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It has been pointed out that there seems to be a mathematical inconsistency in the formulation of the redshift equations in
In equation (A), However, both the September 2007 and the December 2008 papers show that the strength of the ZPE is increasing and the reason why is elucidated there. These papers show that an increasing ZPE strength with time inevitably means that both If we now designate those whole multiples by the letter
In equation (B), the symbol (~) means “proportional to”. This equation means that orbit radii remain fixed as time increases until a whole multiple of
We can then substitute the results from (B) and (C.) back into equation (A). When we do this we find that, in order for equation (A) to balance, the rest-mass of the electron must obey the following proportionality
This is in accord with the observational data which has shown that sub-atomic masses are proportional to The physical reason why the electron rest mass increases at the jump can be found in the nature of the electron itself. Puthoff has shown [in his 11th May 2007 paper in the International Journal of Theoretical Physics, vol 46, pp.3005-3008] that there is a pressure within an electron which comes from its electronic charge which tends to expand its radius. However this is offset by the external pressure of the ZPE which keeps it intact. The equations show that, if the ZPE strength increases, there will be a moment when the external pressure overcomes the internal pressure and the actual electron point radius undergoes a quantum decrease which effectively gives a quantum increase in its mass. There is a reason why there is a mass increase as the electron size reduces. As noted in The quantum jump occurs at the moment when the internal pressure of the electronic charge can no longer resist the increasing Zero Point Energy. At that moment, the ZPE does not make any sudden change, but the 'straw that broke the camel's back' had just occurred and the electron finally reacts. The electron’s actual size has decreased (as distinct from its jiggle volume), and the electron will now resonate or jiggle to waves of a smaller wavelength. Because there are more ZPE waves of smaller wavelengths than longer wavelengths, this reduction in the actual electron size means that the greater numbers of smaller waves will cause the electron to jiggle more violently. This results in an increase in jiggle volume and mass. Let us now return to our redshift analysis. To check the equations so far, the proportionalities in the quantities in (C.) and (D) can be inserted into either equation (4-12) or (4-15) for electron orbit radii as given by M. R. Wehr and J. A. Richards in
will also balance with these proportionalities. In equation (E), the quantity Let us summarize the analysis to this point and show how this results in a redshift. As time progresses and the strength of the ZPE builds up, atomic orbits must adjust to the increased power available to them from the vacuum coupled with increased atomic masses. To offset these two changes, the atom adjusts by making a quantum change in the radii of atomic orbits. Thus, as time moves forward, the radius of each orbit decreases in a series of steps. Each step has the effect of making the orbits further apart. Calculation shows that this occurs because the outermost orbit has essentially no change in its radius, or at most a very minor change, while the innermost orbit moves the most. All other orbits move inwards in proportion. This diagram shows the inner two orbits of electrons in the elements involved, while the outer electrons are remaining at essentially the same distance from the nuclei. When an outside force excites an electron, forcing it out of its normal position relative to the nucleus, it will release the energy from that force as a photon of light when it snaps back into position. However, because the orbits are now further apart, there is a greater energy difference between them. This means the electron requires more energy to be forced into another position and thus will release more energy when it snaps back. The wavelength of light emitted from atoms depends on the energy difference between an outer orbit and an inner orbit as an electron 'falls' from one to the other. The greater the energy difference, the more energetic the photon, and thus the shorter the wavelength and the bluer the light that the electron emits. During the interval between quantum jumps, all orbit positions remain fixed, and so light emitted during that time will have a fixed wavelength. But, as time goes on, a quantum jump occurs, and all orbit radii then become less. The emitted light then becomes more energetic, not smoothly, but in a jump, so the wavelength of that light becomes shorter or bluer in a jump. This is why the redshift measurements are quantized. As we look farther out in space, and thus further back in time, we see that the light was LESS energetic before, and thus it appears red shifted compared to today's standard. The actual point is not so much that the light is 'red shifted' as we look back in time, but that is has become 'blue shifted' and more energetic (in jumps) as we approach our present time. This is a good time to remind the reader that the quantized red shifting is not seen inside of our local group of galaxies for the reasons given in the main paper. The quantized red shifts can be discussed in terms of physics. It needs to hold up mathematically. The equation for the energy of a given orbit can be written (as given by Wehr and Richards, op. cit. p.88 equation 4-18):
In equation (F), the radius of the orbit under discussion,
Therefore, as N increases with time, the magnitude of the orbit energy also increases. Electromagnetic radiation, including visible light, is emitted when an electron falls from an outer orbit to an inner orbit. The energy of the light emitted is equal to the difference in energy between the two orbits. If the outer orbit quantum number is given by
Now it has been shown in
In other words, as time moves forwards and the number of quantum transitions (given by
In equation (K), λ2 is our standard laboratory wavelength of a specific spectral line from an atom, while λ1 is the wavelength of the same spectral line emitted from a distant galaxy. But according to the approach adopted here, the wavelength of light emitted by a distant galaxy is only dependent upon the value of
This therefore means that
where
and that this accords with what has been published in the papers linked above. Therefore, it can be stated that, while the concept was right in |

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