Question about photon energy
Posted: Wed Feb 22, 2017 6:56 pm
Yesterday I did some quick calculations of photon energies. I was curious the scale at which the 1/1 vibrational motion exists - because presumably you cannot have photons emitted in between energies (ie between 1/1 and 1/2 or 1/1 and 2/1) unless it is doppler shifted, so if this scale is somewhere in some reasonable energy range it might be possible to check to see if this is the case.
So far I have read through NBM up to the chapter on cosmic rays. It wasn't entirely clear to me how you convert the energy in the s/t notation to an energy in conventional units. At first I tried the natural unit of energy conversion factor (1.49e-3 ergs) multiplied by s/t. Then I compared this value with the value calculated if I use h * s/(t*t_nat), where h is planck's constant and t_nat is the natural unit of time (1.52e-16 s). I was off by a fairly large factor between the two, so I looked at Nehru's paper on calculating planck's constant - http://reciprocalsystem.org/PDFa/Theore ... Nehru).pdf. Turns out if you use the energy conversion factor for the natural units you need to multiply by s_nat which is the natural unit of space (because planck's constant absorbs this factor due to the fact that current theory views the energy of the photon as a function of its frequency and has no concept of temporal coordinates) and divided by the interregional ratio modified by a secondary mass factor. The reasoning for the interregional ratio is that the motion of the photon is within one unit of space (direction reversals are happening in time).
So if this is the case, why does one need the interregional ratio to modify s/1 type vibrations? If you didn't have this modification, wouldn't there be a very large gap in energies between 1/2 1/1 and 2/1? Also, presumably 1/1 would not need this modification either? I guess by Nehru's reasoning, the motion in time for the s/1 type vibrations are accomplished via direction reversals in space, thus the same factor is needed there too?
Here are the results (using h*s/(t*t_nat) ) for the energies around 1/1:
s/t | Energy [eV]
9/1 2.4477e+02
8/1 2.1757e+02
7/1 1.9038e+02
6/1 1.6318e+02
5/1 1.3598e+02
4/1 1.0879e+02
3/1 8.1590e+01
2/1 5.4393e+01
1/1 2.7197e+01
1/2 1.3598e+01
1/3 9.0655e+00
1/4 6.7992e+00
1/5 5.4393e+00
1/6 4.5328e+00
1/7 3.8852e+00
1/8 3.3996e+00
1/9 3.0218e+00
If this is correct, then we would expect to see gaps around 27.2 eV in terms of possible gamma energies... that doesn't seem right given that this is the UV range.
What is interesting is that 1/2 is 13.6 eV (a consequence of using the Rydberg frequency to set the units) - we know that -13.6 eV is the ground state energy of the electron in the hydrogen atom. In other words, a 13.6 eV gamma, if absorbed by the electron, will ionize the hydrogen atom - turning it into a proton and a free electron. Now in the RS, I *think* this would be as follows (using the single displacement notation):
(1/2) + M 1.5-1.5-(2)
Here we have a few options; from what I understand from NBM, the gamma will get rotated in a probabilistic fashion. Since the hydrogen atom has rotations in each dimension, I think it will either transfer the magnetic or electric rotation depending on which is orthogonal to the photon's translational motion.
If the electric rotation is transferred, then you have
C 0-0-0 + M 1.5-1.5-(1).
Since M 1.5-1.5-(1) is unstable (I think? need to look into this more; not sure what this particle is), a unit of magnetic rotation will be transferred so you end up with
C .5-.5-0 + M 1-1-(1)
C .5-.5-0 is also unstable because you have a negative rotational base with a positive rotational displacement.
That option seems unlikely because of the instability of the products; I wonder if this modifies the probability of this occurrence, or if all possibilities are allowed to occur and within one unit of time the unstable products will dissociate back to their previous components, with the photon exiting in a random direction thus looking like an elastic scatter. Here I'd like to make a quick aside: assuming one can properly calculate the probabilities of these different possibilities, one should be able to convert them to cross sections given the appropriate geometric factors.
The next option is that a unit of positive magnetic rotational displacement gets tranferred to the photon. The problem with this is that the photon is already vibrating with a positive displacement, so it would immediately decay.
Neither of these scenarios result in ionization of the hydrogen atom. Is it possible that I calculated my energies incorrectly? I notice, however, that the 2/1 photon would properly ionize:
(2/1) + M 1.5-1.5-(2) → M 0-0-0 + M 1-1-(2) → M 0-0-(1) + M 1-1-(1)
Which gives us the desired result; a proton and an electron. What if the electric displacement gets transferred instead? Here we have the inverse of the 1/2 case, the negative rotation + negative vibration is unstable and will dissociate immediately. So for this case it seems the only option is ionization (assuming the motions line up properly). So why doesn't 2/1 have an energy of 13.6 keV? What am I missing here? Any insights are greatly appreciated!
Perhaps the missing ingredient I need is charge? I haven't reached this part of NBM yet, so I will update once I do.
So far I have read through NBM up to the chapter on cosmic rays. It wasn't entirely clear to me how you convert the energy in the s/t notation to an energy in conventional units. At first I tried the natural unit of energy conversion factor (1.49e-3 ergs) multiplied by s/t. Then I compared this value with the value calculated if I use h * s/(t*t_nat), where h is planck's constant and t_nat is the natural unit of time (1.52e-16 s). I was off by a fairly large factor between the two, so I looked at Nehru's paper on calculating planck's constant - http://reciprocalsystem.org/PDFa/Theore ... Nehru).pdf. Turns out if you use the energy conversion factor for the natural units you need to multiply by s_nat which is the natural unit of space (because planck's constant absorbs this factor due to the fact that current theory views the energy of the photon as a function of its frequency and has no concept of temporal coordinates) and divided by the interregional ratio modified by a secondary mass factor. The reasoning for the interregional ratio is that the motion of the photon is within one unit of space (direction reversals are happening in time).
So if this is the case, why does one need the interregional ratio to modify s/1 type vibrations? If you didn't have this modification, wouldn't there be a very large gap in energies between 1/2 1/1 and 2/1? Also, presumably 1/1 would not need this modification either? I guess by Nehru's reasoning, the motion in time for the s/1 type vibrations are accomplished via direction reversals in space, thus the same factor is needed there too?
Here are the results (using h*s/(t*t_nat) ) for the energies around 1/1:
s/t | Energy [eV]
9/1 2.4477e+02
8/1 2.1757e+02
7/1 1.9038e+02
6/1 1.6318e+02
5/1 1.3598e+02
4/1 1.0879e+02
3/1 8.1590e+01
2/1 5.4393e+01
1/1 2.7197e+01
1/2 1.3598e+01
1/3 9.0655e+00
1/4 6.7992e+00
1/5 5.4393e+00
1/6 4.5328e+00
1/7 3.8852e+00
1/8 3.3996e+00
1/9 3.0218e+00
If this is correct, then we would expect to see gaps around 27.2 eV in terms of possible gamma energies... that doesn't seem right given that this is the UV range.
What is interesting is that 1/2 is 13.6 eV (a consequence of using the Rydberg frequency to set the units) - we know that -13.6 eV is the ground state energy of the electron in the hydrogen atom. In other words, a 13.6 eV gamma, if absorbed by the electron, will ionize the hydrogen atom - turning it into a proton and a free electron. Now in the RS, I *think* this would be as follows (using the single displacement notation):
(1/2) + M 1.5-1.5-(2)
Here we have a few options; from what I understand from NBM, the gamma will get rotated in a probabilistic fashion. Since the hydrogen atom has rotations in each dimension, I think it will either transfer the magnetic or electric rotation depending on which is orthogonal to the photon's translational motion.
If the electric rotation is transferred, then you have
C 0-0-0 + M 1.5-1.5-(1).
Since M 1.5-1.5-(1) is unstable (I think? need to look into this more; not sure what this particle is), a unit of magnetic rotation will be transferred so you end up with
C .5-.5-0 + M 1-1-(1)
C .5-.5-0 is also unstable because you have a negative rotational base with a positive rotational displacement.
That option seems unlikely because of the instability of the products; I wonder if this modifies the probability of this occurrence, or if all possibilities are allowed to occur and within one unit of time the unstable products will dissociate back to their previous components, with the photon exiting in a random direction thus looking like an elastic scatter. Here I'd like to make a quick aside: assuming one can properly calculate the probabilities of these different possibilities, one should be able to convert them to cross sections given the appropriate geometric factors.
The next option is that a unit of positive magnetic rotational displacement gets tranferred to the photon. The problem with this is that the photon is already vibrating with a positive displacement, so it would immediately decay.
Neither of these scenarios result in ionization of the hydrogen atom. Is it possible that I calculated my energies incorrectly? I notice, however, that the 2/1 photon would properly ionize:
(2/1) + M 1.5-1.5-(2) → M 0-0-0 + M 1-1-(2) → M 0-0-(1) + M 1-1-(1)
Which gives us the desired result; a proton and an electron. What if the electric displacement gets transferred instead? Here we have the inverse of the 1/2 case, the negative rotation + negative vibration is unstable and will dissociate immediately. So for this case it seems the only option is ionization (assuming the motions line up properly). So why doesn't 2/1 have an energy of 13.6 keV? What am I missing here? Any insights are greatly appreciated!
Perhaps the missing ingredient I need is charge? I haven't reached this part of NBM yet, so I will update once I do.