Two photon absorption spectroscopy is well known non-linear optic phenomena [1]. In this phenomena the virtual level is present which allows to absorb the second photon and thus excite the state with energy equal to two times the energy of the original quantum. The corresponding two-photon excited fluorescence is well known (and now three-photon excited fluorescence is known well). The most important observation connected with multiple quanta absorption is the non-linear dependence on power: this allows easily distinguish it from other phenomena.
The fundamental hypothesis outlined in the previous post [2] concerning the harmonics of de Broglie waves may be also stated for the photon itself. Indeed, the initial hypothesis of Plank concerning the photons [3] was the energy of photons itself is: E=n*h*ν [3]. From observation of photoelectric effect Einstein deduced the more commonly known rule: E=h*ν, which eventually lead to the development of the quantum electrodynamics and numerous discoveries.
However, any mathematical expression is only the approximation to the natural law, and the idea of the photons having energy of only E=h*ν may be very successful but not finally correct. Indeed, the double energy photon (with E=2*h*ν) may be so rare that virtually non-observable and thus making the Einstein idea so exceptionally great fit to the natural law that it looks absolute. The double energy photons may easily decay into two ordinary photons or mutate into the photon with double frequency.
Even the probability of the existence of such photons would be governed by the usual Boltzman rule (from [2]):
the population of double energy photons would be exp[-hν/(kT)] less compare to the usual photon. That value for relatively small energy infrared photons (1064 nm wavelength, 1.17 eV ordinary photon energy) would be at room temperature only 2.35*10exp(-20). This means that even such photons exist, they are so rare that virtually non-observable.
However, the two photon excited fluorescence is a convenient way to check theirs presence. Indeed, in addition to the quadratic in power term of such fluorescence (due to virtual levels creation [1]) an extremely small linear in power fluorescence is predicted. This fluorescence is so weak that it is necessary to consider the background created by usual thermal excitation (with some non-zero probability the same excited level may be reached by the usual thermal excitation according to the Boltzman formula P/Po=exp[-E/(kT)].
The trick to subtract background is that the two photon fluorescence is a resonant phenomena. It means that for the deviation of the wavelength from the resonant value it will quickly disappear. Since for the linear phenomena search the laser should not be powerful (to prevent observation of the more common quadratic in power two photon fluorescence) it may be with tuned frequency and thus allowing to observe the linear in power resonant phenomenon. When the frequency of the laser deviates from the frequency necessary for two quanta fluorescence (this frequency may be obtained from the quadratic term of the induced fluorescence) the observed linear term should quickly disappear (and the thermal background stay the same).
In summary: the observation of the linear term in the two photon fluorescence is predicted due to hypothetical existence of double energy photons (from Planks rule E=n*h*ν [3]), the phenomenon would be really weak (20 orders of magnitude weaker compare to one-photon fluorescence at least for infrared photons) but resonant in photon frequency.
References.
1. https://en.wikipedia.org/wiki/Two-photon_absorption
2. https://tipikin.blogspot.com/2020/05/quantization-rule-and-harmonics-of.html
3. http://web.phys.ntnu.no/~stovneng/TFY4165_2013/BlackbodyRadiation.pdf
Sunday, May 24, 2020
Wednesday, May 6, 2020
Quantization rule and harmonics of matter waves.
When modern scientist is recalling the quantization rule for photons, usually the famous E=h*ν is recalled. However, in the original Planck's derivation the more general rule of quantization was assumed: E=n*h*ν [1]. A similar rule of quantization was assumed by Nield Bohr concerning the orbital moment. The values n=2,3,4 .. are responsible for the excited states of the quantum system.
In quantum electrodynamics the quantization rule for electromagnetic field is similar to oscillator:
E=n*h*ν +0.5*h*ν
At the same time the wavelength of the de Broglie wave has only one value: λ=h/p=h/(m*v) not λ=n*h/p, where n is a number 1,2,3..., p is the pulse of the particle (applicable for any particle), m - rest mass and v - velocity of the particle (applicable only for non-relativistic case).
Since the matter waves are not really easy to investigate, it may happened that the de Broglie wavelength also follows the most general rule with the presence of the harmonics:
λ=n*h/p,
But they were simply overlooked and careful experiment would be necessary to discover them.
For de Broglie wave it is would not be easy to find presence of such harmonics, because during the interference experiment they would generate the maxima and minima, which coincide with maxima and minima of the main matter wave. If harmonic is present in the miniscule amount it will lead to some hardly observable effect.
Let's consider for example the case of only one added harmonic. Let the first harmonic has maximum of 1 and decays as exp(-0.1*m), where m is the interference band number, m=0,1,2,3,4... In this case the amplitudes of the interference bands would be: Io=1, exp(-0.1), exp(-0.2), exp(-0.3), exp(-0.4)=1, 0.905, 0.819, 0.741, 0.670...
Second harmonic of de Broglie wave would have the amplitude of 0.01 and decays with distance away from the center according to the same law exp(-0.1*m), here m is the interference band for the second harmonic, which would coincide with a certain band for first harmonic (because wavelength is exactly 2 times larger). The amplitude would be I=0.01, 0.01*exp(-0.1), 0.01*exp(-0.2)… =0.01, 0.00905, 0.00819 ...
The sum of the amplitudes would be:
1.01; exp(-0.1); exp(-0.2)+0.01*exp(-0.1); exp(-0.3); exp(-0.4)+0.01*exp(-0.2); …..=
1.01; 0.905; 0.828; 0.741; 0.679; …..
In order to distinguish the case of the one and multiple harmonics the ratio of the amplitudes of the consecutive bands may be calculated: bamd1/band0; band2/band1, band3/band2.....
For exactly one de Broglie wavelength that would be monotonic function:
0.905, 0.905, 0.905 …. (constant in this example, because the chosen decay function was exponential)
For the sum of harmonics it would be: ratios are:
0.896; 0.915; 0.895; 0.916 …. - non-monotonic function, the superposition of monotonic function and ao*Cos(pi*m), where m is the interference band number.
The third and higher harmonics will add more "waviness" to the smooth function.
How to estimate the amplitude of the harmonics in matter wave? The idea of evaluation is inferred from the reciprocity principle: the particle is both matter and wave [2]. Assuming the matter wave is something real (similar to a photon, but permanently "attached" to the particle), the probability of the excitation of the second energy level would be similar to the idea proposed by Plank [1]:
population of each next level would follow Boltzmann rule [3]:
-log(Ni/N)~Ei/kT
But what is the expected energy of the initial de Broglie wave? Hypothesizing that the particle is both matter and wave it is possible to speculate about this value.
Since de Broglie wave is "attached" to the particle, the only velocity it may have is equals to the velocity of particle v. From the general rule connecting velocity, wavelength and frequency of the wave it follows:
v=λ*ν or λ=v/ν
here v is the velocity of the particle, λ is the wavelength, ν is the frequency of the wave.
Substituting λ into the formula for non-relativistic de Broglie wave:
λ=h/(m*v) and v/ν=h/(m*v)
which may be transformed as follows:
mv2=hν or mv2/2=hν/2
For non-relativistic particle the energy of de Broglie wave can not be larger than the full kinetic energy of the particles and quantized as oscillator (quite reasonable idea, because the zero energy of electromagnetic field has the same value). Assuming the next harmonic will have the energy according to the Planks rule (or quantum electrodynamic rule, similar to oscillator), the difference in energy between two levels for de Broglie wave would be double the kinetic energy of the non-relativistic particle (for relativistic particle the quantization rule is simpler and coincides with the quantization rule for photons).
Than the ratio of the amplitude of the second harmonic of de Broglie wave to the initial amplitude would be equal (from Boltzmann rule):
I/Io=exp(-2Ek/kT)
where Ek is the kinetic energy of the non-relativistic particle. For example for electron with possible to reach energy of 0.1 eV, observed at the room temperature (300 K, at this temperature de Broglie wave is still well resolved since 0.1 eV > kT), the ratio would be:
I/Io=exp(-2Ek/kT)=4.4*10exp(-4)
Which is small, but at numerous averaging is possible to reach and to discover.
References.
1. http://web.phys.ntnu.no/~stovneng/TFY4165_2013/BlackbodyRadiation.pdf
2. https://tipikin.blogspot.com/2019/09/the-possible-way-to-search-for-new.html
3. https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution
In quantum electrodynamics the quantization rule for electromagnetic field is similar to oscillator:
E=n*h*ν +0.5*h*ν
At the same time the wavelength of the de Broglie wave has only one value: λ=h/p=h/(m*v) not λ=n*h/p, where n is a number 1,2,3..., p is the pulse of the particle (applicable for any particle), m - rest mass and v - velocity of the particle (applicable only for non-relativistic case).
Since the matter waves are not really easy to investigate, it may happened that the de Broglie wavelength also follows the most general rule with the presence of the harmonics:
λ=n*h/p,
But they were simply overlooked and careful experiment would be necessary to discover them.
For de Broglie wave it is would not be easy to find presence of such harmonics, because during the interference experiment they would generate the maxima and minima, which coincide with maxima and minima of the main matter wave. If harmonic is present in the miniscule amount it will lead to some hardly observable effect.
Let's consider for example the case of only one added harmonic. Let the first harmonic has maximum of 1 and decays as exp(-0.1*m), where m is the interference band number, m=0,1,2,3,4... In this case the amplitudes of the interference bands would be: Io=1, exp(-0.1), exp(-0.2), exp(-0.3), exp(-0.4)=1, 0.905, 0.819, 0.741, 0.670...
Second harmonic of de Broglie wave would have the amplitude of 0.01 and decays with distance away from the center according to the same law exp(-0.1*m), here m is the interference band for the second harmonic, which would coincide with a certain band for first harmonic (because wavelength is exactly 2 times larger). The amplitude would be I=0.01, 0.01*exp(-0.1), 0.01*exp(-0.2)… =0.01, 0.00905, 0.00819 ...
The sum of the amplitudes would be:
1.01; exp(-0.1); exp(-0.2)+0.01*exp(-0.1); exp(-0.3); exp(-0.4)+0.01*exp(-0.2); …..=
1.01; 0.905; 0.828; 0.741; 0.679; …..
In order to distinguish the case of the one and multiple harmonics the ratio of the amplitudes of the consecutive bands may be calculated: bamd1/band0; band2/band1, band3/band2.....
For exactly one de Broglie wavelength that would be monotonic function:
0.905, 0.905, 0.905 …. (constant in this example, because the chosen decay function was exponential)
For the sum of harmonics it would be: ratios are:
0.896; 0.915; 0.895; 0.916 …. - non-monotonic function, the superposition of monotonic function and ao*Cos(pi*m), where m is the interference band number.
The third and higher harmonics will add more "waviness" to the smooth function.
How to estimate the amplitude of the harmonics in matter wave? The idea of evaluation is inferred from the reciprocity principle: the particle is both matter and wave [2]. Assuming the matter wave is something real (similar to a photon, but permanently "attached" to the particle), the probability of the excitation of the second energy level would be similar to the idea proposed by Plank [1]:
population of each next level would follow Boltzmann rule [3]:
-log(Ni/N)~Ei/kT
But what is the expected energy of the initial de Broglie wave? Hypothesizing that the particle is both matter and wave it is possible to speculate about this value.
Since de Broglie wave is "attached" to the particle, the only velocity it may have is equals to the velocity of particle v. From the general rule connecting velocity, wavelength and frequency of the wave it follows:
v=λ*ν or λ=v/ν
here v is the velocity of the particle, λ is the wavelength, ν is the frequency of the wave.
Substituting λ into the formula for non-relativistic de Broglie wave:
λ=h/(m*v) and v/ν=h/(m*v)
which may be transformed as follows:
mv2=hν or mv2/2=hν/2
For non-relativistic particle the energy of de Broglie wave can not be larger than the full kinetic energy of the particles and quantized as oscillator (quite reasonable idea, because the zero energy of electromagnetic field has the same value). Assuming the next harmonic will have the energy according to the Planks rule (or quantum electrodynamic rule, similar to oscillator), the difference in energy between two levels for de Broglie wave would be double the kinetic energy of the non-relativistic particle (for relativistic particle the quantization rule is simpler and coincides with the quantization rule for photons).
Than the ratio of the amplitude of the second harmonic of de Broglie wave to the initial amplitude would be equal (from Boltzmann rule):
I/Io=exp(-2Ek/kT)
where Ek is the kinetic energy of the non-relativistic particle. For example for electron with possible to reach energy of 0.1 eV, observed at the room temperature (300 K, at this temperature de Broglie wave is still well resolved since 0.1 eV > kT), the ratio would be:
I/Io=exp(-2Ek/kT)=4.4*10exp(-4)
Which is small, but at numerous averaging is possible to reach and to discover.
References.
1. http://web.phys.ntnu.no/~stovneng/TFY4165_2013/BlackbodyRadiation.pdf
2. https://tipikin.blogspot.com/2019/09/the-possible-way-to-search-for-new.html
3. https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution
Saturday, April 18, 2020
Quantization of the gravitational dipole
At the present time gravity is considered by many scientists as the under-investigated force of nature due to its weakness. It is interesting to investigate the hypothetical possibility of the associated with the mass of the elementary particle gravitational dipole. That would be analogous to electric dipole for the electric field and it would reflect the non-uniform distribution of the mass inside the elementary particle.
Since all the physical values which have the dimensions of energy*time (J*s) are quantized (the Plank constant), it would be interesting to see, what physical values may be quantized, too. For example, production m*v*r (mass*velocity*radius is quantized and this is orbital moment). Investigation of quantization of this moment lead to all modern quantum mechanics, started by Niels Bohr. However, the same production may be considered as production of m*r (gravitational dipole, similar to electric dipole q*r - charge times distance) and velocity v of the particle.
Following Niels Bohr steps, it is possible to suppose that such value is quantized too:
(m*r)*v=n*h
here h is Plank's constant.
It may be rewritten as follows:
m*r=n*h/v,
Since h/(m*v) is the de Broglie wavelength λ
m*r=n*m*(h/m*v)=n*m*λ
It means that the mass of the particle is "spread" in the space as de Broglie wavelength. Here n is the number 1,2,3,4...
The most important consequence of the hypothesis - the gravitational dipole moment is not equal to zero! This is a conclusion similar to de Broglie wavelength - it must exist, due to quantum mechanics the particle can not be represented as a point, therefore the dipole moment can not be zero under any circumstances.
Lets estimate the additional gravitational force due to the gravitational dipole moment of the particle. Lets consider the ball with mass M as the second body (the first body has mass m). The gravitational dipole force between the dipole and spherical mass M is:
Fd=m*r*grad(Eg)
here Fd is the force acting onto the dipole m*r, grad(Eg) is the gradient of the gravitational field, what is equal for the spherical mass to:
grad(Eg)=d/dr(M*G/(R*R))=2*M*G/(R*R*R)
Here G is the gravitational constant, M is the mass of the second body, R is the distance between the centers of the attracting masses. Then the gravitational dipole force may be written as:
Fd=n*m*λ*(2GM/R3)=2n*(λ/R)*(GmM/R2)=2n*(λ/R)*Fg
Here Fg is the classical gravitational force between two spherical masses separated by distance R between centers. For the multiple harmonics of the gravitational dipole force (n>1) and for very slow electron (de Broglie wavelength is high) it may be comparable with gravitational force and measurable relatively easily - the electrons will be split into several beams. The gravitational force is not quantizied and the same for all electrons, but the dipole gravitational forced is different depending upon n.
Here comes the different problem discussed in another blog - de Broglie wavelength is unique and not quantizied according to Bohr rule. It may happened that there is no "excited" states for gravitational dipole, only the lowest state exist (n=1).
For the ultraslow electron with the temperature of 1 micro-Kelvin (reachable now in some experiments) the velocity of electron would be 6.7 m/s and de Broglie wavelength is 0.1 mm. For the second body with radius of 0.1 m the ratio of dipole gravitational force to gravitational force is 2*0.0001/0.1=0.002.
The accuracy of the direct measurements of gravitational force today (Kavendish experiment) is much higher than 0.2%, thus making such measurements quite possible.
Additional alleviation may be from the shape of the second mass - the gradient of the gravitational force, similar to the gradient of the electric field, will be much stronger near the sharp edges, so the manipulation with different shapes of the second body with mass M will allow to amplify the gravitational dipole force while keeping the classical gravitational force the same.
Since all the physical values which have the dimensions of energy*time (J*s) are quantized (the Plank constant), it would be interesting to see, what physical values may be quantized, too. For example, production m*v*r (mass*velocity*radius is quantized and this is orbital moment). Investigation of quantization of this moment lead to all modern quantum mechanics, started by Niels Bohr. However, the same production may be considered as production of m*r (gravitational dipole, similar to electric dipole q*r - charge times distance) and velocity v of the particle.
Following Niels Bohr steps, it is possible to suppose that such value is quantized too:
(m*r)*v=n*h
here h is Plank's constant.
It may be rewritten as follows:
m*r=n*h/v,
Since h/(m*v) is the de Broglie wavelength λ
m*r=n*m*(h/m*v)=n*m*λ
It means that the mass of the particle is "spread" in the space as de Broglie wavelength. Here n is the number 1,2,3,4...
The most important consequence of the hypothesis - the gravitational dipole moment is not equal to zero! This is a conclusion similar to de Broglie wavelength - it must exist, due to quantum mechanics the particle can not be represented as a point, therefore the dipole moment can not be zero under any circumstances.
Lets estimate the additional gravitational force due to the gravitational dipole moment of the particle. Lets consider the ball with mass M as the second body (the first body has mass m). The gravitational dipole force between the dipole and spherical mass M is:
Fd=m*r*grad(Eg)
here Fd is the force acting onto the dipole m*r, grad(Eg) is the gradient of the gravitational field, what is equal for the spherical mass to:
grad(Eg)=d/dr(M*G/(R*R))=2*M*G/(R*R*R)
Here G is the gravitational constant, M is the mass of the second body, R is the distance between the centers of the attracting masses. Then the gravitational dipole force may be written as:
Fd=n*m*λ*(2GM/R3)=2n*(λ/R)*(GmM/R2)=2n*(λ/R)*Fg
Here Fg is the classical gravitational force between two spherical masses separated by distance R between centers. For the multiple harmonics of the gravitational dipole force (n>1) and for very slow electron (de Broglie wavelength is high) it may be comparable with gravitational force and measurable relatively easily - the electrons will be split into several beams. The gravitational force is not quantizied and the same for all electrons, but the dipole gravitational forced is different depending upon n.
Here comes the different problem discussed in another blog - de Broglie wavelength is unique and not quantizied according to Bohr rule. It may happened that there is no "excited" states for gravitational dipole, only the lowest state exist (n=1).
For the ultraslow electron with the temperature of 1 micro-Kelvin (reachable now in some experiments) the velocity of electron would be 6.7 m/s and de Broglie wavelength is 0.1 mm. For the second body with radius of 0.1 m the ratio of dipole gravitational force to gravitational force is 2*0.0001/0.1=0.002.
The accuracy of the direct measurements of gravitational force today (Kavendish experiment) is much higher than 0.2%, thus making such measurements quite possible.
Additional alleviation may be from the shape of the second mass - the gradient of the gravitational force, similar to the gradient of the electric field, will be much stronger near the sharp edges, so the manipulation with different shapes of the second body with mass M will allow to amplify the gravitational dipole force while keeping the classical gravitational force the same.
Wednesday, March 4, 2020
Unification of gravitational and electromagnetic force through quantum vacuum. Modification of Cavendish experiment to observe the influence of quantum vaccum excitation by laser
There is a lot of attempts which were trying to create the complete unified field theory. However, some experiments and observations may help to complete smaller but the most important part - unify gravity with any other fundamental force. The possible way to unify gravity and electromagnetism would be use of idea of common source for both forces - quantum vacuum. Indeed, the idea of the direct influence of the quantum vacuum onto the electromagnetic constants (electric force strength and speed of light) is well established: the virtual pairs of particle-antiparticle (mainly electron-positron) are attenuating the electric field strength (in smaller scale the magnetic field strength) and thus limiting the speed of light. A similar idea about gravity was proposed [1]: a massive pairs particle-gravitational antiparticle in quantum vacuum would be responsible for the main contribution of the gravity strength. However, the charged particles are also having mass and thus more common pairs like positron-electron and proton-antiproton will be influencing the gravity force too. Since the quantum vacuum is the same for both interactions, all of the possible pairs having mass will be responsible for the gravity. But some of such pairs are also having charge. The very strong electric field will be able to polarize the quantum vacuum (electromagnetically responsive part of it), which would influence the speed of light (known phenomenon) and simultaneously the gravitational constant (the phenomenon to be discovered), since any pair which has charge and responded to the electric field has also a mass. In the opposite situation the extremely strong gravitational field excites the quantum vacuum (all of the particles, including those which bear charge) and thus influence the speed of light (this is also known phenomenon - the speed of light is smaller in the vicinity of the star or black hole).
The phenomenon of the influence of the gravity onto the speed of light is well known and usually interpreted as the change of time speed [2]. From quantum vacuum point of view it may be interpreted as the excitation of the quantum vacuum by the strong gravitational field, what leads to the change of the parameters of the electric field constant (permittivity and permeability of free space). Indeed, those parameters are known to be changed in the vicinity of the electron (vacuum screening of electron, see [3], which is a confirmed fact). Why would not strong gravitational field modified the same quantum vacuum in a similar way? All the barionic particles which are responsible for virtual pairs in the quantum vacuum have mass and must respond to the strong gravitational field.
But the gravity is responsible for the presence of space and time in our Universe. As the Universe expands, the gravity potential inside the Universe (away from the black holes and stars) will be smaller and smaller (assuming no new mass is added into the Universe). This will lead to the change of the speed of light (change of both permittivity and permeability of free space) - to the increase of speed of light. This value may be estimated as follows:
Speed of light near the massive ball is (according to Einstein, [2,4]):
c=co-2co*α
here α=(GM)/(r*co*co)
Where G is the gravitational constant, M is the mass of the black hole (star), r is the distance from the center of the star and co is the speed of light away from the gravitating star. The value of gravitational potential is expressed as follows:
Φ(r)=-GM/r
c=co+2*Φ(r)/co
Assuming the whole Universe as a ball partially filled with mass it would be possible to evaluate the speed of light inside such a ball using the formula for calculation of the potential inside the charged ball (the analogy to electrostatic is straightforward). Electric potential inside the uniformly charged ball is [5]:
ϕ(r)=[k*Q/(2R)]*(3-r2/R2)
Here k is electric field constant, R is radius of ball, r is the distance from the center of the ball, Q is total charge of the ball. Correspondingly for the gravitational potential (for simplicity at the center of the Universe):
Φ=-3GM/(2*R)
Here M is the total mass of the Universe (1.5*10exp(53) kg) , R is the total radius of the Universe (4.4*10exp(26) m) and Φ=-6.82*10exp(16) m2/s2 (this parameter is related to the cosmological constant, of course [6]).
Thus we got an equation for the speed of light in gravitation-free space (virtual place because according to Einstein the space-time itself is created by gravity, no gravity means no space):
c=co-6.38*10exp(16)/co
Here c is 3*10exp(8) - is the observable speed of light in the present Universe. Solving the quadratic equation, co=4.5*10exp(8) - relatively small change because our Universe is already very inflated.
Assuming no new mass will appear in the Universe, many billions years from now the speed of light will be a just a little larger (if the inflation of the Universe will not influence other properties of the quantum vacuum, for example the probabilities of the appearance of particle-antiparticle pairs).
The difference between the co and observed c is due to the polarization of the quantum vacuum by the total masses present in the Universe.
In summary, the same quantum vacuum may be polarized by different fields and this influences the corresponding constants for both electric and gravitational force (because we are talking about the same vacuum). This may help to unify the gravity and electromagnetism
1. Strong gravitational field polarizes the quantum vacuum and changes electric constant (observed through change of speed of light near the star and black hole) [4]
2. Strong electric field changes the permittivity near the charge ( vacuum screening of electron [3])
3.Perturbation of the quantum vacuum by the electric field should influence the gravitational constant (because the same virtual pairs would be responsible for both forces)
This experiment is the most difficult one, because the gravitational force so much smaller. In a simple way it should be strongly electrically charged objects in Cavendish experiment on gravity [7], but since the electric force is so hugely strongly compare to the gravity, the change in gravity will be completely invisible. Fortunately powerful lasers may already create the electric field strong enough to generate electron-positron pairs (breaking the quantum vacuum) are already available [8]. Illumination of the space between the test masses in Cavendish experiment may create the polarization of the quantum vacuum strong enough to be observed through the measurement of the gravitational constant.
4.In principle the polarization of the quantum vacuum by the strong gravitational field will lead to the different outcome of the Cavendish experiment. This experiment may be performed in the vicinity of Sun or Jupiter and the observed result will be a little different compare to Earth experiment. Such idea may be even closer to the reality because the satellites traveling close to Sun or large planet are already present.
The discoveries of the more elementary particles which would be present as virtual pairs in the quantum vacuum will eventually allow to calculate exactly the strength of electromagnetic constants and gravitational constant from the same principles and general formulas, effectively unifying both fundamental forces [2].
References.
1.http://tipikin.blogspot.com/2019/12/quantum-vacuum-application-to-gravity.html
2.https://arxiv.org/abs/1401.3110
3.https://arxiv.org/ftp/arxiv/papers/1405/1405.5792.pdf
4.https://www.speed-light.info/speed_of_light_gravity.htm
5.http://www.phys.uri.edu/gerhard/PHY204/tsl94.pdf
6.https://en.wikipedia.org/wiki/Observable_universe
7.https://en.wikipedia.org/wiki/Cavendish_experiment
8.https://www.sciencemag.org/news/2018/01/physicists-are-planning-build-lasers-so-powerful-they-could-rip-apart-empty-space
The phenomenon of the influence of the gravity onto the speed of light is well known and usually interpreted as the change of time speed [2]. From quantum vacuum point of view it may be interpreted as the excitation of the quantum vacuum by the strong gravitational field, what leads to the change of the parameters of the electric field constant (permittivity and permeability of free space). Indeed, those parameters are known to be changed in the vicinity of the electron (vacuum screening of electron, see [3], which is a confirmed fact). Why would not strong gravitational field modified the same quantum vacuum in a similar way? All the barionic particles which are responsible for virtual pairs in the quantum vacuum have mass and must respond to the strong gravitational field.
But the gravity is responsible for the presence of space and time in our Universe. As the Universe expands, the gravity potential inside the Universe (away from the black holes and stars) will be smaller and smaller (assuming no new mass is added into the Universe). This will lead to the change of the speed of light (change of both permittivity and permeability of free space) - to the increase of speed of light. This value may be estimated as follows:
Speed of light near the massive ball is (according to Einstein, [2,4]):
c=co-2co*α
here α=(GM)/(r*co*co)
Where G is the gravitational constant, M is the mass of the black hole (star), r is the distance from the center of the star and co is the speed of light away from the gravitating star. The value of gravitational potential is expressed as follows:
Φ(r)=-GM/r
c=co+2*Φ(r)/co
Assuming the whole Universe as a ball partially filled with mass it would be possible to evaluate the speed of light inside such a ball using the formula for calculation of the potential inside the charged ball (the analogy to electrostatic is straightforward). Electric potential inside the uniformly charged ball is [5]:
ϕ(r)=[k*Q/(2R)]*(3-r2/R2)
Here k is electric field constant, R is radius of ball, r is the distance from the center of the ball, Q is total charge of the ball. Correspondingly for the gravitational potential (for simplicity at the center of the Universe):
Φ=-3GM/(2*R)
Here M is the total mass of the Universe (1.5*10exp(53) kg) , R is the total radius of the Universe (4.4*10exp(26) m) and Φ=-6.82*10exp(16) m2/s2 (this parameter is related to the cosmological constant, of course [6]).
Thus we got an equation for the speed of light in gravitation-free space (virtual place because according to Einstein the space-time itself is created by gravity, no gravity means no space):
c=co-6.38*10exp(16)/co
Here c is 3*10exp(8) - is the observable speed of light in the present Universe. Solving the quadratic equation, co=4.5*10exp(8) - relatively small change because our Universe is already very inflated.
Assuming no new mass will appear in the Universe, many billions years from now the speed of light will be a just a little larger (if the inflation of the Universe will not influence other properties of the quantum vacuum, for example the probabilities of the appearance of particle-antiparticle pairs).
The difference between the co and observed c is due to the polarization of the quantum vacuum by the total masses present in the Universe.
In summary, the same quantum vacuum may be polarized by different fields and this influences the corresponding constants for both electric and gravitational force (because we are talking about the same vacuum). This may help to unify the gravity and electromagnetism
1. Strong gravitational field polarizes the quantum vacuum and changes electric constant (observed through change of speed of light near the star and black hole) [4]
2. Strong electric field changes the permittivity near the charge ( vacuum screening of electron [3])
3.Perturbation of the quantum vacuum by the electric field should influence the gravitational constant (because the same virtual pairs would be responsible for both forces)
This experiment is the most difficult one, because the gravitational force so much smaller. In a simple way it should be strongly electrically charged objects in Cavendish experiment on gravity [7], but since the electric force is so hugely strongly compare to the gravity, the change in gravity will be completely invisible. Fortunately powerful lasers may already create the electric field strong enough to generate electron-positron pairs (breaking the quantum vacuum) are already available [8]. Illumination of the space between the test masses in Cavendish experiment may create the polarization of the quantum vacuum strong enough to be observed through the measurement of the gravitational constant.
4.In principle the polarization of the quantum vacuum by the strong gravitational field will lead to the different outcome of the Cavendish experiment. This experiment may be performed in the vicinity of Sun or Jupiter and the observed result will be a little different compare to Earth experiment. Such idea may be even closer to the reality because the satellites traveling close to Sun or large planet are already present.
The discoveries of the more elementary particles which would be present as virtual pairs in the quantum vacuum will eventually allow to calculate exactly the strength of electromagnetic constants and gravitational constant from the same principles and general formulas, effectively unifying both fundamental forces [2].
References.
1.http://tipikin.blogspot.com/2019/12/quantum-vacuum-application-to-gravity.html
2.https://arxiv.org/abs/1401.3110
3.https://arxiv.org/ftp/arxiv/papers/1405/1405.5792.pdf
4.https://www.speed-light.info/speed_of_light_gravity.htm
5.http://www.phys.uri.edu/gerhard/PHY204/tsl94.pdf
6.https://en.wikipedia.org/wiki/Observable_universe
7.https://en.wikipedia.org/wiki/Cavendish_experiment
8.https://www.sciencemag.org/news/2018/01/physicists-are-planning-build-lasers-so-powerful-they-could-rip-apart-empty-space
Tuesday, March 3, 2020
Inherently quantum phenomena reveal itself in macroscopic world. Idea of correlations instead of science fiction "time line".
Landau-Zener formula manifestation in macroscopic world and impossibility of "time-line".
In deterministic world based on classical mechanics the idea of "time-line" appeared (very popular in science fiction in the sense that it should be preserved). Indeed, the classical mechanics is deterministic. After appearance of quantum mechanics this idea disappeared a instead the idea of multiple worlds appeared. At the present time the idea of quantum Darwinism is popular:
https://en.wikipedia.org/wiki/Quantum_Darwinism
which may seemingly allow to preserve the determinism at least for macroscopic world. Unfortunately some of the inherently probabilistic phenomena, governed by quantum mechanics laws may be traced up to macroscopic world. The easiest example would be the motion of electrostatically charged balls, because the electrostatic force is rather macroscopically significant (the coefficient in Coulomb law is 9*10^9 and the force is acting at long distances compare to the inside the nucleus strong force). The charge is quantified and even one electron added or subtracted may change the mechanical motion of the macroscopic object and change the history in the most common sense of this world.
Triboelectrization of polymers includes two steps: at the first step the mechanochemical reaction generates free radicals and at the second stage the interaction between the radicals may lead to recombination of them or to the charge transfer between the contacting surfaces [1].
The second step includes the Landau-Zeener process, where the two energy levels quasi-cross each other and as the system moves along the reaction coordinate, the electron may be transferred between the surfaces, thus creating the charge. Landau-Zeener process law is a quantum law and its application will lead to inherently unpredictable charging of the surfaces (mathematically verified stochastic process). For such process the fluctuations are of the value of sqrt(N), where N is the average value of the quantity (like the distance of the travel in the Brownian motion). The most important consequence of Landau-Zeener determined stochasticity is that it has no hidden parameter.
For the relatively weak charge of 1000 electrons the fluctuation would be around 32 electrons. Triboelectrization takes place between the closely placed surfaces, say 3 angstroms apart. In this case the additional electrostatic force due to 32 electrons (this is the unpredictable fluctuation of average charge of 1000 electrons) would be:
F=k*q*q/(r*r)
here k is coefficient in Coulomb law, q is the charge and r is the distance (say 3 A). Calculations for 32 electrons give force of 2.56*10exp(-6) Newton.
Lets consider lottery where the plastic balls are used with mass of 1 g. The additional acceleration of such ball due to the stochastic electrostatic force would be
a=F/m=2.56*10exp(-3) m/s^2
Being in contact for 1 second the fluctuation in the velocity would be
v=a*t=2.56*10exp(-3) m/s
For the further flying inside the lottery machine for 30 seconds the distance fluctuation is 0.077 m (around 8 cm). Correspondingly the ball will miss the hole and different winning number will appear.
In addition of demonstration that such lottery machine is stochastic on the deepest level possible (no possibility of pre-calculation of the winning number quaranteed by quantum mechanics) it also means the probabilistic events do not stop on microscopic level - they have the way to reveal itself on the macroscopic level as well. Even idea of quantum Darwinism can not return the predictability in the macroscopic world.
From philosophical point of view it means that determinism is not present in our world - it is inherently stochastic. What is preserved is correlations: even in the fully stochastic world there is the range of fluctuations is limited. The correlations between the different values are measurable in the past and due to the laws of correlation function may be used to predict future. This is used by economists to evaluate numerous trends on the market. For example if the consumption of strawberries is increasing consistently for 50 years, the correlation between grows of population and consumption of strawberries is almost 1. By no means may it be that next year it will drop to zero - the correlation function was very strong for around 50 years and it must be equally strong for approximately next decade or so at least.
From science fiction time travel point of view the travel in the past and back into the present will change nothing - the butterfly effect is forbidden by the laws of quantum mechanics. It means that by traveling to the past, doing nothing (no butterfly) and returning back the completely different future will be found. The deviation will depend upon the correlation functions of the event expected and distance in time. For example by traveling back for 50 years and returning to the present minimum changes are expected - the presidents are different, but for example New York is still the largest city of USA (however, some tallest buildings are looking differently and are in a little different places). Since the correlation function associated with city of New York is measured in centuries, 50 years should not lead to big change. The company lifetime is much shorter, so no Google now (but because the Internet has at least comparable lifetime already it must be present and the similar search engine is here, but with different name) etc.
The deeper into the past the travel, the smaller would be the remnant values of correlation function and more changes are to be expected. Traveling back to dinosaur times will lead to the huge change on the return - may be a different species are now making civilization.
The best representation of such attempts may be sci-fi movie "Sliders".
The main conclusion is that contrary to the believe of the scientists of 19th century more and more evidence tells that the world is probabilistic on the deepest level possible. There is no predictable future, but there is also no past at all. History is only recorded in the books, there is no "time-line" at all. The possibility of prediction and use of numerous laws of physics is that the correlation functions for some of them are equal to 1 with enormous accuracy. For example, motion of planets may be predicted forward for billions of years easier. The mechanical motion of macroscopic objects (what lead to the discovery of the Newtons law and the idea of predictability of the motion of any particles) is also very high and predictable - that is why civilization is possible.
Fortunately for everyday life the quantum stochasticity on the macroscopic level is rear. It is only because the electrostatic force is so strong and charge is quantized it is possible in some situations.
References.
1.https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2969192
In deterministic world based on classical mechanics the idea of "time-line" appeared (very popular in science fiction in the sense that it should be preserved). Indeed, the classical mechanics is deterministic. After appearance of quantum mechanics this idea disappeared a instead the idea of multiple worlds appeared. At the present time the idea of quantum Darwinism is popular:
https://en.wikipedia.org/wiki/Quantum_Darwinism
which may seemingly allow to preserve the determinism at least for macroscopic world. Unfortunately some of the inherently probabilistic phenomena, governed by quantum mechanics laws may be traced up to macroscopic world. The easiest example would be the motion of electrostatically charged balls, because the electrostatic force is rather macroscopically significant (the coefficient in Coulomb law is 9*10^9 and the force is acting at long distances compare to the inside the nucleus strong force). The charge is quantified and even one electron added or subtracted may change the mechanical motion of the macroscopic object and change the history in the most common sense of this world.
Triboelectrization of polymers includes two steps: at the first step the mechanochemical reaction generates free radicals and at the second stage the interaction between the radicals may lead to recombination of them or to the charge transfer between the contacting surfaces [1].
The second step includes the Landau-Zeener process, where the two energy levels quasi-cross each other and as the system moves along the reaction coordinate, the electron may be transferred between the surfaces, thus creating the charge. Landau-Zeener process law is a quantum law and its application will lead to inherently unpredictable charging of the surfaces (mathematically verified stochastic process). For such process the fluctuations are of the value of sqrt(N), where N is the average value of the quantity (like the distance of the travel in the Brownian motion). The most important consequence of Landau-Zeener determined stochasticity is that it has no hidden parameter.
For the relatively weak charge of 1000 electrons the fluctuation would be around 32 electrons. Triboelectrization takes place between the closely placed surfaces, say 3 angstroms apart. In this case the additional electrostatic force due to 32 electrons (this is the unpredictable fluctuation of average charge of 1000 electrons) would be:
F=k*q*q/(r*r)
here k is coefficient in Coulomb law, q is the charge and r is the distance (say 3 A). Calculations for 32 electrons give force of 2.56*10exp(-6) Newton.
Lets consider lottery where the plastic balls are used with mass of 1 g. The additional acceleration of such ball due to the stochastic electrostatic force would be
a=F/m=2.56*10exp(-3) m/s^2
Being in contact for 1 second the fluctuation in the velocity would be
v=a*t=2.56*10exp(-3) m/s
For the further flying inside the lottery machine for 30 seconds the distance fluctuation is 0.077 m (around 8 cm). Correspondingly the ball will miss the hole and different winning number will appear.
In addition of demonstration that such lottery machine is stochastic on the deepest level possible (no possibility of pre-calculation of the winning number quaranteed by quantum mechanics) it also means the probabilistic events do not stop on microscopic level - they have the way to reveal itself on the macroscopic level as well. Even idea of quantum Darwinism can not return the predictability in the macroscopic world.
From philosophical point of view it means that determinism is not present in our world - it is inherently stochastic. What is preserved is correlations: even in the fully stochastic world there is the range of fluctuations is limited. The correlations between the different values are measurable in the past and due to the laws of correlation function may be used to predict future. This is used by economists to evaluate numerous trends on the market. For example if the consumption of strawberries is increasing consistently for 50 years, the correlation between grows of population and consumption of strawberries is almost 1. By no means may it be that next year it will drop to zero - the correlation function was very strong for around 50 years and it must be equally strong for approximately next decade or so at least.
From science fiction time travel point of view the travel in the past and back into the present will change nothing - the butterfly effect is forbidden by the laws of quantum mechanics. It means that by traveling to the past, doing nothing (no butterfly) and returning back the completely different future will be found. The deviation will depend upon the correlation functions of the event expected and distance in time. For example by traveling back for 50 years and returning to the present minimum changes are expected - the presidents are different, but for example New York is still the largest city of USA (however, some tallest buildings are looking differently and are in a little different places). Since the correlation function associated with city of New York is measured in centuries, 50 years should not lead to big change. The company lifetime is much shorter, so no Google now (but because the Internet has at least comparable lifetime already it must be present and the similar search engine is here, but with different name) etc.
The deeper into the past the travel, the smaller would be the remnant values of correlation function and more changes are to be expected. Traveling back to dinosaur times will lead to the huge change on the return - may be a different species are now making civilization.
The best representation of such attempts may be sci-fi movie "Sliders".
The main conclusion is that contrary to the believe of the scientists of 19th century more and more evidence tells that the world is probabilistic on the deepest level possible. There is no predictable future, but there is also no past at all. History is only recorded in the books, there is no "time-line" at all. The possibility of prediction and use of numerous laws of physics is that the correlation functions for some of them are equal to 1 with enormous accuracy. For example, motion of planets may be predicted forward for billions of years easier. The mechanical motion of macroscopic objects (what lead to the discovery of the Newtons law and the idea of predictability of the motion of any particles) is also very high and predictable - that is why civilization is possible.
Fortunately for everyday life the quantum stochasticity on the macroscopic level is rear. It is only because the electrostatic force is so strong and charge is quantized it is possible in some situations.
References.
1.https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2969192
Gravitomagnetic Stern-Gerlach experiment in space using Earth gravitomagnetic field. Importance for the direct measurement of quantum mechanical moment of elementary particles.
It is well accepted that gravitomagnetic field is extremely weak and just recently was measured using satellites. However, one of the problems of the physics - the weakness of the gravitational force - may have the answer connected with the presence of very heavy gravitational-antigravitational pairs of virtual particles in the quantum vacuum [1]. Very much like the electrostatic force is limited by the presence of electron-positron virtual pairs in the quantum vacuum, the gravitational field is so weak because the very massive virtual pairs included antigravitational particle are polarized by the gravity of the tested particle and thus attenuates the force perceptibly [1].
But Higgs boson is not fermion from ordinary spin definition and seemingly should not have any antigravitational counterpart. The hypothesis is the presence of one more quantum number, close to spin but revealed by the mechanical moment decoupled from charge. Indeed, Einstein-De Haas experiment revealed that the reverse of the orbital magnetic moment forces the macroscopic object to rotate, thus connecting directly the mechanical moment and magnetic moment. For the orbital moment this experiment demonstrates full mechanical moment. But situation is not so obvious for spin of elementary particles. There is undoubtedly the mechanical moment coupled with electric charge (or electric current) and the flip of the spin will mean the flip of mechanical moment. However, the uncoupled mechanical moment may be still present. Imagine the fast rotating dielectric ball with superconducting strip on equator. The current in such a superconducting strip will be responsible for the magnetic moment of the object (magnetic spin) and cooper pairs would be responsible for the mechanical moment associated with such a magnetic spin. However, the main mechanical moment may be as large as possible and may have different direction. Flip of the current will reveal in this situation only the coupled part of the mechanical moment while the main moment will stay unnoticed. Only gravitomagnetic field will reveal the total mechanical moment of the elementary particle (for macroscopic object, of course, much simpler experiment will work).
The hope of this idea is that such experiment may reveal another quantum number, second spin, which would mean that the Higgs boson is not real boson, but only partial boson (with respect to magnetic spin) and still may have the gravitational antiparticle, thus explaining the weakness of the gravitational force.
How to measure such a spin? At first it would be necessary to evaluate, whether it is possible to measure the usual spin of say electron using any modern day equipment. The only object generating strong enough gravitomagnetic field would be rotating Earth [2].
The easiest experiment to be done is gravitomagnetic Stern-Gerlach experiment: the spin will exert the force in the gradient of gravitomagnetic field. The gradient of the gravitomagnetic force would be (for Earth):
Bg=[G/(5*c*c)]*[M/r]*[2π/T]
dBg/dr=-[G/(5*c*c)]*[M/(r*r)]*[2π/T]
Here Bg is gravitomagnetic field of the rotation ball (Earth), G is gravitational constant, c is speed of light, r is the distance from the center of the Earth, M is the mass of the Earth (5.97*10exp(24) kg), T is the period of the rotation (1 day or 86400 seconds).
The known mechanical moment of the elementary particle would be spin of electron, which is S=h/(4*pi). Here h is Planks constant and pi is 3.14159.
For the electron traveling in the gravitomagnetic field gradient the force between the spin up and spin down particles would be F=2S*dBg/dr (electron will travel in space away from the Earth). Since the gradient is varying with the distance as 1/r^2 law, instead of integration of the force along the path for crude evaluation the distance r is taken to be 8 thousands kilometers (the experiment starts at 6.3 thousands kilometers and ends at 16.3 thousands kilometers). The force for the electron would be:
F=2S*dBg/dr=[h/(2π)]*[G/(5*c*c)]*[M/r*r]*[2π/T]
F=1*10exp(-55) Newton
For the electron traveling with velocity of 0.1 m/s, the distance is 10000 km (1*10exp(7) meters), the time of travel is 1*10exp(8) seconds (~3 years). Using mass of electron 9.1*10exp(-31) kg and simple formula L=a*t*t/2 the expected separation of the electrons due to ordinary spin at the end of travel would be 5.5*10exp(-10) m (5.5 Angstrom - measurable at modern technology).
More accurate double integration will give the similar result:
L=[1/v*v]*[h/(2*π)]*[G/(5*c*c)]*[M/m]*[2π/T]*ln(R1/Ro)
Here v is the velocity of the electron, m is the mass of electron, Ro and R1 are distance from the center of the Earth at the start and at the finish, correspondingly. L is 6.9 Angstrom.
The largest problem is here: the electron is subject to the magnetic field of the Earth and will travel in a circle around the Earth magnetic field line. The only way to compensate such rotation is to put the compensating electric field in the opposite direction during the whole travel of the electron from start to finish. Despite the keeping the whole satellite all the time around the traveling pulse of electrons is an expensive task, it may be done provided the electrons are moving very slow. The electrons and the satellites may, of course rotate around the Earth in the equatorial plane (otherwise such satellite would not work), slowly moving away from the Earth as the bunch of electrons travels away at a speed of 10 cm/s and the separation due to the gravitomagnetic field gradient accumulates.
Another problem would be the presence of the magnetic field gradient (so the classical Stern-Gerlach experiment would be performed in Earth magnetic field gradient). It is possible to carry the compensating magnetic field gradient on the same satellite as well. Actually while the full compensation of the classical Stern-Gerlach splitting would not be possible, the idea here to see the additional splittings in the final picture. The presence of such splittings would mean the presence of one more quantum number - second spin for elementary particles.
Second spin will allow to hypothesize the presence of heavy particle-gravitational antiparticle virtual pairs in the quantum vacuum (like Higgs - antigravitational Higgs pairs proposed in [1]) and explain the gravitational constant in a way similar to the electrostatic one.
References.
1.http://tipikin.blogspot.com/2019/12/quantum-vacuum-application-to-gravity.html
2.https://en.wikipedia.org/wiki/Gravitoelectromagnetism
But Higgs boson is not fermion from ordinary spin definition and seemingly should not have any antigravitational counterpart. The hypothesis is the presence of one more quantum number, close to spin but revealed by the mechanical moment decoupled from charge. Indeed, Einstein-De Haas experiment revealed that the reverse of the orbital magnetic moment forces the macroscopic object to rotate, thus connecting directly the mechanical moment and magnetic moment. For the orbital moment this experiment demonstrates full mechanical moment. But situation is not so obvious for spin of elementary particles. There is undoubtedly the mechanical moment coupled with electric charge (or electric current) and the flip of the spin will mean the flip of mechanical moment. However, the uncoupled mechanical moment may be still present. Imagine the fast rotating dielectric ball with superconducting strip on equator. The current in such a superconducting strip will be responsible for the magnetic moment of the object (magnetic spin) and cooper pairs would be responsible for the mechanical moment associated with such a magnetic spin. However, the main mechanical moment may be as large as possible and may have different direction. Flip of the current will reveal in this situation only the coupled part of the mechanical moment while the main moment will stay unnoticed. Only gravitomagnetic field will reveal the total mechanical moment of the elementary particle (for macroscopic object, of course, much simpler experiment will work).
The hope of this idea is that such experiment may reveal another quantum number, second spin, which would mean that the Higgs boson is not real boson, but only partial boson (with respect to magnetic spin) and still may have the gravitational antiparticle, thus explaining the weakness of the gravitational force.
How to measure such a spin? At first it would be necessary to evaluate, whether it is possible to measure the usual spin of say electron using any modern day equipment. The only object generating strong enough gravitomagnetic field would be rotating Earth [2].
The easiest experiment to be done is gravitomagnetic Stern-Gerlach experiment: the spin will exert the force in the gradient of gravitomagnetic field. The gradient of the gravitomagnetic force would be (for Earth):
Bg=[G/(5*c*c)]*[M/r]*[2π/T]
dBg/dr=-[G/(5*c*c)]*[M/(r*r)]*[2π/T]
Here Bg is gravitomagnetic field of the rotation ball (Earth), G is gravitational constant, c is speed of light, r is the distance from the center of the Earth, M is the mass of the Earth (5.97*10exp(24) kg), T is the period of the rotation (1 day or 86400 seconds).
The known mechanical moment of the elementary particle would be spin of electron, which is S=h/(4*pi). Here h is Planks constant and pi is 3.14159.
For the electron traveling in the gravitomagnetic field gradient the force between the spin up and spin down particles would be F=2S*dBg/dr (electron will travel in space away from the Earth). Since the gradient is varying with the distance as 1/r^2 law, instead of integration of the force along the path for crude evaluation the distance r is taken to be 8 thousands kilometers (the experiment starts at 6.3 thousands kilometers and ends at 16.3 thousands kilometers). The force for the electron would be:
F=2S*dBg/dr=[h/(2π)]*[G/(5*c*c)]*[M/r*r]*[2π/T]
F=1*10exp(-55) Newton
For the electron traveling with velocity of 0.1 m/s, the distance is 10000 km (1*10exp(7) meters), the time of travel is 1*10exp(8) seconds (~3 years). Using mass of electron 9.1*10exp(-31) kg and simple formula L=a*t*t/2 the expected separation of the electrons due to ordinary spin at the end of travel would be 5.5*10exp(-10) m (5.5 Angstrom - measurable at modern technology).
More accurate double integration will give the similar result:
L=[1/v*v]*[h/(2*π)]*[G/(5*c*c)]*[M/m]*[2π/T]*ln(R1/Ro)
Here v is the velocity of the electron, m is the mass of electron, Ro and R1 are distance from the center of the Earth at the start and at the finish, correspondingly. L is 6.9 Angstrom.
The largest problem is here: the electron is subject to the magnetic field of the Earth and will travel in a circle around the Earth magnetic field line. The only way to compensate such rotation is to put the compensating electric field in the opposite direction during the whole travel of the electron from start to finish. Despite the keeping the whole satellite all the time around the traveling pulse of electrons is an expensive task, it may be done provided the electrons are moving very slow. The electrons and the satellites may, of course rotate around the Earth in the equatorial plane (otherwise such satellite would not work), slowly moving away from the Earth as the bunch of electrons travels away at a speed of 10 cm/s and the separation due to the gravitomagnetic field gradient accumulates.
Another problem would be the presence of the magnetic field gradient (so the classical Stern-Gerlach experiment would be performed in Earth magnetic field gradient). It is possible to carry the compensating magnetic field gradient on the same satellite as well. Actually while the full compensation of the classical Stern-Gerlach splitting would not be possible, the idea here to see the additional splittings in the final picture. The presence of such splittings would mean the presence of one more quantum number - second spin for elementary particles.
Second spin will allow to hypothesize the presence of heavy particle-gravitational antiparticle virtual pairs in the quantum vacuum (like Higgs - antigravitational Higgs pairs proposed in [1]) and explain the gravitational constant in a way similar to the electrostatic one.
References.
1.http://tipikin.blogspot.com/2019/12/quantum-vacuum-application-to-gravity.html
2.https://en.wikipedia.org/wiki/Gravitoelectromagnetism
Friday, February 28, 2020
Use of modern centrifuges for discovery of gravitational phenomena on quantum level
Modern centrifuges are improved a lot from the last time their record values were published. Magazine "Popular mechanics) back in 1950 (70 years ago) was already mentioning centrifuges with 166000 rotations per second [1]. Assuming the scientific progress continued today they are even faster. Since from equivalence principle of Einstein the accelerated motion of the object (including atom or molecule) is the same as the motion in gravitational field, such ultracentrifuge may be helpful in discovering and verifications of the new quantum phenomena connected with the gravity.
Most theories talking about the gravity on atomic level are mentioning the vicinity of black hole or neutron star, but modern centrifuges may offer the same accelerations on Earth. For example, even biological centrifuges may easily reach 1 millions g (which is enough for separation of any proteins), but they are not intended for physical experiments and probably the specially made centrifuge may go much further.
There are several possible phenomena relevant for such gravitational force.
1.Deviation of slow light.
The hypothesis that the slow light deviates much stronger inside the stars and may thus generate the gravity force in addition to the usual gravity of baryonic matter is expressed in [2]. However, the deviation of the light in the usual gravity is too weak to be measured directly for light in refracting matter (in the vacuum it was measured during Einstein times and is the confirmation of general theory of relativity). Using the same approach as in [2], for the deviation of light in any weak (compare to the inside of the black hole) it is twice as strong as Newton deviation. For example, for the deviation of the light which travels with the velocity of 0.7c (for example, inside the glass) the formula would be as follows.
For the distance of L=1 meter (reasonably long centrifuge) the time of travel would be:
t=L/(0.7*c)
here t is the time of travel, c is speed of light in vacuum.
Deviation in the perpendicular direction (assuming the light is traveling almost along the axis of the rotation, in uniform gravitational field):
S=a*t*t (this would be twice the Newtonian value of a*t*t/2)
The angle would be:
a=S/L=a*L/(0.49*c*c)=2.3*10exp(-10)
for a equal to 1 million g. The shift for light S is only 2.3 A - too small to be measured easily.
For easy to notice deviation of say 1 mm the velocity of light should be 100000 m/c (or 0.00033*c).
Today the experiments exists for light as slow as 90 m/c [3], so the experiment of observation of slow light will not even need the record centrifuge.
2.Ionization induced by the gravitational field.
In strong enough electric field the tunneling of the electron out of the molecule happened. This called field ionization and usually needs rather high electric field. The observation of the phenomena close to field ionization using the gravitational field may be only possible for the molecules or atoms which are already close to being ionized - excited atoms or molecules, where the electron is in Rydberg state for atoms in vacuum or in Rydberg like state in semiconductors.
Rydberg atoms are capable of detection of the microwaves with frequencies in MHz range already [4](pre-excited by laser atom enters the Rydberg state and gets the final energy from RF quanta). For 100 MHz the energy of quanta is only 4.1*10exp(-7) eV
The idea is that such Rydberg atom being placed in a strong gravitational field (say 10 millions g) will create the potential bending for electron shallow enough to observe the tunneling of electron out of such an atom.
The largest problem to obtain even more excited states Rydberg states is temperature (electron should be on the Rydberg level at least around kT from ionization barrier. For record temperatures achieved on the level of 50 nK that means that the lowest energy detection possible for Rydberg atom hold at this temperature is kT, 6.9*10exp(-31) Joule or 4.3*10exp(-12) eV (assumed it is hold near the thermal bath big enough to absorb the heat created at laser excitation to the Rydberg level)
For the gravitational field of 10 millions g the energy of E=6.9*10exp(-31) J is reached at the distance of:
L=E/F=E/(m*10exp(7)*g)=7.7*10exp(-9) m
So electron should tunnel only 7 nm under barrier to reach the space where it may escape Rydberg atom. This value is a reasonable distance for tunneling of electron (up to 100 Angstroms).
Therefore, such experiment is already at the reach of the modern physics.
The largest problem of the observation of such phenomenon would be the ionization of the material induced by stress (mechanochemistry). Indeed, the gravitational field of 10 millions g is smashing any material very perceptibly. As the huge stress is build inside, the electrons will be emitted merely because near the defects they will be excited enough to leave the material even without help of gravitational pull on the electron itself [6]
Careful choice of materials, long waiting time (conditioning) and modulation of laser beam creating the Rydberg atoms may allow to overcome this problem
References.
1."Merry-go-round of industry"// Popular Mechanics, 1950, January, p. 147
2.https://tipikin.blogspot.com/2019/11/weak-equivalence-principle-is-not-valid.html
3.https://physics.aps.org/story/v3/st37
4. https://arxiv.org/abs/1808.08589
5. https://phys.org/news/2019-02-coldest-quantum-gas-molecules.html
6. https://onlinelibrary.wiley.com/doi/abs/10.1002/masy.19910410105
V.A.Zakrevskii "Electron emission during deformation of polymers"
Most theories talking about the gravity on atomic level are mentioning the vicinity of black hole or neutron star, but modern centrifuges may offer the same accelerations on Earth. For example, even biological centrifuges may easily reach 1 millions g (which is enough for separation of any proteins), but they are not intended for physical experiments and probably the specially made centrifuge may go much further.
There are several possible phenomena relevant for such gravitational force.
1.Deviation of slow light.
The hypothesis that the slow light deviates much stronger inside the stars and may thus generate the gravity force in addition to the usual gravity of baryonic matter is expressed in [2]. However, the deviation of the light in the usual gravity is too weak to be measured directly for light in refracting matter (in the vacuum it was measured during Einstein times and is the confirmation of general theory of relativity). Using the same approach as in [2], for the deviation of light in any weak (compare to the inside of the black hole) it is twice as strong as Newton deviation. For example, for the deviation of the light which travels with the velocity of 0.7c (for example, inside the glass) the formula would be as follows.
For the distance of L=1 meter (reasonably long centrifuge) the time of travel would be:
t=L/(0.7*c)
here t is the time of travel, c is speed of light in vacuum.
Deviation in the perpendicular direction (assuming the light is traveling almost along the axis of the rotation, in uniform gravitational field):
S=a*t*t (this would be twice the Newtonian value of a*t*t/2)
The angle would be:
a=S/L=a*L/(0.49*c*c)=2.3*10exp(-10)
for a equal to 1 million g. The shift for light S is only 2.3 A - too small to be measured easily.
For easy to notice deviation of say 1 mm the velocity of light should be 100000 m/c (or 0.00033*c).
Today the experiments exists for light as slow as 90 m/c [3], so the experiment of observation of slow light will not even need the record centrifuge.
2.Ionization induced by the gravitational field.
In strong enough electric field the tunneling of the electron out of the molecule happened. This called field ionization and usually needs rather high electric field. The observation of the phenomena close to field ionization using the gravitational field may be only possible for the molecules or atoms which are already close to being ionized - excited atoms or molecules, where the electron is in Rydberg state for atoms in vacuum or in Rydberg like state in semiconductors.
Rydberg atoms are capable of detection of the microwaves with frequencies in MHz range already [4](pre-excited by laser atom enters the Rydberg state and gets the final energy from RF quanta). For 100 MHz the energy of quanta is only 4.1*10exp(-7) eV
The idea is that such Rydberg atom being placed in a strong gravitational field (say 10 millions g) will create the potential bending for electron shallow enough to observe the tunneling of electron out of such an atom.
The largest problem to obtain even more excited states Rydberg states is temperature (electron should be on the Rydberg level at least around kT from ionization barrier. For record temperatures achieved on the level of 50 nK that means that the lowest energy detection possible for Rydberg atom hold at this temperature is kT, 6.9*10exp(-31) Joule or 4.3*10exp(-12) eV (assumed it is hold near the thermal bath big enough to absorb the heat created at laser excitation to the Rydberg level)
For the gravitational field of 10 millions g the energy of E=6.9*10exp(-31) J is reached at the distance of:
L=E/F=E/(m*10exp(7)*g)=7.7*10exp(-9) m
So electron should tunnel only 7 nm under barrier to reach the space where it may escape Rydberg atom. This value is a reasonable distance for tunneling of electron (up to 100 Angstroms).
Therefore, such experiment is already at the reach of the modern physics.
The largest problem of the observation of such phenomenon would be the ionization of the material induced by stress (mechanochemistry). Indeed, the gravitational field of 10 millions g is smashing any material very perceptibly. As the huge stress is build inside, the electrons will be emitted merely because near the defects they will be excited enough to leave the material even without help of gravitational pull on the electron itself [6]
Careful choice of materials, long waiting time (conditioning) and modulation of laser beam creating the Rydberg atoms may allow to overcome this problem
References.
1."Merry-go-round of industry"// Popular Mechanics, 1950, January, p. 147
2.https://tipikin.blogspot.com/2019/11/weak-equivalence-principle-is-not-valid.html
3.https://physics.aps.org/story/v3/st37
4. https://arxiv.org/abs/1808.08589
5. https://phys.org/news/2019-02-coldest-quantum-gas-molecules.html
6. https://onlinelibrary.wiley.com/doi/abs/10.1002/masy.19910410105
V.A.Zakrevskii "Electron emission during deformation of polymers"
Subscribe to:
Posts (Atom)