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Re: Why is the universe 13.8 milliards years old ?

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Gary Harnagel wrote:

> On Monday, November 30, 2015 at 11:30:54 PM UTC-7, Thomas 'PointedEars'
> Lahn wrote:

Attribution line, not attribution novel.

>> Gary Harnagel wrote:
>> > On Friday, November 27, 2015 at 4:17:11 PM UTC-7, HGW wrote:
>> > >
>> > > Tom I really feel sorry for you. [And other lies]
>> > > Each one is traveling at 3E8 m/sec.
>> > > If you estimate the volume each one, you will be able to calculate
>> > > that at any instant, only a very small fraction of each cubic metre
>> > > is occupied by 'photonic material'..
>> > 
>> > Poor, poor Ralphie-boy!  He is completely bereft of mathematical
>> > ability.
>> 
>> Knowing math alone is insufficient to solve this problem properly.
> 
> This is true.  One must have some knowledge of physics to even make a WAG.

Obviously, WAGs can be done with insufficient knowledge of physics as well.
 
>> > Most of the photons are from the CMBR which has a nominal temperature
>> > of 2.7 kelvins,
>> 
>> 2.72548±0.00057 K today (Fixsen, 2009)
>> 
>> > i.e., its wavelength is about 6 mm,
>> 
>> How did you get that idea?
> 
> E = k*T = h*c/lambda

  E = k T

where k is the Boltzmann constant and T the absolute temperature, is only 
true for the *thermal* energy of systems with *two* degrees of freedom, as 
the general equation for *thermal* energy is

  E = N 1∕2 k T

where N is the number of the degrees of freedom.

  λ = 2 ℎ c∕(3 k × 2.72548 K) ≈ 3.5199 mm,

but that is still too much because although EM waves propagate in three-
dimensional space, such a system has a lot more degrees of freedom than just 
three.  With 6 degrees of freedom, as expected, you get approximately the 
correct value:

  λ = 2 ℎ c∕(6 k × 2.72548 K) ≈ 1.7597 mm


But in general your approach, and that approach, is _not_ how you can 
calculate the wavelength of the electromagnetic (EM) waves associated with 
EM radiation of a certain absolute temperature.

Instead, the equation that applies here is that of Planck’s law of black-
body radiation, where spectral radiance is

  I(f, T) = 2 ℎ∕c² f³∕(e^(ℎ f∕k T) − 1)

or

  I(λ, T) = 2 ℎ c²∕λ⁵ 1∕(e^(ℎ c∕(λ k T)) − 1) ¹)

For a given absolute temperature T, these functions have a local maximum 
each that defines the *peak* frequency or *peak* wavelength, respectively, 
of the corresponding electromagnetic wave (which you can determine by 
solving numerically the equations dI(f, T)∕df = 0 for f or dI(λ, T)∕dλ = 0 
for λ).

For the CMBR with the absolute temperature as measured above, these are ca. 
160.2 GHz and 1.871 mm, respectively (ibid.)
 
<https://en.wikipedia.org/wiki/Cosmic_microwave_background>
<https://en.wikipedia.org/wiki/Black-body_radiation#Planck.27s_law_of_black-body_radiation>
<https://en.wikipedia.org/wiki/Planck%27s_law>

>> > which is its localization range.
>> 
>> ISTM that "localization range" is a term which in that regard you just
>> invented.
> 
> Sort of.  I assumed that a detector more than one wavelength away from a
> photon would interact weakly with it as the photon went past.

You can view EM radiation as *either* an EM wave that has frequencies and 
wavelengths, *or* as a beam of photons where each one is carrying a distinct 
amount of energy, but _not_ both at the same time (wave–particle duality).
 
>> > This means that each one takes up 2x10^-7 cubic meter, or only
>> > 5 million of them can fill a cubic meter.  20 times that amount will
>> > stuff
>> > that cube quite full.  [...]
>> 
>> How did you get the idea that the wavelength of electromagnetic radiation
>> is related to the number of its photons that could fit within a volume of
>> space?
> 
> WAG,

“Wild Ass Guess”?  Yes, I figured as much.

> which is more than "Wilson" provided with his worse-than-WAG
> assertion. For the record, I wasn't the one that came up with the idea,
> "Wilson" did. My purpose was to demonstrate that his bald-faced assertion
> was baloney (it was a not-even-wrong example of sophistry).

That is not so.  His assertion was that one could do that calculation, and 
your response to that was not (which it should have been) that the 
calculation as such were nonsense but just that the figures were wrong.

The calculation as such is nonsense because photons are _not_ little energy 
balls moving along the waveform.  Instead, they are *quantum* objects.  
Since they have no known inner structure, they must be assumed to be *point-
like*.

For quantum objects one can only specify their position which an uncertainty 
that is limited by how precisely one can tell their momentum (uncertainty 
principle: σₓσₚ ≥ ℏ∕2, where the σ’s are the standard deviation of position 
x and momentum p, respectively, and ℏ = ℎ∕2π).

<https://en.wikipedia.org/wiki/Uncertainty_principle>

So there is a probability greater than 0 that much more than your 5 million 
photons would fit into a volume of a cubic meter.


PointedEars
___________
¹) one can also find ν = f and I = L_ν = B_ν or I = B_λ and other names than
   “spectral radiance” in the literature
-- 
Q: How many theoretical physicists specializing in general relativity
   does it take to change a light bulb?  
A: Two: one to hold the bulb and one to rotate the universe.
(from: WolframAlpha)

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  Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-11-23 19:10 +0000
    Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-11-23 22:39 +0000
      Re: Why is the universe 13.8 milliards years old ? The Starmaker <starmaker@ix.netcom.com> - 2015-11-23 21:04 -0800
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            Re: Why is the universe 13.8 milliards years old ? The Starmaker <starmaker@ix.netcom.com> - 2015-11-24 01:27 -0800
            Re: Why is the universe 13.8 milliards years old ? mlwozniak@wp.pl - 2015-11-24 01:36 -0800
              Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-11-24 10:26 +0000
                Re: Why is the universe 13.8 milliards years old ? mlwozniak@wp.pl - 2015-11-24 02:52 -0800
                Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-11-24 11:48 +0000
                Re: Why is the universe 13.8 milliards years old ? mlwozniak@wp.pl - 2015-11-24 04:02 -0800
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        Re: Why is the universe 13.8 milliards years old ? alsor@interia.pl - 2015-11-24 15:27 -0800
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            Re: Why is the universe 13.8 milliards years old ? alsor@interia.pl - 2015-11-24 17:39 -0800
    Re: Why is the universe 13.8 milliards years old ? John Gogo <jfgogo22@yahoo.com> - 2015-11-23 17:28 -0800
      Re: Why is the universe 13.8 milliards years old ? John Gogo <jfgogo22@yahoo.com> - 2015-11-23 18:07 -0800
        Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-11-24 19:00 +0000
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            Re: Why is the universe 13.8 milliards years old ? HGW <xxx@....> - 2015-11-28 10:17 +1100
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                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-11-28 13:09 -0800
                Re: Why is the universe 13.8 milliards years old ? Carl Heinz Krüger <heinzkrueger@ubernetz.org> - 2015-11-30 16:44 +0000
                Re: Why is the universe 13.8 milliards years old ? Tom Roberts <tjroberts137@sbcglobal.net> - 2015-11-28 17:49 -0600
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                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-11-29 20:13 +0000
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                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-11-30 20:39 +0000
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                Re: Why is the universe 13.8 milliards years old ? Tom Roberts <tjroberts137@sbcglobal.net> - 2015-12-01 10:57 -0600
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-12-01 18:08 +0000
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                Re: Why is the universe 13.8 milliards years old ? alsor@interia.pl - 2015-12-01 14:14 -0800
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-12-02 16:09 +0000
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-11-30 20:52 +0000
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-11-30 15:07 -0800
                Re: Why is the universe 13.8 milliards years old ? alsor@interia.pl - 2015-11-30 17:10 -0800
                Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-12-01 07:30 +0100
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-01 04:13 -0800
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-12-01 18:15 +0000
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-12-01 18:15 +0000
                Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-12-01 22:33 +0100
                Re: Why is the universe 13.8 milliards years old ? Carl Heinz Krüger <heinzkrueger@ubernetz.org> - 2015-12-01 21:47 +0000
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-01 14:57 -0800
                Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-12-02 07:30 +0100
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-02 03:12 -0800
                Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-12-02 15:25 +0100
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-02 06:39 -0800
                Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-12-02 15:57 +0100
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-02 08:25 -0800
                Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-12-02 17:50 +0100
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-02 12:06 -0800
                Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-12-02 22:28 +0100
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-02 14:25 -0800
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-12-03 16:20 +0000
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-03 08:23 -0800
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-12-02 16:29 +0000
                Re: Why is the universe 13.8 milliards years old ? Gary Harnagel <hitlong@yahoo.com> - 2015-12-02 12:10 -0800
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-12-02 16:26 +0000
                Re: Why is the universe 13.8 milliards years old ? Henry Wilson <HGW@home.com> - 2015-12-02 16:21 +0000
      Re: Why is the universe 13.8 milliards years old ? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-11-24 10:25 +0000

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