THE ONLY WAY TO SAVE SPECIAL RELATIVITY

If a light source emits pulses the distance between which is d (e.g. d=300000 km), an observer moving with speed v towards / away from the source measures the frequency of the pulses to be f'=(c±v)/d. Accordingly, the speed of the pulses relative to the observer is c'=c±v, in violation of special relativity.

There is an assumption allowing the speed of the pulses relative to the observer to remain unchanged (c'=c) while the measured frequency is still f'=(c±v)/d. However this assumption is extremely silly and clever Einsteinians would never advance it explicitly. Here it is:

The extremely silly assumption without which special relativity is doomed: When the observer starts moving towards / away from the light source with speed v, the distance between the pulses somehow shifts from d to d'=cd/(c±v), Divine Einstein, yes we all believe in relativity, relativity, relativity.

Pentcho Valev

The actual problem:

A light source emits pulses the distance between which is d (e.g. d=300000 km).

A stationary observer/receiver measures the frequency to be f=c/d; accordingly the speed of the pulses relative to him is c.

An observer/receiver moving with speed v towards the source measures the frequency to be f'=(c+v)/d; accordingly the speed of the pulses relative to him is:

c' = ?

The reasonable answer:

c' = df' = c + v

The unreasonable answer (given by special relativity):

c' = d'f' = c

where d'=cd/(c+v) is an ad hoc requirement without any physical meaning - it is just the factor able to convert the dangerous c'=c+v into the glorious c'=c, Divine Einstein, yes we all believe in relativity, relativity, relativity.

Pentcho Valev

http://www.hep.man.ac.uk/u/roger/PHY.../lecture18.pdf
Roger Barlow, Professor of Particle Physics: "The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. (...) Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/lambda waves pass a fixed point. A moving point adds another vt/lambda. So f'=(c+v)/lambda."

"In time t, ct/lambda waves pass a fixed point." That is, the speed of the waves relative to the fixed point is c.

"A moving point adds another vt/lambda." That is, in time t, (c+v)t/lambda waves pass the moving point, and the speed of the waves relative to the moving point is c'=c+v, in violation of special relativity.

In this interpretation of the Doppler frequency shift special relativity cannot be saved. If v is smaller than c/3 (for v=c/3 gamma is 1.05), the relativistic corrections are negligible and both f'=(c+v)/lambda and c'=c+v are virtually exact formulas.

Pentcho Valev

http://www.einstein-online.info/spotlights/doppler
Albert Einstein Institute: "The frequency of a wave-like signal - such as sound or light - depends on the movement of the sender and of the receiver. This is known as the Doppler effect. (...) Here is an animation of the receiver moving towards the source: (...) By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift - the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. This time, the distances between subsequent pulses are not affected, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened. In this particular animation, which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses."

That is, the speed of the pulses relative to the light source is c=3d/t and relative to the moving receiver is:

c' = c + v = 4d/t

where t is "the time it takes the source to emit three pulses", d is the distance between subsequent pulses and v=c/3 is the speed of the receiver relative to the light source. Clearly special relativity is violated.

The usual relativistic corrections cannot save special relativity - for v=c/3 gamma is 1.05 which makes c' even slightly greater than c+v.

The only (extremely silly) way to save special relativity is to ignore the phrase "the distances between subsequent pulses are not affected" and assume that these distances somehow shift from inertial frame to inertial frame so that the speed of the pulses relative to the moving receiver gloriously remains constant, Divine Einstein, yes we all believe in relativity, relativity, relativity.

Pentcho Valev