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Thread: Discussion of lyndonashmore's ATM idea re H (the Hubble constant)

  1. #301
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    Okay, I am out of here.

    Lyndon is right, I am wrong, or the other way around, I don't fragging care anymore.
    All comments made in red are moderator comments. Please, read the rules of the forum here and read the additional rules for ATM, and for conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    New blog 31-05-2013: Aurora and the Earth's Magnetotial Part 2: From Birkeland to Cluster

  2. #302
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    Quote Originally Posted by lyndonashmore View Post
    [snip]
    Quote Originally Posted by Nereid
    Second, I've read this thread (again), but can't find answers to the following questions, concerning the lyndonashmore idea re the photon-electron interaction:

    1) In the rest frame of the electron, prior to a "lyndonashmore photon-electron interaction", is momentum conserved in that interaction

    Specifically, momentum ("before" photon) + momentum ("before" electron, = 0?) = momentum ("after" photon) + momentum ("after" electron)?
    The princple of momentum holds. In the directon of the photon, h/ λ = mv. In a direction perpendicular to this, when the electron 'quivers' it depends upon your view point. Is the electric field an external force?

    [snip]
    (my bold) Before the photon-electron interaction, there is zero momentum "[i]n a direction perpendicular to" "the directon of the photon".

    If, after the interaction, "the electron 'quivers'" (in this perpedicular direction), how is momentum conserved?

  3. #303
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    Quote Originally Posted by lyndonashmore View Post
    [snip]
    Quote Originally Posted by Nereid
    And now some more questions:

    When (approximately) was the electron-photon interaction that is at the heart of the lyndonashmore idea first discovered?
    By whom?
    Where did they publish the details?
    Standard physics.
    HERE
    and
    French, Special relativity page 128
    the propagaton of light through a medium (even a transparent one) inolves a continual process of absorption of the incident light and its reemission as a secondary radiation by the medium
    and
    Feynman, "QED" transmission and reflection of light is nothng more than an electron picking up a photon, hopping up and down a bit and emitting a new photon.
    and
    The recoil is tied up in the mossbauer effect.
    and.......
    All standard Physics.
    Why is my theory in the ATM section?
    Cheers,
    lyndon
    edit: actually Feynman wrote "transmission and reflection of light is nothng more than an electron picking up a photon, scratching its head and emitting a new photon" - always check your sources first!
    A key aspect of the lyndonashmore idea is that, in (the lyndonashmore) photon-electron interaction, the photon "undergoes an increase in wavelength of h/mc".

    Which "standard Physics" text discusses this "increase in wavelength of h/mc"?

    (the Ask A Scientist Physics Archive webpage you provided a link to does not mention this. Also, that page is about photon-atom interactions, not photon-electron ones).

  4. #304
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    Quote Originally Posted by Nereid View Post
    (my bold) Before the photon-electron interaction, there is zero momentum "[i]n a direction perpendicular to" "the directon of the photon".

    If, after the interaction, "the electron 'quivers'" (in this perpedicular direction), how is momentum conserved?
    He still hasn't answered that question to my satisfaction when I asked pages ago.

  5. #305
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    Quote Originally Posted by lyndonashmore
    Now now, you know quite well why I posted that reference.
    Because you do not have calculations to support your claims, and you think we don't understand that references about plasma oscillations are not relevant to your effect -- as per your own admission.


    Quote Originally Posted by lyndonashmore
    You have always insisted that electrons in plasma do not perform SHM.
    Strawman.
    I said that a single electron is not oscillating back and forth about a position over short length-scales ("short" as in "comparable to the average inter-particle spacing").


    Quote Originally Posted by lyndonashmore
    You have always complained that it was some magical term called the 'charge density' that oscillated.
    The same term used by the physics community, with a well defined physical meaning, which you should understand if you really had studied statistical thermodynamics.
    The same term which is in the equation of simple harmonic motion you keep referring to, despite the fact that plasma oscillations should not be relevant to your effect.


    Quote Originally Posted by lyndonashmore
    In posting Bill's reference I showed you to be wrong (and it is for space too).
    That reference is about plasma oscillations, which is not relevant to your effect -- as per your own admission.


    Quote Originally Posted by lyndonashmore
    I have yet to see the journal itself but it would appear that we are not talking about a theory 'accepted' for publication, but we are now talking about the paper published in a peer reviewed journal..

    A journal with a stated ATM bias, but lacking the rigor necessary to be credible.

  6. #306
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    Quote Originally Posted by lyndonashmore View Post
    Hi Tobin Dax,


    Sorry, already changed it - hope it is correct now!
    You asked about the sources being a student project.
    When i first did this it was in reply to another poster who raised the same point. It was not meant to be a scientific paper and I wanted to show the print out on line.
    It gives the right idea. In an earlier post by Nereid, she talks about a 'doppler footprint' and cites an encyclopeadia reference giving the width. My ref tallies with this too, so it is difficult to separate the two effects. A spread due to thermal motion of the atoms in the gases around a star and the small spread due to random fluctuations in photon collisions.
    Thanks again,
    Lyndon
    In the spectrum of (distant) galaxies, as observed here on Earth, what part of the line width of the K line is due to the 'lyndonashmore effect', and what part due to intrinsic (to the galaxy) effects?

    In the lyndonashmore idea, what systematic changes in the intrinsic effects are expected (e.g. with distance, with Hubble type, with inclination, with age)?

  7. #307
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    Quote Originally Posted by lyndonashmore View Post
    Quote Originally Posted by Nereid
    In post #158 you confirmed that, in the lyndonashmore idea, the mean free path of a 21 cm photon, though a n = 0.5 (electrons per cubic metre) gas, is 0.18 ly.

    If one could track 100 photons, from source to first interaction with (100) electrons, and measure the distance, how many of the 100 would have travelled 0 to <0.1 ly? 0.1 to <0.2 ly? 0.2 to <0.3 ly? >0.3 ly?
    Hi Nereid,
    Have to think about that one.
    What I have done and is more important is to look at the spread in wavelenghts arriving here. i.e i have concentrated on observations and matched my theory to those. What you ask cannot be tested (or can it?)
    Check HERE
    Cheers,
    lyndon
    Have you finished thinking about this yet?

    Do you have an answer to the questions yet?

  8. #308
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    An object is observed to have a z of 0.114, and the rest frame wavelength of an observed (x-ray) line (in the object's spectrum) is calculated to be 6.4 keV.

    Assuming n = 0.5, and 10,000 (redshifted 6.4 keV line) photons detected, how many of these detected photons will have undergone the following number of 'lyndonashmore photon-electron interactions'?

    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    >18

  9. #309
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    Quote Originally Posted by Tobin Dax View Post
    Quote Originally Posted by Nereid
    (my bold) Before the photon-electron interaction, there is zero momentum "[i]n a direction perpendicular to" "the directon of the photon".

    If, after the interaction, "the electron 'quivers'" (in this perpedicular direction), how is momentum conserved?
    He still hasn't answered that question to my satisfaction when I asked pages ago.
    Is this the one you are referring to?
    Quote Originally Posted by Tobin Dax
    But the momentum of the photon is perpendicular the to oscillation. How does an inelastic collision between two point particles result in motion perpendicular to the motion of particle not at rest? (Your wave argument doesn't work. We've been through that before.)
    Or perhaps this?
    Quote Originally Posted by Tobin Dax
    You mean the one about the effects of a coherent group of photons, which is completely different than a single photon, which is what you are talking about with your effect? No.

  10. #310
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    Quote Originally Posted by Nereid View Post
    Is this the one you are referring to?
    Quote Originally Posted by Tobin Dax
    But the momentum of the photon is perpendicular the to oscillation. How does an inelastic collision between two point particles result in motion perpendicular to the motion of particle not at rest? (Your wave argument doesn't work. We've been through that before.)
    That one, though maybe I should rephrase my comment. I'm not satisfied with his answer, mostly because I haven't seen any evidence (presented by lyndon or on my own) that a single photon can cause antenna-like radiation.
    Your question may be different than mine, and I am very interested in lyndon's response. So, just in case it got lost in the shuffle, here is the question:
    Quote Originally Posted by Nereid
    If, after the interaction, "the electron 'quivers'" (in this perpedicular direction), how is momentum conserved?

  11. #311
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    Quote Originally Posted by lyndonashmore View Post
    Hi Fortis,
    Lets do some numbers and then I will answer your question.
    Photon of light comes in, λ = 5x10-7m.
    Frequency is 6x1014Hz.
    It is absorbed by our electron which quivers at this frequency because photon drives it.
    Our lucky electron travels in one direction for half an oscillation - a time of 8.3x10-16seconds.
    Lets then look at our neighbourng electrons which are about 1m away on average.
    You ask "do they stop what they are doing?"
    Well lets see what they are doing in this time.
    temp of plasma 1x105K
    (3/2)kT = (1/2)mv2
    so on average v is 2x106m/s
    In the time it takes for our driven electron to move half a cycle to the right, our "electrons to the right of it" have moved a distance thermally of 1.8x10-9m and this one metre away!
    So you see on our timescales the surrounding charges are like stars in the night - they do not appear to move.
    So what do I think they do?
    I think they just repel our electron in the case of the electrons in front of it and the overall positive charges behind attract it back. SHM
    Cheers,
    Lyndon
    Lyndon, it is possible that due to answering queries from a number of people, you have forgotten the original point of my questions. I'll now try to remind you, so that you are able to understand the context, and hopefully answer within that context.

    Firts of all, in this post, I asked
    Can you write down the equations of motion for a single electron (displaced independently from the rest of the plasma) and show that it will perform SHM?
    In response you quoted this paper extract.
    Initially, I mis-read the extract, in particular I originally didn't spot the assumption that "neighbouring electron orbits do not cross". This I corrected in this post.
    Lyndon, I'm back.

    Would you like to comment on the derivation that you quote, i.e. this one?

    In particular, what do you think the relevance of the line "make the simplifying assumption that neighbouring electron orbits do not cross" is?

    I don't have the whole paper in front of me, but the implication appears to be that for equation 2 to be correct, all of the electrons that where to the right of the one under consideration, remain to the right of it, i.e. we are talking about a collective motion of the bulk.

    Care to comment?
    You then replied to an earlier post (in which I hadn't spotted the assumption regarding crossing of orbits), and said
    Hi Fortis,
    Welcome back!
    Notice that when an electron moves to the right the number of electrons to the right of it stays the same ie they get squashed together and will thus repel it to the left.
    Since it has moved passed a few fixed positive caheges on its way there is an overall, positive charge on the left attractng it back. Hence restoring forces arise.
    What it says is if you were to give an electron an intial kick, it would head off in a straight line, continually slowing down until (to all intents and purposes) it stops
    then it comes back due to the restoring forces .e. it oscillates.
    As I said earlier, I gave the paper as an example of single electrons in plasma performng SHM for those who refused to believe it at all.
    Cheers,
    Lyndon
    (My bold) I replied with
    Consider this.

    In the IGM the electrons are at ~106K. Though non-relativistic, they are travelling with a very high r.m.s. velocity. If I consider our selected electron to be at rest (unlikely w.r.t. the CoM of the plasma, but it makes the picture easier to understand), it is surrounded by electrons that are whizzing all around it. If I give the electron a nudge in one direction at time t=0, do you really believe that all of the electrons that were to the right of it will suddenly stop doing what they were doing in order to remain to the right of it? Particulaly if you consider a quoted number density of 1 m-3?
    (My bold.)

    So, I ask again the question in bold. Please could you answer it in the context of the earlier posts?

  12. #312
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    Quote Originally Posted by lyndonashmore
    Originally Posted by brittannica
    A plasma can be defined in terms of these parameters as a partially or fully ionized gas that satisfies the following criteria: (1) a constituent electron may complete many plasma oscillations before it collides with either an ion or one of the other heavy constituents,
    As mentioned before, you need to keep this quote in context. Full article:
    http://www.britannica.com/eb/article-51956?hook=507064.

    Note that it begins by using the analogy of a cork on an ocean wave; keeping with this analogy, the electron is the cork and the plasma wave is the ocean wave. The article says nothing about electrons oscillating independently. Using it to make such a claim is misleading at best.

    Quote Originally Posted by papageno
    But he also realizes that he cannot support his claims in a scientifically acceptable way, otherwise he would have posted calculations proving his points long ago.
    Well, this was proven months ago when I first asked lyndon to do a dimensional analysis of his claim. He has consistently avoided performing even that very rudimentary mathematical exercise, so why should we be surprised he would refuse to do more complicated "mathinations?"

    Quote Originally Posted by lyndonashmore
    Secondly, in Compton the photons go off at an angle, in mine they travel in a straight line as per transmission of photons in glass.
    Not quite accurate. Glass does also send photons off at an angle… bending, distorting, focusing, separating them. It’s called refraction and it’s actually a closer match to Compton scattering than you would like to admit.

    Quote Originally Posted by lyndonashmore
    Thirdly, In Zwicky's paper he said that his effect was wrong, In my paper I say that I am right.
    Which proves nothing other than Zwicky ran the math and found the error. So far, you haven’t run the math.
    Never attribute to malice that which can be adequately explained by ignorance or stupidity.
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    Hi Nereid,
    Quote Originally Posted by Nereid View Post
    (my bold) Before the photon-electron interaction, there is zero momentum "[i]n a direction perpendicular to" "the directon of the photon".

    If, after the interaction, "the electron 'quivers'" (in this perpedicular direction), how is momentum conserved?
    Already answered this.
    The quivering of electrons in the path of photons is a result that I gave a referenced paper to, and so in any case this is enough to answer your question.
    However, as i said earlier, momentum is only conserved in an isolated system .
    For the electron, the photon is an external force that drives it, so for the electron by itself momentum is not conserved. Momentum 'universe' is though.
    Think of our radio antenna. We make the electrons in the aerial oscillate up and down, is momentum conserved here?(since here the poitive charges cannot move - unlike plasma).
    When the rado waves excite electrons in the ionosphere originally at rest, is momentum conserved then?
    However, as I said I backed my statement with published results in any case.
    Hope this helps,
    Cheers,
    Lyndon

  14. #314
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    Quote Originally Posted by Nereid View Post
    A key aspect of the lyndonashmore idea is that, in (the lyndonashmore) photon-electron interaction, the photon "undergoes an increase in wavelength of h/mc".

    Which "standard Physics" text discusses this "increase in wavelength of h/mc"?

    (the Ask A Scientist Physics Archive webpage you provided a link to does not mention this. Also, that page is about photon-atom interactions, not photon-electron ones).
    French, "Special relativity" pages 176 - 178.does it for an atom, Landau and Lif****z "Quantum Electrodynamics" considers absorption/emission by a "system of electrons i.e. an atom".
    I put the two together to get an original theory.
    French does it in energy loss and i convert that to an increase in wavelength which predicts the observed result.
    Cheers,
    Lyndon

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    Quote Originally Posted by Tobin Dax View Post
    He still hasn't answered that question to my satisfaction when I asked pages ago.
    Hi Tobin Dax,
    'to my satisfaction'
    Are you denying that photons cause electrons to oscillate!!
    At least you recognise that this question has been answered.
    Read feynman.
    Cheers,
    lyndon

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    Quote Originally Posted by papageno View Post
    Because you do not have calculations to support your claims, and you think we don't understand that references about plasma oscillations are not relevant to your effect -- as per your own admission.



    Strawman.
    I said that a single electron is not oscillating back and forth about a position over short length-scales ("short" as in "comparable to the average inter-particle spacing").



    The same term used by the physics community, with a well defined physical meaning, which you should understand if you really had studied statistical thermodynamics.
    The same term which is in the equation of simple harmonic motion you keep referring to, despite the fact that plasma oscillations should not be relevant to your effect.



    That reference is about plasma oscillations, which is not relevant to your effect -- as per your own admission.




    A journal with a stated ATM bias, but lacking the rigor necessary to be credible.
    Thanks for your kind congratulations on my success.
    There is nothng new or that has not been already answered in this post.
    Cheers,
    Lyndon

  17. #317
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    Quote Originally Posted by Nereid View Post
    In the spectrum of (distant) galaxies, as observed here on Earth, what part of the line width of the K line is due to the 'lyndonashmore effect', and what part due to intrinsic (to the galaxy) effects?

    In the lyndonashmore idea, what systematic changes in the intrinsic effects are expected (e.g. with distance, with Hubble type, with inclination, with age)?
    Hi Nereid,
    I calculated the statistical spread in redshifts for you, If you need more time to study it or if you need any more help in understanding it then please let me know.
    Cheers,
    Lyndon

  18. #318
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    Quote Originally Posted by Nereid View Post
    Have you finished thinking about this yet?

    Do you have an answer to the questions yet?
    Yes,
    The calculation that needed doing was done by me and posted here in this thread.
    There is no scientific value in the calculaton you suggest since, unlike mine, it cannot be tested against observation.
    This is what science is about.
    Cheers,
    lyndon

  19. #319
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    Quote Originally Posted by Nereid View Post
    An object is observed to have a z of 0.114, and the rest frame wavelength of an observed (x-ray) line (in the object's spectrum) is calculated to be 6.4 keV.

    Assuming n = 0.5, and 10,000 (redshifted 6.4 keV line) photons detected, how many of these detected photons will have undergone the following number of 'lyndonashmore photon-electron interactions'?

    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    >18
    Why?
    Cheers,
    Lyndon

  20. #320
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    Quote Originally Posted by Tobin Dax View Post
    That one, though maybe I should rephrase my comment. I'm not satisfied with his answer, mostly because I haven't seen any evidence (presented by lyndon or on my own) that a single photon can cause antenna-like radiation.
    Your question may be different than mine, and I am very interested in lyndon's response. So, just in case it got lost in the shuffle, here is the question:
    Feynman, "QED"
    The transmisson of light is just an electron picking up a photon, scratching its head and emitting a new photon.
    Feynman interviewed on t/V
    When we see an electron shaking up and down here and then another one over there shaking up and down we say a photon has travelled from here to there.
    Cheers,
    lyndon

  21. #321
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    Quote Originally Posted by lyndonashmore View Post
    Hi Nereid,
    Quote Originally Posted by Nereid
    (my bold) Before the photon-electron interaction, there is zero momentum "[i]n a direction perpendicular to" "the directon of the photon".

    If, after the interaction, "the electron 'quivers'" (in this perpedicular direction), how is momentum conserved?
    Already answered this.
    The quivering of electrons in the path of photons is a result that I gave a referenced paper to, and so in any case this is enough to answer your question.
    Please state the post number in which you did this (or post a link to it).
    However, as i said earlier, momentum is only conserved in an isolated system .
    So the 'lyndonashmore photon-electron interaction' should be more correctly called the 'lyndonashmore photon-plasma interaction'? or the 'lyndonashmore photon-group electron interaction'?

    Here's what you said here:
    The princple of momentum holds. In the directon of the photon, h/ λ = mv. In a direction perpendicular to this, when the electron 'quivers' it depends upon your view point. Is the electric field an external force?
    This was in answer to my question (my bold): "In the rest frame of the electron, prior to a "lyndonashmore photon-electron interaction", is momentum conserved in that interaction

    Specifically, momentum ("before" photon) + momentum ("before" electron, = 0?) = momentum ("after" photon) + momentum ("after" electron)?
    "
    For the electron, the photon is an external force that drives it, so for the electron by itself momentum is not conserved. Momentum 'universe' is though.
    Think of our radio antenna. We make the electrons in the aerial oscillate up and down, is momentum conserved here?(since here the poitive charges cannot move - unlike plasma).
    When the rado waves excite electrons in the ionosphere originally at rest, is momentum conserved then?
    I cannot see how this is an answer to my question, so let me re-phrase it, in light of your answer (so far).

    What is the 'lyndonashmore photon-{interactor} system' within which momentum is conserved? Please describe it, in terms of the constituents, and show how momentum is conserved.

  22. #322
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    Quote Originally Posted by lyndonashmore View Post
    Quote Originally Posted by Nereid
    A key aspect of the lyndonashmore idea is that, in (the lyndonashmore) photon-electron interaction, the photon "undergoes an increase in wavelength of h/mc".

    Which "standard Physics" text discusses this "increase in wavelength of h/mc"?

    (the Ask A Scientist Physics Archive webpage you provided a link to does not mention this. Also, that page is about photon-atom interactions, not photon-electron ones).
    French, "Special relativity" pages 176 - 178.does it for an atom, Landau and Lif****z "Quantum Electrodynamics" considers absorption/emission by a "system of electrons i.e. an atom".
    I put the two together to get an original theory.
    French does it in energy loss and i convert that to an increase in wavelength which predicts the observed result.
    Cheers,
    Lyndon
    Have you shown the working for this "original theory"? If so, please provide a post number or a link; if not, please provide the calculations and details.

  23. #323
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    Quote Originally Posted by lyndonashmore View Post
    Yes,
    The calculation that needed doing was done by me and posted here in this thread.
    There is no scientific value in the calculaton you suggest since, unlike mine, it cannot be tested against observation.
    This is what science is about.
    Cheers,
    lyndon
    Where (was it "posted here in this thread")?

  24. #324
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    Quote Originally Posted by lyndonashmore View Post
    Quote Originally Posted by Nereid
    An object is observed to have a z of 0.114, and the rest frame wavelength of an observed (x-ray) line (in the object's spectrum) is calculated to be 6.4 keV.

    Assuming n = 0.5, and 10,000 (redshifted 6.4 keV line) photons detected, how many of these detected photons will have undergone the following number of 'lyndonashmore photon-electron interactions'?

    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    >18
    Why?
    Cheers,
    Lyndon
    Is the question unclear in any way?

    If not, then please answer it.

  25. #325
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    Quote Originally Posted by lyndonashmore
    Thanks for your kind congratulations on my success.
    Having a paper published by a journal that gives priority to style over substance is not a success.

    Quote Originally Posted by lyndonashmore
    There is nothng new or that has not been already answered in this post.
    So, you concede that the only simple harmonic motions in a plasma occur in plasma oscillations and when macroscopic EM waves force electrons on oscillations, neither of which is relevant to your effect.

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    Quote Originally Posted by lyndonashmore View Post
    French, "Special relativity" pages 176 - 178.does it for an atom,

    [snip]

    French does it in energy loss and i convert that to an increase in wavelength which predicts the observed result.
    Cheers,
    Lyndon
    Which section is it in (title please)? Which edition of French are you referencing?

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    Quote Originally Posted by lyndonashmore View Post
    Hi Tobin Dax,


    Sorry, already changed it - hope it is correct now!
    You asked about the sources being a student project.
    When i first did this it was in reply to another poster who raised the same point. It was not meant to be a scientific paper and I wanted to show the print out on line.
    It gives the right idea. In an earlier post by Nereid, she talks about a 'doppler footprint' and cites an encyclopeadia reference giving the width. My ref tallies with this too, so it is difficult to separate the two effects. A spread due to thermal motion of the atoms in the gases around a star and the small spread due to random fluctuations in photon collisions.
    Thanks again,
    Lyndon
    What is the galaxy whose observed K line you used?

    Clicking the link, "Here" does not take you to "an actual print out of the spectrum" - where is this spectrum?

    What proportion of the observed K line line width, of this galaxy, arises from causes other than the 'lyndonashmore effect'?

    Using your website, and what you have posted earlier in this thread, I calculate the following as the linewidths (± 1 σ) predicted by the 'lyndonashmore effect'. Are they correct?

    z = 0.1
    5000 A: 7 A
    21 cm: 452 nm
    6.4 keV: 0.45 keV

    z = 1
    5000 A: 22 A
    21 cm: 1.4 μ
    6.4 keV: 1.4 keV

  28. #328
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    Quote Originally Posted by Nereid View Post
    Clicking the link, "Here" does not take you to "an actual print out of the spectrum" - where is this spectrum?
    That appears to have happened around the time Lyndon updated the page, when the course webpage he linked to changed. He does need to do something about that. I did save a copy of the plot with the shifted H and K lines if someone needs to see it, as long as falls under fair use.

  29. #329
    Join Date
    Apr 2004
    Posts
    1,270
    Hi Nereid,
    Quote Originally Posted by Nereid View Post
    Have you shown the working for this "original theory"? If so, please provide a post number or a link; if not, please provide the calculations and details.
    No problem it's here
    Cheers,
    Lyndon

  30. #330
    Join Date
    Apr 2004
    Posts
    1,270
    H Tobin Dax,
    Quote Originally Posted by Tobin Dax View Post
    That appears to have happened around the time Lyndon updated the page, when the course webpage he linked to changed. He does need to do something about that. I did save a copy of the plot with the shifted H and K lines if someone needs to see it, as long as falls under fair use.
    Can I have a copy please? I will then post 'an artists impression!!!" on my site.
    My e Mail is at the bottom of my home page
    Thanks.
    Lyndon

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