Exact value of Hydrogen line?
Jay Bala
1) Whats the exact value of Hydrogen line?
2) And under what condition(s) is this value holds true?
Regards,
Jay Bala.
Chalky
> A few simple questions:
>
> 1) Whats the exact value of Hydrogen line?
> 2) And under what condition(s) is this value holds true?
There are lots of them. See eg http://en.wikipedia.org/wiki/Hydrogen_spectral_series
If you mean the H-alpha line, it is given to 6 sig. fig. at
http://en.wikipedia.org/wiki/H-alpha
Exact value would be what you would expect to see if emitter and
detector are in the same state of motion at essentially the same
location.
Uncle Al
At rest with respect to the observer in vacuum. Which hydrogen line?
The "21 cm" hyperfine transition is 1.4204057517667 GHz. The H-alpha
transition is 656.281 nm. There are lots more.
http://en.wikipedia.org/wiki/Hydrogen_spectral_series
http://en.wikipedia.org/wiki/Lyman_series
etc.
The Lyman transition is 121.6 nm - and it's a doublet, n = 2 orbital,
j = 1/2 and j = 3/2.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Jay Bala
c/f= gives just a little over 21 cm right?
Also, what is the measurement error of this frequency?
Considering the time (seconds) and length (meters) are man made
numbers, is there some measurements or ratios that expresses these
values where these units cancel?
Regards,
Jay Bala.
Richard Saam
delta E delta t => h/(4pi)
delta (h*f/2) * delta t => h/(4pi)
delta (f) * delta t => 1/(2pi)
delta t is the life time of the excited state
delta E is energy of transition
which is extremely long in case of the 21 cm line
as observed in the astrophysical context
making its "natural width" very small
as Uncle Al's number would imply.
Richard D. Saam
Chalky
> Jay Bala wrote:
> > Lets take the hyperfine, appears to be a basic and simpler model,
>
> > c/f= gives just a little over 21 cm right?
>
> > Also, what is the measurement error of this frequency?
>
> > Considering the time (seconds) and length (meters) are man made
> > numbers, is there some measurements or ratios that expresses these
> > values where these units cancel?
>
> > Regards,
> > Jay Bala.
>
> > On Jul 13, 5:42 pm, Uncle Al <Uncle...@hate.spam.net> wrote:
>
> >> The "21 cm" hyperfine transition is 1.4204057517667 GHz.
>
> The "natural width" is determined by Heisenberg Uncertainty
>
> delta E delta t => h/(4pi)
>
> delta (h*f/2) * delta t => h/(4pi)
>
> delta (f) * delta t => 1/(2pi)
>
> delta t is the life time of the excited state
> delta E is energy of transition
This doesn't sound right.
Delta t relates to the length of the wave train, hence the duration of
the transition, not the lifetime of the excited state, before it
relaxes.
Delta E relates to the spread of frequencies in the wave train, not to
the energy of the transition (which determines the centre frequency)
It is probably also worth mentioning that this "tight" uncertainty
constraint of h/(4pi) applies when the uncertainty is defined as the
standard deviation (sigma) for each component. Hence a more
conservatively meaningful interpretation of the duration of the wave
train would be 2 sigma....wouldn't it? You would then have nearly a
70% (fighting) chance of finding it somewhere in the range where you
think it is.
Richard Saam
In terms of the 21 cm hydrogen line,
http://en.wikipedia.org/wiki/Hydrogen_line#Cause_of_the_hydrogen_line
"This transition is highly forbidden with an extremely small probability
of 2.9E−15 /sec. This means that the time for a single isolated atom of
neutral hydrogen to undergo this transition is 1/2.9E−15 or 3.4E14 seconds"
from above:
delta f * delta t => 1/(2pi)
delta f * 3.4E14 => 1/(2pi)
delta f => 4.68E-16 Hz
The above observed significant digit frequency
1.4204057517667 GHz = 1,420,405,751.7667 Hz
Apparently other effects (doppler )
are broadening the width beyond the
natural lifetime Heisenberg uncertainty line width.
Richard D. Saam
Chalky
> neutral hydrogen to undergo this transition is 1/2.9E-15 or 3.4E14 seconds"
>
> from above:
>
> delta f * delta t => 1/(2pi)
>
> delta f * 3.4E14 => 1/(2pi)
>
> delta f => 4.68E-16 Hz
>
> The above observed significant digit frequency
>
> 1.4204057517667 GHz = 1,420,405,751.7667 Hz
>
> Apparently other effects (doppler )
> are broadening the width beyond the
> natural lifetime Heisenberg uncertainty line width.
The observed error margin is ~ 5 E-5
The theoretical error margin is ~ 5 E-16
Just as the theoretical error margin requires an emission time of ~ 10
million years, the same applies for the required detection time. The
difference between the 2 error margins is ~ E 11 corresponding to a
required detection time of ~ 1 hour. This sounds reasonable.
Chalky
> neutral hydrogen to undergo this transition is 1/2.9E-15 or 3.4E14 seconds"
>
> from above:
>
> delta f * delta t => 1/(2pi)
>
> delta f * 3.4E14 => 1/(2pi)
>
> delta f => 4.68E-16 Hz
>
> The above observed significant digit frequency
>
> 1.4204057517667 GHz = 1,420,405,751.7667 Hz
>
> Apparently other effects (doppler )
> are broadening the width beyond the
> natural lifetime Heisenberg uncertainty line width.
These figures do seem to make a nonsense of the idea that del t in the
uncertainty relationship also represents the time window needed to
observe the radiation to that accuracy of resolution.
Clearly we haven't had mirowave detectors on Earth for 10 million
years, or even for the thousand years or more needed for the observed
(lesser) resolution.
I'm not sure how that point is resolved.
C
Richard Saam
>
> The observed error margin is ~ 5 E-5
> The theoretical error margin is ~ 5 E-16
>
> Just as the theoretical error margin requires an emission time of ~ 10
> million years, the same applies for the required detection time. The
> difference between the 2 error margins is ~ E 11 corresponding to a
> required detection time of ~ 1 hour. This sounds reasonable.
>
It would be interesting to know
if the observational error margin ~ 5 E-5 Hz
in the observed frequency of astrophysical hydrogen 21 cm
1.4204057517667 GHz = 1,420,405,751.7667 Hz
represents a limit
below which astrophysical electromagnetic frequencies
cannot be observed.
Are any electromagnetic waves observed below 5 E-5 Hz ?
Richard D. Saam
Jay Bala
Regards,
Jay Bala.
Chalky
In principle, yes, but we are now straying into areas of practical
eletronics. If it were possible to produce a sufficiently high Q tuned
filter to admit a still tighter pass band, then that would pick out
which ever frequency it was tuned to. However, you would still end up
with the pulse from fthe filter being ten times as long if the spread
was reduced by a factor of ten.
Richard Saam
1/ 5 E-5 Hz = 20,000 seconds (333 minutes) (5.6 hours)
may be an extreme test of practical electronic instrumentation,
but given such practical electronic instrumentation:
Are any electromagnetic astrophysical waves observed below 5 E-5 Hz ?
Richard D. Saam
Chalky
The point is that ALL frequencies within this range exist, via Fourier
analysis.
A 5.6 hour aperture for an astrophysical source would introduce
serious Doppler shifts due to the Earth's rotation. This would broaden
not narrow the spectrum (unless you, personally, are prepared to
finance a radio observatory at the South Pole)
Richard Saam
From where was the frequency range observed
(including the +/- 5 E-5 Hz)?
1.4204057517667 GHz = 1,420,405,751.7667 Hz
The fundamental question is:
What broadens the Heisenberg Uncertainty 5E-16 Hz to 5E-5 Hz?
Chalky
I have already answered that. The limited time available to make the
observation.
Chalky
Given that hydrogen is the simplest thing to model theoretically, I
would not be too surprised if it turns out to have been derived from
theory.
> The fundamental question is:
> What broadens the Heisenberg Uncertainty 5E-16 Hz to 5E-5 Hz
Under that theoretical scenario, that would be the limit of accuracy
of the theoretical model.
Ulf Torkelsson
>
> Are any electromagnetic astrophysical waves observed below 5 E-5 Hz ?
>
order of some kHz, which means that electromagnetic waves of lower
frequency will be rapidly damped out. Of course, any observatory that
we build will at least be located inside the solar wind, and usually
even inside the Earth's ionosphere, where the plasma frequency is even
higher (MHz in case of the ionosphere), which sets the lower limit on
the frequency of astrophysical electromagnetic waves that we can observe.
Ulf Torkelsson
Richard Saam
Yes, there are these plasma frequencies as you describe but:
What is the 'rapidly damped out' time of other incident frequencies
and can this dampening be used as an observational tool?
Assuming there is some type of ~1E-5 hz astrophysical generator
(dark matter and/or energy as in post 'hypothesis for dark matter'),
do we see these plasma frequency damping out effects
on a complementary frequency order of 1E-5 hz (or harmonics thereof)
in accordance with the following observations:
***D. Saul Davis, Paul Hickson, Glen Herriot, Chiao- Yao She Temporal
variability of the telluric sodium layer Science 24
http://arxiv.org/abs/astro-ph/0609307
***K. Pounds , R. Edelson, A. Markowitz, S. Vaughan X-ray Power Density
Spectrum of the Narrow Line Seyfert1 Galaxy Akn 564,
http://arxiv.org/abs/astro-ph/0101542
***Kotov V.A., Lyuty V. M., Haneychuk V. I. :
"New evidences of the 160-minute oscillations
in active galactic nuclei", 1993,
Izv. Krym. Astrofiz. Obs., Tom 88, p. 47-59.
***Interstellar scintillation of AGN
http://www.jive.nl/science/iss.html
***Kiwamu Nishida, Naoki Kobayashi, Yoshio Fukao Resonant Oscillations
Between the Solid Earth and the Atmosphere Science 24 March 2000 Vol.
287. no. 5461, pp. 2244 – 2246
and perhaps these damping effects result in tidal forces
of a magnitude to affect planetary flybys:
***John D. Anderson, James K. Campbell, Michael Martin Nieto,
The energy transfer process in planetary flybys
http://arxiv.org/abs/astro-ph/0608087
and cause the anomalous Gravity Probe B Polhode motions of superconductor
supercurrents:
***Gravity Probe B Gyro #1 Polhode Motion Animations
http://einstein.stanford.edu/Media/Polhode_motion-animation.html
Richard D. Saam
Ulf Torkelsson
> Ulf Torkelsson wrote:
>> Richard Saam skrev:
>>> Are any electromagnetic astrophysical waves observed below 5 E-5 Hz ?
>>>
>> The typical plasma frequency of the interstellar medium is on the
>> order of some kHz, which means that electromagnetic waves of lower
>> frequency will be rapidly damped out. Of course, any observatory that
>> we build will at least be located inside the solar wind, and usually
>> even inside the Earth's ionosphere, where the plasma frequency is even
>> higher (MHz in case of the ionosphere), which sets the lower limit on
>> the frequency of astrophysical electromagnetic waves that we can
>> observe.
>>
>> Ulf Torkelsson
>>
>
> Yes, there are these plasma frequencies as you describe but:
> What is the 'rapidly damped out' time of other incident frequencies
> and can this dampening be used as an observational tool?
The electromagnetic waves become evanescent below the plasma
frequency and are damped out within at most a few wavelengths or periods
if you prefer to think in terms of the time scale. For that reason
there is no way of observing these waves from an astrophysical source.
Having said this though one should keep in mind that there are other
forms of waves that can propagate through a plasma at a frequency below
the plasma frequency, for instance Alfven waves. Such waves can be
measured in situ in the magnetosphere and the solar wind.
One should also keep in mind that although one cannot have an
electromagnetic wave at a frequency below the plasma frequency it is
possible to observe slow modulations in waves with higher frequencies,
which is the way a radio works.
>
> Assuming there is some type of ~1E-5 hz astrophysical generator
> (dark matter and/or energy as in post 'hypothesis for dark matter'),
> do we see these plasma frequency damping out effects
> on a complementary frequency order of 1E-5 hz (or harmonics thereof)
> in accordance with the following observations:
>
Assuming some new physics you can always explain any observation that
you want to explain, but most of the time the same phenomenon can also
be explained by more mundane mechanisms that are based on established
physics. As far as I can tell essentially all of the observations that
you list can be explained in the latter way, and sometimes it is even
possible to find more than one explanation based on conventional
physics, because there is insufficient data.
> ***D. Saul Davis, Paul Hickson, Glen Herriot, Chiao- Yao She Temporal
> variability of the telluric sodium layer Science 24
> http://arxiv.org/abs/astro-ph/0609307
>
> ***K. Pounds , R. Edelson, A. Markowitz, S. Vaughan X-ray Power Density
> Spectrum of the Narrow Line Seyfert1 Galaxy Akn 564,
> http://arxiv.org/abs/astro-ph/0101542
>
> ***Kotov V.A., Lyuty V. M., Haneychuk V. I. :
> "New evidences of the 160-minute oscillations
> in active galactic nuclei", 1993,
> Izv. Krym. Astrofiz. Obs., Tom 88, p. 47-59.
>
> ***Interstellar scintillation of AGN
> http://www.jive.nl/science/iss.html
>
> ***Kiwamu Nishida, Naoki Kobayashi, Yoshio Fukao Resonant Oscillations
> Between the Solid Earth and the Atmosphere Science 24 March 2000 Vol.
> 287. no. 5461, pp. 2244--2246
>
> and perhaps these damping effects result in tidal forces
> of a magnitude to affect planetary flybys:
>
> ***John D. Anderson, James K. Campbell, Michael Martin Nieto,
> The energy transfer process in planetary flybys
> http://arxiv.org/abs/astro-ph/0608087
>
> and cause the anomalous Gravity Probe B Polhode motions of superconductor
> supercurrents:
>
> ***Gravity Probe B Gyro #1 Polhode Motion Animations
> http://einstein.stanford.edu/Media/Polhode_motion-animation.html
>
The last two examples illustrate another problem. These are small
effects in highly complex experiments, which are also influenced by the
environment in a number of different ways, which might not even be
completely understood by the experimentalists themselves, since they
only have a limited knowledge of and control of the environment
surrounding their instruments.
Ulf Torkelsson
Richard Saam
On the subject of Alfen_wave:
http://en.wikipedia.org/wiki/Alfven_wave
"The ion mass density (ni mi) provides the inertia
and the magnetic field (B) line tension
provides the restoring force."
such that:
v = B / sqrt(4 pi ni mi)
v = velocity
B = magnetic field
ni = ion number concentration
mi = ion mass
mu = magnetic permeability
then:
mi v^2 ~ B^2 volume / (4 pi)
To which Enrico Fermi in 1949 nodded his head exclaiming "of course".
Eugene Parker
"Conversations on Electric and Magnetic Fields in the Cosmos
(Princeton Series in Astrophysics)"
does not say 'of course' could be applied
to an analogous argument for
an electric field (E) and its displacement (D) in that same 'volume'
mi v^2 ~ D E volume / (4 pi)
But if electric fields (E & D) as well as (H & B)
were involved as restoring forces,
all of the examples could be explained
in terms of gravitational tidal effects related
to a significant portion
of the observable universe critical mass (~1E56 g)
(dark energy dark matter?)
oscillating in accordance with these restoring forces
at ~1e-5 hz with a related van Alfen wave mechanism
As an aside, Eugene Parker makes a strong case
for the cgs system use in research analysis
because dimensional units are the same for E,D,H & B
(g ^ (1/2) cm ^ (-1/2) sec ^ -1)
and can be compared on that basis,
an attribute that does not exist in the SI system.
Richard D. Saam