Stars are full of trapped light. May this fact help to explain dark matter presence?

"Light Matter" may help to explain dark matter absence, at least partially.
Light is bended by the gravity - this is very old phenomenon, once confirmed the general theory of relativity. The Einstein formula for the light bending is:
ϒ=4*G*M/(r*c²)
where ϒ is the angle of the deviation of the light near the star, M is the mass of star, G is gravitational constant, c is speed of light and r is the shortest distance between the light and star.

From this formula it follows that the light, being traveled near the star, influenced the star, too, transferring part of its pulse to star. While for passing light this is truly negligible, what about the light trapped inside the star itself? It is well known fact, that the gamma quantum generated during the fusion in the Suns core, will spend millions of years till it is emitted by the Sun. During all this time the quantum of the light will be subject of the gravitational pull of other stars (Galaxy in general to explain the additional force added to the usual gravity which may help to explain dark matter partially). This force will mean that some kind of gravitational mass equivalent is added to the star. According to the weak equivalence principle the amount of inertial mass of the star does not change at such process.
The evaluation of the importance of such additional force from the photons back onto the barionic matter may be done as follows:
For the formal consideration (just to have the formula) the photon is treated as having mass m. Then deviation of the light near the star would be:
V_p=a*t, a=F/m, F=G*m*M_s/(r²) → a=G*M_s/(r²)
here
V_p is the perpendicular component of the velocity of the photon of formal mass m, t is time of flight near the star, a is the formal acceleration of the photon of formal mass m, M_s 

is the mass of the star, G is gravitational constant, r is the effective distance between the star and the photon, t is the effective time of flight of the photon near the star. Knowing the values of the acceleration and time it would be possible to evaluate the perpendicular component of velocity:

V_p=G*M_s*t/(r²) Evaluation of the time of flight will lead to "classical" formula for the deviation angle:
t=2r/c and
ϒ=V_p/c=G*M_s*2r/(r²*c²)=2G*M_s/(r*c²) which is exactly 2 times smaller than the Einstein results, what confirmed the general theory of relativity.

The same formal approach may be used to evaluate the influence of the galactic pull onto the all the photons inside the star (multiplying later the result by 2 to account to general theory of relativity).
The photons generated inside the star during the fusion are not leaving it immediately but essentially trapped inside for millions of years. During all this time all the numerous trapped photons are generating the pull toward the center of galaxy, which may be estimated as follows:
Using the same formal approach the formal "force" onto the photon is:

F=G*m*M/(r²)

Here G is gravitational constant, M is the effective mass of the Galaxy, r is the distance between the photon and the Galaxy center, m is the formal "mass" of the photon (the idea of such approach is that since it allows to obtain Einstein formula with accuracy of factor 2, it will allow to evaluate this pull with the same accuracy - later final formula to be multiplied by 2).
The force on the photon toward the center of Galaxy:

F=ma, a=G*M/(r²), V_p=at=G*M*Δt/(r²)

Here F is the force onto the photon toward the center of Galaxy, a is the acceleration created by such force, Vp is the perpendicular component of the velocity the photon obtained during the time Δt of its stay inside the star.

What would be the change of pulse of the photon during such stay? It may be evaluated assuming the velocity of the photon equals to   c/(n)^1/2
where n is the effective refraction coefficient for the light in the star medium (since the interior of star is enormously dense and hot plasma, this value is not 1)
The change of pulse of photon is:
Δp=V_p*n*P/c
here Δp is the change of pulse of photon, P is the total pulse of photon, Vp is the obtained perpendicular component of the velocity, c/n
is the velocity of light inside the star. The obtained velocity Vp is considered very small compare to the initial velocity - despite million of years, the photon inside the star is moving as a photon only for small time periods - it is absorbed and re-emit almost instantly. Using the formula for Vp it is possible to obtain:
Δp=G*M*Δt*n*P/(r²*c)
where Δp is the full change of pulse during time period Δt, G is the gravitational constant, M is the mass of Galaxy, n is the effective refraction coefficient, P is the full pulse of the photon, r is the distance from the star to the Galaxy center, c is speed of light.
But Δp/Δt is the effective force (toward the center of the Galaxy) expressed through pulse of photon instead of time Δt. For one photon:
F=Δp/Δt=G*M*P*n/(r²*c) Here F is the pull onto the photon toward the center of the Galaxy, M is the effective mass of the Galaxy P is the pulse of the photon, n is the effective refraction coefficient, c is speed of light, G is the gravitational constant, r is the distance from the star to the center of Galaxy.
The pulse of photon is P=n*E/c for the refracted light (Minkowski formula [1]) and:
F=Δp/Δt=G*M*e*(n)²/(r²*c²)
Where e is the energy of one photon. For the total force exhibited by all the photons this force would be:F=Δp/Δt=G*M*E*(n)²/(r²*c²)
Where E is the total energy of the photons inside the star. Now it is possible to calculate the ratio of this force to the gravitational force exhibited by the star (as derived from weak equivalence principle E=mc*c). The gravitational force

F_g=G*M_s*M/(r²) where G is gravitational constant, Ms is the mass of star, M is the mass of Galaxy, r is the distance between the star and Galaxy. The ratio of those forces

is:
F/F_g=E*(n)²/(M_s*c²)
Adding multiple 2 from Einstein's formula:
F/F_g=2*E*(n)²/(M_s*c²) This value may be somehow estimated using the data for Sun. Mass of the Sun is

2*10³⁰ kg, energy release is 3.9*10²⁶ Watt and assuming photons are trapped inside for 10 millions years ( 3.15*10¹⁴ s) the ratio would be:

F/F_g=(n)²*1.4*10^-6

which is very small if n=1. However, the star matter is relative not investigated and the effective refraction coefficient may be very high (in metals, for example it is supposed to be infinity). Essentially the light inside the Sun may be traveling very slow. If in the highly conductive full ionized plasma value of n is 100, the added force may jump to 1.4 % and become noticable
Still there is no additional gravitational pull for the Sun, which lives for billion of years. The dark matter however usually associated with the presence of young stars in the sleeves of Galaxy. For the star with the big initial mass the life time may be just 10 millions of years. It means that such star will emit the equivalent of 10^-7 of its mass per year as radiation and if the photons are still trapped inside for 10 millions of years that means that the ratio of forces

now is 2*n²

^{That means that for the star of larger mass the pull toward the center of Galaxy, associated with the light matter may be many times larger than the gravitational pull from the ordinary matter. But this trapped light still makes contribution to inertial mass E=m*c*c (according to weak equivalence principle), which would  mean that it will be rotating faster compare to pure barionic mass body like planet. This may explain the dark matter, at least partially.}

 

 

In a broad sense this idea is in today track of unification of matter and wave behavior. In addition to being full with trapped for long time quanta (pure wave), inside the star the process of tunneling of baryonic particles takes place (during the fusion). However, during the tunneling the baryonic particle is pure wave (the energy is negative, what is inconsistent with particle). Thus inside the star more energy is in wave form and waves are attracted gravitationally differently, so the overall star may have larger than possible orbital speed without presence of dark matter. More experimentation with plasma in fusion reactors may be necessary to understand the behavior of stars.

References.
1. https://en.wikipedia.org/wiki/Abraham%E2%80%93Minkowski_controversy

 
 
 
 
 
 

 

 
 












 
 
 



 

 




 
 
 


 

 




 












 
 
 




 



 

 
 

 
 

 







 





 


 



 















 

The possible way to search for new discoveries in physics: reciprocity between the matter and wave behaviour of matter

The idea of the matter-wave dualism is very old. Actually De Broglie himself was strong supporter of non-zero mass of photon, what means that from his point of view, not only all the mass particles have a wave associated with them (De Broglie wave), but all the waves (photons) have something with mass associated with them (see, for example [1]). I am trying to infer some new ideas from the following hypothesis: any matter is simultaneously particle and wave. How to describe it mathematically is a difficult problem and probably such mathematical formalism does not exist yet. However, some interesting ideas may be inferred from the mere fact of such duality. The most obvious is the mass of photon - it should have a mass, despite it is clear that it is very, enormously  small. However, this fact will instantly explain the quantization of the light absorption - the light is quantized because it is countable very much like any other particle.
The easiest phenomenon which would be possible to predict has already an analog in nuclear physics. This is Ramsauer Model for cross-sections of different events (like nuclear fission) [2]. According to this result, the smaller the energy of neutron, the better his chances to start fission, what is consistent with the quantum mechanics idea of De Broglie wave around the neutron. A similar contrary to usual sense behavior is observed in Ramsauer-Townsend effect - at certain low energy of electron the gas in the chamber becomes transparent (the De Broglie wavelength is around the mean free path for electrons). For future use the ultracold neutrons with De Broglie wavelength of 10 A are supposed to be generated in new sources [3]. So the idea of finding a phenomena, reciprocal to phenomena well known for light but being applied to matter wave considered as the main part of the wave-matter particle is appealing.
Some research groups are already observing for matter waves the phenomena, exactly like those previously described for light. For example, the rotation of particle beams in space without external fields was described in [4]. Authors correctly described the behavior as impossible from classical point of view for electrons (particles), easily observed for photons (wave) and now observed for electrons but created by the De Broglie part of electrons (wave part of the matter). This phenomena confirms the reciprocity idea: the phenomenon exists for pure waves (photons), thus it must exist for matter waves (in the case the wave part of the particle is essential, as for the case of ultra slow electrons [4])
The unusual example of the appearance of the wave properties of the particles (electron) would be
 observation of the cathodoluminescence in some compounds for extremely low energies of electrons (1-3 eV). Usually the cathodoluminescence is easily observed and important phenomenon for energies of  few kV. At this region the electron is working essentially as a particle only and simply creating excitation through hit of particle. But for usual light the luminescence is easily observed for energies of few eV - because they are waves. Even despite charge interactions, if the electron is working as a wave (reciprocity principle), the resonances may be predicted for very low energy electrons in the range 1-3 eV. The idea is that electron in this region has the essential wave admixture. Despite the De Broglie wavelength is still much smaller compare to light with this energy, it may be enough to be absorbed as a wave, not interact as a particle. In this situation the sharp in energy resonance is expected for the electron created luminescence due to the interaction of electron as wave, not as a particle.




References.
1. https://arxiv.org/pdf/hep-ph/0107122.pdf
2. https://en.wikipedia.org/wiki/Neutron_cross_section
3. https://physicsworld.com/a/neutrons-for-the-future/
4. https://iopscience.iop.org/article/10.1088/1367-2630/ab152d/pdf

Neutron enigma and Einstein's second coefficient: may the smaller lifetime of ultra-cold neutrons be explained by the induced decay (similar to fission process and lasers)?
Modern physics is quickly developing the unified theory of wave-particle mathematical formalism. While the exact equations, which would describe in one limit the particle (pure mass, Newton-Einstein mechanic) and in another limit the pure wave (Maxwell equation) are far from completion, the preliminary use of such concept may allow to explain some modern phenomena and predict new.
The idea is: any matter is neither particle nor wave but both. It means that it has two intrinsic parts: matter and wave, considered for some approximation as a sum. The closest modern approach would be consider De-Broglie wave as material and consider any particle as consisted of two parts: usual particle (inertial mass) and De-Broglie wave. In this case the photon must have a finite (despite enormously small) mass and any moving particle has the added energy associated with dragging De-Broglie wave. Photon is almost pure De-Broglie wave and stopped classical particle (neutron) is almost pure particle. However, even the highest energy gamma-quantum has some finite mass inside and even ultra-cold neutron has some energy associated with De-Broglie wave - the matter and wave are inseparable in principle.
In this case the idea of reciprocity of physical phenomena may appear: each phenomena for particles has the similar phenomena for waves and vice versa. Photon - almost pure wave - has Einstein's first and second coefficients associated with him. Any particle like neutron must have reciprocal coefficients associated with De-Broglie part of particle. First coefficient A is responsible for spontaneous decay of excited atom and the corresponding coefficient is simply spontaneous decay of neutron. Einstein's second coefficient is responsible for induced decay of excited atom (lasers) and the corresponding second coefficient for neutron would be the induced decay of excited nucleus (another neutron).
It is interesting that such idea is already applied to fission process, where the energy dependence of the cross-section of fission induced by neutron has in excellent agreement with squared De-Broglie wavelength (at least at lower energies and without consideration of resonances). From the wave-particle unification point of view the fission process is laser like process but for nuclei. It may be even possible that in fission the created neutrons have exactly the same De-Broglie wave as the initial neutron, but since in neutrons contrary to photons the De-Broglie part of matter is small, the neutrons as a whole are not looking exactly coherent as created photons in laser. The matter part of neutrons is obviously not synchronized and de-coherent. And the cross-section of both processes is governed by the similar equations:
Ramsauer model for fission: σ(E)~π(R+λ)²~ λ² for small energies

Einstein's second coefficient:

σ₂₁=A₂₁*g(λ)*(λ²)/(8π*n²)

In both cases the cross-section is proportional to λ²
For the case of neutron enigma it means that the effect of deviation of lifetime for neutrons would be even more pronounced in the case of ultra-ultra cold neutrons and it will also strongly depend upon the concentration of neutrons (very much like for efficient nuclear explosion the critical mass is necessary or critical density).
Hopefully the future experiments concerning the neutron enigma will involve more and more slow neutrons and this predicted effect will be observed.
Einstein's second coefficient was derived using perturbation theory by Dirak (P.A.M. Dirac, Proc.Roy.Soc., A114, 243, 1927 "The quantum theory of the Emission and Absorption of Radiation")
Most probably exactly the same formalism may lead to the derivation of the cross-section in the case of fission process and for neutron enigma, assuming the De-Broglie wave is considered instead of photons as in the article.
That does  not mean that the De-Broglie wave may be treated separately as a similar to photons (see the beginning of the blog). The idea is that particle is a sum of De-Broglie wave and particle is a very rough approximation. The real mathematical description of such matter-wave object is absent now. However, even the simplistic treatment of the particle as a sum of matter and wave may help to establish the reciprocal phenomena for both particles and waves (like the idea of existence of Einstein's second coefficient for the particles).

About the correlation function between two vectors and quantum superposition of photons.
For many years, starting 1982 numerous researchers are investigating the so-called quantum entanglement - quantum superposition of polarized photons. The work started by Alain Aspect, who found that the correlation function between the two simultaneously generated photons in a radiative cascade of calcium [1] is not linear, but follows the law Cos(F), where F is the angle between the polarizers. For intensity that would mean Cos²(F) law. This is exactly the law expected for two completely independent by equally polarized photons (Malus Law).
The deviation from Bell's inequality was thought to occur because of the idea (wrong idea) that for classical case the correlation function between the polarization vectors would be linear (that is directly proportional to angle between polarizers). This is not possible because of the mathematical definitions of vectors: according to [2] the correlation function between any vectors (quantum or classical) must be expressed as a function of Cos and Sin and by no means may be simply proportional to angle. In [2] the correlation function between any vectors is to be proved to be Cos(F) (because it is actually simply normalized dot product of two vectors):

Correlation=Cos(a^.b)=(a^.b)/(|a|^.|b|)

In this case either classical or quantum correlation will follow the Cos(F) law (simple Malus law) and no deviation from Bell's inequality is observed. In [1] a simple generation of two equally polarized photons was observed without any quantum superposition between them.
Linear function of an angle is not possible for correlation function because it will have two special points (at 0 and at 90 degrees), where the derivative is discontinuous, which is not possible for correlation function which must be smooth function. Thus the zig-zag correlation function for classical vectors is equally impossible as for quantum vectors, and the presence of Cos(F) is not proof of quantum behavior of the two independent photons in [1].
This does not exclude the possibility of quantum superposition of photons (and action at the distance), simply the present papers are not proof of it.

References.
1.Alain Aspect, Philippe Grangier, Gerard Roger "Experimantal realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell's inequalities"//Physical Review Letters, Vol.49, No 2, p.p.91-94, 1982.
2.Zenon Gniazdowsi "Geometric interpretation of correlation" // Zeszyty Naukowe Warszawsiej Szkoly Informatyki, No 9, Vol.7, 2013 p.p.27-35.

3D television and what is the origin of discomfort

3D television is a great thing, especially for the people who weared glasses half a life. Indeed, when I looked through the glasses to the screen, the nice picture of the shaped figures sprang into the view. Some people are talking about the problem of the vision, that looks layered, that is a little blurred on the corners, but this is only temporily. The childhood problem of 3D television is easily understood by the people, who wear glasses in everyday life. Not every glasses works well, in addition to different lenses for different eyes (right versus left) the problem of astigmatism is very important and the problem of the ceparation between the centers of the lenses. That is why I was visiting my physician (optometrist) every year in the childhood till the vision is finally stabilized. She measured carefully the distance between the pupils, the slightes possible askew view and finally the pharmasist was able to manufacture exactly what I need. The same is true for TV. Not just the modern glasses for 3D TV are looking ugly and nonfashion, they should be adopted for everybody's eyes. So very soon the long lines of people will be standing to optometrists offices, looking for prescription of the 3D glasses. It is interesting to  note, that wearing of glasses over glasses is very bad and now the persons with the bad eyes will be trying to make the additional set of spectacles with polarized lenses (3D demand) and with different dioptries for every eye to have the same clear and cristall view the modern spectacles can give for everybody.

Crosscountry skiing in Ithaca

There are two types of skiing - skiing at mountain resort and cross-country. The first one is expensive and more to spend time, not for real sporting hard work. The crossc-ountry skiing is not for lazy people, because the gravitational force of the Earth, that pulling you down from the mountain at mountain resort is not helping you now. Sometimes it works against you, when you climb a hill, sometimes allows some relaxation, when you race down the hill, but on average, like in running, you are working hard to complete the distance. In Russia this tipe of sport is extremely popular among all because of a three snow months. In Ithaca in normal year it is possible to catch 3-4 weekends, when the trail is good. Again, at mountain resort the people are making the artificial snow, but nobody is making artificial snow for cross-country and now the weather alone is responsible for strong enough snow layer to run the distance competing with the seconds on the chronometer. In 2007 I found an exellent place to run - Poddunk center near the Ithaca, on route 96 north. If the sun is shining brightly and the snow is good enough to cover all the remnants of the farmers crop in the fields, the trail will be in an exellent condition and in this case the distance is especially fun to run. The good trail means I am not thinking about where to put the ski on the next step and all the efforts are concentrated onto the wide step and stronger pushes with ski sticks. At those moments, when I running down the hill, I feel myself very excited about the velocity I can develop and how strong I am and how strong are my pushes. If the weather is not so good and windy, the trail is normally half covered by snow delivered by wind and more efforts are necessary to guess the trail with the ski and less fun remains. Still, the exersize is good and after couple of hours, what corresponds to 10-20 km depending on conditions of trail the feeling of an exellent outdoor relaxation persists.

Grocery shopping in finger lakes region

Grocery shopping is something everybody is doing every day, and many are interested in local farmers production. These are good quality, definetly organic and fun to shop cabbages, eggs, redish, potatoes, pumpkins. Especially reddish, since in retailer shops the black reddish and white reddish are rear guests, and for those who has a strong habit for it (like Russians) it will be quite a problem to check many local farmers markets to buy some. Among the big retailers the best is Wegmans, followed by Tops and others. Actually due to great choice Wegmans is the most popular despite the higher price compare to Tops. Both have one more important advantage - they work overnight, this is especially good when I had have sleeplesness, I used to walk to the nearest shop at midnight and buy stuff. Couple of hours being spent walking and choosing and buying and bringing the grocery  back, the sleeplesness was over and morning was bright without any sleep problems. Compare to Wegmans in Tops the prices are lower and  cakes, juices, milk cartoons  are of different style (for example, in Tops I bought unsulted buttermilk that was possible to buy previously just in ShopRite near Atlantic City - for a person from Moscow unsalted buttermilk is really a great drink, as well as unsalted cottege cheese). But in Wegmans the real rye bread is present, with the quality outweighting the Moscow "black bread". This Kostenbrot is sold in huge loafs or in smaller size loafs and has an exellent taste. The rest of grocery shopping is similar in both Wegmans and Tops, but in the smaller retailer shops not all the variety is present.