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k constant shows a mistake in wavelength equation in the wave-particle duality and presents a new formula

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Bahram Kalhor at Shahid Beheshti University
Bahram Kalhor
Farzaneh Mehrparvar
Farzaneh Mehrparvar
Farzaneh Mehrparvar
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Abstract

We use k constant for investigating the correctness of the equation of the wave-particle duality. We show that the equation of the wavelength of a massive object is not correct unless it moves in the speed of the light. According to the equations of the quantum of the mass, we rewrite the equation of the wave-particle duality.
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k constant shows a mistake in wavelength equation in the wave-particle duality and presents
a new formula
Bahram Kalhor
1
, Farzaneh Mehrparvar1
Abstract
We use quantum of the mass for investigating the correctness of the equation of the wave-particle
duality. We show that the equation of the wavelength of a massive object is not correct unless it
moves in the speed of the light. According to the equations of the quantum of the mass, we rewrite
the equation of the wave-particle duality.
Introduction
In 1924 de Broglie proposed wave-particle
duality. In this theory, all objects have their
frequency [1]. de Broglie used Einstein’s
equation [2] for formulating his theory. He
proposed that the wavelength of each object
is related to its linear momentum and
Planck’s constant. In 1927 Thomson
discovered wave property of the electron.
Also, Davisson and Germer showed that the
electron makes diffraction patterns. These
experimental results confirmed wave-particle
duality. However, experimental results were
based on the electron and molecules when
they move close to the light speed [3-11].
Although according to the equation,
physicists believe that the wavelength of the
massive object is too low and we can deny it,
we show that the de Broglie’s equation does
not work in the speeds less than the speed of
the light.
In this paper, we use k constant [12] and show
that de Broglie’s formula is not correct. Our
paper result is not against to concept of the
wave-particle duality and we do not refuse
the wave-nature of matter. We just refuse
de Broglie’s equation. We show that the
1
Independent researcher form Alborz, IRAN
Corresponding author. Email: Kalhor_bahram@yahoo.com
wavelength of an object is related to its mass,
Planck’s constant, and the speed of the light,
while the particle moves in the speed of the
light. This new formula is suitable for
describing phenomena and investigating the
path of stars in the galaxies and the formation
of supermassive objects in the space [13-15].
de Broglie’s wavelength and its problem
de Broglie related wavelength, momentum,
and Planck’s constant in a simple formula:
 
where is the wavelength of the particle, is
the Planck’s constant, and is the linear
momentum of the particle. In the classic
physic, the linear momentum of each particle
is equal to the multiplication of its mass by its
speed
     and then
 
=
 (1)
on the other hand, we showed that (8) we can
present h and m based on the quantum of the
mass
   (2)
where is the quantum of the mass, is the
Planck’s constant, and  is the speed of the
light. Also, the mass of the object is given by:
   or    (3)
where is the mass, k is the quantum of the
mass, and v or f is the frequency of the
particle.
 
  
According to equations (2) and (3)
 
 


the relation can also be expressed as
 
 (4) or
   
using that the speed of the particle    ,
therefore
   
  
  
as we can see, de Broglie’s equation is true
when the particle moves with the speed of the
light.
 
 (5)
Equation (5) shows that when a particle or
photon moves with the speed of the light, its
wavelength relates to its mass. Hence, a
photon with more mass or energy has less
wavelength.
On the other hand, when the speed of the
particle is less than the speed of the light, we
can see that de Broglie’s equation is not
correct. Hence using de Broglie’s equation
for calculating the wavelength of the object
in the speeds less than the speed of the light
not recommended.
New formula of wavelength based on the
quanta mass
Equation (3) shows the relation between
mass and frequency of all objects. According
to equation (3):
 
Also, we know that    or  
hence
  
(6)
Equation (6) shows the relation between the
wavelength of an object and its speed and
mass.
For instance, according to the equation (6)
wavelength of an electron that moves with
half of the speed of the light is equal to:
  
     m
or the wavelength of the sun is equal to:
  
If we use the speed of the sun relative to the
cosmic microwave background:
 
     m
Conclusion
We presented a new formula based on the
quantum of the mass for calculating
wavelength of the objects. We showed that
de Broglie’s equation is correct when the
speed of the object is equal to the speed of the
light.
References
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12. Kalhor, B., and Mehrparvar, F. (2020). "k constant",
Figshare. DOI: 10.6084/m9.figshare.12249479
13. Kalhor, B., and Mehrparvar, F. (2020). "Where is
antimatter?", Figshare. DOI:
10.6084/m9.figshare.12200717
14. Kalhor, B., and Mehrparvar, F. (2020). "Do stars in a
spiral galaxy simulate 4-dimensional movement in a 3-
dimensional space ", Figshare. DOI:
10.6084/m9.figshare.12234617
15. Kalhor, B., and Mehrparvar, F. (2020). “Theory of
black hole structure ", Figshare. DOI:
10.6084/m9.figshare.12198213
16. Gladen, R. W., Chirayath, V. A., Fairchild, A. J.,
Koymen, A. R., & Weiss, A. H. (2020). Digital methods
for the coincident measurement of the energies of
positron-induced electrons and Doppler-shifted
annihilation gamma quanta. Nuclear Instruments and
Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment,
953, 162887.
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