• Enhancements to the Wikipedia article on the Ives-Stilwell experiment

    From Prokaryotic Capase Homolog@21:1/5 to All on Sun Sep 3 01:05:17 2023
    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    Expanded discussion of the experimental challenges.
    Added a new "Theory" section.
    Expanded the description of the experiment.
    Added several new figures.

    My authorship of the article now stands at 48%

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Sun Sep 3 06:51:27 2023
    On Sunday, September 3, 2023 at 1:05:20 AM UTC-7, Prokaryotic Capase Homolog wrote:
    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    Expanded discussion of the experimental challenges.
    Added a new "Theory" section.
    Expanded the description of the experiment.
    Added several new figures.

    My authorship of the article now stands at 48%


    The theory section is weak. The main reason is that it rests on the assumption that the cathode rays can be directed exactly at 0 and 180 degrees wrt the source. The genius of Ives was to realize that , while that was physically impossible, all that need
    to happen was that the light rays were at 180 degrees opposition. So, the correct equations have to be based on the general Doppler effect:

    f_receiver=\gamma(1-\beta*cos (\alpha) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi) f_source -------------------------------------------------------------------------------------------
    (f_receiver+f'_receiver)/2=\gamma*f_source

    You can do the above with the wavelenghts just as well.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Dono. on Sun Sep 3 07:05:55 2023
    On Sunday, September 3, 2023 at 6:51:30 AM UTC-7, Dono. wrote:
    On Sunday, September 3, 2023 at 1:05:20 AM UTC-7, Prokaryotic Capase Homolog wrote:
    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    Expanded discussion of the experimental challenges.
    Added a new "Theory" section.
    Expanded the description of the experiment.
    Added several new figures.

    My authorship of the article now stands at 48%
    The theory section is weak. The main reason is that it rests on the assumption that the cathode rays can be directed exactly at 0 and 180 degrees wrt the source. The genius of Ives was to realize that , while that was physically impossible, all that
    need to happen was that the light rays were at 180 degrees opposition. So, the correct equations have to be based on the general Doppler effect:

    f_receiver=\gamma(1-\beta*cos (\alpha) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi) f_source -------------------------------------------------------------------------------------------
    (f_receiver+f'_receiver)/2=\gamma*f_source

    You can do the above with the wavelenghts just as well.


    Added missing RHS parens

    f_receiver=\gamma(1-\beta*cos (\alpha)) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi)) f_source

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Sun Sep 3 08:35:28 2023
    On Sunday, September 3, 2023 at 8:51:30 AM UTC-5, Dono. wrote:
    On Sunday, September 3, 2023 at 1:05:20 AM UTC-7, Prokaryotic Capase Homolog wrote:
    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    Expanded discussion of the experimental challenges.
    Added a new "Theory" section.
    Expanded the description of the experiment.
    Added several new figures.

    My authorship of the article now stands at 48%
    The theory section is weak. The main reason is that it rests on the assumption that the cathode rays can be directed exactly at 0 and 180 degrees wrt the source. The genius of Ives was to realize that , while that was physically impossible, all that
    need to happen was that the light rays were at 180 degrees opposition. So, the correct equations have to be based on the general Doppler effect:

    f_receiver=\gamma(1-\beta*cos (\alpha) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi) f_source -------------------------------------------------------------------------------------------
    (f_receiver+f'_receiver)/2=\gamma*f_source

    You can do the above with the wavelenghts just as well.

    A. P. French started with the general Doppler effect, and
    an earlier version of my article did, in fact, begin with those
    equations in wavelength form. However, Michael Richmond's
    Physics 314 web page, *which you recommended,* began
    with the formula for relativistic longitudinal Doppler effect. http://spiff.rit.edu/classes/phys314/lectures/doppler/doppler.html

    Since cos 7 deg = 0.9925, I figured that the error between
    a presentation using the longitudinal formula versus the
    general formula probably wasn't enough to really worry
    about. This is especially so, since the intent of Ives and
    Stilwell *WAS NOT TO DISTINGUISH BETWEEN THE
    RELATIVISTIC FORMULA VS THE CLASSIC FORMULA*,
    which is the way that both A. P. French and Michael
    Richmond (and in fact, most textbook authors) treat
    the experiment, but rather to determine the value of "n"
    in Ives' 1937 test theory. So far as Ives was concerned,
    the classic formula had already long been dead and
    buried.

    As Robertson noted, MMX and KTX by themselves are
    insufficient to completely test the Lorentz transformation.
    The addition of I-S, however, does make it possible to
    replace Einstein's postulates with findings drawn inductively
    from observation. https://cds.cern.ch/record/1061896/files/RevModPhys.21.378.pdf

    My choice to start with the longitudinal relativistic
    Doppler equation rather than the general form was
    a deliberate one, since the web page that you linked
    to was a little "dumbed down" compared with the
    presentation in A. P. French, which I otherwise would
    have followed.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Sun Sep 3 10:02:09 2023
    On Sunday, September 3, 2023 at 8:35:30 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Sunday, September 3, 2023 at 8:51:30 AM UTC-5, Dono. wrote:
    On Sunday, September 3, 2023 at 1:05:20 AM UTC-7, Prokaryotic Capase Homolog wrote:
    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    Expanded discussion of the experimental challenges.
    Added a new "Theory" section.
    Expanded the description of the experiment.
    Added several new figures.

    My authorship of the article now stands at 48%
    The theory section is weak. The main reason is that it rests on the assumption that the cathode rays can be directed exactly at 0 and 180 degrees wrt the source. The genius of Ives was to realize that , while that was physically impossible, all that
    need to happen was that the light rays were at 180 degrees opposition. So, the correct equations have to be based on the general Doppler effect:

    f_receiver=\gamma(1-\beta*cos (\alpha) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi) f_source -------------------------------------------------------------------------------------------
    (f_receiver+f'_receiver)/2=\gamma*f_source

    You can do the above with the wavelenghts just as well.
    A. P. French started with the general Doppler effect, and
    an earlier version of my article did, in fact, begin with those
    equations in wavelength form. However, Michael Richmond's
    Physics 314 web page, *which you recommended,* began
    with the formula for relativistic longitudinal Doppler effect. http://spiff.rit.edu/classes/phys314/lectures/doppler/doppler.html

    Since cos 7 deg = 0.9925, I figured that the error between
    a presentation using the longitudinal formula versus the
    general formula probably wasn't enough to really worry
    about. This is especially so, since the intent of Ives and
    Stilwell *WAS NOT TO DISTINGUISH BETWEEN THE
    RELATIVISTIC FORMULA VS THE CLASSIC FORMULA*,
    which is the way that both A. P. French and Michael
    Richmond (and in fact, most textbook authors) treat
    the experiment, but rather to determine the value of "n"
    in Ives' 1937 test theory. So far as Ives was concerned,
    the classic formula had already long been dead and
    buried.

    As Robertson noted, MMX and KTX by themselves are
    insufficient to completely test the Lorentz transformation.
    The addition of I-S, however, does make it possible to
    replace Einstein's postulates with findings drawn inductively
    from observation. https://cds.cern.ch/record/1061896/files/RevModPhys.21.378.pdf

    My choice to start with the longitudinal relativistic
    Doppler equation rather than the general form was
    a deliberate one, since the web page that you linked
    to was a little "dumbed down" compared with the
    presentation in A. P. French, which I otherwise would
    have followed.


    The whole brilliancy of the IS experiment is the extraction of the tiny transverse effect from the mostly longitudinal effect . The general formula of the relativistic DE needs to be used in order to illustrate that. Experimentally, it is impossible to
    get \alpha=0, Ives figured out a way how to do that and the wiki page is left wanting if you don't explain the above.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Sun Sep 3 10:47:37 2023
    On Sunday, September 3, 2023 at 12:02:12 PM UTC-5, Dono. wrote:
    On Sunday, September 3, 2023 at 8:35:30 AM UTC-7, Prokaryotic Capase Homolog wrote:

    My choice to start with the longitudinal relativistic
    Doppler equation rather than the general form was
    a deliberate one, since the web page that you linked
    to was a little "dumbed down" compared with the
    presentation in A. P. French, which I otherwise would
    have followed.
    The whole brilliancy of the IS experiment is the extraction of the tiny transverse effect from the mostly longitudinal effect . The general formula of the relativistic DE needs to be used in order to illustrate that. Experimentally, it is impossible to
    get \alpha=0, Ives figured out a way how to do that and the wiki page is left wanting if you don't explain the above.

    I am rather puzzled by that statement of yours. By the time
    they get to explaining how to extract the tiny transverse
    effect from the mostly longitudinal effect, both French and
    Richmond are using the simplified, strictly longitudinal
    formula. In the Taylor series expansion, the linear terms
    have opposite sign, while the second order terms have the
    same sign, so that in taking the average of the direct and
    reflected Doppler-shifted emission lines, the second order
    effect should be manifest as a displacement of the computed
    center of gravity of the two Doppler-shifted lines from the non-Doppler-shifted line.

    *** ALL THAT IS IN MY PRESENTATION. ***

    If you want to maintain use of the general formulas for
    Doppler effect throughout, you need to go to Ives' 1937
    paper. The graphs in this paper are complex to interpret,
    and the Taylor series expansions are definitely non-trivial,
    far beyond what I think would be appropriate for an
    encyclopedia article at this level. Here is also where you
    will get details of the parameterized test theory that Ives
    had developed.
    Ives, Herbert E. (1937). "The Doppler Effect Considered
    in Relation to the Michelson-Morley Experiment".
    Journal of the Optical Society of America. 27: 389–392

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Sun Sep 3 11:37:31 2023
    On Sunday, September 3, 2023 at 11:35:28 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Sunday, September 3, 2023 at 1:16:53 PM UTC-5, Dono. wrote:

    There no need of any Taylor expansion, the averaging of the two frequencies, as I showed you does the job. No expansion is needed, resorting to it is actually unnecessary and detracts from the beauty of the method.
    Yes, but Wikipedia has rules against "original research."
    All derivations need to be traceable against reliable sources,
    and both Pound and Richmond go the power series route.
    You should not have given me the link to Richmond's
    class notes if you thought that his was an inferior
    presentation.
    I gave you the Richmond link in order to illustrate how bad the wiki page is.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Sun Sep 3 11:16:50 2023
    On Sunday, September 3, 2023 at 10:47:40 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Sunday, September 3, 2023 at 12:02:12 PM UTC-5, Dono. wrote:
    On Sunday, September 3, 2023 at 8:35:30 AM UTC-7, Prokaryotic Capase Homolog wrote:

    My choice to start with the longitudinal relativistic
    Doppler equation rather than the general form was
    a deliberate one, since the web page that you linked
    to was a little "dumbed down" compared with the
    presentation in A. P. French, which I otherwise would
    have followed.
    The whole brilliancy of the IS experiment is the extraction of the tiny transverse effect from the mostly longitudinal effect . The general formula of the relativistic DE needs to be used in order to illustrate that. Experimentally, it is impossible
    to get \alpha=0, Ives figured out a way how to do that and the wiki page is left wanting if you don't explain the above.
    I am rather puzzled by that statement of yours. By the time
    they get to explaining how to extract the tiny transverse
    effect from the mostly longitudinal effect, both French and
    Richmond are using the simplified, strictly longitudinal
    formula. In the Taylor series expansion, the linear terms
    have opposite sign, while the second order terms have the
    same sign, so that in taking the average of the direct and
    reflected Doppler-shifted emission lines, the second order
    effect should be manifest as a displacement of the computed
    center of gravity of the two Doppler-shifted lines from the non-Doppler-shifted line.

    *** ALL THAT IS IN MY PRESENTATION. ***

    If you want to maintain use of the general formulas for
    Doppler effect throughout, you need to go to Ives' 1937
    paper. The graphs in this paper are complex to interpret,
    and the Taylor series expansions are definitely non-trivial,
    far beyond what I think would be appropriate for an
    encyclopedia article at this level. Here is also where you
    will get details of the parameterized test theory that Ives
    had developed.
    Ives, Herbert E. (1937). "The Doppler Effect Considered
    in Relation to the Michelson-Morley Experiment".
    Journal of the Optical Society of America. 27: 389–392
    There no need of any Taylor expansion, the averaging of the two frequencies, as I showed you does the job. No expansion is needed, resorting to it is actually unnecessary and detracts from the beauty of the method.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Sun Sep 3 11:38:12 2023
    On Sunday, September 3, 2023 at 1:37:34 PM UTC-5, Dono. wrote:
    On Sunday, September 3, 2023 at 11:35:28 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Sunday, September 3, 2023 at 1:16:53 PM UTC-5, Dono. wrote:

    There no need of any Taylor expansion, the averaging of the two frequencies, as I showed you does the job. No expansion is needed, resorting to it is actually unnecessary and detracts from the beauty of the method.
    Yes, but Wikipedia has rules against "original research."
    All derivations need to be traceable against reliable sources,
    and both Pound and Richmond go the power series route.
    You should not have given me the link to Richmond's
    class notes if you thought that his was an inferior
    presentation.
    I gave you the Richmond link in order to illustrate how bad the wiki page is.

    (sigh)

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Sun Sep 3 11:35:25 2023
    On Sunday, September 3, 2023 at 1:16:53 PM UTC-5, Dono. wrote:

    There no need of any Taylor expansion, the averaging of the two frequencies, as I showed you does the job. No expansion is needed, resorting to it is actually unnecessary and detracts from the beauty of the method.

    Yes, but Wikipedia has rules against "original research."
    All derivations need to be traceable against reliable sources,
    and both Pound and Richmond go the power series route.
    You should not have given me the link to Richmond's
    class notes if you thought that his was an inferior
    presentation.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From J. J. Lodder@21:1/5 to Dono. on Sun Sep 3 21:00:28 2023
    Dono. <eggy20011951@gmail.com> wrote:

    On Sunday, September 3, 2023 at 1:05:20?AM UTC-7, Prokaryotic Capase Homolog:
    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    Expanded discussion of the experimental challenges.
    Added a new "Theory" section.
    Expanded the description of the experiment.
    Added several new figures.

    My authorship of the article now stands at 48%


    The theory section is weak. The main reason is that it rests on the assumption that the cathode rays can be directed exactly at 0 and 180
    degrees wrt the source. The genius of Ives was to realize that , while
    that was physically impossible, all that need to happen was that the light rays were at 180 degrees opposition. So, the correct equations have to be based on the general Doppler effect:

    f_receiver=\gamma(1-\beta*cos (\alpha)) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi)) f_source --------------------------------------------------------------------------- (f_receiver+f'_receiver)/2=\gamma*f_source

    You can do the above with the wavelenghts just as well.

    Yes, but why would you want to?
    It spoils the conceptual framework. [1]
    (note: question not adressed to you personally)

    Jan

    [1] For Prokary: note that the original Ives-Stilwell paper is titled:
    An Experimental Study of -the Rate- of a Moving Atomic Clock. [emp. JJL]

    That is -rate-, not wavelength.
    To see how silly it is: compare it for example with the discussions
    of -the rate- of atomic clocks aboard GPS sats.
    No one in his right mind would want to discuss that in terms of the
    wavelength emitted by its radio transmitter.
    Modern refinements of the Ives-Stilwell experiment such as <https://arxiv.org/pdf/1309.0549>
    are written entirely in terms of frequency shifts. (or time dilation)

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Sun Sep 3 22:01:09 2023
    On Sunday, September 3, 2023 at 1:05:20 AM UTC-7, Prokaryotic Capase Homolog wrote:
    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    Expanded discussion of the experimental challenges.
    Added a new "Theory" section.
    Expanded the description of the experiment.
    Added several new figures.

    My authorship of the article now stands at 48%


    You write: "For v ≪ c , } the average of the direct and reflected wavelengths may be approximated by "


    The above is total rubbish, as I have shown you, the correct sentence is:

    "For any speed v of the ions, for any angle \alpha, the average of the direct and reflected wavelengths is exactly (no approximation)...."

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Mon Sep 4 01:02:50 2023
    On Monday, September 4, 2023 at 12:01:13 AM UTC-5, Dono. wrote:

    You write: "For v ≪ c , } the average of the direct and reflected wavelengths may be approximated by "


    The above is total rubbish, as I have shown you, the correct sentence is:

    "For any speed v of the ions, for any angle \alpha, the average of the direct and reflected wavelengths is exactly (no approximation)...."

    For frequency, \gamma(1-\beta*cos (\alpha)) is in the numerator
    The \beta*cos (\alpha) and \beta*cos (\alpha+\pi) terms cancel out in taking the average of the direct and reflected frequencies

    For wavelength, \gamma(1-\beta*cos (\alpha)) is in the denominator
    Do the\beta*cos (\alpha) and \beta*cos (\alpha+\pi) terms cancel out in taking the average of the direct and reflected wavelengths?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Mon Sep 4 07:25:34 2023
    On Monday, September 4, 2023 at 1:02:53 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Monday, September 4, 2023 at 12:01:13 AM UTC-5, Dono. wrote:

    You write: "For v ≪ c , } the average of the direct and reflected wavelengths may be approximated by "


    The above is total rubbish, as I have shown you, the correct sentence is:

    "For any speed v of the ions, for any angle \alpha, the average of the direct and reflected wavelengths is exactly (no approximation)...."
    For frequency, \gamma(1-\beta*cos (\alpha)) is in the numerator


    Err, you need a refresher:

    https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Einstein_Doppler_shift_equation




    The \beta*cos (\alpha) and \beta*cos (\alpha+\pi) terms cancel out in taking the average of the direct and reflected frequencies

    Sure they do. Do you have problems with elementary trigonometry?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Mon Sep 4 07:32:46 2023
    On Monday, September 4, 2023 at 9:25:36 AM UTC-5, Dono. wrote:
    On Monday, September 4, 2023 at 1:02:53 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Monday, September 4, 2023 at 12:01:13 AM UTC-5, Dono. wrote:

    You write: "For v ≪ c , } the average of the direct and reflected wavelengths may be approximated by "


    The above is total rubbish, as I have shown you, the correct sentence is:

    "For any speed v of the ions, for any angle \alpha, the average of the direct and reflected wavelengths is exactly (no approximation)...."
    For frequency, \gamma(1-\beta*cos (\alpha)) is in the numerator
    Err, you need a refresher:

    https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Einstein_Doppler_shift_equation
    The \beta*cos (\alpha) and \beta*cos (\alpha+\pi) terms cancel out in taking the average of the direct and reflected frequencies

    Sure they do. Do you have problems with elementary trigonometry?

    I was asking about wavelengths, not frequency.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Mon Sep 4 08:29:51 2023
    On Monday, September 4, 2023 at 7:32:48 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Monday, September 4, 2023 at 9:25:36 AM UTC-5, Dono. wrote:
    On Monday, September 4, 2023 at 1:02:53 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Monday, September 4, 2023 at 12:01:13 AM UTC-5, Dono. wrote:

    You write: "For v ≪ c , } the average of the direct and reflected wavelengths may be approximated by "


    The above is total rubbish, as I have shown you, the correct sentence is:

    "For any speed v of the ions, for any angle \alpha, the average of the direct and reflected wavelengths is exactly (no approximation)...."
    For frequency, \gamma(1-\beta*cos (\alpha)) is in the numerator
    Err, you need a refresher:

    https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Einstein_Doppler_shift_equation
    The \beta*cos (\alpha) and \beta*cos (\alpha+\pi) terms cancel out in taking the average of the direct and reflected frequencies

    Sure they do. Do you have problems with elementary trigonometry?
    I was asking about wavelengths, not frequency.


    https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Motion_in_an_arbitrary_direction

    Now, \lambda=c/f

    Substitute f from the above link. You need to stop this, it is getting embarrassing.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Dono. on Mon Sep 4 08:32:17 2023
    On Sunday, September 3, 2023 at 7:05:58 AM UTC-7, Dono. wrote:
    On Sunday, September 3, 2023 at 6:51:30 AM UTC-7, Dono. wrote:
    On Sunday, September 3, 2023 at 1:05:20 AM UTC-7, Prokaryotic Capase Homolog wrote:
    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    Expanded discussion of the experimental challenges.
    Added a new "Theory" section.
    Expanded the description of the experiment.
    Added several new figures.

    My authorship of the article now stands at 48%
    The theory section is weak. The main reason is that it rests on the assumption that the cathode rays can be directed exactly at 0 and 180 degrees wrt the source. The genius of Ives was to realize that , while that was physically impossible, all that
    need to happen was that the light rays were at 180 degrees opposition. So, the correct equations have to be based on the general Doppler effect:

    f_receiver=\gamma(1-\beta*cos (\alpha) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi) f_source -------------------------------------------------------------------------------------------
    (f_receiver+f'_receiver)/2=\gamma*f_source

    You can do the above with the wavelenghts just as well.
    Added missing RHS parens

    f_receiver=\gamma(1-\beta*cos (\alpha)) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi)) f_source


    If you want to do the above in terms of wavelength (JJ Lodder pointed out that it is not agood idea) you only need to substitute \lambda instead of f and + instead of -.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Mon Sep 4 13:02:26 2023
    On Monday, September 4, 2023 at 12:51:51 PM UTC-7, Prokaryotic Capase Homolog wrote:
    On Sunday, September 3, 2023 at 9:05:58 AM UTC-5, Dono. wrote:

    f_receiver=\gamma(1-\beta*cos (\alpha)) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi)) f_source
    You made a rather gross typo that mislead me for a while.
    Things weren't making sense, and I didn't think to double-check,
    since I hadn't expected you to be making that sort of error

    Set alpha = pi/2 so that we are looking at right angles to the beam.
    Then cos (alpha) = 0
    Let the frequency of the source = 1000 THz
    If beta = 0.9, then gamma = 2.294
    According to what you have written, the received light is blue-shifted
    to 2294 THz



    You don't get it, do you? There are two different expressions (both equally valid) for the relativistic Doppler effect. They depend on whether the angle \alpha is measured in the source frame or in the receiver frame. The wiki article I linked in is
    quite explicit on this. So, what you wrote above is yet another piece of rubbish. You would be getting the correct expression if you took \alpha=\pi/2 in the correct frame. Then, you would get the correct shift (red).



    You made a valid point earlier, but you expressed yourself in an
    offensive manner, and you are always too convinced that you are
    immune to brain farts to bother checking what you wrote.

    We are ALL capable of making brain farts.



    ...and you just made another one.


    Regardless of whether you made any sort of valid points, (you had
    both valid points and committed silly mistakes),

    All mistakes are yours, due to lack of understanding of basics. Own it.





    I am required by
    Wikipedia rules to follow "reliable sources" in my presentation.
    In this case, my presentation is adapted from a textbook developed
    by MIT, and class notes given an imprimatur by the Rochester
    Institute of Technology.


    Doing that inserts some major misunderstandings:

    1. The IS results are valid for ANY v, not only for v<<c
    2. The IS results are exact, not an approximation
    3. There is absolutely no need for the use of the Taylor expansion, simple algebra gives the correct results

    You ask me to critique your writeup, this is what I did.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Mon Sep 4 12:51:48 2023
    On Sunday, September 3, 2023 at 9:05:58 AM UTC-5, Dono. wrote:

    f_receiver=\gamma(1-\beta*cos (\alpha)) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi)) f_source

    You made a rather gross typo that mislead me for a while.
    Things weren't making sense, and I didn't think to double-check,
    since I hadn't expected you to be making that sort of error

    Set alpha = pi/2 so that we are looking at right angles to the beam.
    Then cos (alpha) = 0
    Let the frequency of the source = 1000 THz
    If beta = 0.9, then gamma = 2.294
    According to what you have written, the received light is blue-shifted
    to 2294 THz

    You made a valid point earlier, but you expressed yourself in an
    offensive manner, and you are always too convinced that you are
    immune to brain farts to bother checking what you wrote.

    We are ALL capable of making brain farts.

    Regardless of whether you made any sort of valid points, (you had
    both valid points and committed silly mistakes), I am required by
    Wikipedia rules to follow "reliable sources" in my presentation.
    In this case, my presentation is adapted from a textbook developed
    by MIT, and class notes given an imprimatur by the Rochester
    Institute of Technology.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Mon Sep 4 13:42:39 2023
    On Monday, September 4, 2023 at 3:02:29 PM UTC-5, Dono. wrote:
    On Monday, September 4, 2023 at 12:51:51 PM UTC-7, Prokaryotic Capase Homolog wrote:
    On Sunday, September 3, 2023 at 9:05:58 AM UTC-5, Dono. wrote:

    f_receiver=\gamma(1-\beta*cos (\alpha)) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi)) f_source
    You made a rather gross typo that mislead me for a while.
    Things weren't making sense, and I didn't think to double-check,
    since I hadn't expected you to be making that sort of error

    Set alpha = pi/2 so that we are looking at right angles to the beam.
    Then cos (alpha) = 0
    Let the frequency of the source = 1000 THz
    If beta = 0.9, then gamma = 2.294
    According to what you have written, the received light is blue-shifted
    to 2294 THz

    You don't get it, do you? There are two different expressions (both equally valid) for the relativistic Doppler effect. They depend on whether the angle \alpha is measured in the source frame or in the receiver frame. The wiki article I linked in is
    quite explicit on this. So, what you wrote above is yet another piece of rubbish. You would be getting the correct expression if you took \alpha=\pi/2 in the correct frame. Then, you would get the correct shift (red).

    Even if I allow that, then you are ***STILL*** making a gross error
    that you are blinding yourself to in your fanatic insistence that you
    can never possibly be in the wrong.

    I don't expect you to be able to find your mistake. You've never
    been able to in the past, and I don't expect you ever to be able to
    in the future.

    I am in the process of incorporating the valid points that you made,
    and I am ignoring your offensive remarks.

    I still need to be able to trace what I write to reliable sources. In this case,
    it is apparent by careful study of French's exact wording that he was NOT limiting himself to the first few terms of the Taylor series, but was considering
    the entire series. On the other hand, Richmond limited himself to looking only at the second order term, and that threw me off.

    By the way, I wrote that section to which you refer, and I am quite familiar with the differences between measurements in the source frame versus
    receiver frame. Experimentalists (including Ives and Stilwell) generally
    use the receiver frame, although there are definitely exceptions. https://xtools.wmcloud.org/articleinfo/en.wikipedia.org/Relativistic_Doppler_effect
    Slightly less than 74% authorship.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Mon Sep 4 14:29:02 2023
    On Monday, September 4, 2023 at 1:42:42 PM UTC-7, Prokaryotic Capase Homolog wrote:
    On Monday, September 4, 2023 at 3:02:29 PM UTC-5, Dono. wrote:
    On Monday, September 4, 2023 at 12:51:51 PM UTC-7, Prokaryotic Capase Homolog wrote:
    On Sunday, September 3, 2023 at 9:05:58 AM UTC-5, Dono. wrote:

    f_receiver=\gamma(1-\beta*cos (\alpha)) f_source

    f'_receiver=\gamma(1-\beta*cos (\alpha+\pi)) f_source
    You made a rather gross typo that mislead me for a while.
    Things weren't making sense, and I didn't think to double-check,
    since I hadn't expected you to be making that sort of error

    Set alpha = pi/2 so that we are looking at right angles to the beam. Then cos (alpha) = 0
    Let the frequency of the source = 1000 THz
    If beta = 0.9, then gamma = 2.294
    According to what you have written, the received light is blue-shifted to 2294 THz

    You don't get it, do you? There are two different expressions (both equally valid) for the relativistic Doppler effect. They depend on whether the angle \alpha is measured in the source frame or in the receiver frame. The wiki article I linked in is
    quite explicit on this. So, what you wrote above is yet another piece of rubbish. You would be getting the correct expression if you took \alpha=\pi/2 in the correct frame. Then, you would get the correct shift (red).
    Even if I allow that,

    So the "error" is not my error, it is your error.


    then you are ***STILL*** making a gross error
    that you are blinding yourself to in your fanatic insistence that you
    can never possibly be in the wrong.



    Looks like you are talking to your mirror. Look, you messed up, own it.


    I don't expect you to be able to find your mistake. You've never
    been able to in the past, and I don't expect you ever to be able to
    in the future.



    Looks like you are talking to your mirror. Look, you messed up, own it.

    I am in the process of incorporating the valid points that you made,
    and I am ignoring your offensive remarks.


    We;ll see what you do.


    I still need to be able to trace what I write to reliable sources. In this case,
    it is apparent by careful study of French's exact wording that he was NOT limiting himself to the first few terms of the Taylor series, but was considering
    the entire series. On the other hand, Richmond limited himself to looking only
    at the second order term, and that threw me off.



    There is absolutely no need for any Taylor expansion. The moment one uses the Taylor expansion one limits the validity of the experiment to v<<c and that is plain wrong. You need to remember that the theory of the IS experiment was written by Einstein.
    He did not make that kind of mistakes.


    By the way, I wrote that section to which you refer, and I am quite familiar with the differences between measurements in the source frame versus receiver frame. Experimentalists (including Ives and Stilwell) generally
    use the receiver frame, although there are definitely exceptions. https://xtools.wmcloud.org/articleinfo/en.wikipedia.org/Relativistic_Doppler_effect
    Slightly less than 74% authorship.

    Then you would not have made the gross mistake of accusing me that I got the wrong kind of shift.
    BTW, Einstein's genius in envisaging the experiment was to make it independent of the angle \alpha.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to All on Wed Sep 6 01:26:58 2023
    On Monday, September 4, 2023 at 4:29:05 PM UTC-5, Dono. wrote:

    [snip rant]

    Please examine the article now, focusing on the experimental
    section. As I have repeatedly tried to explain to you, since both
    of my references use Taylor expressions and analysis in terms
    of the longitudinal relativistic Doppler effect, I will continue to use
    them since to do otherwise would be to perform what is known
    as "original research", which is highly discouraged in Wikipedia.
    You may read Wikipedia policy here: https://en.wikipedia.org/wiki/Wikipedia:No_original_research

    Incidentally, Ives' 1937 article where he develops a "test theory"
    as a framework for performing the 1938 experiment does
    indeed do the analysis in terms of arbitrary viewing angle, but
    since he is developing a test theory, he does NOT presuppose
    the Lorentz transformations.

    In their 1938 article, I particularly enjoyed reading about
    how the molecular absorption spectrum of the fill gas
    interfered with their wavelength measurements. (See the
    discussion associated with Fig. 5)

    There were other fascinating experimental details in their
    article that I appreciated, but refrained from mentioning
    because of their lessened importance to the modern reader.
    For example, having had experience using a Gaertner
    measuring engine to measure astrograph plates, I really
    appreciated how they managed to reach 0.25 micron precision
    in their plate measurements, but their methods would be of
    little relevance to any current wannabe experimentalists
    who would instead be using scanners or direct CCD recording
    of their spectra.

    As I expected, you refuse to acknowledge your blunder.
    Make that MULTIPLE blunders.

    The correct expression for relativistic Doppler frequency shift
    with the angle measured in the receiver frame is
    f_receiver = f_source / ( \gamma ( 1 - \beta * cos(\alpha) ) )
    whereas you had written
    f_receiver=\gamma(1-\beta*cos (\alpha) f_source

    Note how 1 - \beta * cos(\alpha) is in the denominator in
    the one case, and in the numerator in the other case.

    Ives and Stilwell considered the transverse Doppler effect to
    be REDSHIFT, therefore they were considering measurements
    of angle to be in the RECEIVER frame.

    So whereas taking the average WAVELENGTHS of a beam and
    its mirror reflection does indeed yield gamma regardless of
    alpha (an observation for which I thank you), taking the
    average FREQUENCIES of a beam and its mirror reflection
    will not generally yield 1/gamma, which is what you claimed
    in your earlier post.

    For those people using newsgroup services with limited
    historical retention, here is a google link to see Dono's post. https://groups.google.com/g/sci.physics.relativity/c/vPy1OD_7rEs/m/QUwYIO5YAwAJ

    I expect you to continue to bullshit your way into maintaining
    your absolute, total correctness in this exchange.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Wed Sep 6 06:50:53 2023
    On Wednesday, September 6, 2023 at 1:27:02 AM UTC-7, Prokaryotic Capase Homolog wrote:

    Please examine the article now, focusing on the experimental
    section.

    I looked at it. You replaced v/c with \beta and you used this in order to surreptitiously remove the fact that one can ignore the higher order terms of the Taylor expansion if v<<c. A sleigh of hand, you are not only incompetent, you are dishonest as
    well.



    As I have repeatedly tried to explain to you, since both
    of my references use Taylor expressions and analysis in terms
    of the longitudinal relativistic Doppler effect, I will continue to use
    them since to do otherwise would be to perform what is known
    as "original research", which is highly discouraged in Wikipedia.

    In doing so, you are :

    1. Doing great injustice to the fact that the formalism is true for any angle \alpha
    2. Even worse, you are contradicting the experimental section above that shows that IS intentionally dithered the angle by \plusminus 1 degree
    3. Embarrassingly, you (and French) fail to notice that there is absolutely no need for the Taylor expansion since \sqrt{\frac{1-\beta}{1+\beta}}-\sqrt{\frac{1+\beta}{1-\beta}} equals \frac{1}{\gamma}. exactly :-)

    Incidentally, Ives' 1937 article where he develops a "test theory"
    as a framework for performing the 1938 experiment does
    indeed do the analysis in terms of arbitrary viewing angle, but
    since he is developing a test theory, he does NOT presuppose
    the Lorentz transformations.


    But, you, in your narrowmindness, fail to reflect this in the "Theory" section.





    As I expected, you refuse to acknowledge your blunder.
    Make that MULTIPLE blunders.

    The correct expression for relativistic Doppler frequency shift
    with the angle measured in the receiver frame is
    f_receiver = f_source / ( \gamma ( 1 - \beta * cos(\alpha) ) )
    whereas you had written
    f_receiver=\gamma(1-\beta*cos (\alpha) f_source


    Dumbfuck,


    I did not specify in what frame the angle was measured. This is why I gave you the hint (multiple times) that you can replace the frequency with the wavelength in the equations I gave you.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Wed Sep 6 07:34:08 2023
    On Wednesday, September 6, 2023 at 7:31:01 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:20:25 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 6:50:56 AM UTC-7, Dono. wrote: \sqrt{\frac{1-\beta}{1+\beta}}-\sqrt{\frac{1+\beta}{1-\beta}} equals \gamma. Exactly.
    No need for any Taylor expansion. No need to continue to embarrass yourself.
    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use . them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research


    How do you explain your idiotic personal attacks? Is this also from the wiki set of rules?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Wed Sep 6 07:30:59 2023
    On Wednesday, September 6, 2023 at 9:20:25 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 6:50:56 AM UTC-7, Dono. wrote: \sqrt{\frac{1-\beta}{1+\beta}}-\sqrt{\frac{1+\beta}{1-\beta}} equals \gamma. Exactly.
    No need for any Taylor expansion. No need to continue to embarrass yourself.

    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use .
    them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to All on Wed Sep 6 07:20:22 2023
    On Wednesday, September 6, 2023 at 6:50:56 AM UTC-7, Dono. wrote:
    \sqrt{\frac{1-\beta}{1+\beta}}-\sqrt{\frac{1+\beta}{1-\beta}} equals \gamma. Exactly.
    No need for any Taylor expansion. No need to continue to embarrass yourself.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Wed Sep 6 07:36:15 2023
    On Wednesday, September 6, 2023 at 7:31:01 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:20:25 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 6:50:56 AM UTC-7, Dono. wrote: \sqrt{\frac{1-\beta}{1+\beta}}-\sqrt{\frac{1+\beta}{1-\beta}} equals \gamma. Exactly.
    No need for any Taylor expansion. No need to continue to embarrass yourself.
    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use . them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research


    If you insist on using the Taylor expansion, why did you take out the fact that your stuff is valid only for \beta<<1? It was in there originally (put by you), why did you remove it?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Wed Sep 6 08:01:46 2023
    On Wednesday, September 6, 2023 at 9:36:18 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 7:31:01 AM UTC-7, Prokaryotic Capase Homolog wrote:

    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use . them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research
    If you insist on using the Taylor expansion, why did you take out the fact that your stuff is valid only for \beta<<1? It was in there originally (put by you), why did you remove it?

    I included "dot dot dot" to mean that I was using the complete
    expansion going on to infinity.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Wed Sep 6 07:58:38 2023
    On Wednesday, September 6, 2023 at 9:34:10 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 7:31:01 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:20:25 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 6:50:56 AM UTC-7, Dono. wrote: \sqrt{\frac{1-\beta}{1+\beta}}-\sqrt{\frac{1+\beta}{1-\beta}} equals \gamma. Exactly.
    No need for any Taylor expansion. No need to continue to embarrass yourself.
    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use . them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research
    How do you explain your idiotic personal attacks? Is this also from the wiki set of rules?

    I think that all readers of this exchange between us realize who
    has been using an abundance of foul language.

    The purpose of the Wiki rules is as a first line of defense against
    self-styled "experts" such as yourself who might attempt to insert
    their own flawed original research into articles. The requirement
    for a reliable source provides a simple criterion for ANY editor to
    immediately throw out, say, your hammock paradox analysis, or
    your unusual interpretation of the role of the TDE in the Sagnac
    effect, or your infamous diagrams illustrating a directional
    dependence of the Lorentz transforms. Long-time readers of
    this newsgroup know of what I speak, but there is a whole new
    generation of newsgroup participants who might get a kick out
    of them.

    By rigorously adhering to the no-original-research rules, even a
    decided NON-expert such as myself can edit Wiki articles with
    a reasonable amount of confidence that I am not inserting
    nonsense into an article. On the occasions when I do goof, I
    am lucky to have good friends and associates in Wikipedia who
    know that I will take getting slapped down with good humor. :-)

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Maciej Wozniak@21:1/5 to Prokaryotic Capase Homolog on Wed Sep 6 08:03:50 2023
    On Wednesday, 6 September 2023 at 16:58:40 UTC+2, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:34:10 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 7:31:01 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:20:25 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 6:50:56 AM UTC-7, Dono. wrote: \sqrt{\frac{1-\beta}{1+\beta}}-\sqrt{\frac{1+\beta}{1-\beta}} equals \gamma. Exactly.
    No need for any Taylor expansion. No need to continue to embarrass yourself.
    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use .
    them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research
    How do you explain your idiotic personal attacks? Is this also from the wiki set of rules?
    I think that all readers of this exchange between us realize who
    has been using an abundance of foul language.

    The purpose of the Wiki rules is as a first line of defense against self-styled "experts" such as yourself who might attempt to insert
    their own flawed original research into articles. The requirement
    for a reliable source provides a simple criterion for ANY editor to immediately throw out, say, your hammock paradox analysis, or
    your unusual interpretation of the role of the TDE in the Sagnac
    effect, or your infamous diagrams illustrating a directional
    dependence of the Lorentz transforms. Long-time readers of
    this newsgroup know of what I speak, but there is a whole new
    generation of newsgroup participants who might get a kick out
    of them.

    By rigorously adhering to the no-original-research rules, even a
    decided NON-expert such as myself can edit Wiki articles with
    a reasonable amount of confidence that I am not inserting
    nonsense into an article. On the occasions when I do goof, I
    am lucky to have good friends and associates in Wikipedia who
    know that I will take getting slapped down with good humor. :-)

    And thus another of the lies of physics is exposed:
    yes, "how many are repeating it" - does matter.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Wed Sep 6 08:09:20 2023
    On Wednesday, September 6, 2023 at 8:01:49 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:36:18 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 7:31:01 AM UTC-7, Prokaryotic Capase Homolog wrote:

    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use .
    them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research
    If you insist on using the Taylor expansion, why did you take out the fact that your stuff is valid only for \beta<<1? It was in there originally (put by you), why did you remove it?
    I included "dot dot dot" to mean that I was using the complete
    expansion going on to infinity.

    This hilarious comeback shows that you do not understand basic calculus. Hint: has nothing to do with "the expansion going to infinity".

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Wed Sep 6 08:07:49 2023
    On Wednesday, September 6, 2023 at 7:58:40 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:34:10 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 7:31:01 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:20:25 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 6:50:56 AM UTC-7, Dono. wrote: \sqrt{\frac{1-\beta}{1+\beta}}-\sqrt{\frac{1+\beta}{1-\beta}} equals \gamma. Exactly.
    No need for any Taylor expansion. No need to continue to embarrass yourself.
    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use .
    them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research
    How do you explain your idiotic personal attacks? Is this also from the wiki set of rules?
    I think that all readers of this exchange between us realize who
    has been using an abundance of foul language.


    ...and who is the incompetent crook (that would be you).

    On the occasions when I do goof, I
    am lucky to have good friends and associates in Wikipedia who
    know that I will take getting slapped down with good humor. :-)

    You don't, as evidenced by this exchange.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Dono. on Wed Sep 6 08:14:45 2023
    On Wednesday, September 6, 2023 at 8:09:23 AM UTC-7, Dono. wrote:
    On Wednesday, September 6, 2023 at 8:01:49 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 9:36:18 AM UTC-5, Dono. wrote:
    On Wednesday, September 6, 2023 at 7:31:01 AM UTC-7, Prokaryotic Capase Homolog wrote:

    As I have repeatedly tried to explain to you, since both .
    of my references use Taylor expansions and analysis in terms .
    of the longitudinal relativistic Doppler effect, I will continue to use .
    them since to do otherwise would be to perform what is known .
    as "original research", which is highly discouraged in Wikipedia .
    You may read Wikipedia policy here : https://en.wikipedia.org/wiki/Wikipedia:No_original_research
    If you insist on using the Taylor expansion, why did you take out the fact that your stuff is valid only for \beta<<1? It was in there originally (put by you), why did you remove it?
    I included "dot dot dot" to mean that I was using the complete
    expansion going on to infinity.
    This hilarious comeback shows that you do not understand basic calculus. Hint: has nothing to do with "the expansion going to infinity".


    ...and one more thing: 1+beta^2/2 does not equal \gamma. Unless....

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Prokaryotic Capase Homolog@21:1/5 to Dono. on Wed Sep 6 09:16:51 2023
    On Wednesday, September 6, 2023 at 10:14:47 AM UTC-5, Dono. wrote:

    ...and one more thing: 1+beta^2/2 does not equal \gamma. Unless....

    What are you copying from?
    For beta << 1, that would be approximately true.
    You can add a few terms to make it a better approximation.

    γ=1 + (1/2)β^2 + (3/8)β^4 + (5/16)β^6 + (35/128)β^8 + . . .

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dono.@21:1/5 to Prokaryotic Capase Homolog on Wed Sep 6 09:27:40 2023
    On Wednesday, September 6, 2023 at 9:16:54 AM UTC-7, Prokaryotic Capase Homolog wrote:
    On Wednesday, September 6, 2023 at 10:14:47 AM UTC-5, Dono. wrote:

    ...and one more thing: 1+beta^2/2 does not equal \gamma. Unless....
    What are you copying from?
    For beta << 1, that would be approximately true.
    You can add a few terms to make it a better approximation.

    γ=1 + (1/2)β^2 + (3/8)β^4 + (5/16)β^6 + (35/128)β^8 + . . .


    I am simply pointing out that your analysis is true only for beta << 1 and that you have taken this out of the original page (that you wrote earlier).
    The approximation is definitely not true for the general case.
    Basically, what you have done is you have taken a very smart experiment (independent of \alpha angle on of v/c) and you have produced a very dumb analysis.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)