Red Shift is Due to the Doppler Effect . . . Isn't It ?
Copyright © 2004 - 2013 David V Connell.
We begin this analysis with the situations where there is a recessional velocity v between a light source and an observer, the distance between them commonly referred to as space. Most physicists, probably all, agree with the classical equation for the ratio of the predicted wavelength d of light emitted at speed c from a source and received by the above observer, to the wavelength do (when the rececessional velocity is zero). This classical ratio is
d/do = 1 / (1 - v/c) , (1)
provided that the speed of propagation of the light is not changed by an entity in the intervening space, so the waves are therefore received at speed c-v. This formula predicts a red shift of the wavelengths, but does not agree with Einstein's claim regarding the speed being measured c by the observer.
Let the intervening space be the Frame of Reference (FoR). If it contains an external entity, such as an aether, that controls the speed of propagation to be also c (what a coincidence!), the emitted speed c from a stationary source will not be changed, and eq.1 above is applicable. But the speed of light received by a stationary observer from a receding source will be changed from c-v to c, causing the wavelength to be stretched by the increase in speed, and a different equation results, which is
d/do = 1 + v/c . (2)
Thus there are two different equations for the recessional situation. Eq.(1) assumes that there is no interference to the emitted speed of light, so that the speed of light propagation is c relative to its source. Eq.2 assumes that interference to the emitted speed takes place and that the speed of light propagation is c relative to the interfering entity and the observer, which is the situation assumed in most text books for deriving the equations.
The above equations were derived for a manuscript  submitted in 2004 to Nature and Europhysics Letters magazines, but not published. The manuscript went on to point out that eqs.1 and 2 were expected to be the same, since in relativity which one is moving is arbitrary, that the SRT method of producing a single equation to be used instead is invalid, and that eq.2 was clearly not true, leading to the downfall of SRT, as indicated below.
Equation 2 is clearly not true, for as v approaches c the ratio of wavelengths approaches the value 2, whereas eq.1 gives the expected infinite result. If it were true, astronomical evidence indicates that no stars or galaxies are receding from us, but we are receding from all of them ! Obviously impossible.
To replace eqs.1 and 2 with just one equation (this assumes an interfering entity exists), the arithmetic mean of, or the geometric mean of, the derived values could have been chosen.
The arithmetic mean, where x = v/c, is
1 + x + 1/2(x² + x³ +   + . . . . ) . (3)
The geometric mean is the square root of the product, or
((1+v/c)/(1-v/c)) 1/2 (4)
and the resulting adjustment factor is the sq.root of the ratio, or
(1- v²/c²)-1/2 (5)
Expression (4) is familiar as being the algorithm for the SRT Relativistic Doppler Effect and was chosen presumably because the adjustment factor (5) is the same as the mass ratio factor in SRT. What a coincidence! The lower value (1 + v/c) is multiplied by the factor, the other divided. The idea that any valid reason exists for doing that is refuted. Light is not mass, so it does not merit a relativistic change. That such a change appears to produce the required result is empirical and not a valid reason. Eq.1 is the only valid equation, is valid whichever participant is moving when there is no interfering entity. The results with an interfering entity do not comply with the principle of relativity.
This author has never seen a reference to the "time dilation/relativity" adjustment as being the "geometric mean" adjustment. (Perhaps no one else has noticed they are the same!).
An alternative would have been to discard the controlled light speed assumptions and use eq.1, when no adjustments would be necessary. But this would have invalidated SRT, so it didn't get done.
Equation (2) results only when the speed of light is assumed to be a constant in space independent of the speed of the source. Therefore, since eq.2 is obviously wrong, the assumption must be wrong and a basic assumption of SRT is invalid. This is confirmed by the fact that the velocity of light relative to a receding source would then be greater than c, and that is not allowed in SRT. So another fix had to be applied (that being the idea that the addition of velocities must never exceed the speed of light), and so on, to keep patching it up.
The Doppler Effect equations for relative approach of source and observer are obtained by changing the sign of v in the above equations.
If, someday, the measured speed of red shifted light is found to be c, then the red shift cannot be due to the Doppler Effect of relative recession and a different explanation must be sought. And the universe would not be assumed to be expanding. Several other origins of red shift are known, but are not adequate to explain the large shifts found. At least one more must exist if the Doppler Effect is to be challenged as the main cause. A possible, simple mechanism for this is offered below.
A Simple Mechanism for Non-Doppler Red Shift.
A commonly offered explanation of the red shift is that known as "tired light", which comes from the Planck equation E = hf, suggesting that a reduction in frequency f can be explained by a slow loss of energy E over long periods of time. Many theories of how this slow loss occurs have been developed, some being perhaps possible but rather complicated. This loss of energy accompanied by a reduction in frequency is difficult to explain when the model of a photon is considered. A simple mechanism for this does not readily suggest itself. But, an emitted photon has a fixed amount of energy which will not be changed by a detector moving relative to the source, and since a resulting (Doppler) red shift with no energy loss must still obey the same equation, it needs to be modified to E=hfe, where fe is the emitted frequency, and is shown in NR (Ref. 4) to be valid in all inertial frames of reference.
However, if the length of the photon increases slowly over long periods of time (it is already expanding at right angles to the direction of motion), then the frequency will slowly reduce (proportional to distance), but the total energy will stay the same.
In fact, a Doppler red shift also results from receiving a stretched photon with no loss of energy. If 'tired light' is also at work the red shift will be even greater and there will be some loss of energy. Do red shifted photons from distant galaxies have less total energy than when emitted? If not, the 'tired light' theory is eliminated. Have any experiments (photoelectric probably) been made to determine this?
Incidentally, papers purporting to detect an aether and also assume a light source is stationary in it (but don't say so), overlook the fact that the resulting equation for the wavelength ratio is independent of an aether, therefore do NOT confirm its existence. Other published papers, e.g. [2, 3] also indicate that Einstein's assumption regarding the velocity of light is invalid. A new theory of Relativity not using that assumption seems to be urgently necessary. This author has outlined the main results of such a theory (much simpler than SRT), on this website ("SR's Problems") and submitted the full theory for publication to a well known physics journal (subsequently published).
 David.V.Connell, "Errors in Physics Theory Affecting Astronomical Redshift and Relativity", 2004 (Not published).
 H.E.Ives, Proc.Am.Philos.Soc 95, 125, (1951).
 S.J.G.Gift, "The Invalidation of a Sacred Principle of Modern Physics", Phys.Essays 17.3, 338-341 (2004)
 David.V.Connell, "Natural Effects of Applied Energy, Motion and Gravity on Mass" Phys. Essays, 22, 3, 402-412(2009).
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