Doppler phenomenon for electromagnetic waves and new
equations for relativity quantum
What is the Doppler effect?
Because of Doppler phenomenon importance in cosmology, it is
necessary to have a short revision. Doppler phenomenon is considered
in classic physic for changes in frequency of sound source.
According to this effect, whenever an observer is on move compared
to a sound source, he will receive another frequency which
dispatched by source. For example, if an ambulance with certain
speed is on move toward us, its alert sound makes change in sending
waves because of sound source movement, and more closing us more
acute alert (more frequency and shorter wavelength) is heard and
when it passes beside us and far away, the alert becomes graver
(shorter frequency and longer wavelength).
This phenomenon is called Doppler Effect which is same in light too.
It means whenever light resource is on move toward observer , the
frequency of receiving light will change, if observer and source may
being far away, the frequency of receiving light will go toward red
and if may being near, the frequency of receiving light will go
toward blue. After presenting relativity theory, Doppler Effect for
electromagnetic waves has discussed. In relativity Doppler Effect,
because wave dispatching source shines electromagnetic waves and
behavior of these category of waves described by Special relativity,
therefore it differs with classic Doppler. Because according to
special relativity - based on unifying physical rules in all inertia
reference frames - the existence of any supreme reference frame in
universe will disavow. Because of this, source
moving towards observer or observer moving toward source has no
difference. In this phenomenon, if source moving towards observer or
observer moving toward source, there will be a displacing toward
blue spectrum. It means below equation:
Which λ0
is receiving wave length, and λe
is wavelength that sends by light source. It is clear that in this
situation receiving wavelength is smaller than sending wavelength.
If source from observer or observer from source is far away, with
increasing in receiving light wavelength, there will be a displacing
in absorbing or emission as below equation:
Now this subject will survey under classic mechanic, relativity and
quantum mechanics:
In below picture, the source of green spectrum (central circle) is
spotted consonant. For its wavelength and frequency have:
C is light speed, λ
is wavelength, and f is frequency of electromagnetic wave. Now if
source of green spectrum displace with v speed, we have:
λ' is received
wavelength, v is source speed,
λ
is source wavelength, f is source frequency and f ' is receiving
frequency. In latest equation, v is speed of wave - for example
sound - and Vs is wave or sound
source speed. The above equations are referred to classic equations
for Doppler Effect. For example a police car is dispatching alert
with 4000 Hz and closing to a static passenger with 72km/hour speed
and far away from another, what is the amount of sound frequency?
The speed of sound in air is 340m/s:
But as we knew, by
increasing speed of light source, the time will be slow and length
will be short, so observer beside
the light
source won't understand difference in frequency and wavelength and
also will reach to previous result in light speed measurement. But
in view of other observer not with light source, the more increase
in speed and slower in time and shorter in length, the more decrease
in frequency of spectrum. It means moving toward yellow spectrum
from green spectrum that no observer could see it, else it will be
beside source of light and makes changes in measurement units of
length and time. This spectrum is understood just by observation
based on Gerald - Lawrence contraction. So the classic equation will
change to below equation that f'' is frequency of on move source
spectrum with V speed.
As we knew the units of frequency is cycle per second and by slowing
time, surely the frequency of source spectrum, will be decreased for
observers that they don't beside the source. It means:
t is time, t' is
slowed time, and f " is frequency of on move source. Its ease and
advantage compared old formula is that we just change a sign in
numerator of the equation which simplify its learning and
application.
The below curve shows shortening in wavelength by increasing speed
of closing source to observer (blue tendency) and upper curve shows
lengthen in wavelength by increasing speed of far away source from
observer (red tendency).
Now we compare result from new formulas and old formulas:
As it is clear, the results are same and now after confidence of
equation accuracy, try to merge these equations with equations in
quantum mechanics and catch new formulas:
The above equation shows the
frequency of received electromagnetic waves from a source which is
closing or far away to observer. That f is source frequency and f'
is received frequency to observer.
The upper curve shows frequency increase, by increasing speed of
source closing to observer (blue tendency) and the below curve shows
frequency decrease, by increasing speed of source far away observer
(red tendency).
E is photon energy
and h is Plank consonant. The above equation and limit shows energy
of electromagnetic wave of the on move source. As it is clear by
closing to light speed, the energy of radiant wave is decreased by
source that this will cause balance in source and prevent explosion
and mass convert to energy. In fact by closing to light speed, the
temperature will close to absolute zero which will discussed in next
discussions.
And this is the general and
final equation to achieve energy of electromagnetic waves received
from on move source. The general conclusion is that energy in some
ranges of space - time is quantized that referred to second and
paced distance by light in a second. Which express this fact that
common time division as second, minute, hour and ... was not done by
human, but done by super intelligent life who use professional
geometry and mathematics as dozen calculation and they transferred
us these time and calendar knowledge and first watch, means time
showing was made by them. Because the unit of frequency in Plank
formula is cycle per second, and this means electromagnetic energy
is quantized and packaged in time and unit of it is second and also
length with meter unit. We can consider this package as mechanical
bit like photon or a string of c.t length and t=1 which will be
discussed after.
