Electronics and Nanotechnology, April 12-14, 2011, Kyiv, Ukraine
5
Doppler Effect and Absolute Motion
O.A. Vityaz
National Technical University of Ukraine “Kiev Polytechnic Institute”, e-mail: [email protected]
Abstract – evidence of insolvency of the special
relativity theory postulate on the equality of
inertial frames of reference is provided based
on a Doppler effect analysis. A cinematic
equation describing the motion in a medium
excited by a moving source is derived.
Keywords – absolute motion, state of the rest,
medium perturbation, medium disturbance,
space period, space event, simultaneity in
space.
I. INTRODUCTION
The world consists of matter. Space and time
are needed to describe the motion of matter. One
example of how the matter behaves in space and
time is the effect discovered by Christian Doppler in
1842 and named after him.
The classical formulation of the Doppler effect
is the following: frequency of vibrations of a
medium detected by an observer differs from the
frequency of a signal source if the source and the
observer are in a relative motion. A theoretical
study of this effect traditionally involves two inertial
frames of reference. The first is associated with a
moving signal source, and the second is
associated with a moving observer. However, the
medium perturbed by the source is also involved in
motion and should be taken into account. To
describe the law of medium perturbation, time is
required.
Motion of medium has a special feature. The
medium, free from external actions, comes to a
motionless state, while a material body, free from
external actions, continues to move. Consequently,
there are two kinds of motion, a real motion of the
material body and a motion of the disturbed
medium. To describe these types of motion, space
is needed.
Motion of the material body is characterized by
the direction of displacement. The disturbance of
medium
takes
place
in
all
directions
simultaneously. Both types of motion are
characterized by speed. The speed of perturbation
propagation in a homogeneous isotropic medium is
constant and it is a property of the medium. The
velocity of a body may vary and it is a characteristic
of the motion in space.
We show that the classical formulation does
not reveal all the essence of the Doppler effect.
II. PERTURBATION AND DISTURBANCE
Motionless medium is different from a disturbed
one by the fact that all physical parameters that
characterize the state of the medium are constant.
The value of any physical parameter characterizing
the medium is the same at any time at any point of
space occupied by the medium. This state of
medium is called the state of the rest. Disturbance
of medium due to perturbation by a source at some
point in space means that some parameter of
medium at this point starts to change its value over
time.
A time instance when the source began to
change a value of the medium parameter is called
the initial time instance. The subsequent change of
the parameter value at this point is the process of
the medium perturbation. Change of the parameter
value in space is the process of the medium
disturbance. The process of the medium
disturbance depends on the medium properties.
The perturbation process depends on the
properties of the source and its interaction with the
medium.
The process of medium perturbation at a point
of space can be described as a function of time.
Fig 1a shows an example of the process, where  e
is the perturbation duration. Excitation, the duration
of which is equal to zero, is called an event (see
Fig 1b), where  (t) is the impulse Dirac function.
Such impulse excitation of a homogeneous
isotropic medium causes a spherical wave
disturbance that can be called as a medium
impulse characteristic. This characteristic can be
used for coordination of clocks in space.
Using the analysis of events propagation in
space the cinematic equation of motion is derived.
III. CONCLUSION
Each of the two popular theories of physics is
based on a pair of postulates:
• classical mechanics is based on the postulates of
the absoluteness of time and the relativity of
velocity;
• special relativity is based on the postulates of the
absoluteness of velocity and the relativity of time.
In this paper through the Doppler effect
analysis it is shown that a justifiable pair of
postulates is the absoluteness of time in space and
the absoluteness of velocity in medium, and hence,
the absoluteness of motion as such. What the
medium is – air, ether, vacuum, or dark matter – it
does not matter.
p
p
e
  S( e ) (t)
p(t)
S( e )   p(t)dt
0
0
e
t
0
t
a
b
Fig. 1. Medium perturbation: a) continuous finite
excitation; b) Dirac impulse excitation.