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Thread: Tired Light Theory

  1. #1

    Tired Light Theory

    I am fully aware that this subject has probably been discussed and found extremely wanting, but I am new to this forum, and I would like to get as much accurate info. about it as possible. Any help is sincerely appreciated.

    Thanx,

    PM

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    Re: Tired Light Theory

    Quote Originally Posted by Prozacman
    ...I would like to get as much accurate info. about it as possible...
    Why? It is a roundly discredited theory that is best relegated to the dustbin of history.
    Everyone is entitled to his own opinion, but not his own facts.

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    What is this theory?

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    It says that light loses energy as it travels through space, and that the red-shift is due to the emitting objects simply being far away, and not to them moving away from us.

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    tired light

    Tired light is fighting back. The hubble constant at 64 km/s per Mpc is, when you convert it into SI units, exactly equal to hr/m in each cubic metre of space. This result can't be purely by chance. The electron and H must be related. Therefore the Universe is not expanding. See 'ashmore's paradox' at www.lyndonashmore.com
    h = planck constant, r = classical electron radius, m = rest mass of electron and H is the Hubble constant.

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    But there's nothing fundamental about the parsec unit. It's based soley on the legnth of the major axis of the Earth's orbit. Therefore, justifying anything like this by using a number per megaparsec is pure garbage.

    Additional:
    I couldn't even get your numbers, and it took me a minute to figure out why.

    2.1exp(-18 ) is NOT the notation for 2.1^-18. It's the notiaton for 2.1e^-18, which is a very different number.

    Moreover, I don't get 2.1^-18 for your A, I get 2.04977336e^-18, where as H/Mpc = 2.07409712^-18, using the best numbers I could find. Those aren't the same numbers.

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    Re: tired light

    Quote Originally Posted by lyndonashmore
    Tired light is fighting back. The hubble constant at 64 km/s per Mpc is, when you convert it into SI units, exactly equal to hr/m in each cubic metre of space. This result can't be purely by chance. The electron and H must be related. Therefore the Universe is not expanding. See 'ashmore's paradox' at www.lyndonashmore.com
    h = planck constant, r = classical electron radius, m = rest mass of electron and H is the Hubble constant.
    Well, first of all, the current best estimate for Hubble's constant is 71 km/s per Mpc. This would seem to falsify your claims right off the bat.

    Then, your page says, "In astronomical units, hr/m per cubic metre of space is also equal to 64 km/s per Mpc." I'm pretty confused by the units you're using here, particularly since H has a time component, and your ratio hr/m simply has no time component. So how can you even think of comparing the two in any meaningful way?

    And even if one ratio was in the same ballpark as the other, so what? There are certainly many numerical coincidences in Nature. How would that have anything to do with disproving the big bang theory as you claim?

    Your webpage says that you are not "...too happy with the Big Bang theory and expanding Universe cosmology..." but you give no reason for your unhappiness. As a physics teacher, you ought to know that this is not a very scientific attitude. To make a long story short, I think you would be wise to get happy with this prevailing theory. Unlike your rather unfocused assertions, the big bang theory is very well supported by careful and repeated observational evidence.
    Everyone is entitled to his own opinion, but not his own facts.

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    Re: tired light

    Quote Originally Posted by Cougar
    Then, your page says, "In astronomical units, hr/m per cubic metre of space is also equal to 64 km/s per Mpc." I'm pretty confused by the units you're using here, particularly since H has a time component, and your ratio hr/m simply has no time component. So how can you even think of comparing the two in any meaningful way?
    h has units Js=kg m^2/s^2 * s = kg m^2/s
    r has units of m
    m has units of kg.

    So hr/m has units of (kg m^2/s)(m)(1/kg) = m^3/s
    So "hr/m" does have a time component. Of course the units
    still don't match. Lets figure out the units.

    Units of H are km/s/Mpc = unit of length/unit of time/unit of length.
    So in SI units, H is in terms of inverse seconds.


    This guy, is in effect telling us,

    [some number] s^-1 = [some number] m^3 s^-1


    This is a false statement since meters are not dimentionless. Therefore his assumption used to show this is false. Therefore his "H=hr/m" equation is false. QED.


    That the two numbers stripped of their units are "close" is very underwhelming. If the numbers are not "close" with one set of units, convert to another set of units: meters to miles or whatever. Eventually one will find one that makes the measurments stripped of their units "close."

    And what is worse is that this guy gives H as "64 ± 3 km per sec per Mpc." Now lets ignore whether or not he is giving the current estimate of H and just take him at his word that this is H. Lets rephase the measurement as 64 ± 5% km/s/Mpc. Without some other reason to
    suppose an equality, one would be hard presses to state that two things are exactly equal when one has such a significant uncertainty.

    In short, this is stuff that any one with a few weeks of high school physics should be able to debunk.

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    No, what Couger means is that the Hubble constant isn't a constant. It varies with time, where as hr/m does not.

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    Quote Originally Posted by Ut
    But there's nothing fundamental about the parsec unit. It's based soley on the legnth of the major axis of the Earth's orbit. Therefore, justifying anything like this by using a number per megaparsec is pure garbage.

    Additional:
    I couldn't even get your numbers, and it took me a minute to figure out why.

    2.1exp(-18 ) is NOT the notation for 2.1^-18. It's the notiaton for 2.1e^-18, which is a very different number.

    PARDON??????

    Moreover, I don't get 2.1^-18 for your A, I get 2.04977336e^-18, where as H/Mpc = 2.07409712^-18, using the best numbers I could find. Those aren't the same numbers.
    There is no such thing as a 'fundamental unit'. All units are decided by 'convention'. The only point worth making is that the units, whatever they may be must be the same on either side of the equation. This is true in my paradox and so it is very justifiable to do this (ashmore's paradox www.lyndonashmore.com).

    I am comfortable with my position on arithmetic. Why not check again.

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    Re: tired light

    Well, first of all, the current best estimate for Hubble's constant is 71 km/s per Mpc. This would seem to falsify your claims right off the bat

    Who says this is this 'best estimate'? The people who did it? The average of all the last 24 results is 64 km/s per Mpc. this is the scientific way to do it rather than choosing a result to suit your case. My claims are spot on since I take account of all results and methods for finding H. Secondly Wendy's result, quoted above, includes an element of uncertainty and when you take this into account the possible range includes ashmore's paradox.

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    Re: tired light

    Quote Originally Posted by Cougar
    Quote Originally Posted by lyndonashmore
    Tired light is fighting back. The hubble constant at 64 km/s per Mpc is, when you convert it into SI units, exactly equal to hr/m in each cubic metre of space. This result can't be purely by chance. The electron and H must be related. Therefore the Universe is not expanding. See 'ashmore's paradox' at www.lyndonashmore.com
    h = planck constant, r = classical electron radius, m = rest mass of electron and H is the Hubble constant.
    Well, first of all, the current best estimate for Hubble's constant is 71 km/s per Mpc. This would seem to falsify your claims right off the bat.

    Then, your page says, "In astronomical units, hr/m per cubic metre of space is also equal to 64 km/s per Mpc." I'm pretty confused by the units you're using here, particularly since H has a time component, and your ratio hr/m simply has no time component. So how can you even think of comparing the two in any meaningful way?

    see below you have conveniently lost the 'per cubic metre' from hte paradox. I wonder why?

    And even if one ratio was in the same ballpark as the other, so what? There are certainly many numerical coincidences in Nature. How would that have anything to do with disproving the big bang theory as you claim?

    Your webpage says that you are not "...too happy with the Big Bang theory and expanding Universe cosmology..." but you give no reason for your unhappiness. As a physics teacher, you ought to know that this is not a very scientific attitude. To make a long story short, I think you would be wise to get happy with this prevailing theory. Unlike your rather unfocused assertions, the big bang theory is very well supported by careful and repeated observational evidence.
    firstly, ashmore's paradox www.lyndonashmore.com is that H = 'hr/m per cubic meter of space'. this has base units of 'per sec' the same as H so your poit is invalid.

    secondly, Name me three numerical coincidences in nature where the numbers are the same to two sig figs and they both have the same base units.

    The paradox is my reason for being unhappy with the BB theory. As a Physicist I was always taught to be suspicious of things that have the same value but are seemingly unrelated.

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    Re: tired light

    Quote Originally Posted by harlequin
    Quote Originally Posted by Cougar
    Then, your page says, "In astronomical units, hr/m per cubic metre of space is also equal to 64 km/s per Mpc." I'm pretty confused by the units you're using here, particularly since H has a time component, and your ratio hr/m simply has no time component. So how can you even think of comparing the two in any meaningful way?
    h has units Js=kg m^2/s^2 * s = kg m^2/s
    r has units of m
    m has units of kg.

    So hr/m has units of (kg m^2/s)(m)(1/kg) = m^3/s
    So "hr/m" does have a time component. Of course the units
    still don't match. Lets figure out the units.

    Units of H are km/s/Mpc = unit of length/unit of time/unit of length.
    So in SI units, H is in terms of inverse seconds.


    This guy, is in effect telling us,

    [some number] s^-1 = [some number] m^3 s^-1

    NOW DIVIDE THIS BY m^3 AND YOU GET..... s^-1

    QED


    This is a false statement since meters are not dimentionless. Therefore his assumption used to show this is false. Therefore his "H=hr/m" equation is false. QED.


    That the two numbers stripped of their units are "close" is very underwhelming. If the numbers are not "close" with one set of units, convert to another set of units: meters to miles or whatever. Eventually one will find one that makes the measurments stripped of their units "close."

    And what is worse is that this guy gives H as "64 ± 3 km per sec per Mpc." Now lets ignore whether or not he is giving the current estimate of H and just take him at his word that this is H. Lets rephase the measurement as 64 ± 5% km/s/Mpc. Without some other reason to
    suppose an equality, one would be hard presses to state that two things are exactly equal when one has such a significant uncertainty.

    In short, this is stuff that any one with a few weeks of high school physics should be able to debunk.
    I will debunk your answer if 5 seconds. "hr/m per cubic metre of space' has the units of "per sec" the same as H (you conveniently forgot the cubic metre -I wonder why! I have corrected your reply above.

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    Re: Tired Light Theory

    Quote Originally Posted by Prozacman
    I am fully aware that this subject has probably been discussed and found extremely wanting, but I am new to this forum, and I would like to get as much accurate info. about it as possible. Any help is sincerely appreciated. Thanx, PM
    Welcome to the board.

    Astronomer Ned Wright's "Cosmology Tutorial" has a section debunking Tired Light models:

    http://www.astro.ucla.edu/~wright/tiredlit.htm

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    Yes, I realized afterwords that you were deviding by metres, and not parsecs. I take back the statement about units in so much that I said you were using them incorrectly. I stand by my "fundamental units" statement, though, because each system of units has a set of basic, or fundamental units to them which cannot be reduced to others. The parsec is not one of these.

    Quote Originally Posted by lyndonashmore
    I am comfortable with my position on arithmetic. Why not check again.
    I suggest you go back and look at your numbers. 2.1E-18 is really stretching the rounding on hr/m.

    m = 9.1093897E-31 kg
    h = 6.6260755E-34 Js
    r = 2.817940285E-15 m

    hr/m = 2.04974051E-18 != 2.1E-18

    You do the math. I'm more than confident in that number, and feel it's one of the biggest arguments against your theory.

    As for H being 64 km/s/Mpc, this is from one of the papers you list as confirming it.

    Quote Originally Posted by Freedman et al
    Based on the Key Project Cepheid calibration and its application to five secondary methods (type Ia supernovae, the Tully-Fisher relation, surface brightness fluctuations, type II supernovae, and the fundamental plane for elliptical galaxies), a combined value of H0 = 72±8 km/sec/Mpc is obtained.
    ± 8 km/s? That's a pretty high error. What kind of error do you get when you average them?

    72±8
    67±3
    61±3
    69±12
    72±8
    -------
    341±34

    => H0~68.2±6.8

    That was just quickly, using a number of your examples. Others pull up confidenes between 50 and 80%. Those aren't particularly good, either. But at least they're given. You don't seem to give any. That makes me thing it's large.

    Coincidences and constants...
    Well, I've got a good 2 for you, anyway. Both the lenth of my thumbs and my big toes, from the last knuckle to the tip, are 2.7cm in length. That's Euler's number to 2 sig figs.

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    Quote Originally Posted by Ut
    Yes, I realized afterwords that you were deviding by metres, and not parsecs. I take back the statement about units in so much that I said you were using them incorrectly. I stand by my "fundamental units" statement, though, because each system of units has a set of basic, or fundamental units to them which cannot be reduced to others. The parsec is not one of these.

    Quote Originally Posted by lyndonashmore
    I am comfortable with my position on arithmetic. Why not check again.
    I suggest you go back and look at your numbers. 2.1E-18 is really stretching the rounding on hr/m.

    m = 9.1093897E-31 kg
    h = 6.6260755E-34 Js
    r = 2.817940285E-15 m

    hr/m = 2.04974051E-18 != 2.1E-18

    You do the math. I'm more than confident in that number, and feel it's one of the biggest arguments against your theory.

    As for H being 64 km/s/Mpc, this is from one of the papers you list as confirming it.

    Quote Originally Posted by Freedman et al
    Based on the Key Project Cepheid calibration and its application to five secondary methods (type Ia supernovae, the Tully-Fisher relation, surface brightness fluctuations, type II supernovae, and the fundamental plane for elliptical galaxies), a combined value of H0 = 72±8 km/sec/Mpc is obtained.
    ± 8 km/s? That's a pretty high error. What kind of error do you get when you average them?

    72±8
    67±3
    61±3
    69±12
    72±8
    -------
    341±34

    => H0~68.2±6.8

    That was just quickly, using a number of your examples. Others pull up confidenes between 50 and 80%. Those aren't particularly good, either. But at least they're given. You don't seem to give any. That makes me thing it's large.

    Coincidences and constants...
    Well, I've got a good 2 for you, anyway. Both the lenth of my thumbs and my big toes, from the last knuckle to the tip, are 2.7cm in length. That's Euler's number to 2 sig figs.
    Can you combine errors in this way? You only do it your way when you are adding or subtracting two quantities and want to find the uncertainty in the final total. These are all results for H - the same thing and so they must all surely agree with each other.
    You have 72+/- 8 which means that they say that H MUST lie between 64 and 80.
    You have H = 61 +/- 3 from another worker which means that they say that H MUST lie between 58 and 64.
    Clearly the two results must agree otherwise somebody must be wrong (in which case you can't include them in your average as you have done above - can't include false results) so the value of H must be in the region where the two uncertainties overlap. WHICH IS ^64 km/s per Mpc or 'hr/m per cubic metre of space for the electron"

    PS the two uncertainties you quote are not independent and therefore only count as one. So I need two more. Oh! by the way lets add another condition. They must be related in the same way as H, h, r, m i.e. H is related to redshift which is related to the the energy of photons (E=hf), To measure redshift we look at spectral lines which are related to the electron in absorption and emission - hence r and m.
    The only relation between your fingers and toes and Eulers number is that you have to take your gloves and socks off to count to 2.7!

  17. #17
    Quote Originally Posted by lyndonashmore
    These are all results for H - the same thing and so they must all surely agree with each other.
    You have 72+/- 8 which means that they say that H MUST lie between 64 and 80.
    You have H = 61 +/- 3 from another worker which means that they say that H MUST lie between 58 and 64.
    Clearly the two results must agree otherwise somebody must be wrong (in which case you can't include them in your average as you have done above - can't include false results) so the value of H must be in the region where the two uncertainties overlap. WHICH IS ^64 km/s per Mpc or 'hr/m per cubic metre of space for the electron"
    It depends on what you're using for the uncertainty. For statistical uncertainty it could be one, two or three standard deviations of a gaussian distribution. The number does not have to lie within the bounds of the error - you have a certain confidence that they do.

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    Quote Originally Posted by swansont
    Quote Originally Posted by lyndonashmore
    These are all results for H - the same thing and so they must all surely agree with each other.
    You have 72+/- 8 which means that they say that H MUST lie between 64 and 80.
    You have H = 61 +/- 3 from another worker which means that they say that H MUST lie between 58 and 64.
    Clearly the two results must agree otherwise somebody must be wrong (in which case you can't include them in your average as you have done above - can't include false results) so the value of H must be in the region where the two uncertainties overlap. WHICH IS ^64 km/s per Mpc or 'hr/m per cubic metre of space for the electron"
    It depends on what you're using for the uncertainty. For statistical uncertainty it could be one, two or three standard deviations of a gaussian distribution. The number does not have to lie within the bounds of the error - you have a certain confidence that they do.
    But what is the probability, that Baldrick, is the question. once you get outside your uncertainties the probabilities of the value lying there drops to zilch. 64 km/s per Mpc is the most likely and this is 'hr/m per cubic metre of space', and this reeks of tired light. ashmore's paradox www.lyndonashmore.com
    These varying values of H show that the BB is incorrect (amongst a lot of other things). You should get the same rate of expansion wherever you look. But, some scientists get values of H repeatably small and others find values of H repeatably large. Surely in a Big Bang Universe they should all get the same value for H within experimental uncertainty. With tired light we just say that it is due to fluctuations in the density of space. No problem to us, but to the BB it is fatal.

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    Re: tired light

    Quote Originally Posted by harlequin
    ...So "hr/m" does have a time component....
    Ah, my mistake.

    Still, averaging the last 24 estimates of the Hubble constant is not the way science is done. The most current, best estimate is from WMAP...
    Everyone is entitled to his own opinion, but not his own facts.

  20. #20
    Quote Originally Posted by lyndonashmore
    once you get outside your uncertainties the probabilities of the value lying there drops to zilch.
    No. If the uncertainty represents 2 standard deviations, that means that the chances of being inside is ~95%, not 100%. If it's only one standard deviation, it's ~68%.

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    Re: tired light

    Quote Originally Posted by Cougar
    Quote Originally Posted by harlequin
    ...So "hr/m" does have a time component....
    Ah, my mistake.

    Still, averaging the last 24 estimates of the Hubble constant is not the way science is done. The most current, best estimate is from WMAP...
    Wow...what a motherload of parameters! Found at your site... here (pdf file at bottom).

    It's amazing what they have accomplished especially since I can hardly get my microwaves to make popcorn.

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    Quote Originally Posted by swansont
    Quote Originally Posted by lyndonashmore
    once you get outside your uncertainties the probabilities of the value lying there drops to zilch.
    No. If the uncertainty represents 2 standard deviations, that means that the chances of being inside is ~95%, not 100%. If it's only one standard deviation, it's ~68%.
    So I take it that you are saying that there is less than a 5% probability (1 in 20) that these results confirm the Big Bang theory?

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    Re: tired light

    Quote Originally Posted by Cougar
    Quote Originally Posted by harlequin
    ...So "hr/m" does have a time component....
    Ah, my mistake.

    Still, averaging the last 24 estimates of the Hubble constant is not the way science is done. The most current, best estimate is from WMAP...
    Is this the NASA that sent a 125 million dollar spacecraft to Mars that crashed because they got the units wrong? One group worked in metric the other worked in Imperial!
    Is this the NASA that had to put spectacles on the Hubble telescope because it was designed wrong?
    Is this the NASA that failed to realise that their values for the Hubble constant, H was just the electron in disguise? (until I told them)
    Why should we take their value over everyone elses?
    George is correct here. You are nit picking over one or two percent when the two values H and 'hr/m per cubic metre of space' are clearly the same. Admit it, and lets move on to the big picture.

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    No, he's saying that there is a 5% probability that the Hubble constant lies outside those bounds. This doesn't invalidate the Big Bang theory all of a sudden. While the numbers not working for you would invalidate your theory that H has to be this particular value, Big Bang theory does not demand this precise number.

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    Quote Originally Posted by Lyndon Ashmore
    In the Big bang theory, the age of the Universe is 1/H. This means that the Big bang theory and the expanding Universe say that the age of the Universe is (mass of electron)/{(planck constant)x(electron radius)}. This is clearly nonsense. It cannot be correct for the age of the Universe to be related to the parameters of the electron. Therefore either 26 experimental results must be wrong or the theory must be wrong. It is the theory that is wrong. The Universe is not expanding - Ashmore's paradox
    Is is precisely 31416 days since the Royal Air Force formed (yes, it really is). But this means that the age of the R.A.F. is related to the ratio between the circumference and the diameter of its logo, measured to an accuracy of 5 significant figures, or 1000 times as accurate as Ashmore's Paradox has been 'proved'. This is clearly nonsense. Therefore all measurements of Pi are incorrect, or the R.A.F. doesn't really exist.

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    Quote Originally Posted by Iain Lambert
    Quote Originally Posted by Lyndon Ashmore
    In the Big bang theory, the age of the Universe is 1/H. This means that the Big bang theory and the expanding Universe say that the age of the Universe is (mass of electron)/{(planck constant)x(electron radius)}. This is clearly nonsense. It cannot be correct for the age of the Universe to be related to the parameters of the electron. Therefore either 26 experimental results must be wrong or the theory must be wrong. It is the theory that is wrong. The Universe is not expanding - Ashmore's paradox
    Is is precisely 31416 days since the Royal Air Force formed (yes, it really is). But this means that the age of the R.A.F. is related to the ratio between the circumference and the diameter of its logo, measured to an accuracy of 5 significant figures, or 1000 times as accurate as Ashmore's Paradox has been 'proved'. This is clearly nonsense. Therefore all measurements of Pi are incorrect, or the R.A.F. doesn't really exist.
    At the risk of repeating myself, H, h, r and m are related. In order to find the Hubble constant you have to look at absorption lines in the spectra of distant galaxies. These are due to electrons in atoms absorbing certain frequencies of light because the energy of a photon (E=hf) is equal to the difference in energy levels of the electron (r and m).
    Now if you are trying to say that the Hubble constant is a variable and at some point in the age of the Universe it must equal hr/m per cubic metre of space then:
    1) why not say so instead of trying to ridicule an excellent organisation such as the RAF.
    2) I would have been quite happy if someone had measured H and said Oh! in x days time it will equal hr/m lets have a big party to celebrate. I would have joined in with the rest of you.
    But they didn't. At the very first time that we measure H precisely, it is exactly equal to 'hr/m per cubic metre' for the electron. WHAAAAAT a coincidence. No way! How do we know that H varies with time? because the Big Bang codsmologists tell us so. Experimental evidence is that H = hr/m per m^3. The rest is speculation.
    Come back in a million years or so and we will see if H has changed.
    What you are saying is that if H is a variable then we are at a very special time and place in the history of the Universe - one where the rate of expansion is equal to a combination of the parameters of the electron. Scientists have had their fingers burned too often doing that, so I for one am not falling for it. remeber those who said the Earth was at the centre of the Universe?

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    My point is that you seem to be stating that it can't be coincidence, when such coincidences can always be found if you go looking for them - see the 23-related madness I accidentally sparked off in BaBBling a while back. Maybe it isn't, but until we've tied down the current value to something an awful lot more precise we can't say that your equation is even correct - I'm seeing a search for numbers that fit, and not a theory that leads to this value in the first place.

    So I perhaps shouldn't be so dismissive, but instead file it under "Interesting - lets see what the value does end up measuring to, before we go further however".

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    Quote Originally Posted by Iain Lambert
    No, he's saying that there is a 5% probability that the Hubble constant lies outside those bounds. This doesn't invalidate the Big Bang theory all of a sudden. While the numbers not working for you would invalidate your theory that H has to be this particular value, Big Bang theory does not demand this precise number.
    I am uncertain as to the accuracy of this statement. :wink:

    Uncertainty of measurement acknowledges that no measurements can be perfect and is defined as a '… parameter, associated with the result of a measurement, that characterises the dispersion of values that could reasonably be attributed to the measurand. It is typically expressed as a range of values in which the value is estimated to lie, within a given statistical confidence, but it does not attempt to define or rely on a unique true value.

    In summary, common usage of the word accuracy for quantitatively describing the characteristics of measuring instruments, is incompatible with its official meaning but, even ignoring this point, its common usage definition is significantly cruder than the proper metrological term uncertainty.
    From >>> here <<<

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    Quote Originally Posted by lyndonashmore
    PS the two uncertainties you quote are not independent and therefore only count as one. So I need two more. Oh! by the way lets add another condition. They must be related in the same way as H, h, r, m i.e. H is related to redshift which is related to the the energy of photons (E=hf), To measure redshift we look at spectral lines which are related to the electron in absorption and emission - hence r and m.
    Ok. I've measured the thumbs of my roommates. Two out of three of them have thumb lengths which round off to 2.7 cm. Plus myself, that makes 3.

    Yes, yes, another "You've made a point which makes my argument look weaker. Let's invalidate your point by adding after-the-fact qualifiers" responce. I'm surprised by how often people make such statements around here. See, the thing is, I don't believe there is a realtionship between H, h, r, and m. I think at the very best, the relationship you've found is a very weak coincidence based on some poor rounding by yourself.

    Also, I noticed that you didn't comment on the calculation of hr/m ~ 2.0E-18.

    You realize that the energy that can be absorbed by an electron depends entirely on the atom/molecule it's bound to, right? The potential well created by an atom is a major contributer in the Schroedinger equation. For a free electron -- one for which the potential is zero -- the phenomenon of energy quantization of the state isn't even found, and thus one would not expect to see spectral lines. At least, that's what I've been lead to believe. I'm open to corrections.

    The only relation between your fingers and toes and Eulers number is that you have to take your gloves and socks off to count to 2.7!
    Funny. I can't tell if you're insinuating that between all of my appendages, I have only 2.7 digits, or if you're implying that I don't have the mental capacity to count higher than 2 without visual aide. Such attacks do little to help your argument, and much to invalidate your opinion.

  30. #30
    Just wishing everyone in and/or connected with the RAF a happy myriapi days!

    If I should live so long, I will be a myriapi of days old on 2038 September 14!

    Just a note: my dictionary shows myria- as a metric prefix and gives myriameter (10,000 m) as an example. I'm not sure if it is still accepted as an SI prefix, I'll check on this later tonight.

    Once again, happy myriapi days to the RAF!

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