A few simple questions:

1) Whats the exact value of Hydrogen line?
2) And under what condition(s) is this value holds true?

Regards,
Jay Bala.

On Jul 13, 3:35 am, Jay Bala wrote:
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.

Jay Bala wrote:

A few simple questions:

1) Whats the exact value of Hydrogen line?
2) And under what condition(s) is this value holds true?

Regards,
Jay Bala.

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

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 wrote:

The "21 cm" hyperfine transition is 1.4204057517667 GHz.

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 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
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

On Jul 18, 12:07 pm, Richard Saam wrote:
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 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.

Chalky wrote:
On Jul 18, 12:07 pm, Richard Saam wrote:
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 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)


In terms of the 21 cm hydrogen line,

http://en.wikipedia.org/wiki/Hydroge..._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

On Jul 24, 8:25 pm, Richard Saam wrote:
Chalky wrote:
On Jul 18, 12:07 pm, Richard Saam wrote:
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 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)

In terms of the 21 cm hydrogen line,

http://en.wikipedia.org/wiki/Hydroge..._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.


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.

On Jul 24, 8:25 pm, Richard Saam wrote:
Chalky wrote:
On Jul 18, 12:07 pm, Richard Saam wrote:
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 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)

In terms of the 21 cm hydrogen line,

http://en.wikipedia.org/wiki/Hydroge..._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.

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

Chalky wrote:

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