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2nd article of the book "Great mistakes of the physicists"
(Edited May 3, 1999)
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Compton effect is a Doppler effect
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Abstract
--------
An electromagnetic wave with the wavelength L, which has some 
energy, descends on an electron and makes it move in the same direction
of propagation of the wave. The wave makes the moving electron oscillate
with a lower frequency. A very much simple analysis shows that this moving 
oscillating electron radiates, in the direction making angle T with the
direction of the descending wave, an electromagnetic wave which its
wavelength is bigger by a factor proportional to L(1-cosT). In this manner
we see that probably determination of the drift velocity of electrons in
electric currents is possible in practice.

I. Introduction
---------------
When an electromagnetic wave descends on a target, bound electrons of the 
target are made to oscillate with the same frequency of the descending 
wave. These oscillating electrons radiate electromagnetic waves in every
direction with the same frequency of their oscillation.

Further to these radiations, it is observed in practice that there is 
another electromagnetic wave with a wavelength longer than the 
wavelength of the descending wave. Difference between the wavelengths
of this wave and the descending wave is different in different
directions being proportional to the factor 1-cosT in which T is the
scattering angle (ie the angle relative to the line of propagation
of the descending wave in which the detector sees the target).

The empirical linear proportion of the above difference of the 
wavelengths to the factor 1-cosT is justified by the Compton's
reasoning in the form of 

<delta>L=L'-L=(h/(m0c))(1-cosT)                           (1)

in which it is assumed that the electromagnetic wave in the form of 
photon hits the electron and causes its recoiling.

What is intended by this article is obtaining the above mentioned 
empirical linear proportion in a simple classical manner. The use of
this act is that firstly no longer we can consider the Compton effect
as a quantum (and relativistic) phenomenon and recognize it among
the phenomena which only the quantum (or relativistic) physics is able
to justify them probably, and secondly the proportion of <delta>L   
to L will appear absence of which in Compton's reasoning has been
always surprising!

II. The reasoning
-----------------
Since an electromagnetic beam descending on a target has energy, it causes
that the relatively free valence electrons of the target start moving
into the target in the direction of propagation of the wave. Indeed we can
say that the beam gives energy to the gas molecules adjacent to the 
target causing their warmth or in fact local increase of their mobility
which in turn causes much impacts of them on the target. A part of these
impacts is transferred to the free electrons of the target and cause them 
to move towards the inside of the target in the direction of the wave
propagation. It is obvious that, when the descending beam is normal
to the target surface, since these impacts are in all possible directions,
the mean effect of them will be the motion of the free electrons of the
target in the direction of the incident beam. In fact motion of the 
electrons in this manner produces a kind of local closed electric current
which is not concerned here. (We must also believe in such a current in
Compton's reasoning produced by the recoiling electrons moving inwards.)

The wave descended on the target not only makes the bound electrons of
the target oscillate making scattered waves with the same wavelength
of the beam, but also makes  the free electrons moving towards the 
inside of the target oscillate. We are to study the mechanism of the
oscillation of the free electrons and the wavelengths produced by
them in different directions.

                                
                              /'
                            /, 
        i            s ___/__|
      ,--,            | /'
     /    \           /'T angle
   -/------\------/-*'====>
            \    /  e   v
             `--'
  Fig. 1

The wave i with the wavelength L descends on the electron e which is
moving in the same direction of the wave i with the speed v. We want
to obtain the oscillation frequency that the electron gains from the
wave i descending on it. The speed of propagation of the wave i is c.
Then, for obtaining the above mentioned oscillation frequency, we can
suppose that the electron is stationary but the wave i descends on it
with the speed c-v. Therefore, the frequency received by the electron
will be (c-v)/L.

Now we have an electron moving with the velocity v and oscillating with
the frequency (c-v)/L. It is obvious that such an oscillating electron
radiates electromagnetic wave. We want to obtain the wavelength of this
radiated wave in the direction related to the angle T.

Since the electron has the speed v in the direction of propagation of
the wave i, the situation is as if it has the speed vcosT in the
direction related to the angle T. Now it is sufficient to see which
wavelength will be radiated in the direction of motion (ie T-direction)
by an electron moving with the speed vcosT and oscillating with the
frequency (c-v)/L. Since the speed of this radiated wave is also c,
the situation is as if the electron is stationary and while it is
oscillating with the frequency (c-v)/L, radiates a wave with the speed
c-vcosT in the T-direction. It is obvious that the wavelength of such
a wave is L'=(c-vcosT)/((c-v)/L)=((c-vcosT)/(c-v))L.
Now we can calculate <delta>L=L'-L. The result will be

  <delta>L=(vL/(c-v))(1-cosT)                                (2)

As we see <delta>L is directly proportional to the wavelength of the
descended wave (L) too. If accurate experiments indicates dependence
of <delta>L to L, the only acceptable reasoning will be the one 
presented in this article not Compton's one.

It is noticeable that in some texts to the trying for justifying this
phenomenon as a Doppler effect has been pointed but in this incomplete
form that because of the Doppler effect the moving electron accepts some
wavelength longer than the descending wavelength and then radiates just
this wavelength in all the directions. But, in the current opinion of the
physicists, since the electron is accepting continuously the descending
wavelength from a stationary state to its final speed we must expect a
continuous distribution of scattered wavelengths from the descended
wavelength to the Dopplery lengthened wavelength (and since this is not
the case, the classical reasoning is not acceptable and the interaction 
between the wave and the electron is impulsive not continuous). It was only
sufficient that, as in fact has been done in this article, researchers
in this phenomenon would take one other step forwards and, as they accept
that the moving electron accepts lower frequency, they would accept that
this electron (accepting the lower frequency) would radiate just this
lower frequency only if it is motionless, but now that it is in motion,
again, Doppler effect will be effective and it radiates different
wavelengths in different directions (according to what has come in this 
article).

Point
~~~~~
After accepting the validity of the relation (2) we can use it to obtain 
v when other parameters are experimentally known. v is in fact the drift
velocity of the electrons in the local closed electric current produced
by the incidence of the beam (which has acted here as a source of potential).

The above material suggests an experiment that not only can test the theory
but also can be a means for determining the drift velocity of the electrons
in different electric currents (see the 9th article of this book):

We can write the relation (2) as <delta>L=(L/((c/v)-1))(1-cosT). 
If both the term (1-cosT) and v increase, obviously <delta>L will increase
significantly. To provide such situation that these terms increase let
the beam descend normally on a straight wire of the same kind as the
above-mentioned target (our beam is perpendicular to this wire).
Select a specified direction, eg T in Fig. 2.

                               A|
                          \     |
                           \    |Straight wire
                            \   |
                             \~-,_ T
              Beam            \ | ~-_
           -------------------->|....\..........
                                |
                                |
                                |
                                |
                                |
                               B|
     Fig. 2

When the straight wire is not connected to any source of potential (and
then there is no ordinary electric current in it) determine <delta>L in 
this direction (related to T in Fig. 2).

Now connect the two ends of the straight wire to a source of potential
such that an ordinary current of electrons from A to B in Fig. 2  flows in
the wire. In this state the drift velocity of the electrons in their
ordinary current is added vectorially to the velocity v in Fig. 1 we 
discussed earlier. Since in the relation (2) v is in fact the velocity
of the electron and T is the angle between the vector of this velocity
and the line connecting the detector to the point of incidence, we 
conclude that here the new v is the vector sum of the old v and the 
above-mentioned ordinary drift velocity, and this causes not only 
the magnitude of the new v to be larger than of the old one but also 
the new T angle to be larger than the old one. Both of these should 
cause the new <delta>L to be larger than the old one. Certainly we 
can devise other similar methods to determine drift velocities.

A request 
~~~~~~~~~
The author requests the society of science not hesitate to help him to
be placed in the main flow of the world physics if really his talent is
capable of flourishing widely arousing the motive for many world-wide
physical researches and experiments.

Hamid V. Ansari
jc626@cleveland.Freenet.Edu
esfahan@math.ui.ac.ir