Doppler Shift and the Principle of Relativity
Principle of Relativity: Most people understand that if two ships are far from land, it is impossible to tell which is moving simply by observing one from the other. Any motion relative to the sea can be detected by the wake or bow wave, but the sea is providing a third frame of reference.
Similarly we know a plane is moving through air which also provides a third reference frame, but anybody that has ever flown and looked down at the ground sees the ground moving beneath them. In the immense void of space the same rule applies. We cannot tell if the other ship is moving or we are moving, all we can say is that there is relative motion between us and the other ship. In this animation this principle is demonstrated, and the source of light is a star.
The 3rd image above would apply if there were any aether, but none has been detected. The 4th image is impossible, it would imply the ship caused the light from the star to change by it's own motion and is therefore a violation of physics and the Principle of Relativity.
Note that only if the star accelerates can there be any change in the concentric circles, which having left the star are then independent of any motion the star may have.
Doppler Shift:
According to Professor Christian Andreas Doppler of the University of Vienna, competent mathematician and physicist,
Source:
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Doppler.html
NOTE that u, the greek letter 'nu' representing frequency, is not the roman letter v representing velocity.
According to Albert ('God of physics' to many) Einstein, who in 1895 failed an examination that would have allowed him to study for a diploma as an electrical engineer at the Eidgenössische Technische Hochschule in Zurich (couldn't even pass the SATs),
which is Doppler's equation divided by Einstein's cuckoo malformation.
Source: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Einstein.html
Let us program a spreadsheet for comparison. We'll use 8 Hz and let f remain zero, since the symbol f can be misinterpreted as angle of phase and as angle of the incidence. We'll let v = 0 as a check, and of course
This necessitates the removal of x.
This is simple:
yielding t in its perspicacious form.
z
Now we'll enter in a velocity and see what happens. For simplicity I'll use v = 0.866c where c is the velocity of light.
Where are the missing cycles?
Well, of course they never happened, they also represent Stella's heartbeats in 6 or 7 seconds and she doesn't age as much as Terence - See 'Twin Paradox' from the index page and the explanation from the incompetent phuckwit Professor John Baez of University of California, Riverside. Curiously, Terence notices a frequency from Stella that never happened that is double the frequency Doppler predicts.
For -0.866c:
For v = 0.99c, in agreement with experience we further assume Einstein's statement
"It follows from these results that to an observer approaching a source of light with the velocity c, this source of light must appear of infinite intensity"
to be accurately modelled here:
Persons of mathematical competence may download
http://www.androcles01.pwp.blueyonder.co.uk/Wave.xls
and check the veracity of the spreadsheet.