Recent discovery of Higgs boson which has a relation to gravity but should be the boson particle with respect to the statistic poses some problems with gravitational constant origin and strength. Since boson is the antiparticle to itself, it may be created from the vacuum without any pair and since it may condense into the lowest state, the increased fluctuations of quantum vacuum near any particle will grow the final mass to infinity.
Fluctuations of quantum vacuum long ago were used to explain the origin of speed of light [1]. For the attenuation of the electric field near the charge the use of virtual dipoles from vacuum is relatively straightforward: the particle-antiparticle pair composed of fermions, which can not occupy the same state and thus can not accumulate near the charge up to infinite amounts, completely eliminating the electric field. Unfortunately, application of the same idea to the gravity fails simply because any particle has a mass and they all attract to the initial mass. While the usual particles like protons, neutrons, electrons etc will be attracted to the particle but being fermions can not accumulate infinitely, the Higgs boson can. It means that the virtual Higgs bosons will be clumping to any mass to infinity, creating infinitely heavy condensate, thus making the gravity impossible.
The plausible explanation is given in [2]: similar to the particle-antiparticle dualism, there are virtual gravitational dipoles formed by pairs matter- antigravitational matter (the mass being considered as independent quantum number, the whole set of antigravity particles should exist for both particles and antiparticles, effectively doubling the number of existing particles).
Those gravitational dipoles are formed by the particles, which may be bosons with respect to usual matter-antimatter relations but not with respect to gravity. Similar to the creation of the electron-positron pair in the intense electric field, those virtual dipoles will create pair particle - gravitational antiparticle in strong enough gravitational field (inside the dark hole, according to [2]).
Fortunately, antiparticles are formed not only in electric field, but also in any interactions of highly accelerated particles (that is how antiprotons are manufactured and separated by the electric and magnetic field). In a similar way the antigravitational particles should be formed (and may be already produced from time to time, but since the gravity is so much weaker compare to electric force, the usual separation methods in accelerators will render them unnoticed).
Using the formula derived for electric permittivity of vacuum from [1] it is even possible to estimate the mass of one component of such virtual dipole
εo=[(Kw2-1)3/2/Kw]*2e2/(3π*h*c)
here εo
- is the vacuum permittivity, e is the charge of electron, h is Planks constant, c is speed of light and Kw - is the coefficient received after the summation of all the possible fermion pairs in the vacuum near the charge.
The gravitational constant being considered similar to Coulomb constant for vacuum permittivity:
k=1/(4*π*εo
), that is εo
=1/(4π*k), where k=9*10exp(9) is Coulomb constant,
The equation would be (mass is instead of charge and gravitational constant instead of Coulomb constant):
1/(4π*G)=[(Kw2-1)3/2/Kw]*2m2/(3π*h*c)
where G is gravitational constant and m is the mass of the particle- gravitational antiparticle pair.
Using value of 32 for Kw- the constant calculated in [1] the value of mass is 1.84*10exp(-9) kg or 166 GeV
Assuming the evaluations are very approximate, the only close in energy particle is Higgs boson (125 GeV).
Thus it is possible to predict that during the Higgs boson production at CERN, from time to time the antigravitational Higgs boson will be generated (like in the case with antiparticles, it will have the same mass, but of the opposite sign). It may be easily distinguished because the decay path of it will include antigravitational particles instead of normal particles and antiparticles, which would move differently at decay. The Higgs boson and antigravitational Higgs boson will be born in pairs, of course, so the total energy would be 250 GeV, but this is still well below the possible energy of BAC, which is 14 TeV.
Being discovered, such antigravitational particle would allow to justify the quantum vacuum virtual particles approach to the gravitational constant value calculations (combining approaches of [1] and [2]) thus effectively unifying electricity and gravity on the basis of quantum vacuum properties.
References.
1. https://arxiv.org/abs/1302.6165
2. https://arxiv.org/abs/1405.5792
3.
Friday, December 20, 2019
Tuesday, December 10, 2019
Light matter attraction as a driving force for Galaxy rotation - the energy transformed from thermonuclear to mechanical
The dark matter modern approach to the explanation of galaxies rotation has one drawback - it is still considers stars as equivalent to rocks (planets). In reality stars have one distinct difference from planets (for planets the third Kepler Law explains all the motion perfectly) - they are generating energy by themselves. If only a small fraction of that energy is transformed through any mechanism into the mechanical energy, that may easily explain any rotation curve of the galaxy without any new hypothesis about predominant non-observable matter. Let's consider the bright star with luminocity of 1260 Sun and total inertial mass of 5.4 Sun (Polaris star). The total energy release would be 5*10exp(+29) J/s and mass would be 1.1*10exp(31) kg. If only 1% of the energy released is somehow transformed into the mechanical energy, the star may reach the rotational speed of 230000 m/s (Sun surrounding) for only 1.8 million of years (estimation done from 1/2*mV^2 formula). This is smaller than life time of the star of such initial mass (10 millions of years).
Thus the difference between the star and planet is essentially inside the star. The idea of the strongly gravitating slow light [1,2], may not only explain the too fast rotation of the stars in the galaxy (the effective gravitational mass is higher compare to the inertial mass) but also the overall dynamic of the stars in the galaxy (origin of spiral arms) and the difference between the elliptical and spiral galaxy (why the elliptical galaxy stopped rotating).
According to the hypothesis of [1], the stars has a lot of trapped photons inside. Not only the gamma quanta from the nuclear reaction but softer light like X-ray and visible light due to bremsstrahlung scattering of electron and ions inside the fully ionized plasma inside the star. Those photons are inside the environment with enormous value of effective refraction coefficient (inside the fully conductive media) and thus are moving really slow and gravitating very strongly (similar idea is expressed in [3]). The gravity-like behavior of slow photons is demonstrated in [4] experimentally (polaritons are exactly what is expected for photons inside the stars).
The photons inside the stars are gravitating according to general relativity, of course, they are not creating the mutually reciprocal force like the baryonic matter. The slow photons are attracted to the galaxy center (and much strongly if calculated per energy compare to baryonic matter) but not creating the additional distortion of time-space themselves (except for the equivalent inertial mass they have in vacuum, from E=m*c^2). Thus they create the additional force to the bright stars, which forces them toward the center of gravity (center of galaxy). This force moves the star to the new position and according to the momentum conservation law the star is accelerating (new equilibrium position closer to the center of rotation needs higher velocity). This mechanism effectively transforms the energy of the thermonuclear fusion into the mechanical energy necessary for the accelerated rotation. Thus the energy of the nuclear fusion is transformed into the rotation energy of the whole galaxy (the effect is smaller for light stars like Sun, but stars are created and dying continuously). In this situation the rotation of the galaxy is more like dynamo phenomena than static rotation of planets around the star.
That additional force might be expressed in the following formula:
F=K*E*M/(R*R)
The force is concentrated in the star, so for the outside space it will be the central force. The 1/(R*R) law follows from the attraction formula for light and from geometry of space-time (should be similar to Newtonian law in the weak gravitational limit). The force is proportional to the inertial mass of the object which attracts the star (or to the curvature created by the inertial mass in the weak gravitation limit of general relativity), since light is "attracted" due to the curvature of space-time (similar to the deviation of light near the star). But the force does not proportional to the inertial mass of the star which attracts, but rather to the total energy of trapped light inside E (and the coefficient K depends upon the type of star, upon the effective refraction coefficient inside, which makes the whole force non-universal). When the E of trapped light is zero the force is zero only the usual gravitation exist,
For the evaluation it is possible to assume that the value of F will depend upon the luminosity I of the star (it is an idea that the amount of light still trapped inside the star should correlate with the light emitted by star every second).
F=K*I*M/(R*R)
For evaluations it is possible to assume that the force from light matter should be at least equal to the gravitational force:
K*I*M/(R*R)~G*m*M/(R*R)
and then for the stars like Sun K=3.3*10exp(-7) m*s/kg
for bright stars like Polaris K=1.46*10exp(-9) m*s/kg
and taking the average (geometric one):
K~2*10exp(-8) m*s/kg
With this force the origin of spiral arms would be the higher velocity of bright stars compare to the rest of stars: the bright stars are short lived, but they are the main driving force for the rotation of galaxy - the additional force accelerates them very much like the rotation of the skater is accelerates when he or she pulls the leg in. This acceleration of rotation transfers to the rest of stars and the galaxy starts to rotate.
The gravitational force only is seemingly not enough to sustain the rotation: the elliptical galaxies are contracting radially, not rotating. Only young galaxies, full of new stars have enough energy to start rotation and hold it at the almost constant for all galaxies speed (the energy originates from the drain of stars in the black hole, very much like the rotation of water in the tub originates from the energy of the drained water). The comparison is not really quite well because the friction is much smaller, but it was found that the vortex in bathtub also need some threshold discharge rate [5] - if the discharge is too small, water drains pure radially.
It puts the elliptical galaxies as the final evolution stage of galaxy: it starts from protogalaxy, starts to rotate around the central black hole (spiral galaxy), slowly uses all of the necessary molecular clouds - no bright stars any more - and turns into the elliptical galaxy with huge black hole and aging low luminosity stars.
References.
1. https://tipikin.blogspot.com/2019/10/stars-are-full-of-trapped-light-may.html
2. https://tipikin.blogspot.com/2019/09/accelerated-rotation-of-star-because-of.html
3. https://arxiv.org/abs/0710.0273
4. https://funsizephysics.com/gravity-for-photons/
5.T.Kawakubo Y.Tsuchiya M. Sugaya K.Matsumura "Formation of a vortex around a sink: a kind of phase transition in a nonequilibrium open system" // Physics Letters A, Vol.68, No1, p.p.65-66, 1978
Thus the difference between the star and planet is essentially inside the star. The idea of the strongly gravitating slow light [1,2], may not only explain the too fast rotation of the stars in the galaxy (the effective gravitational mass is higher compare to the inertial mass) but also the overall dynamic of the stars in the galaxy (origin of spiral arms) and the difference between the elliptical and spiral galaxy (why the elliptical galaxy stopped rotating).
According to the hypothesis of [1], the stars has a lot of trapped photons inside. Not only the gamma quanta from the nuclear reaction but softer light like X-ray and visible light due to bremsstrahlung scattering of electron and ions inside the fully ionized plasma inside the star. Those photons are inside the environment with enormous value of effective refraction coefficient (inside the fully conductive media) and thus are moving really slow and gravitating very strongly (similar idea is expressed in [3]). The gravity-like behavior of slow photons is demonstrated in [4] experimentally (polaritons are exactly what is expected for photons inside the stars).
The photons inside the stars are gravitating according to general relativity, of course, they are not creating the mutually reciprocal force like the baryonic matter. The slow photons are attracted to the galaxy center (and much strongly if calculated per energy compare to baryonic matter) but not creating the additional distortion of time-space themselves (except for the equivalent inertial mass they have in vacuum, from E=m*c^2). Thus they create the additional force to the bright stars, which forces them toward the center of gravity (center of galaxy). This force moves the star to the new position and according to the momentum conservation law the star is accelerating (new equilibrium position closer to the center of rotation needs higher velocity). This mechanism effectively transforms the energy of the thermonuclear fusion into the mechanical energy necessary for the accelerated rotation. Thus the energy of the nuclear fusion is transformed into the rotation energy of the whole galaxy (the effect is smaller for light stars like Sun, but stars are created and dying continuously). In this situation the rotation of the galaxy is more like dynamo phenomena than static rotation of planets around the star.
That additional force might be expressed in the following formula:
F=K*E*M/(R*R)
The force is concentrated in the star, so for the outside space it will be the central force. The 1/(R*R) law follows from the attraction formula for light and from geometry of space-time (should be similar to Newtonian law in the weak gravitational limit). The force is proportional to the inertial mass of the object which attracts the star (or to the curvature created by the inertial mass in the weak gravitation limit of general relativity), since light is "attracted" due to the curvature of space-time (similar to the deviation of light near the star). But the force does not proportional to the inertial mass of the star which attracts, but rather to the total energy of trapped light inside E (and the coefficient K depends upon the type of star, upon the effective refraction coefficient inside, which makes the whole force non-universal). When the E of trapped light is zero the force is zero only the usual gravitation exist,
For the evaluation it is possible to assume that the value of F will depend upon the luminosity I of the star (it is an idea that the amount of light still trapped inside the star should correlate with the light emitted by star every second).
F=K*I*M/(R*R)
For evaluations it is possible to assume that the force from light matter should be at least equal to the gravitational force:
K*I*M/(R*R)~G*m*M/(R*R)
and then for the stars like Sun K=3.3*10exp(-7) m*s/kg
for bright stars like Polaris K=1.46*10exp(-9) m*s/kg
and taking the average (geometric one):
K~2*10exp(-8) m*s/kg
With this force the origin of spiral arms would be the higher velocity of bright stars compare to the rest of stars: the bright stars are short lived, but they are the main driving force for the rotation of galaxy - the additional force accelerates them very much like the rotation of the skater is accelerates when he or she pulls the leg in. This acceleration of rotation transfers to the rest of stars and the galaxy starts to rotate.
The gravitational force only is seemingly not enough to sustain the rotation: the elliptical galaxies are contracting radially, not rotating. Only young galaxies, full of new stars have enough energy to start rotation and hold it at the almost constant for all galaxies speed (the energy originates from the drain of stars in the black hole, very much like the rotation of water in the tub originates from the energy of the drained water). The comparison is not really quite well because the friction is much smaller, but it was found that the vortex in bathtub also need some threshold discharge rate [5] - if the discharge is too small, water drains pure radially.
It puts the elliptical galaxies as the final evolution stage of galaxy: it starts from protogalaxy, starts to rotate around the central black hole (spiral galaxy), slowly uses all of the necessary molecular clouds - no bright stars any more - and turns into the elliptical galaxy with huge black hole and aging low luminosity stars.
References.
1. https://tipikin.blogspot.com/2019/10/stars-are-full-of-trapped-light-may.html
2. https://tipikin.blogspot.com/2019/09/accelerated-rotation-of-star-because-of.html
3. https://arxiv.org/abs/0710.0273
4. https://funsizephysics.com/gravity-for-photons/
5.T.Kawakubo Y.Tsuchiya M. Sugaya K.Matsumura "Formation of a vortex around a sink: a kind of phase transition in a nonequilibrium open system" // Physics Letters A, Vol.68, No1, p.p.65-66, 1978
Accelerated rotation of stars in the galaxy
Accelerated rotation of the star because of the difference between the effective gravitational mass and real inertial mass.
For baryonic matter the gravitational mass is equal for the inertial mass (Einstein's postulate). For light the inertial mass is still zero but the effective gravitational mass may be assumed (the light deviates near the star). If the enormous amount of light is trapped inside the star, the overall effective gravitational mass of the star Mg may be larger than the effective inertial mass Mi. How it will influence the rotation of the star around the galaxy center?
From Newton mechanics:
where G is gravitational constant, M is effective mass of the galaxy (for simplicity), v is the linear velocity of the star around center of galaxy, mg is the effective gravitational mass of the star, mi is the inertial mass of the star, R is the radius of rotation. If due to the trapped light the effective gravitational mass is much larger compare to inertial mass, so the velocity of the rotation. In this case the dark matter is not necessary for the accelerated rotation of the stars in the galaxy
For baryonic matter the gravitational mass is equal for the inertial mass (Einstein's postulate). For light the inertial mass is still zero but the effective gravitational mass may be assumed (the light deviates near the star). If the enormous amount of light is trapped inside the star, the overall effective gravitational mass of the star Mg may be larger than the effective inertial mass Mi. How it will influence the rotation of the star around the galaxy center?
From Newton mechanics:
mi*v2/R=G*mg*M/R2 and v=[(G*M/R)*(mg/mi)]1/2
where G is gravitational constant, M is effective mass of the galaxy (for simplicity), v is the linear velocity of the star around center of galaxy, mg is the effective gravitational mass of the star, mi is the inertial mass of the star, R is the radius of rotation. If due to the trapped light the effective gravitational mass is much larger compare to inertial mass, so the velocity of the rotation. In this case the dark matter is not necessary for the accelerated rotation of the stars in the galaxy
Wednesday, November 27, 2019
Weak equivalence principle is not valid for stars - observations of mass-luminosity relation for visual binaries
Stars are special objects in the sense of the possible gravitational deviations: they have both barionic and non-barionic matter (like trapped and slowly advancing to the surface light) inside. While for barionic matter the weak equivalence principle was established by Kepler (planets orbiting around stars) it was never checked for stars.
The good example are binaries. There are many binary stars which are visible as double stars with resolved period and axis and ratio of inertial masses (through measurements of the velocities of stars). Many parameters of such stars are published in [1]
The usual formula applied to the stars from the third Kepler Law:
However, the light theoretically may have much higher gravitational pull compare to the inertial mass from E=mc*c relation (it is assumed that the inertial mass of light being emitted and reabsorbed inside star is still according to E=mc*c, as it was proved by Einstein himself) [2]. The presence of slow light may modify the gravitational pull, making it much stronger for the star which has more trapped light (and other non-barionic matter). While the exact amount of trapped light is difficult to calculate (not much is known about the light content of the interior of fully ionized plasma), it is obvious that this amount is correlated with luminosity of the star - the higher the luminosity, the higher the amount of trapped light and the higher the additional gravitational pull on the star (the higher the deviation between the gravitational and inertial mass).
In the derivation of the formula (1) the gravitational masses are always comes as a product [3]:
The modified third Kepler Law:
To determine the masses from the observation of binaries we need: T, a, and ratio of masses m1/m2=n. Since the ratio of masses is determined through the Doppler shift of spectra of stars, is a ratio of inertial masses. We have two equations for masses m1, m2:
Then:
m2=4π2*a3/[G*T2*K1*K2*(n+1)]
m1=4π2*a3*n/[G*T2*K1*K2*(n+1)]
Suppose we decided to determine the inertial masses from the visual binaries with two distinct masses m1>>m2. How it would influence the mass-luminosity correlation (like in [1])?
It is possible to show, that contrary to the case of valid third Kepler Law the slope of the dependence will be depended upon the ratio of masses!
Lets consider three cases:
1.Binary m1 and m1
2.Binary m2 and m2
3.Binary m1 and m2
In the first case the value of m1 is (because n=1)
m1=m1(old)/[K1*K1], here m1(old)=4π2*a3/[G*T2*2]
Here m1(old) is real inertial mass. K1 is large and the value of m1 is shifted strongly toward smaller mass compare to real inertial mass.
In the second case the value of m2 (n is equal to 1)
m2=m2(old)/[K2*K2]
If K2 is smaller than 1 (supposedly Sun has the value of K exactly one) the mass of smaller star will shifted strongly toward larger mass
In the third case the value of m1 is
m1=m1(old)/[K1*K2], m1(old)=m1(old)=4π2*a3*n/[G*T2*(n+1)]
Since both coefficients K1 and K2 are here, one is small and one is big, the shift compare to the real inertial mass is smaller
m2=m2(old)/[K1*K2]
This idea may be immediately checked. If the mass-luminosity curve is plotted using first only stars with close masses, it will be compressed because of K1*K1 and K2*K2 coefficients along the x-axis (the slope will be larger). If the same curve is plotted using the stars with different masses (preferably with large difference, but I used what we have in [1]) it will be much more spread. I manually chose approximately half of visual binaries (17 binaries or 34 stars) from Table 1A from [1] with close masses and obtained the relation between the luminosity and mass:
Absolute luminosity= -3.2119*ln(m)+5.1264
And for the rest of the binaries (21 binaries, 42 stars) - masses are different:
Absolute luminosity = -2.495*ln(m)+5.4042
The white dwarfs were excluded, like in [1].
The scattering in the second case is much larger (as expected, because the product of coefficients K1 and K2 is highly unpredictable), but they must give much smoother curve if the coefficients are the same - the shift is larger, but it is more predictable - obviously it is some smooth function of luminosity and can not jump from star to star).
Indeed as predicted the slope is larger beyond any error for the subset of close in masses stars compare to the far in masses stars.
Since the deviation from Newton law for the barionic matter of such large scale would be noticed long ago in our Solar system (some small deviation due to GR are not considered), the only possible explanation is that the weak equivalence principle does not hold for gravitation of stars (mixture of barionic and non-barionic matter), possibly due to mechanism outlined in [2].
![]()
References.
1.George E. McCluskey, Jr, Yoji Kondo "On the mass-luminosity relation" // Astrophysics and Space Science 17 (1972), p.p.134-149
http://articles.adsabs.harvard.edu//full/1972Ap%26SS..17..134M/0000137.000.html
2.D.S.Tipikin, publication on blog
https://tipikin.blogspot.com/2019/10/stars-are-full-of-trapped-light-may.html
3.http://www.astro.caltech.edu/~george/ay20/Ay20-Lec4x.pdf
The good example are binaries. There are many binary stars which are visible as double stars with resolved period and axis and ratio of inertial masses (through measurements of the velocities of stars). Many parameters of such stars are published in [1]
The usual formula applied to the stars from the third Kepler Law:
T2=4π2*a3/[G(m1+m2)] (1)
Here T is the period of rotation of one star around the second one, a is semi-axis, m1 and m2 are masses of the stars (assuming gravitational mass is equal to inertial mass) and G is gravitational constant.However, the light theoretically may have much higher gravitational pull compare to the inertial mass from E=mc*c relation (it is assumed that the inertial mass of light being emitted and reabsorbed inside star is still according to E=mc*c, as it was proved by Einstein himself) [2]. The presence of slow light may modify the gravitational pull, making it much stronger for the star which has more trapped light (and other non-barionic matter). While the exact amount of trapped light is difficult to calculate (not much is known about the light content of the interior of fully ionized plasma), it is obvious that this amount is correlated with luminosity of the star - the higher the luminosity, the higher the amount of trapped light and the higher the additional gravitational pull on the star (the higher the deviation between the gravitational and inertial mass).
In the derivation of the formula (1) the gravitational masses are always comes as a product [3]:
F=G*M1*M2/r2
Here M1 and M2 are gravitational masses. Assuming the added pull is proportional to luminosity which is proportional to mass (whether gravitational or inertial) [1], it is possible to assume:
F=G*K1*K2*m1*m2/r2
Here K1 and K2 are multiplicity coefficients, the value of K may be especially high to ultra-bright star. It is important that both coefficients for binaries are always a product. The modified third Kepler Law:
T2=4π2*a3/[G*K1*K2*(m1+m2)]
Here m1 and m2 are inertial masses. When K1=K2=1, the third Kepler Law for barionic matter is obtained.To determine the masses from the observation of binaries we need: T, a, and ratio of masses m1/m2=n. Since the ratio of masses is determined through the Doppler shift of spectra of stars, is a ratio of inertial masses. We have two equations for masses m1, m2:
G*K1*K2*(m1+m2)=4π2*a3/T2
m1/m2=nThen:
m2=4π2*a3/[G*T2*K1*K2*(n+1)]
m1=4π2*a3*n/[G*T2*K1*K2*(n+1)]
Suppose we decided to determine the inertial masses from the visual binaries with two distinct masses m1>>m2. How it would influence the mass-luminosity correlation (like in [1])?
It is possible to show, that contrary to the case of valid third Kepler Law the slope of the dependence will be depended upon the ratio of masses!
Lets consider three cases:
1.Binary m1 and m1
2.Binary m2 and m2
3.Binary m1 and m2
In the first case the value of m1 is (because n=1)
m1=m1(old)/[K1*K1], here m1(old)=4π2*a3/[G*T2*2]
Here m1(old) is real inertial mass. K1 is large and the value of m1 is shifted strongly toward smaller mass compare to real inertial mass.
In the second case the value of m2 (n is equal to 1)
m2=m2(old)/[K2*K2]
If K2 is smaller than 1 (supposedly Sun has the value of K exactly one) the mass of smaller star will shifted strongly toward larger mass
In the third case the value of m1 is
m1=m1(old)/[K1*K2], m1(old)=m1(old)=4π2*a3*n/[G*T2*(n+1)]
Since both coefficients K1 and K2 are here, one is small and one is big, the shift compare to the real inertial mass is smaller
m2=m2(old)/[K1*K2]
This idea may be immediately checked. If the mass-luminosity curve is plotted using first only stars with close masses, it will be compressed because of K1*K1 and K2*K2 coefficients along the x-axis (the slope will be larger). If the same curve is plotted using the stars with different masses (preferably with large difference, but I used what we have in [1]) it will be much more spread. I manually chose approximately half of visual binaries (17 binaries or 34 stars) from Table 1A from [1] with close masses and obtained the relation between the luminosity and mass:
Absolute luminosity= -3.2119*ln(m)+5.1264
And for the rest of the binaries (21 binaries, 42 stars) - masses are different:
Absolute luminosity = -2.495*ln(m)+5.4042
The white dwarfs were excluded, like in [1].
The scattering in the second case is much larger (as expected, because the product of coefficients K1 and K2 is highly unpredictable), but they must give much smoother curve if the coefficients are the same - the shift is larger, but it is more predictable - obviously it is some smooth function of luminosity and can not jump from star to star).
Indeed as predicted the slope is larger beyond any error for the subset of close in masses stars compare to the far in masses stars.
Since the deviation from Newton law for the barionic matter of such large scale would be noticed long ago in our Solar system (some small deviation due to GR are not considered), the only possible explanation is that the weak equivalence principle does not hold for gravitation of stars (mixture of barionic and non-barionic matter), possibly due to mechanism outlined in [2].
References.
1.George E. McCluskey, Jr, Yoji Kondo "On the mass-luminosity relation" // Astrophysics and Space Science 17 (1972), p.p.134-149
http://articles.adsabs.harvard.edu//full/1972Ap%26SS..17..134M/0000137.000.html
2.D.S.Tipikin, publication on blog
https://tipikin.blogspot.com/2019/10/stars-are-full-of-trapped-light-may.html
3.http://www.astro.caltech.edu/~george/ay20/Ay20-Lec4x.pdf
Friday, October 11, 2019
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.
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:
Vp=a*t, a=F/m, F=G*m*Ms/(r2) → a=G*Ms/(r2)
here
Vp 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, Ms
t=2r/c and
ϒ=Vp/c=G*Ms*2r/(r2*c2)=2G*Ms/(r*c2)
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:
The force on the photon toward the center of Galaxy:
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=Vp*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)
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/Fg=E*(n)2/(Ms*c2)
Adding multiple 2 from Einstein's formula:
F/Fg=2*E*(n)2/(Ms*c2) This value may be somehow estimated using the data for Sun. Mass of the Sun is
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
References.
1. https://en.wikipedia.org/wiki/Abraham%E2%80%93Minkowski_controversy
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:
Vp=a*t, a=F/m, F=G*m*Ms/(r2) → a=G*Ms/(r2)
here
Vp 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, Ms
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:
Vp=G*Ms*t/(r2)t=2r/c and
ϒ=Vp/c=G*Ms*2r/(r2*c2)=2G*Ms/(r*c2)
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), Vp=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=Vp*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)
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
Fg=G*Ms*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/Fg=E*(n)2/(Ms*c2)
Adding multiple 2 from Einstein's formula:
F/Fg=2*E*(n)2/(Ms*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/Fg=(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 noticableStill 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
Thursday, September 26, 2019
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
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
Thursday, September 5, 2019
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:
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).
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 λ2For 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).
Wednesday, August 28, 2019
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):
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.
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.
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