All submissions of the EM system will be redirected to Online Manuscript Submission System. Authors are requested to submit articles directly to Online Manuscript Submission System of respective journal.

Original Article

, Volume: 5( 4)

About the Gravitational Interaction of Photons

Peter Rafay I Institute for Nuclear Research of the Russian Academy of Sciences, Tel: +972 1-800-660-660; E-mail:

Received Date: October 28, 2017 Accepted Date: November 10, 2017 Published Date: November 16, 2017

Citation: Peter Rafay I. About the Gravitational Interaction of Photons. J Phys Astron. 2017; 5(3):130


In the following article, the author theoretically proved that during a threshold frequency of electromagnetic radiation equal to Planck’s frequency, this radiation, under the influence of the force of gravity between photons, will stop. The energy will transform itself into so-called ‘dark energy’. This ‘dark energy’ affects gravity, yet it does not move, or does not oscillate in the real sense of the term. Another observation regarding gravitational energy is that it is dependent upon the ratio of Planck’s length and the distance between two interacting objects, as well as the ratio of the multiplied energies of two interacting particles to Planck’s energy, which are a part of the constants of nature. Further results can be obtained through further theoretical and practical research.


Absolute Zero; Bound State; Dark Energy; Electromagnetism; Frequency; Gravity; Kinetic Energy; Oscillation; Photons; Planck’s Constants; Radiation


The author has finished a technical university education with a Slovak equivalent of the Masters of Science, or MSc., and has further educated himself in the fields of physics and mathematics throughout his life. Mathematical language used is only trivial in nature, as its transcription into vector and tensor script has been deemed unnecessary by the author in the early stages of research, yet it can be supplied if required. The author has discovered multiple irregularities within his studies of physics, which were often caused by not always accurate obtainment of results. The field of mathematics contains certain limits for the analytical calculation of functions of differential equations, and while numerical methods can give us the expected values, the analytical descriptions of functions are not known in their full range of values. These numerical methods fail especially in borderline conditions, which is exactly what the author focuses on. Hence, the priority is not to define borderline conditions and then use numerical methods to solve the course of values of functions in particular intervals, but to correctly identify these boundaries and then use the force of numerical solutions. Furthermore, while it is not yet possible to prove the practical implications of this theory, it is useful to have a theoretical basis which would motivate us towards such improvements in technology, rather than slow this progress, unlike the current theories of Special and General Relativity Theories.

The author believes that the main objective of physics is discussion, which is currently not maintained in the field of Einstein’s physics, which can be taken quite dogmatically. The base of Einstein’s Special and General Relativity Theories present a barrier to the evolution of physics, and the author would like to disturb these stereotypes and offer his own critical opinion. Throughout this article the only idea in accordance to Einstein’s theory is that the speed of light is equal to the speed of photons (particles with zero rest mass). For particles that do not have zero rest mass the limitation of maximum speed is in accordance to quantum-mechanical constants. The author wants to suggest that the main disproportions are only apparent when mass is included in the formulas, which is not necessary when dealing with photons, as their resting mass is equal to zero.

In the following article the author consciously prioritised the original Newtonian view on gravitation, over Einstein’s General Relativity Theory and his geometrical interpretation of space-time curved by mass, in combination with the theory of quantum-mechanics.


During the so-called threshold frequency of electromagnetic radiation, equal to Planck’s frequency, will this radiation, under the influence of gravity between photons, stop and become ‘dark energy’.

Practical limitations

Energy equal to around 14 000 GeV is currently used in existing accelerators, which is approximately 10-6 Joules, and the energy required to prove the practical implications of this theory is 109 Joules, which represents energy 15 times greater than what is possible in current accelerators.

According to the author, the practical proof could also be acquired through using the reverse order, and that is to cool down the mass, or photons, to the temperature of absolute zero, during which the photons exist in a bound state of gravitational and kinetic energy (they have the same size, they are just oriented in an opposite manner). Once the barrier of the temperature of absolute zero is overcome, this bound state will break and both energies are going to be separated from each other, which will cause an immediate rise of the temperature of photons to Planck’s temperature equal to Tp = 9,455 x 1031 K. The author believes that absolute zero and the highest temperature within the limit of Planck’s radiation frequency are equal. This means that there is a pulsation around these temperatures, pulsating from maximum temperature to minimal temperature and back. This is shown in Figure 1.


Figure 1: Figure

The author is unaware of any other methods of obtaining the above stated energy, and in his opinion it can only be found in observations of space, such as evaporation or interaction of black holes [1,14].


Take a ray, which is created by a flow of localized quantities of concentrated energy (photons). We are going to define the energy of these quanta within the range of corpuscular wave dualism using frequency f and Planck’s constant h, also known as reduced Planck’s constant equation and the circular frequency ω:


The relationship between the frequency of the photon and its circular frequency is:


We then define the quantity T = the duration of vibration of the photon:


The wavelength of the photon λ is defined as:


The radius of the photon R is equal to the distance between photons and it is defined as:


We are assuming that the composition of the ray is made up of entities of equal frequency (monochromatic radiation), with the distance between them being equal to the radius of the photon R, as shown by Figure 2.


Figure 2: Figure

We apply Newton’s gravitational law in the following way:- gravitational force can be written in the following way:



mf dynamic weight of the photon in kg (while the rest mass is equal to zero) The coefficient of proportion k will be identified using Planck’s constants:



X=1,61624.10-35 m smallest also known as Planck’s length

Tp=5,391.10-44 s Planck’s shortest time

Ep=1,956.109 J Planck’s energy

C=2.998.108 m.s-1 the speed of light in a vacuum

h=6,625.10-34 J.s Planck’s constant

h=1,055.10-34 J.s Reduced Planck’s constant

Then gravitational force can be written as:


and gravitational energy can be written as:


where equation Einstein’s kinetic energy of a photon While the following applies:




then the gravitational energy of two photons can be written as:


therefore: equation

(This equation of gravitation is true in general for two particles with both zero resting mass and resting mass that does not equal to zero.)

We can define the relative decrease in the energy of the photon as a consequence of gravitation as a ratio of gravitational to kinetic energy:


For example, for medium yellow radiation with the angular frequency equation the kinetic energy is equal to:



and gravitational energy:


and lastly the relative decrease of the energy of the photon as a result of gravity:


If we set the gravitational energy to be equal to the kinetic energy of the photon equation we will get the threshold value of the frequency, during which the gravitational pull of the photons will be equal to the kinetic energy of the photons and the flow of currents will calm down (stop):

EP = Eg



Hence the threshold frequency equation


During the angular frequency of 1,855×1043 s-1, which is Planck’s angular frequency ωp the gravitational power of photons will outweigh the kinetic energy of photons and the flow of localised quant-energy will stop, hence the hypothesis that the photon flow will collapse into singularity emerges, and the temperature of photons will be equal to Planck’s temperature


Maximum temperature will jump to the temperature of absolute zero, because the flow of photons will come to a stop. It is questionable whether the photon called the ‘black photon’ will also have the properties of a graviton, as particles of gravitational interaction. The duration of its lifespan will be equal to Planck’s time tp=5,39×10-44 s and the remaining parameters are given in the Table 1.

Name of quantity Angular frequency of photon Duration of oscillation Radius of photon Frequency of photon Wavelength of photon
Formula ω T=1/ω R=cT f=ω/2π λ=2πR=2πcT=2πc/ω
Unit s-1=Hz s m s-1=Hz m
Name of photon/number of colon 1 2 3 4 5
Biggest photon 1, 000E+00 1, 000E+00 2, 998E+08 1, 592E-01 1, 883E+09
Technical alternating currents 5, 000E+01 2, 000E-02 5, 996E+06 7, 962E+00 3, 765E+07
  1, 000E+02 1, 000E-02 2, 998E+06 1, 592E+01 1, 883E+07
  1, 000E+03 1, 000E-03 2, 998E+05 1, 592E+02 1, 883E+06
  1, 000E+04 1, 000E-04 2, 998E+04 1, 592E+03 1, 883E+05
Long waves 2, 000E+05 5, 000E-06 1, 499E+03 3, 185E+04 9, 413E+03
Medium waves 1, 000E+06 1, 000E-06 2, 998E+02 1, 592E+05 1, 883E+03
Very short waves 3, 000E+08 3, 333E-09 9, 993E-01 4, 777E+07 6, 276E+00
Microwaves 1, 000E+10 1, 000E-10 2, 998E-02 1, 592E+09 1, 883E-01
  2, 000E+10 5, 000E-11 1, 499E-02 3, 185E+09 9, 413E-02
  4, 000E+10 2, 500E-11 7, 495E-03 6, 369E+09 4, 707E-02
  8, 000E+10 1, 250E-11 3, 747E-03 1, 274E+10 2, 353E-02
  1, 600E+11 6, 250E-12 1, 874E-03 2, 548E+10 1, 177E-02
  3, 200E+11 3, 125E-12 9, 369E-04 5, 096E+10 5, 883E-03
  6, 400E+11 1, 563E-12 4, 684E-04 1, 019E+11 2, 942E-03
Infrared radiation 1, 280E+12 7, 813E-13 2, 342E-04 2, 038E+11 1, 471E-03
  2, 560E+12 3, 906E-13 1, 171E-04 4, 076E+11 7, 354E-04
  5, 120E+12 1, 953E-13 5, 855E-05 8, 153E+11 3, 677E-04
  1, 024E+13 9, 766E-14 2, 928E-05 1, 631E+12 1, 839E-04
  2, 048E+13 4, 883E-14 1, 464E-05 3, 261E+12 9, 193E-05
  4, 096E+13 2, 441E-14 7, 319E-06 6, 522E+12 4, 596E-05
  8, 192E+13 1, 221E-14 3, 660E-06 1, 304E+13 2, 298E-05
Visible radiation 3, 800E+14 2, 632E-15 7, 889E-07 6, 051E+13 4, 954E-06
Medium red radiation 4, 600E+14 2, 174E-15 6, 517E-07 7, 325E+13 4, 093E-06
Medium yellow radiation 5, 200E+14 1, 923E-15 5, 765E-07 8, 280E+13 3, 621E-06
Medium green radiation 5, 750E+14 1, 739E-15 5, 214E-07 9, 156E+13 3, 274E-06
Medium blue radiation 6, 700E+14 1, 493E-15 4, 475E-07 1, 067E+14 2, 810E-06
Medium violet radiation 7, 500E+14 1, 333E-15 3, 997E-07 1, 194E+14 2, 510E-06
  3, 300E+15 3, 030E-16 9, 085E-08 5, 255E+14 5, 705E-07
Ultraviolet radiation 1, 000E+16 1, 000E-16 2, 998E-08 1, 592E+15 1, 883E-07
  1, 000E+17 1, 000E-17 2, 998E-09 1, 592E+16 1, 883E-08
X-Rays 1, 000E+18 1, 000E-18 2, 998E-10 1, 592E+17 1, 883E-09
  1, 000E+19 1, 000E-19 2, 998E-11 1, 592E+18 1, 883E-10
Gamma radiation 7, 761E+20 1, 289E-21 3, 863E-13 1, 236E+20 2, 426E-12
  1, 000E+21 1, 000E-21 2, 998E-13 1, 592E+20 1, 883E-12
  1, 000E+22 1, 000E-22 2, 998E-14 1, 592E+21 1, 883E-13
  1, 000E+23 1, 000E-23 2, 998E-15 1, 592E+22 1, 883E-14
Cosmic radiation 1, 425E+24 7, 018E-25 2, 104E-16 2, 269E+23 1, 321E-15
  3, 097E+24 3, 228E-25 9, 679E-17 4, 932E+23 6, 078E-16
  3, 097E+24 3, 228E-25 9, 679E-17 4, 932E+23 6, 078E-16
  3, 512E+24 2, 848E-25 8, 537E-17 5, 592E+23 5, 361E-16
  3, 512E+25 2, 848E-26 8, 537E-18 5, 592E+24 5, 361E-17
  3, 512E+26 2, 848E-27 8, 537E-19 5, 592E+25 5, 361E-18
  3, 512E+27 2, 848E-28 8, 537E-20 5, 592E+26 5, 361E-19
  3, 512E+28 2, 848E-29 8, 537E-21 5, 592E+27 5, 361E-20
  3, 512E+29 2, 848E-30 8, 537E-22 5, 592E+28 5, 361E-21
  3, 512E+30 2, 848E-31 8, 537E-23 5, 592E+29 5, 361E-22
  3, 512E+31 2, 848E-32 8, 537E-24 5, 592E+30 5, 361E-23
  3, 512E+32 2, 848E-33 8, 537E-25 5, 592E+31 5, 361E-24
  1, 509E+33 6, 625E-34 1, 986E-25 2, 404E+32 1, 247E-24
  9, 479E+33 1, 055E-34 3, 163E-26 1, 509E+33 1, 986E-25
  1, 000E+34 1, 000E-34 2, 998E-26 1, 592E+33 1, 883E-25
  1, 000E+35 1, 000E-35 2, 998E-27 1, 592E+34 1, 883E-26
  1, 000E+36 1, 000E-36 2, 998E-28 1, 592E+35 1, 883E-27
  1, 000E+37 1, 000E-37 2, 998E-29 1, 592E+36 1, 883E-28
  1, 000E+38 1, 000E-38 2, 998E-30 1, 592E+37 1, 883E-29
  1, 000E+39 1, 000E-39 2, 998E-31 1, 592E+38 1, 883E-30
  1, 000E+40 1, 000E-40 2, 998E-32 1, 592E+39 1, 883E-31
  1, 000E+41 1, 000E-41 2, 998E-33 1, 592E+40 1, 883E-32
  1, 600E+42 6, 249E-43 1, 874E-34 2, 548E+41 1, 177E-33
Black photon 1, 855E+43 5, 391E-44 1, 616E-35 2, 954E+42 1, 015E-34

Table. 1. Table showing certain calculated quantities for various angular frequencies of radiation/ photons

Even though we cannot measure the wave sources of such frequency and we also do not have the ability of constructing such a source, we can possibly gather such sources from the universe during extraordinary circumstances (such as during the gravitational impact of black holes etc.).

The author has theoretically proven the afore mentioned hypothesis mostly using Newton’s Law of Gravity for two physical bodies (photons): equation expression of Newton’s gravitational constant through Planck’s constants equation and modelling photons as particles (e.g. balls which move very close behind each other = localized energies of photons and hence their distance from the middle is equal to: equation as well as electromagnetic waves, which is representative of the duality of particles and oscillation. The author used Einstein’s law for calculating energy equation and Planck’s quantummechanical relationship for calculation of energy equation which are equal to each other. From the afore mentioned laws, the author has deduced a formula for the calculation of threshold frequency equation which the author has calculated to be on the level of Planck’s frequency, and hence voiced a hypothesis claiming the creation of ‘dark energy’ through the transformation of real energy, from electromagnetic oscillation, where during the appropriate frequency (Planck’s), under the influence of gravitational effect of photons, will become immobile. When something becomes immobile, the temperature of the particles becomes equal to absolute zero. Hence the temperature 31 9,45.1031 K becomes 0 K.

It needs to be re-stated, that the results are only based upon theoretical research, and it is necessary for them to be verified. However, if the theoretical basis of this research is at least confirmed it would provide motivation for the practical verification to be provided, as it would change our view on a part of physics, particularly in the field of threshold values [1,2].


The author found inconsistencies in Einstein’s Special Relativity Theory, particularly regarding infinite values of mass, zero length (contraction of length) and frequency (dilatation of time), which more likely fulfill the quantum-mechanical limitations, such as Planck’s mass, smallest length, largest frequency and other constants given in Table 2, 3. The principle of superposition of individual particles, which mass is made up of, is applicable for the bonding of particle theories for micro and macro particles.

Name of quantity Mass of photon Momentum of the photon Energy of photon Gravitational energy of photon Gravitational energy as a percentage of kinetic energy Temperature of photon
Formula m=E/c2 p=mc=h/l=hf/c E=hf/qe Eg=κm2/R Eg/E t=E/kB
Unit kg kgms-1 eV J   st. K
Name of photon/number of column 7 8 9 10 11 12
Biggest photon 1.17E-48 3.52E-40 6.59E-13 3.07E-118 2.91E-84 7, 65E-12
Technical alternating currents 5.87E-47 1.76E-38 3.29E-11 3.83E-113 7.27E-81 3, 82E-10
  1.17E-46 3.52E-38 6.59E-11 3.07E-112 2.91E-80 7, 65E-10
  1.17E-45 3.52E-37 6.59E-10 3.07E-109 2.91E-78 7, 65E-09
  1.17E-44 3.52E-36 6.59E-09 3.07E-106 2.91E-76 7, 65E-08
Long waves 2.35E-43 7.04E-35 1.32E-07 2.45E-102 1.16E-73 1, 53E-06
Medium waves 1.17E-42 3.52E-34 6.59E-07 3.07E-100 2.91E-72 7, 65E-06
Very short waves 3.52E-40 1.06E-31 1.98E-04 8.28E-93 2.62E-67 2, 29E-03
Microwaves 1.17E-38 3.52E-30 6.59E-03 3.07E-88 2.91E-64 7, 65E-02
  2.35E-38 7.04E-30 1.32E-02 2.45E-87 1.16E-63 1, 53E-01
  4.70E-38   2.63E-02 1.96E-86 4.65E-63 3, 06E-01
  9.39E-38 2.82E-29 5.27E-02 1.57E-85 1.86E-62 6, 12E-01
  1.88E-37 5.63E-29 1.05E-01 1.26E-84 7.44E-62 1, 22E+00
  3.76E-37 1.13E-28 2.11E-01 1.01E-83 2.98E-61 2, 45E+00
  7.51E-37 2.25E-28 4.22E-01 8.04E-83 1.19E-60 4, 89E+00
Infrared radiation 1.50E-36 4.51E-28 8.43E-01 6.43E-82 4.76E-60 9, 79E+00
  3.01E-36 9.01E-28 1.69E+00 5.14E-81 1.91E-59 1, 96E+01
  6.01E-36 1.80E-27 3.37E+00 4.12E-80 7.62E-59 3, 91E+01
  1.20E-35 3.60E-27 6.74E+00 3.29E-79 3.05E-58 7, 83E+01
  2.40E-35 7.21E-27 1.35E+01 2.63E-78 1.22E-57 1, 57E+02
  4.81E-35 1.44E-26 2.70E+01 2.11E-77 4.88E-57 3, 13E+02
  9.62E-35 2.88E-26 5.40E+01 1.69E-76 1.95E-56 6, 26E+02
Visible radiation 4.46E-34 1.34E-25 2.50E+02 1.68E-74 4.20E-55 2, 91E+03
Medium red radiation 5.40E-34 1.62E-25 3.03E+02 2.99E-74 6.15E-55 3, 52E+03
Medium yellow radiation 6.11E-34 1.83E-25 3.43E+02 4.31E-74 7.86E-55 3, 98E+03
Medium green radiation 6.75E-34 2.02E-25 3.79E+02 5.83E-74 9.61E-55 4, 40E+03
Medium blue radiation 7.87E-34 2.36E-25 4.41E+02 9.22E-74 1.31E-54 5, 12E+03
Medium violet radiation 8.81E-34 2.64E-25 4.94E+02 1.29E-73 1.64E-54 5, 73E+03
  3.87E-33 1.16E-24 2.17E+03 1.10E-71 3.17E-53 2, 52E+04
Ultraviolet radiation 1.17E-32 3.52E-24 6.59E+03 3.07E-70 2.91E-52 7, 65E+04
  1.17E-31 3.52E-23 6.59E+04 3.07E-67 2.91E-50 7, 65E+05
X-Rays 1.17E-30 3.52E-22 6.59E+05 3.07E-64 2.91E-48 7, 65E+06
  1.17E-29 3.52E-21 6.59E+06 3.07E-61 2.91E-46 7, 65E+07
Gamma radiation 9.11E-28 2.73E-19 5.11E+08 1.43E-55 1.75E-42 5, 93E+09
  1.17E-27 3.52E-19 6.59E+08 3.07E-55 2.91E-42 7, 65E+09
  1.17E-26 3.52E-18 6.59E+09 3.07E-52 2.91E-40 7, 65E+10
  1.17E-25 3.52E-17 6.59E+10 3.07E-49 2.91E-38 7, 65E+11
Cosmic radiation 1.67E-24 5.02E-16 9.39E+11 8.87E-46 5.90E-36 1, 09E+13
  3.64E-24 1.09E-15 2.04E+12 9.11E-45 2.79E-35 2, 37E+13
  3.64E-24 1.09E-15 2.04E+12 9.11E-45 2.79E-35 2, 37E+13
  4.12E-24 1.24E-15 2.31E+12 1.33E-44 3.58E-35 2, 68E+13
  4.12E-23 1.24E-14 2.31E+13 1.33E-41 3.58E-33 2, 68E+14
  4.12E-22 1.24E-13 2.31E+14 1.33E-38 3.58E-31 2, 68E+15
  4.12E-21 1.24E-12 2.31E+15 1.33E-35 3.58E-29 2, 68E+16
  4.12E-20 1.24E-11 2.31E+16 1.33E-32 3.58E-27 2, 68E+17
  4.12E-19 1.24E-10 2.31E+17 1.33E-29 3.58E-25 2, 68E+18
  4.12E-18 1.24E-09 2.31E+18 1.33E-26 3.58E-23 2, 68E+19
  4.12E-17 1.24E-08 2.31E+19 1.33E-23 3.58E-21 2, 68E+20
  4.12E-16 1.24E-07 2.31E+20 1.33E-20 3.58E-19 2, 68E+21
  1.77E-15 5.31E-07 9.94E+20 1.06E-18 6.62E-18 1, 15E+22
  1.11E-14 3.34E-06 6.24E+21 2.61E-16 2.61E-16 7, 25E+22
  1.17E-14 3.52E-06 6.59E+21 3.07E-16 2.91E-16 7, 65E+22
  1.17E-13 3.52E-05 6.59E+22 3.07E-13 2.91E-14 7, 65E+23
  1.17E-12 3.52E-04 6.59E+23 3.07E-10 2.91E-12 7, 65E+24
  1.17E-11 3.52E-03 6.59E+24 3.07E-07 2.91E-10 7, 65E+25
  1.17E-10 3.52E-02 6.59E+25 3.07E-04 2.91E-08 7, 65E+26
  1.17E-09 3.52E-01 6.59E+26 3.07E-01 2.91E-06 7, 65E+27
  1.17E-08 3.52E+00 6.59E+27 3.07E+02 2.91E-04 7, 65E+28
  1.17E-07 3.52E+01 6.59E+28 3.07E+05 2.91E-02 7, 65E+29
  1.88E- 5.63E+02 1.05E+30 1.26E+09 7.44E+00 1, 22E+31
Black photon 2.18E-05 6.53E+03 1.22E+31 1.96E+12 1.00E+03 1, 42E+32

Table. 2. Table showing certain calculated quantities for various angular frequencies of radiation/ photons

No. Name of quantity Lettering chosen to mark the quantity Formula for calculation Value of quantity Unit for quantity
1 Speed of light c equation equation ms-1
2 Planck’s constant h   equation Js
3 Planck’s smallest length xp   equation m
4 Planck’s shortest time tp   equation s
5 Planck’s area sp equation equation m2
6 Planck’s angular frequency ωp equation equation s-1
7 Planck’s frequency fp equation equation s-1
8 Planck’s energy Ep equation equation J
9 Planck’s mass mp equation equation kg
10 Planck’s momentum Pp equation equation kg ms-1
11 Planck’s volume Vp equation equation m3
12 Planck’s time-volume VTp equation equation m4
13 Planck’s density ρp equation equation kg m-3
14 Planck’s acceleration (gravitation) ap equation equation ms-2
15 Planck’s force Fp equation equation N
16 Wavelength of Planck’s radiation λp equation equation m
17 Gravitational energy of Planck’s photon Eg equation equation J
18 Gravitational constant k equation equation equation

Table 3. Table showing chosen Planck’s quantities and its values and chosen values of certain constants.

The Heisenberg’s uncertainty principle can be solved in the same way, when we observe uncertainty and inability to observe certain parameters, in which the threshold values of Planck’s constants are manifested. It is important to understand that the observation of real parameters can be done using real instruments, yet the properties of virtual parameters cannot be investigated in such a way, only their threshold expressions can be investigated. In order to be able to investigate the whole process, machines would have to be built which would be able to capture such values, which is motivational only after a thorough theoretical background is given. Hence first a motivational, theoretical background is obtained, and then finances, which would be necessary for such research. Author’s motivation is to aid the acquisition of such theoretical background and possibly start the work for obtaining such goals.

The given work on gravitational interaction of photons is just an introduction into the field of ‘New Physics’, which the author is currently working on. However, the results are adequate for the military industrial complex hence, the release of further theoretical research should be handled with care [1,2].