Professors Mohazzbi and Luo [1] published “Despite several attempts have been made to explain the twin paradox … none of the explanations … resolved the paradox. If the paradox can be ever resolved, it requires a m...Professors Mohazzbi and Luo [1] published “Despite several attempts have been made to explain the twin paradox … none of the explanations … resolved the paradox. If the paradox can be ever resolved, it requires a much deeper understanding … of the theory of relativity”. The deeper understanding of resolving the paradox is by applying more explicit definitions of proper time interval, Lorentz transform, time dilation, and aging time.展开更多
The origin of elementary particle mass is considered as a function of n-valued graviton quanta. To develop this concept we begin in a cold region of “empty space” comprised of only microscopic gravitons oscillating ...The origin of elementary particle mass is considered as a function of n-valued graviton quanta. To develop this concept we begin in a cold region of “empty space” comprised of only microscopic gravitons oscillating at angular frequency ω. From opposite directions enters a pair of stray protons. Upon colliding, heat and energy are released. Customarily, this phase and what follows afterward would be described by Quantum Chromodynamics (QCD). Instead, we argue for an intermediary step. One in which neighboring gravitons absorb discrete amounts of plane-wave energy. Captured by the graviton, the planewave becomes a standing wave, whereupon its electromagnetic energy densities are converted into gravitational quanta. Immediately thereafter an elementary particle is formed and emitted, having both mass and spin. From absorption to conversion to emission occurs in less than 3.7 × 10−16 s. During this basic unit of hybrid time, general relativity and quantum physics unite into a common set of physical laws. As additional stray protons collide the process continues. Over eons, vast regions of spacetime become populated with low-mass particles. These we recognize to be dark matter by its effects on large scale structures in the universe. Its counterpart, dark energy, arises when the conversion of gravitational quanta to particle emission is interrupted. This causes the gravitational quanta to be ejected. It is recognized by its large scale effects on the universe.展开更多
In this article, we address the solution of the Einstein’s equations in the vacuum region surrounding a spherically symmetric mass distribution. There are two different types of mathematical solutions, depending on t...In this article, we address the solution of the Einstein’s equations in the vacuum region surrounding a spherically symmetric mass distribution. There are two different types of mathematical solutions, depending on the value of a constant of integration. These two types of solutions are analysed from a physical point of view. The comparison with the linear theory limit is also considered. This leads to a new solution, different from the well known one. If one considers the observational data in the weak field limit this new solution is in agreement with the available data. While the traditional Schwarzschild solution is characterized by a horizon at r=2GM/c2, no horizon exists in this new solution.展开更多
This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the me...This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.展开更多
In a very recent article of mine I have corrected the traditional derivation of the Schwarzschild metric thus arriving to formulate a correct Schwarzschild metric different from the traditional Schwarzschild metric. I...In a very recent article of mine I have corrected the traditional derivation of the Schwarzschild metric thus arriving to formulate a correct Schwarzschild metric different from the traditional Schwarzschild metric. In this article, starting from this correct Schwarzschild metric, I also propose corrections to the other traditional Reissner-Nordstrøm, Kerr and Kerr-Newman metrics on the basis of the fact that these metrics should be equal to the correct Schwarzschild metric in the borderline case in which they reduce to the case described by this metric. In this way, we see that, like the correct Schwarzschild metric, also the correct Reissner-Nordstrøm, Kerr and Kerr-Newman metrics do not present any event horizon (and therefore do not present any black hole) unlike the traditional Reissner-Nordstrøm, Kerr and Kerr-Newman metrics.展开更多
The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified,...The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified, to include Newton’s Shell Theorem (NST). By including NST for r, both Schwarzschild singularity at r = 2GM/c2 and at r → 0 singularities are removed from the metric. Near R → 0, the question of maximal density is considered based on Schwarzschild’s modified metric, and compared to the quantum limit of maximal mass density put by Planck’s quantum-based universal units. It is asserted, that General relativity, when combined with Planck’s universal units, inevitably leads to quantization of gravity.展开更多
A complementarity hypothesis concerning outsider and insider perspectives of a gargantuan black hole is proposed. The two thought experiments presented herein are followed by a brief discussion of a new interpretation...A complementarity hypothesis concerning outsider and insider perspectives of a gargantuan black hole is proposed. The two thought experiments presented herein are followed by a brief discussion of a new interpretation of black hole interior “space-and-time-reversal”. Specifically, it is proposed that the “singularity” space of the black hole interior is time-like and the expansion time of the black hole interior is space-like. The resemblance of this new insider interpretation to our own expanding and redshifting big bang universe is compelling.展开更多
Null geodesics for massless particles in Schwarzschild spacetime are obtained by direct integration of the trajectory equation in spatial coordinates without transformation to the inverse space. The results are classi...Null geodesics for massless particles in Schwarzschild spacetime are obtained by direct integration of the trajectory equation in spatial coordinates without transformation to the inverse space. The results are classified following Chandrasekhar depending on the ratio of the impact parameter of the trajectory to its critical value. In the subcritical and supercritical cases the geodesics are expressed in terms of elliptic integrals of the first kind. Some results are formally different from the classical ones, but in fact equivalent to them, being at the same time more compact and descriptive.展开更多
In this paper we rewrite the gravitational constant based on its relationship with the Planck length and based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In t...In this paper we rewrite the gravitational constant based on its relationship with the Planck length and based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In this way we are able to quantize a series of end results in Newton and Einstein’s gravitation theories. The formulas will still give exactly the same values as before, but everything related to gravity will then come in quanta. This also gives some new insight;for example, the gravitational deflection of light can be written as only a function of the radius and the Planck length. Numerically this only has implications at the quantum scale;for macro objects the discrete steps are so tiny that they are close to impossible to notice. Hopefully this can give additional insight into how well or not so well (ad hoc) quantized Newton and Einstein’s gravitation is potentially linked with the quantum world.展开更多
Physicists possess an intuitive awareness of Euclidian space and time and Galilean transformation, and are then challenged with Minkowski space-time and Einstein’s curved space-time. Relativistic experiments support ...Physicists possess an intuitive awareness of Euclidian space and time and Galilean transformation, and are then challenged with Minkowski space-time and Einstein’s curved space-time. Relativistic experiments support the “time-dilation” interpretation and others support “curved space-time” interpretation. In this, and related work, we investigate the key issues in terms of the intuitive space-time frame. In particular, we provide alternative approaches to explain “time dilation” and to explain the energy density for gravity systems. We approach the latter problem from an information perspective.展开更多
A new simpler mathematic method is proposed to study fermions tunneling from black holes. According to this method, by using semiclassical approximation theory, it simplifies the Dirac equation of curved spacetime and...A new simpler mathematic method is proposed to study fermions tunneling from black holes. According to this method, by using semiclassical approximation theory, it simplifies the Dirac equation of curved spacetime and then the relationship of the gamma matrix and the component of contravariant metric is considered in order to transform the set of difficult quantum equations into a simple equation. Finally, the fermion tunneling and Hawking radiation of black holes are obtained. The method is very effective and simple, and we will take the Schwarzschild black hole with global monopole and the higher-dimensional Reissner-Nordstrom de Sitter black hole as two examples to show the fact.展开更多
Applying Parikh＇s quantum tunnelling method, this paper has studied the quantum tunnelling radiation of Schwarzschild de Sitter black hole with a global monopole. The result shows that the tunnelling rates at the eve...Applying Parikh＇s quantum tunnelling method, this paper has studied the quantum tunnelling radiation of Schwarzschild de Sitter black hole with a global monopole. The result shows that the tunnelling rates at the event horizon and the cosmological horizon are related to Bekenstein-Hawking entropy and the derived radiation spectrum is not precisely thermal when considering energy conservation and self-gravitation interaction.展开更多
Haug has recently introduced a new theory of unified quantum gravity coined “<em>Collision Space-Time</em>”. From this new and deeper understanding of mass, we can also understand how a grandfather pendu...Haug has recently introduced a new theory of unified quantum gravity coined “<em>Collision Space-Time</em>”. From this new and deeper understanding of mass, we can also understand how a grandfather pendulum clock can be used to measure the world’s shortest time interval, namely the Planck time, indirectly, without any knowledge of G. Therefore, such a clock can also be used to measure the diameter of an indivisible particle indirectly. Further, such a clock can easily measure the Schwarzschild radius of the gravity object and what we will call “Schwarzschild time”. These facts basically prove that the Newton gravitational constant is not needed to find the Planck length or the Planck time;it is also not needed to find the Schwarzschild radius. Unfortunately, there is significant inertia towards new ideas that could significantly alter our perspective on the fundamentals in the current physics establishment. However, this situation is not new in the history of science. Still, the idea that the Planck time can be measured totally independently of any knowledge of Newton’s gravitational constant could be very important for moving forward in physics. Interestingly, an old instrument that today is often thought of as primitive instrument can measure the world’s shortest possible time interval. No atomic clock or optical clock is even close to be able to do this.展开更多
Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ...Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ago by Penrose, and many papers have since extended the concept. Currently there is no satisfactory physical understanding of the nature of quasi-local mass. In this paper I review the key issues, the current status, and propose an alternative interpretation of the problem of local mass and energy density for gravity systems from an information perspective.展开更多
The authors have developed an experimental system for the studies of extreme ultraviolet projection lithography at 13.0nm wavelength, which includes a laser plasma source, an ellipsoidal condenser, a transmission mask...The authors have developed an experimental system for the studies of extreme ultraviolet projection lithography at 13.0nm wavelength, which includes a laser plasma source, an ellipsoidal condenser, a transmission mask and a Schwarzschild optics. The optical system is optimized to achieve 0.1μm resolution over a 0.1mm diameter image field of view and the mirrors of the objective were coated with Mo/Si multilayer to provide 60% reflectance at near normal incidence angle for 13.0nm radiation.展开更多
This article presents the hypothesis that the vacuum is endowed with a quantum structure;the vacuum particles would be Friedmann-Planck micro-universes. For this, the article introduces a quantization of a closed Frie...This article presents the hypothesis that the vacuum is endowed with a quantum structure;the vacuum particles would be Friedmann-Planck micro-universes. For this, the article introduces a quantization of a closed Friedmann universe, then a quantization of the photon spheres filling this universe. This approach gives a numerical value consistent with cosmological measurements for the current dark energy density of our Universe. Next, the article takes the content of a model published in Physics Essays in 2013 [<a href="#ref1" target="_blank">1</a>], assuming that elementary particles are Schwarzschild photon spheres;these could be derived from the Friedmann photon spheres composing the vacuum particles. It is further recalled that the model presents a unified structure of elementary particles and allows us to calculate the value of the elementary electric charge as well as the mass of the elementary particles.展开更多
A few physicists have recently constructed the generating compatibility conditions (CC) of the Killing operator for the Minkowski (M), Schwarzschild (S) and Kerr (K) metrics. They discovered second order CC, well know...A few physicists have recently constructed the generating compatibility conditions (CC) of the Killing operator for the Minkowski (M), Schwarzschild (S) and Kerr (K) metrics. They discovered second order CC, well known for M, but also third order CC for S and K. In a recent paper (DOI:10.4236/jmp.2018.910125) we have studied the cases of M and S, without using specific technical tools such as Teukolski scalars or Killing-Yano tensors. However, even if S(<em>m</em>) and K(<em>m</em>, <em>a</em>) are depending on constant parameters in such a way that S <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span></span> M when <em>m</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span></span> 0 and K<span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><span style="white-space:nowrap;"><span style="white-space:nowrap;"></span></span> S when <em>a</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span></span> 0, the CC of S do not provide the CC of M when <em>m</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span> 0 while the CC of K do not provide the CC of S when a <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span> 0. In this paper, using tricky motivating examples of operators with constant or variable parameters, we explain why the CC are depending on the choice of the parameters. In particular, the only purely intrinsic objects that can be defined, namely the extension modules, may change drastically. As the algebroid bracket is compatible with the <em>prolongation/projection</em> (PP) procedure,展开更多
文摘Professors Mohazzbi and Luo [1] published “Despite several attempts have been made to explain the twin paradox … none of the explanations … resolved the paradox. If the paradox can be ever resolved, it requires a much deeper understanding … of the theory of relativity”. The deeper understanding of resolving the paradox is by applying more explicit definitions of proper time interval, Lorentz transform, time dilation, and aging time.
文摘The origin of elementary particle mass is considered as a function of n-valued graviton quanta. To develop this concept we begin in a cold region of “empty space” comprised of only microscopic gravitons oscillating at angular frequency ω. From opposite directions enters a pair of stray protons. Upon colliding, heat and energy are released. Customarily, this phase and what follows afterward would be described by Quantum Chromodynamics (QCD). Instead, we argue for an intermediary step. One in which neighboring gravitons absorb discrete amounts of plane-wave energy. Captured by the graviton, the planewave becomes a standing wave, whereupon its electromagnetic energy densities are converted into gravitational quanta. Immediately thereafter an elementary particle is formed and emitted, having both mass and spin. From absorption to conversion to emission occurs in less than 3.7 × 10−16 s. During this basic unit of hybrid time, general relativity and quantum physics unite into a common set of physical laws. As additional stray protons collide the process continues. Over eons, vast regions of spacetime become populated with low-mass particles. These we recognize to be dark matter by its effects on large scale structures in the universe. Its counterpart, dark energy, arises when the conversion of gravitational quanta to particle emission is interrupted. This causes the gravitational quanta to be ejected. It is recognized by its large scale effects on the universe.
文摘In this article, we address the solution of the Einstein’s equations in the vacuum region surrounding a spherically symmetric mass distribution. There are two different types of mathematical solutions, depending on the value of a constant of integration. These two types of solutions are analysed from a physical point of view. The comparison with the linear theory limit is also considered. This leads to a new solution, different from the well known one. If one considers the observational data in the weak field limit this new solution is in agreement with the available data. While the traditional Schwarzschild solution is characterized by a horizon at r=2GM/c2, no horizon exists in this new solution.
文摘This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.
文摘In a very recent article of mine I have corrected the traditional derivation of the Schwarzschild metric thus arriving to formulate a correct Schwarzschild metric different from the traditional Schwarzschild metric. In this article, starting from this correct Schwarzschild metric, I also propose corrections to the other traditional Reissner-Nordstrøm, Kerr and Kerr-Newman metrics on the basis of the fact that these metrics should be equal to the correct Schwarzschild metric in the borderline case in which they reduce to the case described by this metric. In this way, we see that, like the correct Schwarzschild metric, also the correct Reissner-Nordstrøm, Kerr and Kerr-Newman metrics do not present any event horizon (and therefore do not present any black hole) unlike the traditional Reissner-Nordstrøm, Kerr and Kerr-Newman metrics.
文摘The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified, to include Newton’s Shell Theorem (NST). By including NST for r, both Schwarzschild singularity at r = 2GM/c2 and at r → 0 singularities are removed from the metric. Near R → 0, the question of maximal density is considered based on Schwarzschild’s modified metric, and compared to the quantum limit of maximal mass density put by Planck’s quantum-based universal units. It is asserted, that General relativity, when combined with Planck’s universal units, inevitably leads to quantization of gravity.
文摘A complementarity hypothesis concerning outsider and insider perspectives of a gargantuan black hole is proposed. The two thought experiments presented herein are followed by a brief discussion of a new interpretation of black hole interior “space-and-time-reversal”. Specifically, it is proposed that the “singularity” space of the black hole interior is time-like and the expansion time of the black hole interior is space-like. The resemblance of this new insider interpretation to our own expanding and redshifting big bang universe is compelling.
文摘Null geodesics for massless particles in Schwarzschild spacetime are obtained by direct integration of the trajectory equation in spatial coordinates without transformation to the inverse space. The results are classified following Chandrasekhar depending on the ratio of the impact parameter of the trajectory to its critical value. In the subcritical and supercritical cases the geodesics are expressed in terms of elliptic integrals of the first kind. Some results are formally different from the classical ones, but in fact equivalent to them, being at the same time more compact and descriptive.
文摘In this paper we rewrite the gravitational constant based on its relationship with the Planck length and based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In this way we are able to quantize a series of end results in Newton and Einstein’s gravitation theories. The formulas will still give exactly the same values as before, but everything related to gravity will then come in quanta. This also gives some new insight;for example, the gravitational deflection of light can be written as only a function of the radius and the Planck length. Numerically this only has implications at the quantum scale;for macro objects the discrete steps are so tiny that they are close to impossible to notice. Hopefully this can give additional insight into how well or not so well (ad hoc) quantized Newton and Einstein’s gravitation is potentially linked with the quantum world.
文摘Physicists possess an intuitive awareness of Euclidian space and time and Galilean transformation, and are then challenged with Minkowski space-time and Einstein’s curved space-time. Relativistic experiments support the “time-dilation” interpretation and others support “curved space-time” interpretation. In this, and related work, we investigate the key issues in terms of the intuitive space-time frame. In particular, we provide alternative approaches to explain “time dilation” and to explain the energy density for gravity systems. We approach the latter problem from an information perspective.
基金supported by the National Natural Science Foundation of China(Grant Nos.10773008 and 11075224)the Chongqing University Postgraduates Science and Innovation Fund,China(Grant No.200811B1A0100299)
文摘A new simpler mathematic method is proposed to study fermions tunneling from black holes. According to this method, by using semiclassical approximation theory, it simplifies the Dirac equation of curved spacetime and then the relationship of the gamma matrix and the component of contravariant metric is considered in order to transform the set of difficult quantum equations into a simple equation. Finally, the fermion tunneling and Hawking radiation of black holes are obtained. The method is very effective and simple, and we will take the Schwarzschild black hole with global monopole and the higher-dimensional Reissner-Nordstrom de Sitter black hole as two examples to show the fact.
基金Proiect suooorted by the National Natural Science Foundation of China （Grant No 10347008）.
文摘Applying Parikh＇s quantum tunnelling method, this paper has studied the quantum tunnelling radiation of Schwarzschild de Sitter black hole with a global monopole. The result shows that the tunnelling rates at the event horizon and the cosmological horizon are related to Bekenstein-Hawking entropy and the derived radiation spectrum is not precisely thermal when considering energy conservation and self-gravitation interaction.
文摘Haug has recently introduced a new theory of unified quantum gravity coined “<em>Collision Space-Time</em>”. From this new and deeper understanding of mass, we can also understand how a grandfather pendulum clock can be used to measure the world’s shortest time interval, namely the Planck time, indirectly, without any knowledge of G. Therefore, such a clock can also be used to measure the diameter of an indivisible particle indirectly. Further, such a clock can easily measure the Schwarzschild radius of the gravity object and what we will call “Schwarzschild time”. These facts basically prove that the Newton gravitational constant is not needed to find the Planck length or the Planck time;it is also not needed to find the Schwarzschild radius. Unfortunately, there is significant inertia towards new ideas that could significantly alter our perspective on the fundamentals in the current physics establishment. However, this situation is not new in the history of science. Still, the idea that the Planck time can be measured totally independently of any knowledge of Newton’s gravitational constant could be very important for moving forward in physics. Interestingly, an old instrument that today is often thought of as primitive instrument can measure the world’s shortest possible time interval. No atomic clock or optical clock is even close to be able to do this.
文摘Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ago by Penrose, and many papers have since extended the concept. Currently there is no satisfactory physical understanding of the nature of quasi-local mass. In this paper I review the key issues, the current status, and propose an alternative interpretation of the problem of local mass and energy density for gravity systems from an information perspective.
文摘The authors have developed an experimental system for the studies of extreme ultraviolet projection lithography at 13.0nm wavelength, which includes a laser plasma source, an ellipsoidal condenser, a transmission mask and a Schwarzschild optics. The optical system is optimized to achieve 0.1μm resolution over a 0.1mm diameter image field of view and the mirrors of the objective were coated with Mo/Si multilayer to provide 60% reflectance at near normal incidence angle for 13.0nm radiation.
文摘This article presents the hypothesis that the vacuum is endowed with a quantum structure;the vacuum particles would be Friedmann-Planck micro-universes. For this, the article introduces a quantization of a closed Friedmann universe, then a quantization of the photon spheres filling this universe. This approach gives a numerical value consistent with cosmological measurements for the current dark energy density of our Universe. Next, the article takes the content of a model published in Physics Essays in 2013 [<a href="#ref1" target="_blank">1</a>], assuming that elementary particles are Schwarzschild photon spheres;these could be derived from the Friedmann photon spheres composing the vacuum particles. It is further recalled that the model presents a unified structure of elementary particles and allows us to calculate the value of the elementary electric charge as well as the mass of the elementary particles.
文摘A few physicists have recently constructed the generating compatibility conditions (CC) of the Killing operator for the Minkowski (M), Schwarzschild (S) and Kerr (K) metrics. They discovered second order CC, well known for M, but also third order CC for S and K. In a recent paper (DOI:10.4236/jmp.2018.910125) we have studied the cases of M and S, without using specific technical tools such as Teukolski scalars or Killing-Yano tensors. However, even if S(<em>m</em>) and K(<em>m</em>, <em>a</em>) are depending on constant parameters in such a way that S <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span></span> M when <em>m</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span></span> 0 and K<span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><span style="white-space:nowrap;"><span style="white-space:nowrap;"></span></span> S when <em>a</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span></span> 0, the CC of S do not provide the CC of M when <em>m</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span> 0 while the CC of K do not provide the CC of S when a <span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span></span> 0. In this paper, using tricky motivating examples of operators with constant or variable parameters, we explain why the CC are depending on the choice of the parameters. In particular, the only purely intrinsic objects that can be defined, namely the extension modules, may change drastically. As the algebroid bracket is compatible with the <em>prolongation/projection</em> (PP) procedure,
