How does the quantum structure of electromagnetic waves describe quantum redshift?
The redshift of the electromagnetic waves is a powerful tool for calculating the distance of the
objects in space and studying their behavior. However, physicists' misinterpretation of why
Redshift occurs has led us to a misunderstanding of the most cosmological phenomena. The paper
introduces Quantum Redshift (QR) by using the quantum structure of the electromagnetic waves
(QSEW) In the Quantum Redshift, although the Planck constant is the smallest unit of three-
dimensional energy, it is consisting of smaller units of one-dimensional energy. The maximum
energy of each period of the electromagnetic waves is equal to the Planck constant hence, the
capacity of each period is carrying one-dimensional quanta energy.
However, in the QR, at the emitting time of the electromagnetic waves, their periods are not fully
filled. On the other hand, they are interested in sharing quanta energies with each other to have
fully filled periods. Sharing the quanta energies ofا some periods between other periods is the
reason for destroying some periods and decreasing the frequency of the electromagnetic waves.
Our other studies show Quantum Redshift can well explain the whole phenomenon of the universe,
and real data support our theory. The quantum redshift rejects the big bang theory, expansion of
space and dark energy. It predicts dark matters and describes CMB. The paper obtains the basic
equation of the QR for use in future papers.
Cosmic redshift or shift in spectral lines is a powerful tool for calculating the distance of the objects
in the universe. It belongs to the electromagnetic waves area and usually happens when the
wavelength of a wave decrease by traveling in space. The measurement parameter of the cosmic
redshift is z. The value of the z usually is a positive number, and more distance is equal to the
greater z value. In some cases, the value of the z is negative, and we have blueshift.
Although the redshift is known by name of the Edwin Hubble , Vesto Slipher (1875-1969) was
the first astronomer who measured it . Also, the redshift of the cosmic waves has measured by
Carl W. Wirtz (1922) and the Swede Knut Lundmark (in 1924) [3,4].
There are many theories for describing the behavior of the wave in space and increasing its
wavelength. Doppler effect is the most similar theory that has been used for investigating the
cosmic redshift [5-9]. In the Doppler effect, changing the wavelength is due to changing the
distance between emitter and observer during the traveling of the wave between them. In 1848
Hippolyte Fizeau proposed that cosmic redshift is like the Doppler effect. In 1968 William
Huggins measured the velocity of the stars by using the Doppler effect formula. According to this
Shahid Beheshti University, Faculty of Electrical & Computer Engineering
Corresponding author. Email: Kalhor_bahram@yahoo.com
method, objects that come toward us have the blueshift, while objects that move away have the
Using spectral lines and the Doppler effect method showed that the speed of some stars and
galaxies should be more than the speed of light. This issue disagreed with Einstein's special
relativity [13-16]. Hence, the expanding universe theory is proposed. In the expanding space
theory, the distance between two objects in space will be increased along time even they do not
move. In the expanding space theory, the reason for the redshift of the waves is expanding the
space. Also, by increasing the distance between the objects their expansion rate will be increased.
If we accept the expansion of the space, we should find dark energy that makes this expansion.
The expanding space theory has two problems. Dark energy is not discovered yet, and not possible
to build a realistic model of the universe on modes of unrestrained expansion .
The gravitational redshift is another theory that tries to describe the spectral displacement by using
general relativity [18-22]. Although there is a significant redshift for massive objects, it is a weak
effect for non-massive stars.
The purpose of this work is to represent quantum redshift for measuring the distance of the objects.
The quantum redshift disagrees with the accelerated expansion of space. The results of the
quantum redshift show the real distances of the objects are less than the distances that have been
obtained in the theory of expanding universe. Concepts of the quanta energy  and the quantum
structure of the electromagnetic waves  are the main parts of this paper.
In the quantum structure of the electromagnetic waves, regardless of the frequency of the waves,
the capacity of each period of the wave is an equal number of the quanta
energies. Each period of the wave is called the virtual k box. The number of quanta energies in
each period will be changed by traveling in space.
In the quantum structure of the electromagnetic waves, the capacity of each virtual k box (period)
is equal to the quanta energies, where and =1. A fully filled
period contains one quanta mass in the first dimension, quanta energies in the second dimension,
and quanta energies in the third dimension.
Fig.1.a demonstrates a virtual cube and free positions for bullets as one-dimensional energies.
While in the real world, the distance between the one-dimensional energies (k constants or quanta
energies) is not static, in this model we have used static positions for better understanding.
Each cube is an equivalence of one period of the electromagnetic waves. Hence, the frequency is
equal to the number of cubes per second. The width and height of the cube are not Fixed. The
maximum width of the cube is equal to the value of the speed of light and belongs to an
electromagnetic wave with a frequency of 1 Hz.
Fig.1: A model for showing the three-dimensional structure of Planck’s constant energy, and bullets as the one-
dimensional energy in the electromagnetic waves. a) The capacity of Planck’s constant for carrying one-
dimensional quanta energies in each period plus one quanta mass. b) An unfulfilled period at the emitting time. Each
green bullet is one quanta energy.
Fig.2 shows a simple model of the arrangement of k boxes or periods of the waves. The Green
positions have been occupied by the one-dimensional quanta energies (k constant). Depending on
the mass of the emitter, the number of occupied positions varies. Though the capacity of all k
boxes (periods) is constant, the k boxes are not fully filled at the time of emitting.
By accepting the Quantum Redshift, we should replace by
Planck's equation can only calculate the maximum energy of electromagnetic waves due to their
Fig.2: The frequency is equal to the number of cubes per second. The width and height of the cubes are not Fixed.
The maximum width of the cube is equal to the value of the speed of light and belongs to an electromagnetic wave
with a frequency equal to 1 Hz.
After emitting the electromagnetic waves, all periods are not fully filled, and they are interested in
observing quanta energies for fully filling of their free positions. The best candidates are quanta
energies in the neighbor periods. The older periods take quanta energies from the near younger
periods. The mechanism is time-consuming and depends on the number of free positions and the
amount of losing quanta energies over time can take billions of years.
Fig.3 is a simple unreal model to demonstrate the QR mechanism. Sharing of quanta energies of
one period between other periods is the reason for the QR. The older periods on the left side
observe the quanta energies from the younger period on the right side (a box with red quanta
energies). The electromagnetic wave loses its right box while other periods have obtained its
quanta energies. As a result of losing some periods, the frequency and number of electromagnetic
waves per second will be decreased.
Fig.3: An unreal model for describing sharing quanta energies between periods: All periods are interested in
observing quanta energies from the space or neighbor periods. The quanta energies of the right period (Red
bullets) share between other periods.
Recursive quantum redshift
The frequency of the wave is equal to the total number of the virtual k boxes (periods) that carry
in a second. On the other hand, while k boxes move in a vacuum, in each second, one or more
quanta energies will be decreased from new periods for fulling other periods. Hence, in each
second, the total number of the decreased quanta energies that have distributed in a second or in
299792458 meters is equal to the frequency of the wave multiplied by the number of the quanta
energies that will be decreased in each second from each period. Hence, the total number of sharing
and even losing the quanta energies in each second is equal to where p is the number of the
quanta energies that will be decreased in each second from each k box, and is the frequency of
the wave at the start of each second.
If result of the be less than the capacity of the k box, the frequency will not be decreased,
and this operation will be continued until the sum of the lost (shared) quanta energies for all the k
boxes (periods) reaches the capacity of the one period.
After passing seconds, the total number of the shared quanta energies reaches the capacity of
one period. Hence, it is an equivalent of destroying one period and send their remain quanta
energies to other k boxes (periods), this operation will be decreased frequency of the wave.
The value of the is given by:
where is the counts of the seconds that k boxes lose their quanta energies until the sum of the
lost quanta energies reaches the capacity of the one k box (q). Also, If then
The equation (1) provides the time for decreasing frequency in each step. The total number of the
decreased quanta energies in second is given by:
where is the total number of the lost quanta energies in the seconds and is the remain
number of divisions
in the previous step (
After passing seconds and reaching the number of the lost quanta energies ( to the equal or
greater than the capacity of the one k box (q), k boxes will be reconstructed, and the wave will be
lost some k boxes (periods). Hence, frequency will be decreased. Equation is given by:
where is the amount of the frequency that will be decreased.
Table.1 illustrates the value of parameters of the quantum redshift in each step and obtain a
Table.1: Parameters of the Recursive quantum redshift in each step.
The results of the equation
is not an integer number, hence a few numbers of the quanta energies
will be remained, and we should consider them in the next step, hence:
on the other hand,
in the quantum redshift
using (6) and (7)
on the other hand,
The equation (11) provides the amount of the frequency in the next step based on the frequency of
the current step. In the quantum redshift for calculating the distance of a remote galaxy we use the
total time of traveling the wave between the galaxy and the observer, the equation is given by:
In the equations (13) and (14) value of the parameter n is not specified at the first. These equations
represent recursive procedure; hence we need a computer program that according to the step
by step calculate previous frequencies and time of that step until the frequency reaches the .
Approximating recursive quantum redshift to non-recursive quantum redshift
Although environmental parameters such as temperature and mass, have an impact on the
parameter p, in a normal space we can use it as a value that will be decreased overtime. Also, the
value of the q is invariant. On the other hand, in the equation (4), the amount of the is too small
and we can omit it. Hence, a simple relationship between and in each second is given by:
where q = 89875518173474223
Hence, t seconds after emitting, would be obtained depend on by using this equation:
The equation (16) is a non-recursive quantum redshift.Table.2 shows the changes of the
frequency in consequence seconds, respectively.
Table.2: Parameters of the non-Recursive quantum redshift in each step.
Calculating time by using frequency
By using the equation of the non-recursive quantum redshift and according to the definition of
the parameter z, we can calculate the time distance between the emitter and observer.
In the normal electromagnetic waves, at the emitting time the value of the p is greater than 1 but
after passing time it will be decreased to less than 1. For Instance, with p = 1 and q =
Calculating distance by using frequency
The equation (16) represents the relationship between the and .
on the other hand,
Calculating distance by using z
Using equations (20) and (25)
In the real world, scientists obtain the value of parameter z of the objects in space and calculate
their distance to the observer. The equation (14) provides a recursive quantum redshift method for
calculating the distance of the objects while the equation (31) represents a non-recursive quantum
redshift method. The advantage of the non-recursive quantum redshift method is its higher speed
of calculation. For calculating the distance of the object by using the equation (14) we need a
computer program and a fast computer, but equation (31) is a simple equation that could be
calculated by a professional calculator. The only restriction of the equation (31) is the value of the
or the value of the parameter p. It is not a constant value. Our studies on the real data of more
than 90,000 nearby stars show at the begging years after the time of emitting, the value of the p is
more than hundreds and its value will be decreased to the less than one after traveling more than
millions of years we will publish these results in another paper. For calculating we need a
calculator that supports this kind of calculation. In this paper for simulating the Quantum redshift
we assumed a constant value for the parameter p=1 and in future paper we will discussed in more
detail. We have used an online calculator from this internet address
However, we should compare the results of both methods to ensure that the results of the non-
recursive quantum redshift method are reliable. For this reason, we wrote a program and calculate
the parameter z for distances between zero to almost 8 billion light-years with a constant value for
the parameter p = 1. Although choosing a constant value for the parameter p makes an inaccurate
distance, we can use it for comparing recursive and no recursive methods. This range of distances
covers z parameters between zero and 12. In the table.3 the columns (1) and (2) represent the
relation between the special distances and their z value in the recursive quantum redshift,
In the next step, we used all z parameters in column (2) for calculating the distances of the objects
in equation (31). The results have been shown in column (3). The difference between the two
methods is too small, and less than percent, hence results of the non-recursive quantum
method are reliable.
Another thing that we should consider is the value of the . Although, the value of the q is invariant
(q = 89875518173474223), the value of the p is not constant. The parameter p is the average
number of quanta energies that each individual period of the wave loses in each second at the time
t, and it could mainly depend on the mass of the emitter and a little on the environmental
parameters such as the temperature of the space. We should consider that p is the average number
of the decreased quanta energies in a second.
We should consider that result in the quantum redshift disagrees with the accelerated expansion
universe theory, hence the distances that would be obtained from each value of the parameter z by
the quantum redshift would be less than the distances that have been calculated by the accelerated
expansion universe method
Table.3: Comparing distances in the Recursive quantum
redshift and non-Recursive quantum redshift.
Fig.4 illustrates the relationship between distances and their z parameters in the quantum redshift
theory. By increasing the distance, the z will be increased more. Meanwhile, this graph shows that
the percent of the increase in the z parameter is more than the increasing percentage of the distance
even with a constant value of the parameter p. This agrees with the real data of the universe.
Fig.4: distances and their z parameters in the quantum redshift
Quantum redshift claims the reason for redshift is the existence of free energy capacity in the
periods of the electromagnetic waves, and they're interested in obtaining quanta energies for full
filling. After the time of emitting, the older periods absorb quanta energies from the younger
periods continuously. Sharing the quanta energies along with traveling in space is the main
reason for destroying some periods and decreasing the frequency of the waves.
The relationship between the and is given by:
where q = 89875518173474223 and the parameter p is not a constant value, and its initial value
depends on the mass of the emitter. In the begging years after the time of emitting, the value of the
p is more than hundreds and its value will be decreased to less than one after traveling more than
millions of years.
Observational evidence supports the QR theory. In a future paper, we will show that data of 93,060
nearby space objects show an agreement with the Quantum Redshift theory. The Quantum
Redshift rejects the accelerating expansion of the universe and dark energy. The QR theory not
Distance (light Year)
only can describe the reason for the Redshift but prove a higher rate of increasing Redshift of the
1. Chrisitanson, Gale E. Edwin Hubble: mariner of the nebulae. Routledge, 2019.
2. Slipher, Vesto Melvin. "The radial velocity of the Andromeda Nebula." Lowell Observatory Bulletin 2
3. Duerbeck, Hilmar W. "Carl Wirtz—An early observational cosmologist." Morphological Cosmology.
Springer, Berlin, Heidelberg, 1989. 405-407.
4. Soares, Domingos, and Luiz Paulo R. Vaz. "Solar-Motion Correction in Early Extragalactic
Astrophysics." Journal of the Royal Astronomical Society of Canada 108.3 (2014).
5. Kündig, Walter. "Measurement of the transverse doppler effect in an accelerated system." Physical
Review 129.6 (1963): 2371.
6. Nezlin, Mikhail V. "Negative-energy waves and the anomalous Doppler effect." UsFiN 120 (1976):
7. Compton, Arthur H., and Ivan A. Getting. "An apparent effect of galactic rotation on the intensity of
cosmic rays." Physical Review 47.11 (1935): 817.
8. Byrd, G. G., and M. J. Valtonen. "Origin of redshift differentials in galaxy groups." The Astrophysical
Journal 289 (1985): 535-539.
9. Skeivalas, J., V. Turla, and M. Jurevicius. "Predictive models of the galaxies’ movement speeds and
accelerations of movement on applying the Doppler Effect." Indian Journal of Physics 93.1 (2019): 1-
10. Zhao, HongSheng, John A. Peacock, and Baojiu Li. "Testing gravity theories via transverse Doppler
and gravitational redshifts in galaxy clusters." Physical Review D 88.4 (2013): 043013.
11. Albrecht, H-E., et al. Laser Doppler and phase Doppler measurement techniques. Springer Science &
Business Media, 2013.
12. Walker, Jack L. "Range-Doppler imaging of rotating objects." IEEE Transactions on Aerospace and
Electronic systems 1 (1980): 23-52.
13. Wolf, Peter, and Gérard Petit. "Satellite test of special relativity using the global positioning system."
Physical Review A 56.6 (1997): 4405.
14. Daszkiewicz, M., K. Imilkowska, and J. Kowalski-Glikman. "Velocity of particles in doubly special
relativity." Physics Letters A 323.5-6 (2004): 345-350.
15. Delva, P., et al. "Test of special relativity using a fiber network of optical clocks." Physical Review
Letters 118.22 (2017): 221102.
16. Tsamparlis, Michael. "Waves in Special Relativity." Special Relativity. Springer, Cham, 2019. 647-702.
17. Ranzan, Conrad. "Cosmic redshift in the nonexpanding cellular universe." American Journal of
Astronomy and Astrophysics 2.5 (2014): 47-60.
18. Kaiser, Nick. "Measuring gravitational redshifts in galaxy clusters." Monthly Notices of the Royal
Astronomical Society 435.2 (2013): 1278-1286.
19. Müller, Holger, Achim Peters, and Steven Chu. "A precision measurement of the gravitational
redshift by the interference of matter waves." Nature 463.7283 (2010): 926-929.
20. Di Dio, Enea, and Uroš Seljak. "The relativistic dipole and gravitational redshift on LSS." Journal of
Cosmology and Astroparticle Physics 2019.04 (2019): 050.
21. Delva, Pacôme, et al. "A new test of gravitational redshift using Galileo satellites: The GREAT
experiment." Comptes Rendus Physique 20.3 (2019): 176-182.
22. Savalle, Etienne, et al. "Gravitational redshift test with the future ACES mission." Classical and
Quantum Gravity 36.24 (2019): 245004.
23. Kalhor, Bahram, Farzaneh Mehrparvar, and Behnam Kalhor. "k constant: a new quantum of the
energy that is smaller than the Planck’s constant." Available at SSRN 3771223 (2021).
24. Kalhor, Bahram, Farzaneh Mehrparvar, and Behnam Kalhor. "How quantum of the mass, k box, and
photon make light and matter?." Available at SSRN 3667603 (2020).
25. Picqué, Nathalie, and Theodor W. Hänsch. "Frequency comb spectroscopy." Nature Photonics 13.3
26. Gaeta, Alexander L., Michal Lipson, and Tobias J. Kippenberg. "Photonic-chip-based frequency
combs." Nature Photonics 13.3 (2019): 158-169.
27. Probst, Rafael A., et al. "A crucial test for astronomical spectrograph calibration with frequency
combs." Nature Astronomy (2020): 1-6.
28. Wang, Ning, et al. "Room-temperature heterodyne terahertz detection with quantum-level
sensitivity." Nature Astronomy 3.11 (2019): 977-982.
29. Kalhor, Bahram, Farzaneh Mehrparvar, and Behnam Kalhor. "Is Einstein’s special relativity
wrong?." Available at SSRN 3650796 (2020).
30. Kalhor, Bahram, Farzaneh Mehrparvar, and Behnam Kalhor. "Unexpected Redshift of nearby
stars." Available at SSRN 3777341 (2021).
31. Lara-Avila, S., et al. "Towards quantum-limited coherent detection of terahertz waves in charge-
neutral graphene." Nature Astronomy 3.11 (2019): 983-988.
32. Adams, Elizabeth AK, and Joeri van Leeuwen. "Radio surveys now both deep and wide." Nature
Astronomy 3.2 (2019): 188-188.
33. Zhao, HongSheng, John A. Peacock, and Baojiu Li. "Testing gravity theories via transverse Doppler
and gravitational redshifts in galaxy clusters." Physical Review D 88.4 (2013): 043013.