## APPENDIX 6: Doppler Shifts and the ZPE

(i). What is being Measured?

A varying ZPE, with an inversely varying c, calls into question what is being measured in the cases where there are genuine Doppler shifts involved rather than the cosmological redshifts of distant galaxies discussed above. It is expected that these Doppler effects will usually be non-relativistic at their point of origin. Consequently, the basic Doppler formula becomes

Δλ / λ  =  v/c      (125)

Here, λ is the laboratory wavelength and Δλ is the change in wavelength compared with the laboratory standard. The velocity producing the Doppler shift is given by v, while the speed of light is c. The relativistic counterpart can be found in reference [191]. It has the same primary term v/c as in (125) but also includes higher order terms.  Now it has been shown above that wavelengths remain unchanged in transit through space. Thus, apart from any ZPE induced red-shifting, the term Δλ remains unchanged in transit. The laboratory wavelength, λ, also remains unchanged. Thus the left hand side of equation (125) is independent of changing conditions in transit and depends entirely on conditions at the time of emission. If we now designate the speed of light at the time of emission as c1, and the velocity involved as being v1, then, retaining c as the velocity of light now and v the inferred velocity at reception, we can write (125) as

Δλ / λ  =  v1 /c1 =  v/c       (126)

From (126) it follows that

v1  =  v (c1/c)      (127)

Therefore, the actual velocity at the point of emission that we are measuring is (c1/c) times greater than the velocity v that we are inferring from the measurements. The practical outcome of this conclusion may be assessed by two examples.

(ii). Data From a Supernova

This conclusion is of some importance in view of data from supernova SN 1993J in M81 (NGC 3031). The rate of expansion of the supernova was observed in optical, radio and ultraviolet wavelengths. For example, optical spectroscopy using Doppler shifts of the blue edge of the hydrogen alpha line absorption trough determined the expansion rate based on a constant speed of light. These data gave a distance to M81 that closely agreed with Cepheid data [192-195]. But if c was higher at emission and slowed in transit, then we, the observers, were seeing those events in slow motion. However, the Doppler shift calculated on the current speed of light would exactly correspond with the observed sequence of events. This result is obtained since the actual velocity of expansion, v1, and the actual velocity of light, c1, were both proportionally greater. Because of this proportionality, the ratio (v1/c1) at the point of emission is still the same as the inferred (v/c) at reception, so measured Doppler velocities will always be in agreement with observed phenomena under conditions of varying ZPE & c.

(iii). Rotation Rates of Distant Galaxies

The other important conclusion is that galaxy rotation rates will be faster than suspected from the Doppler measurements. One aspect of this problem has already given rise to the idea of the ‘missing mass’ or ‘dark matter’, and has been dealt with in Appendix 3. However, this development with Doppler shifts has been seen as a distinct problem by some. There is an effective answer to this, and it comes from the Plasma Model of galaxy formation which was elaborated by Anthony Peratt in two major articles in the IEEE Journal of Plasma Physics. There, Peratt published photographs of experiments in the laboratory with plasma filaments and Birkeland currents [220].

The photographs reveal that every form of galaxy can be reproduced as a sequence starting with a double radio galaxy and a quasar and ending up with a spiral galaxy simply by the interaction of two or more plasma filaments. The interaction time governs the final form of the object [220]. The experiments demonstrate that the rotation rates of spiral arms in galaxies are not controlled by gravitation, but rather by the strength of the Birkeland current in the filaments [221]. The animated versions of the experimental photographs reveal this clearly [222]. As the current strength drops off, so, too, does the rotation rate of the spiral arms about the galaxy center. It has nothing to do with gravity and orbital mechanics. Thus when the Birkeland current strength is greater, the galaxy rotation rate is faster [223].

It is to be expected that the strength of the Birkeland currents would decline with time after the formation of the universe. For this reason alone, it would be expected that actual galaxy rotation rates would be faster the closer they are to the inception of the cosmos. This situation approximates to what we are seeing if the Doppler velocities are corrected for higher lightspeed at the time of emission. However, we can go further than this.

(iv). Electric Currents Expected to be Stronger With Lower ZPE

It can be shown that when the ZPE strength is lower and lightspeed is higher, then electric current strengths will be intrinsically greater. Equation (7A) shows that e2/ε = constant. Since the permittivity of space, ε is shown to be proportional to the ZPE strength, U, and hence to 1/c, then we have the strength of the electronic charge, e, being proportional to √U and hence to √(1/c). Thus the Hall resistance h/e2 is a constant from (2) and (7A). It can be shown that all resistances, R, generally follow this constancy with ZPE variation. Importantly, the expression for electrostatic force, F, is given by (e2/ε)[1/(4π r2)].

Now from (7A) it can be stated that F is a constant with varying ZPE since r is unchanged. But we also have F = eE = constant, where E is the electric field strength. Therefore the field strength, E, is proportional to √c.  Equation (4) indicates that we have symmetry between the electric and magnetic properties of space. Therefore the force between two parallel currents is constant. If those currents are of equal magnitude I, then the force is proportional to (μI2) and is constant. So from (4), the electric current, I, is proportional to √c. Furthermore, since F is proportional to IB, where B is the magnetic flux density or the magnetic induction, then it follows that B is proportional to √U and hence √(1/c). Now since electric currents, I, will be intrinsically higher with higher c values and lower ZPE strengths, then it follows that galaxy rotation rates will also be higher on the various Plasma Models for galaxies, This supports the evidence from galaxy Doppler shifts with changing c and ZPE.

(v). Implications for Plasma Models of the Sun

Intrinsically stronger currents in earlier epochs of the Universe have implications for other aspects of the Plasma Model that can only be touched on here. Along with stronger currents goes a higher voltage or potential, since voltage, V = IR, where R is resistance and I is current as above. Since we have shown that R is unchanged with changing ZPE strengths, then it follows that V is proportional to I. But since I is proportional to √(1/U), or the √c, so too is V.  In addition, since power, P, in an electrical circuit is given by the relation P = IV, it necessarily follows that this power must be proportional to 1/U or c.

This treatment means that, if the Plasma Model for the Sun is followed [224], then for a Birkeland current, I, and potential difference, V, this process has a power output, P, which is proportional to c. This is the same result as that obtained for the thermonuclear case treated in Appendix 2 (ii). Now equation (77) in Appendix 2 points out that the energy density of all radiation, ρ, is proportional to 1/c. This is still true on the Plasma Model. Furthermore, the radiation intensities (and hence stellar luminosities) are given by the quantity ρc [148-150] as in (86A). But ρc is constant for changing ZPE strength on both models, so stellar luminosities must also be constant in these conditions for both models. Thus the only two models which have been proposed for the Sun’s light output, the thermonuclear and the plasma approach, both give the same result. Note that a full discussion of how Plasma Models behave with a varying ZPE requires another paper.

References

[148]F.A. Jenkins & H.E. White, “Fundamentals of Optics” 3rd Edition, (McGraw-Hill, 1957). pp. 412-414.
[149] S. G. Starling & A. J. Woodall, “Physics,”  Longmans, (1958) 1129.
[150] A.P. French,op. cit., p.40. (see ref. #73)

[191]F.A. Jenkins & H.E. White, op.cit. p.403 (see ref.#148)
[192] W.L. Freedman et al., Astrophysical Journal, 427:2 (1994), pp. 628-655.
[193] N. Bartel et al., Nature, 368 (No. 6472), pp. 610-613 (1994).
[194] J.M. Marcaide et al., Nature 373(No. 6509), pp. 44-45, (1995).
[195] J.M. Marcaide et al., Astrophysical Journal, 486 (1997), pp. L31-L34.

[220] A.L. Peratt, IEEE Transactions on Plasma Science, Vol. PS-14 No.6 (Dec. 1986), pp. 639-778.
[221] D.E. Scott, op. cit., p.180. (see ref. #213)
[222] “Thunderbolts” – The Tutorial Part 1 - on CD Rom from Silver Wolf Productions & the Kronia Group (2006).
[223] D.E. Scott, private communication, 11th January 2007.
[224] D.E. Scott, op. cit., p. 90.(see ref. #213, linked above)

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