful on 7 Aug 2010 00:51
On Aug 7, 2:50 pm, BURT <macromi...(a)yahoo.com> wrote: > On Aug 6, 9:46 pm, artful <artful...(a)hotmail.com> wrote: > > > > > > > > What does time do if not slow down from a fastest point? > > > > > What a stupid question from a stupid person. > > > > There are Two Times that can slow down. One is from gravity. The other > > > is from mass in motion. > > > > > One time comes from Einstein's theory of gravity and the second comes > from his theory of motion. These are the Two times. Now you're just spouting nonsense. Yours is a typical response from a troll .. can't say anything relevant and meaningful, so spout some nonsense assertion and try to divert the topic. |