Abstract

The non-linear Doppler effect shows that the acceleration is able to change the spectral image of the sample significantly. The effect may have great influence on cosmologic theories due to Hubble dilatation of space. The recent examination of the Fine structure constant shows that the constant was not being stable over the time. One explanation is that the acceleration of the dilatation of space has influence on it so we may conclude that it was changing over the time. The goal of the text is following formula:

(6)

Above formula shows that the Doppler effect is connected to all derivatives not with the just first one.

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FREQUENCY SHIFT THAT IS CAUSED BY OBSERVER MOVEMENT

Watching the wave itself we can conclude that next equation is valid:

(1)

Whereas:

- c
- = speed of light,
- f
- = the source frequency,
- f
_{0}- = the frequency noticed by observer,
- v
- = velocity of observer related to source.

Regarding the Taylor series we have:

(2)

Thus it can be written:

(3)

Further is obtained:

(4)

As the following formula is valid:

(5)

It is obtained the final implicit formula of frequency shift:

(6)

Approximation with first two items, velocity and acceleration, of the Taylor approximation of the previous formula has practical application:

(7)

Further is obtaining:

(8)

Whereas:

- c
- = speed of light,
- f
- = the source frequency,
- f
_{0}- = the frequency noticed by observer,
- v
- = velocity of observer related to source,
- a
- = acceleration of the observer related to source.

It can be solved on **f**:

(9)

It is interesting that acceleration causes non-linear deformation of the spectrum
and thus the spectrum of the chemical elements may be deformed significantly by strong acceleration.

The approximation is:

(10)

The less accurate approximation yields:

(11)

It can be notices that the frequency spectrum could be changed only by acceleration,
and that may explain the change of a constant of the fine structure.

The formula (9) can be used for
derivation of third Newton low.

DERIVATION OF THE THIRD NEWTON LAW

Lets us start from formula for light momentum:

(12)

Whereas:

- h
- = Planck constant,
- P
- = photon momentum,
- c
- = speed of light,
- v
- = scalar velocity of source related to observer,
- f
_{0}- = original frequency.

⇒

(13)

Where is:

In approximation:

(15)

The formula shows that the Doppler effect is sufficient for theoretical derivation of
the ^{th}

Author of this article is Andrija S. Radović,

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Author:

Dipl.-Ing. Andrija S. Radović

Tel: +381 64 1404075