Now I switch to a different venue for my thought experiment. It will involve two automobiles traveling down a smooth straight level section of turnpike. Each auto will set their cruise controls at a constant velocity, v, which they have agreed upon beforehand. Each driver has fully operational digital clocks, annoyingly loud horns, and bright halogen lights on board. It is dusk on a clear windless day.

As the convoy (a lead auto and a following auto) makes its way down the road, the pair are rolling in tandem with each other; neither accelerating, nor decelerating, relative to one another. They can be regarded as at rest relative to one other. However, the air is at rest relative to both autos as they are moving down the road (the air and road are both at rest relative to the autos).

So to check that they are a safe distance, L, apart (stopping distance at this speed) the driver of the following auto conjures up a test. She makes a hands free cell phone call to the driver in the lead car. When he answers she tells him her plan.

On a windless day they are rolling down the turnpike in tandem, thus they at rest relative to each other; but at the same time, they are in motion, at the same velocity, relative to the road and air. She proposes to flash her headlights as a signal to her comrade‘s auto. When he sees the light signal, he is to honk his horn. At the same that she flashes her lights, she starts her digital clock. Thusly, the time she measures, since the light signal is effectively instantaneous, will be for the horn sound to return to her:

The distance they are apart will not be L = ct, but rather L = ct + vt, where v is the velocity of the tandem relative to the road and still air (c is the velocity of sound). They will begin at the distance L apart, then her auto and the sound pulse will meet somewhere within L by algebra. This reflects the forward motion of her vehicle at the same time as the sound wave is traveling rearwards. This accounts for all the variables and determines the distance they are apart.

The pair travels on further, after checking their safe distance. Now, towards the end of their trip, they have reached the familiar environs near the exit for her town. He speeds up to a new constant velocity, u, to make time without risk of losing her. At this new velocity, he gradually pulls away from her. He will travel on to the next town alone. Then, she imagines a continuance for their little thought experiment.

As he is gradually separating, she realizes that the source (he) and the receiver (she) are no longer in tandem, now a Doppler effect appears because they are no longer traveling at the same speed. An aspect of Doppler (sound waves through air) is that when the source approaches the receiver, there is a slight mathematical difference than when the receiver approaches the source (introducing a sort of wind in either reference frame).

So if she makes the measurement of the change in frequency from her friend’s auto horn while he gradually separates from her, then she will find the source sound wave to have apparently changed frequency. She knows the frequency of the horn from when the autos are at rest relative to each other.

In other words she can determine the frequency of the sound of the auto horn while the autos are rolling in tandem (they are at rest relative to each other but moving at the same velocity relative to the air, so ff = f0 ). She can now discern whether she is in motion relative to the air, earth and his auto (which she thinks could be at rest); or whether the air (wind) , earth and his auto are in motion while she is at rest.

This can seen by a comparison of the two formulas that fit these two scenarios (the different frequencies can be used to solve for using their different velocities); if the frequency she measures is one value of f then she concludes that she is moving; if the frequency has some other value f, then she concludes she is at rest:

♦ f = [ c / (c + v_s)] f₀

♦ f = [(c + v_r ) / c] f₀

These formulae are clearly different, just by appearance. Therein, the nature of her motion is revealed. Either she is stationary, with the medium in motion; or she is in motion, with the medium being stationary. She has a mathematical means of determining this.

She can distinguish, by her thought experiment, whether the autos are in motion with the Earth stationary; or the autos are stationary, with the Earth in motion. This is contrary to the principles of relativity which state that both situations are equivalent, or equally valid descriptions of her motion, thus they are interchangeable in a way. But her thought experiment shows that this is unsound.

http://en.wikipedia..../Doppler_effect

http://gerrybharris.blogspot.com/