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%
On Sunday, September 3, 2023 at 1:05:20 AM UTC-7, Prokaryotic Capase Homolog wrote: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:
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
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.
On Sunday, September 3, 2023 at 1:05:20 AM UTC-7, Prokaryotic Capase Homolog wrote: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:
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
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.
On Sunday, September 3, 2023 at 8:51:30 AM UTC-5, Dono. wrote: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:
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
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.
On Sunday, September 3, 2023 at 8:35:30 AM UTC-7, Prokaryotic Capase Homolog wrote: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.
My choice to start with the longitudinal relativisticThe 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
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.
On Sunday, September 3, 2023 at 1:16:53 PM UTC-5, Dono. wrote:I gave you the Richmond link in order to illustrate how bad the wiki page is.
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.
On Sunday, September 3, 2023 at 12:02:12 PM UTC-5, Dono. wrote: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.
On Sunday, September 3, 2023 at 8:35:30 AM UTC-7, Prokaryotic Capase Homolog wrote:
My choice to start with the longitudinal relativisticThe 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
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.
I am rather puzzled by that statement of yours. By the timeThere 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.
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
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:
I gave you the Richmond link in order to illustrate how bad the wiki page is.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.
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.
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.
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)...."
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
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:
Err, you need a refresher:"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
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?
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:
Err, you need a refresher:"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
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.
On Sunday, September 3, 2023 at 6:51:30 AM UTC-7, Dono. wrote: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:
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
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
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_sourceYou 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),
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.
f_receiver=\gamma(1-\beta*cos (\alpha)) f_source
f'_receiver=\gamma(1-\beta*cos (\alpha+\pi)) f_source
On Monday, September 4, 2023 at 12:51:51 PM UTC-7, Prokaryotic Capase Homolog wrote: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).
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_sourceYou 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
On Monday, September 4, 2023 at 3:02:29 PM UTC-5, Dono. wrote: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).
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_sourceYou 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
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.
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.
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.
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
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.As I have repeatedly tried to explain to you, since both .
No need for any Taylor expansion. No need to continue to embarrass yourself.
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
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.
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.As I have repeatedly tried to explain to you, since both .
No need for any Taylor expansion. No need to continue to embarrass yourself.
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
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 .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?
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
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:How do you explain your idiotic personal attacks? Is this also from the wiki set of rules?
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.As I have repeatedly tried to explain to you, since both .
No need for any Taylor expansion. No need to continue to embarrass yourself.
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
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:I think that all readers of this exchange between us realize who
On Wednesday, September 6, 2023 at 9:20:25 AM UTC-5, Dono. wrote:How do you explain your idiotic personal attacks? Is this also from the wiki set of rules?
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.As I have repeatedly tried to explain to you, since both .
No need for any Taylor expansion. No need to continue to embarrass yourself.
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
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. :-)
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:
I included "dot dot dot" to mean that I was using the completeAs I have repeatedly tried to explain to you, since both .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?
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
expansion going on to infinity.
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:I think that all readers of this exchange between us realize who
On Wednesday, September 6, 2023 at 9:20:25 AM UTC-5, Dono. wrote:How do you explain your idiotic personal attacks? Is this also from the wiki set of rules?
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.As I have repeatedly tried to explain to you, since both .
No need for any Taylor expansion. No need to continue to embarrass yourself.
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
has been using an abundance of foul language.
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. :-)
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:
This hilarious comeback shows that you do not understand basic calculus. Hint: has nothing to do with "the expansion going to infinity".I included "dot dot dot" to mean that I was using the completeAs I have repeatedly tried to explain to you, since both .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?
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
expansion going on to infinity.
...and one more thing: 1+beta^2/2 does not equal \gamma. Unless....
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 + . . .
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