CN114822182A

CN114822182A - Method for renormalizing universal gravitation law based on experimental data

Info

Publication number: CN114822182A
Application number: CN202210483053.8A
Authority: CN
Inventors: 马龙
Original assignee: Individual
Current assignee: Individual
Priority date: 2021-10-12
Filing date: 2022-05-05
Publication date: 2022-07-29
Also published as: CN113888937A

Abstract

A method of renormalizing the law of universal gravitation based on experimental data, comprising preparing two objects with masses m1 and m2, respectively, without weighing them; preparing a device for measuring the constant of universal gravitation; by using the device for measuring the constant of the universal gravitation, the magnitude of the universal gravitation F1 between two objects with the mass of m1 and m2 respectively is measured, and the distance between the two objects is measured to be R1. The method can solve the obvious defect of the existing universal gravitation law, obtains a renormalization constant in the universal gravitation law, further obtains a new universal gravitation constant C according to the renormalization constant, calculates the field intensity of a gravitational field of electrons at a field source, calculates the field intensity of the gravitational field of a black hole at the field source, and calculates the size of the universal gravitation when the distance between a pi meson and other mesons is zero based on experimental data.

Description

Method for renormalizing universal gravitation law based on experimental data

Technical Field

The invention relates to a method for renormalizing universal gravitation law based on experimental data.

Background

The Law of universal gravitation (Law of univarial visualization) was published by Isaac Newton in 1687 in the mathematical theory of nature. Newton's universal law of gravity is expressed as follows:

any two particles m ₁ 、m ₂ By a force F in a direction passing through the center line ₁₂ Attract each other by the attraction force F ₁₂ Product m of size and their mass ₁ m ₂ Proportional, inversely proportional to the square of the distance r between them, independent of the chemical composition of the two bodies and the kind of medium between them.

The existing universal gravitation law has an obvious defect that two mass points m ₁ 、m ₂ In the case where the distance therebetween tends to zero, the attractive force F ₁₂ It tends to infinity or the gravitational field strength at which the origin (singularity) of the particle is located is infinite. However, this is clearly not true of the fact that there are two particles m ₁ 、m ₂ When the distance between the two mass points is zero, the two mass points m ₁ 、m ₂ The interaction force F between ₁₂ Nor may it be infinite.

Existing physical experiments can qualitatively demonstrate that when two particles coincide, infinite energy is not released, e.g., annihilation of a positive and negative electron pair, as an example.

Based on two particles m ₁ 、m ₂ The fact that the distance between them tends to zero and the energy released is finite, makes it reasonable to assume that in this case the two particles m ₁ 、m ₂ Between the gravity F ₁₂ Tends to be a constant and not infinite. In addition, if the field strength of the gravitational field at the origin of the particle is physically infinite, even if the detection is performed away from the origin (singular point) of the particle, the field strength of the infinite gravitational field is not decreased slightly due to the distance, and still is infinite. However, enough experiments can prove that the field intensity of the gravitational field is a limited physical quantity when the point away from the origin (singularity) of the particle is detected. Therefore, from the experiment, the existing law of universal gravitation needs to be renormalized to avoid the situation that the field intensity of the gravitational field is infinite. To this endThe existing law of universal gravitation needs to be corrected based on data of physical experiments to solve the problem that the existing law of universal gravitation is located at two mass points m ₁ 、m ₂ The distance between them tends to zero. Needless to say, the correction is to maximally accommodate the experimental fact that the existing law of universal gravitation conforms to the inverse square law, and the experimental result cannot be violated.

Disclosure of Invention

The invention aims to provide a method for renormalizing the universal gravitation law based on experimental data, which can solve the obvious defects of the existing universal gravitation law, obtain a renormalization constant in the universal gravitation law, calculate the field intensity of a gravitational field of electrons at a field source of the gravitational field, calculate the field intensity of a gravitational field of a black hole at the field source of the black hole, calculate the size of the universal gravitation when the distance between a pi meson and other mesons is zero, and can recalculate the mass of each celestial body including the earth, the sun and the moon to obtain a more accurate value, thereby better serving scientific and technological projects such as various satellite launching, space launching and the like.

The invention discloses a method for renormalizing universal gravitation law based on experimental data, which comprises the following steps:

A. two objects with mass m1 and m2 respectively are prepared without weighing the objects;

B. preparing a device for measuring the constant of universal gravitation;

C. by utilizing the device for measuring the universal gravitation constant, the universal gravitation between two objects with the mass of m1 and m2 is measured to be F1, the distance between the two objects is measured to be R1, then the distance between the two objects is changed to be R2, and the universal gravitation between the two objects with the mass of m1 and m2 is measured to be F2 after the distance between the two objects is changed to be R2;

E. according to the formula of the corrected law of universal gravitation

F ₁₂ ＝G m ₁ m ₂ /(r+r _m ) ² (21)

Substituting the secondary measurement result into the formula to respectively obtain:

F1＝G m ₁ m ₂ /(R1+r _m ) ² (22)

F2＝G m ₁ m ₂ /(R2+r _m ) ² (23)

the two equations of formula (22) and formula (23) are simplified to obtain:

F1/F2＝(R2+r _m ) ² /(R1+r _m ) ² (24)

substituting F1, F2, R1 and R2 measured by experiments into the formula (24) to obtain the renormalization constant R in the law of universal gravitation _m The specific numerical value of (1).

Preferably, the field strength Ee of the gravitational field of the electron at the field source is calculated by using the corrected law of universal gravitation as follows:

Ee＝C me/r _m (11)

wherein C is modified universal gravitation constant C, r _m Is the renormalization constant in the law of universal gravitation, me is the mass of the electron.

Preferably, the field intensity E of the gravitational field of the black hole at the field source is calculated by using the modified law of universal gravitation as follows:

E＝C M/r _m (12)

wherein C is modified universal gravitation constant C, r _m Is the renormalization constant in the law of universal gravitation, and M is the mass of the black hole.

Preferably, the universal gravitation F when the distance between the pi meson and other hadrons is zero is calculated by using the corrected universal gravitation law _π The size of (A) is as follows:

F _π ＝C M _π M/r _m (13)

wherein C is modified universal gravitation constant C, r _m Is a renormalization constant in the law of universal gravitation, M _π The mass of pi mesons and M the mass of other hadrons.

Preferably, the device for measuring the gravitational constant is a cavendian torsion balance, and the two objects with the mass m1 and the mass m2 are solid spherical bodies made of metal respectively.

The method for renormalizing the law of universal gravitation based on experimental data comprises the steps of preparing two objects with the mass of m1 and m2 respectively without weighing the objects; preparing a device for measuring the constant of universal gravitation; by using the device for measuring the universal gravitation constant, the universal gravitation between two objects with the mass of m1 and m2 is measured to be F1, the distance between the two objects is measured to be R1, then the distance between the two objects is changed to be R2, the universal gravitation between the two objects with the mass of m1 and m2 after the distance between the two objects is changed to be R2 is measured again to be F2, and the data are substituted into a corresponding calculation formula, so that the weight normalization constant R in the universal gravitation law can be obtained _m The specific numerical value of (1). Therefore, the method for renormalizing the law of universal gravitation based on experimental data can overcome the obvious defect of the conventional law of universal gravitation and obtain the renormalization constant r in the law of universal gravitation _m Then according to the renormalization constant r _m Further obtaining a new universal gravitation constant C, calculating the field intensity of the gravitational field of the electron at the field source, calculating the field intensity of the gravitational field of the black hole at the field source, calculating the universal gravitation size when the distance between the pi meson and other mesons is zero, and recalculating the mass of each celestial body including the earth, the sun and the moon to obtain a more accurate value, thereby better serving scientific and technological projects such as various satellite launching, space launching and the like, and further reducing the fuel consumption of various satellite launching and space launching.

The following describes in detail a specific embodiment of the method for normalizing law of universal gravitation based on experimental data according to the present invention.

Detailed Description

Based on two particles m ₁ 、m ₂ The fact that the distance between them tends to zero and the energy released is finite, we have the reason to assume that in this case the two particles m ₁ 、m ₂ Between the gravity F ₁₂ Tends to be a constant and not infinite. In addition, if the field strength of the gravitational field at the origin of the particle is physically infinite, even if the detection is performed away from the origin (singular point) of the particle, the field strength of the infinite gravitational field is not decreased slightly due to the distance, and still is infinite. However, enough experiments can prove that the field intensity of the gravitational field is a limited physical quantity when the point away from the origin (singularity) of the particle is detected. Therefore, from the experiment, the existing law of universal gravitation needs to be renormalized to avoid the situation that the field intensity of the gravitational field is infinite. Therefore, it is necessary to correct the existing law of universal gravitation based on data of physical experiments to obtainSolves the problem that the solution is at two mass points m ₁ 、m ₂ The distance between them tends to zero. Needless to say, the correction is to maximally accommodate the experimental fact that the existing law of universal gravitation conforms to the inverse square law, and the experimental result cannot be violated.

Based on the above requirements, the present invention is a solution for renormalizing the existing law of universal gravitation by inserting a constant from physical experiments into the denominator term of the existing law of universal gravitation, and the basic principle of the insertion is to make the law of universal gravitation be in two mass points m ₁ 、m ₂ Two particles m with zero distance between them ₁ 、m ₂ The interaction force F between ₁₂ Not infinite.

The law of universal gravitation corrected by renormalization treatment, namely the law of universal gravitation under the singularity mechanics, can be expressed as follows:

any two particles m ₁ 、m ₂ By a force F in a direction passing through the center line ₁₂ Attract each other by the attraction force F ₁₂ Product m of size and their mass ₁ m ₂ Proportional to the distance r between them plus a renormalization constant r _m Is inversely proportional to the square of the two mass points m, independent of the chemical composition of the two bodies and the type of medium between them ₁ 、m ₂ Cannot be zero, i.e.:

in the formula r _m The method is a renormalization constant in the law of universal gravitation under singularity mechanics, the physical unit of the renormalization constant is a length unit of meter, and the volume of two mass points cannot be zero.

The universal gravitation law under the singularity mechanics pursues a mathematical expression which is more consistent with an experimental result, and obviously, the universal gravitation law under the singularity mechanics can be used for analyzing and processing two mass points m ₁ 、m ₂ In the "superposed" state with universal attraction between each otherHowever, due to the highly idealized characteristics of the mathematical tool and the fact that the data of the physical experiment inevitably have measurement errors, it is obvious that whether the mathematical formula is strictly established cannot be completely verified, and the pursuit goal is only approximately established and only 'available'.

The physical meaning of the renormalization constant in the law of universal gravitation under the singularity mechanics is as follows: two particles with a volume of not zero, m ₁ 、m ₂ A space constant brought by the action of gravitational field is shown under the condition that the distance between the two is zero, and the constant r is renormalized _m Within a spatial range of (c), two mass points m ₁ 、m ₂ Even if there is relative motion between them, they should be regarded as two mass points m ₁ 、m ₂ At zero distance, i.e. two particles m ₁ 、m ₂ Is in a position superposed state without space interval. Note that this position superimposed state is a position superimposed state under a gravitational field, and its magnitude is different from that under an electromagnetic field.

Correspondingly, a mass point with mass m has the field intensity E of the gravitational field under the singularity mechanics _m Comprises the following steps:

at the point where r is 0, the position of r,

this relationship indicates that the maximum value of the gravitational field strength of the mass point is the position of the mass point with mass m.

Potential function U of gravity field under singularity mechanics of mass point with mass m _m Comprises the following steps:

for a stationary mass point with mass m, at r-0, the following relationship can be obtained:

because the volumes of two mass points under the singularity mechanics cannot be zero, any two mass points m ₁ 、m ₂ The distance between the two is r + r under the singularity mechanics _m R in the prior knowledge no longer; that is, even if r is 0, there is one r between any two particles in the gravitational field _m Due to two particles m ₁ 、m ₂ And (4) a result in a position superposition state.

Renormalization constant r generated based on position stacking state _m Unlike conventional distances, if described in a coordinate system, due to the renormalization constant r from physical experiments _m Not a mathematical point but a length of space that is not detachable for mathematical processing, and therefore has a renormalization constant r _m The formula (2) may encounter some difficulties in the mathematical process of transformation using a coordinate system. A possible solution is to first renormalize the constant r before performing the mathematical derivation _m Withdrawing from the formula, and normalizing the constant r after the mathematical derivation is completed _m Reinserted into the formula.

Intuitively, the renormalization constant r in the law of universal gravitation under the singularity mechanics _m The geometry of the field source of (a) is a sphere, which brings about a series of problems:

1. first, we can determine the renormalization constant r _m Outside the range, i.e. outside the field source sphere, two particles m ₁ 、m ₂ The smaller the distance between the two particles is, the larger the gravitational force is, the two particles m are on the field source spherical surface ₁ 、m ₂ If the film is stuck on the renormalization constant r _m There will be two particles m ₁ 、m ₂ The maximum value of universal gravitation therebetween.

2. Second, due to two particles m ₁ 、m ₂ Bonding to the renormalization constant r _m The maximum value of gravity appears in the two partsParticle m ₁ 、m ₂ On the field source sphere, i.e. at a distance r _m Has the smallest potential energy, i.e. has the most stable physical state.

3. When two mass points m ₁ 、m ₂ Are continuously overlapped with each other so as to enter a renormalization constant r _m After the "inside of field source" range, it is out of the minimum potential energy state, so it needs to have kinetic energy to overcome this potential energy.

4. The mathematical formula of the universal gravitation law under the singularity mechanics cannot provide a mass point m ₁ At another particle m ₂ Renormalization constant r of _m The magnitude of the internal gravitational pull (if it can also be called gravitational pull) because the physical model into which our experimental data is substituted cannot handle this.

5. From the results of particle collision experiments, a more reasonable assumption is that such gravitational interactions may not exist, i.e., a particle m ₁ At another particle m ₂ Renormalization constant r of _m Should be free and free from gravitational forces because of the renormalization constant r _m Should be zero.

We cannot exclude a particle m ₂ Renormalization constant r of _m Has a renormalization constant r inside _m The field strength of the external gravitational field is opposite in direction. But because we cannot enter a particle m ₂ Renormalization constant r of _m The field source of (a) is internally physically tested, so this can only be handled by guessing.

6. Since we have identified two particles m ₁ 、m ₂ The external distance between the two is r + r _m If two particles m ₁ 、m ₂ Is a mathematical point without volume size, then two mass points m ₁ 、m ₂ Must not be less than the renormalization constant r _m Because it is smaller than two particles m ₁ 、m ₂ When the distance between the two magnetic poles is an external mathematical distance, the field intensity of the gravitational field is larger than the maximum field intensity of the gravitational field obtained by experiments.

While at renormalization constant r _m Inside the field source we can only consider two particles m ₁ 、m ₂ The distance between them is a true, physical negative spatial dimension, and two particles m in this state appear to all observers in our "positive" physical space ₁ 、m ₂ No physical separation between the two particles occurs regardless of the movement. Two particles m ₁ 、m ₂ The 'intrinsic distance of the field source' and the 'intrinsic speed of the field source' between the two have more intuitive physical meanings in quantum mechanics.

Suppose particle m ₁ Satisfies the following equation:

Ψ(r+r _m ,t)＝Ψ ₀ exp{ik(r+r _m )-iωt}

the imaginary coordinate in the above formula represents the particle m ₁ I.e. the position function of the "particles" in the geometric space of the field source. When r is 0, it represents the mass point m ₁ At renormalization constant r _e A position function within the range.

7. The inventors prefer to consider the renormalization constant r _m Representing an important physical property of the real gravitational field. The position limit of a particle is the position where the maximum of the field strength of the particle is located, the field is the particle, the particle can be described by the field strength of the field source, and besides, no other physical quantity can be used for describing the position and the size of the particle.

Then, how should we understand the location of the "particles" of the gravitational field nature? The explanation of the singularity mechanics is: the "particles" of the gravitational field properties, i.e. the "field source" of the gravitational field and the "extended source" part outside the field source, can simultaneously have states of position at different mathematical points, which states are called superimposed states. In other words, the renormalization constant r _m It can be made to have different (under mathematical point) positions at the same time, and when you do not want to find one of the mathematical points with a measurement to define the position of the "particle" of the force field property, such a measurement will make you randomly obtain one of themThe state and when you measure it, the wave function of the system in the superimposed state collapses randomly into one of the wave functions.

For example, the mathematical point coordinates of the field source of the gravitational field of electrons can be simultaneously at its renormalization constant r _m At different places within. If you really measure the exact location of one of the mathematical points, you measure that is its renormalization constant r _m One of the specific locations within, as to which mathematical coordinate point is specific, is completely random.

You prepare 100 identical test objects and measure their status and you will get 100 results. But it is likely that some of the results will occur more frequently and some will occur less frequently, the highest occurring should be at the renormalization constant r _m Is located at the renormalization constant r _m The probability of the occurrence of the mathematical coordinate points outside the field source is lower, and the distribution of this frequency is a probability distribution, i.e., a wave function.

Based on two mass points m in gravitational field ₁ 、m ₂ Must not be less than the renormalization constant r _m In the gravity field under the singularity mechanics, a transformation and inverse transformation formula of a right-handed Cartesian rectangular coordinate and a spherical coordinate which are established on a physical particle is given:

z＝R cosθ＝(r+r _m )cosθ

wherein R is R + R _m That is, a physical and volumetric mass point is used as a coordinate origin point under the singularity mechanics and is located between other coordinate points in the coordinate systemThe distance of (d); note that r, the renormalization constant in the law of universal gravitation under singularity mechanics here _m Is directly interpolated by experimental data, renormalized by a constant r _m Can be used for describing two mass points m in a position superposition state ₁ 、m ₂ Coordinate transformation relation between them.

Note that the renormalization constant r is obtained based on physical experiments _m Unlike conventional distances, if the positional relationship is described by coordinate points of a coordinate system, the renormalization constant r is used _m Not a mathematical point but a length of space that is not detachable for mathematical processing, and therefore has a renormalization constant r _m The formula (2) may encounter some difficulties in the mathematical process of transformation using a coordinate system. A possible solution is to first renormalize the constant r before performing the mathematical derivation _m Withdrawing from the formula, and normalizing constant r after the mathematical derivation is completed _m Reinserted into the formula.

When r is 0, that is, the distance between two particles is zero, under the force field singularity mechanics, the transformation and inverse transformation formula of the right-handed cartesian coordinate and the spherical coordinate established on the physical mass point is as follows:

z＝R cosθ＝r _m cosθ

in the force field under singularity mechanics, if the spatial coordinate q of a particle with a volume ₁ 、q ₂ 、q ₃ The change over time is expressed by a single-valued law, then the motion of this particle is completely fixed, so:

q ₁ ＝q ₁ (t)+r _m ；q ₂ ＝q ₂ (t)+X _m ；q ₃ ＝q ₃ (t)+r _m ；

these equations are simple vector equations

R＝r(t)+r _m

And equivalence. Where R is the connecting coordinate origin and the moving mass point M (q) ₁ +q ₂ +q ₃ ) The sagittal diameter of (1). If particle M (q) ₁ +q ₂ +q ₃ ) Is equal to x, y, z, then

R＝r(t)+r _m ＝xi+yj+zk

Where i, j, k are unit vectors corresponding to the positive directions of the coordinate axes Ox, Oy, Oz, and vectors xi, yj, zk are vector diameters R (t) + X _m Components along the Ox, Oy, Oz coordinate axes.

In singularity mechanics, the vector R ═ R (t) + R of the moving particles _m And coordinates q ₁ 、q ₂ 、q ₃ The derivative with respect to time can be expressed as:

based on two mass points m in gravitational field ₁ 、m ₂ The external distance between the two electrodes cannot be less than the renormalization constant r _m In the following, we directly give that in the gravitational field under singularity mechanics, the origin of the stationary coordinate system and the origin of the moving coordinate system are both galileo coordinate transformations established on mass points whose volume is not zero:

x-x′＝r _m +vt

y-y′＝r _m

z-z′＝r _m

t-t′＝t _m ＝r _m /v

based on two mass points m in gravitational field ₁ 、m ₂ Must not be less thanRenormalization constant r _m In the following, we directly give that in the gravitational field under the singularity mechanics, the origin of the stationary coordinate system and the origin of the moving coordinate system are lorentz coordinate transformations established on the particles whose volume is not zero:

y-y′＝r _m

z-z′＝r _m

again, the renormalization constant r generated based on the position stacking state _m Unlike conventional distances, if the positional relationship is described by coordinate points of a coordinate system, the renormalization constant r is used _m Not a mathematical point but a length of space that is not detachable for mathematical processing, and therefore has a renormalization constant r _m The formula (2) may encounter some difficulties in the mathematical process of transformation using a coordinate system. A possible solution is to first renormalize the constant r before making the mathematical derivation _m Withdrawing from the formula, and normalizing the constant r after the mathematical derivation is completed _m Reinserting into the formula.

Based on two mass points m in gravitational field ₁ 、m ₂ Must not be less than the renormalization constant r _m We define that under singularity mechanics, if particle m ₁ 、m ₂ The motion state is changed under the action of gravitational field, so that the motion distance of the particle can adopt two mass points m ₁ 、m ₂ Between R and R _m From this we find out that under the singularity mechanics, two mass points m ₁ 、m ₂ The singularity velocity concept in between, namely:

1. singular point average speed: in Δ t time, if two particles m ₁ 、m ₂ The non-position superposition state displacement between the two is delta R, then the singular point displacement is R ═ RΔr+r _m Then, the ratio of the singularity shift to the time Δ t, i.e. the average singularity velocity V of the particle at the time Δ t, is:

note that during Δ t, when two particles m ₁ 、m ₂ When the distance between the two particles is zero, the two particles m ₁ 、m ₂ There may also be a superimposed state displacement motion between them, i.e. two particles m ₁ 、m ₂ The motion in the position superposition state, the singular point average velocity V under the displacement of the superposition state is:

in this case, two particles m ₁ 、m ₂ The mean speed V of the singularities in between is an intrinsic movement of the singularities. We can also see that when two particles m ₁ 、m ₂ When the displacement between is zero, two mass points m ₁ 、m ₂ In fact, the two parts of a particle are merged into a single particle, and there may be an intrinsic motion between the two parts of a particle, i.e. a motion in a position superimposed state, which tends to make the two particles m ₁ 、m ₂ Separated from each other by a time interval Δ t required for the separation of the two particles _m The method comprises the following steps:

2. singular instantaneous speed V: in dt time, if two particles m ₁ 、m ₂ The non-position superposition state displacement between the two is dr, then the singular point displacement is R ═ Deltar + R _m Then, the ratio of the singularity displacement to the time dt, i.e. the singularity instantaneous velocity V of the charge of the point in the time dt, is:

making circular motion two mass points m ₁ 、m ₂ The singularity instantaneous speed V in between:

the upper omega is the rotation motion of the mass point under the singularity mechanics.

Note that in dt times, when two particles m ₁ 、m ₂ When the non-position superposition state rotary displacement between the two is zero, the singular point instantaneous speed V of the circular motion under the singular point mechanics is as follows:

in this case, two particles m ₁ 、m ₂ The singularity instantaneous velocity V in between is a kind of superimposed state spin motion of the singularity.

Assuming that the singularity instantaneous velocity V of the intrinsic motion is the light velocity c, a new constant can be obtained, i.e. the zero time constant dt ═ r under the singularity mechanics _m /c。

At the speed of light, we have c ═ r _m ω。

3. Singularity instantaneous acceleration a:

4. for circular motion, centripetal acceleration at odd points a:

when the value of r is equal to 0,

5. newton's second law of motion under singularity mechanics:

6. a calculation formula of the circumference L under the singularity mechanics:

L＝2πR＝2π(r+r _m )

when r is equal to 0, the compound is,

L＝2πR＝2πr _m

7. the formula for calculating the circle area S under the singularity mechanics is as follows:

S＝πR ² ＝π(r+r _m ) ²

when r is equal to 0, the compound is,

S＝πR ² ＝πr _m ²

8. the formula for calculating the volume V of a sphere under singularity mechanics is as follows:

when r is equal to 0, the compound is,

when r is 0, for a particle with mass m, the mass density ρ of the particle is:

9. a calculation formula of acting under the singularity mechanics:

if it is not

Then

The potential function U of the gravity field under singularity mechanics of a mass point with mass m is:

coulomb's law is a law of stationary point charge interaction force, french scientist C, -a.de Coulomb in 1785 is derived from experiments, a common expression of Coulomb's law:

the product of the interaction force between two stationary point charges in vacuum and their charge amount (q) ₁ q ₂ ) Proportional to the square of their distance (mathematical distance) (r) ² ) In inverse proportion, the force is directed on the connecting line, like charges repel and opposite charges attract. Namely:

similar to the law of universal gravitation, the existing coulomb law also has a obvious defect that the charge q at two points is ₁ 、q ₂ In the case of a distance between the two tending to zero, the electric field force F ₁₂ Will tend to be infinite, however, this is clearly not in line with the fact that the charge q is at two points ₁ 、q ₂ With a distance of zero, two point charges q ₁ 、q ₂ The interaction force F between ₁₂ Nor may it be infinite. In fact, even two point charges q ₁ 、q ₂ The distance between the two tends to zero, and the electric field force F ₁₂ It is also only approximately constant and never infinite.

Therefore, from the experiment, the existing coulomb's law needs to be renormalized to avoid the situation that the field intensity of the electric field is infinite, for this purpose, a constant can be inserted into the denominator term of the coulomb's law, and the basic principle of the insertion is to make the coulomb's law have charges q at two points ₁ 、q ₂ In the case where the distance therebetween tends to zero, the two point charges q ₁ 、q ₂ The interaction force F between ₁₂ Not infinite. Needless to say, this correction should maximally accommodate the experimental fact that the existing coulomb's law conforms to the inverse square law, and cannot violate the experimental result.

The coulomb's law after correction by renormalization, that is, the coulomb's law under the singularity mechanics, can be expressed as follows:

arbitrary two point charges q ₁ 、q ₂ By a force F in a direction passing through the center line ₁₂ Are mutually attracted, the electric field force F ₁₂ The product q of the magnitude and their electrical quantities ₁ q ₂ Proportional to the distance r between them (distance in the non-superimposed state) plus the renormalization constant r _e Is inversely proportional to the square of the two point charges q ₁ 、q ₂ Cannot be zero. Namely:

in the formula r _e Is the renormalization constant of coulomb's law under singularity mechanics, the physical unit of the renormalization constant is the length unit'm ', we specify simultaneously that two point charges q ₁ 、q ₂ Cannot be zero.

The coulomb's law under the singularity mechanics pursues a mathematical expression which better accords with the experimental result, and obviously, the coulomb's law under the singularity mechanics can be used for analyzing and processing charges at two pointsq ₁ 、q ₂ The universal gravitation between the two is in an overlapped state, but due to the highly ideal characteristics of the mathematical tool and the fact that the data of the physical experiment inevitably have measurement errors, obviously, whether the mathematical formula is strictly established or not cannot be completely verified, and the pursuit goal is only approximately established and only can be used.

Renormalization constant r in coulomb's law under singularity mechanics _e The physical meaning of (a) is: two point charge q whose volume cannot be zero ₁ 、q ₂ At two points of charge q ₁ 、q ₂ A space constant due to the action of electrostatic field, represented by zero distance, at renormalization constant r _e Within a range of two point charges q ₁ 、q ₂ Even if there is relative motion between them, it should be considered as two point charges q ₁ 、q ₂ At zero distance, i.e. two point charges q ₁ 、q ₂ Is in a position superposed state without space interval.

It should be emphasized here that any two point charges q ₁ 、q ₂ There is a singular point distance R under the singular point mechanics, and the charges q of any two points under the singular point mechanics ₁ 、q ₂ The singular point distance R between is R + R _e And is no longer the non-superimposed state distance r in the prior knowledge. That is, even if the non-superimposed state distance r is 0, the electric charges q at any two points ₁ 、q ₂ There is also a r between _e Is constant distance of the position superposition state. Namely: for singularity mechanics, any two point charges q ₁ 、q ₂ The singular point distance between R-R + R _e 。

Corresponding thereto, an electric quantity q ₁ Point charge of (2) field strength E of electric field under singularity mechanics _e Comprises the following steps:

at the point where r is 0, the position of r,

this relationship indicates the point charge q ₁ Is the point charge q at the maximum value of the electric field intensity ₁ The location of the same.

One electric quantity is q ₁ Potential U of electric field under the singularity mechanics of point charges _e Comprises the following steps:

intuitively, the renormalization constant r in the coulomb law under the singularity mechanics _e The geometry of (2) is a sphere, which brings the following series of problems:

1. first, we can determine the renormalization constant r _e Outside the range, i.e. outside the field source sphere, two point charges q ₁ 、q ₂ The smaller the distance between the two points is, the larger the coulomb force is, the more the spherical surface is, namely, the two point charges q ₁ 、q ₂ Are laminated to each other at a renormalization constant r _e At this point, two point charges q appear ₁ 、q ₂ The maximum value of the coulomb force in between.

2. Secondly, due to the two point charges q ₁ 、q ₂ Bonding to the renormalization constant r _e The result of the maximum coulomb force is that two point charges q ₁ 、q ₂ On the field source sphere, i.e. at a distance r _e Has the smallest potential energy, i.e. has the most stable physical state there.

3. When the charge q is two points ₁ 、q ₂ Are continuously overlapped with each other so as to enter a renormalization constant r _e After the range of the 'inside of the spherical surface of the field source', the field source is separated from the minimum potential energy state, so that the field source can be realized only by having kinetic energy for overcoming the potential energy.

4. The mathematical formula of the coulomb law under the singularity mechanics of the invention can not give a point charge q ₁ At another point of charge q ₂ Renormalization constant r of _e The magnitude of the coulomb force (if we can also refer to it as coulomb force) experienced inside the field source, since the physical model into which our experimental data is substituted cannot handle this.

5. From the results of particle-collision experiments, a more reasonable assumption is that there is a possibility that coulomb force interaction does not exist, i.e., a point charge q ₁ At another point of charge q ₂ Renormalization constant r of _e Should be free and free from gravitational forces because of the renormalization constant r _e Should be zero.

We cannot exclude one point charge q ₁ Renormalization constant r of _e Has a renormalization constant r inside _e The field strength of the external electric field is opposite. But since we cannot get into one point charge q ₁ Renormalization constant r of _e The field source of (a) is internally subjected to physical experiments, so that this can only be handled as a guess.

6. Since we have identified two point charges q ₁ 、q ₂ The external distance between the two is r + r _e If two points of charge q ₁ 、q ₂ Is a mathematical point without volume size, two points charge q ₁ 、q ₂ The external mathematical distance between the two can not be less than the renormalization constant r _e Since this would allow the field strength of the electric field to be greater than the experimentally obtained physical field strength.

While at renormalization constant r _e Inside the field source, we can only consider two point charges q ₁ 、q ₂ The distance between is a true, physical negative spatial dimension, and the two point charges q in this state appear to all observers in our "positive" physical space ₁ 、q ₂ No physical separation between the two particles occurs regardless of the movement. Two point charge q ₁ 、q ₂ The 'intrinsic distance of the field source' and the 'intrinsic speed of the field source' between the two have more intuitive physical meanings in quantum mechanics.

Assuming point charge q ₁ Satisfies the following equation:

Ψ(r+r _e ,t)＝Ψ ₀ exp{ik(r+r _e )-iωt}

the imaginary coordinate in the above formula represents the point charge q ₁ I.e. the position function of the "particle" in the geometric space of the field source. When r is 0, it represents the point charge q ₁ At renormalization constant r _e A position function within the range.

7. The inventors prefer to consider the renormalization constant r _e Representing an important physical property of a real electric field. The position limit of a particle is the position of the maximum of the field strength of the particle, the field is the particle, the particle can be described by the field strength as well as the position, besides, no other physical quantity can be used to describe the position and the size of the particle.

Then, how should we understand the location of the "particles" of the electric field properties? The explanation of the singularity mechanics is: the "particles" of the nature of the electric field, i.e. the "field source" of the electric field and the "extended source" part outside the field source, can simultaneously have states of position at different mathematical points, this state being called the superimposed state. In other words, the renormalization constant r _e It is possible to let them have different (under mathematical points) states at the same time, such measurements let you randomly get one of them when you do not want to look for one of them with the measurement to define the position of the "particle" of the force field property, and when you measure it, the wave function of the system in the superimposed state collapses randomly into one of them.

For example, the mathematical point coordinates of the field source of the electric field of the electrons may be at the same time at its renormalization constant r _e At different places within. If you really measure the exact location of one of the mathematical points, you measure that is its renormalization constant r _m One of the specific locations within, as to which mathematical coordinate point is specific, is completely random.

You prepare 100 identical test objects and measure their status and you will get 100 results. But it is possible that some of the results occur more frequently, and some of themThe frequency of occurrence of the result is low, and the highest occurrence should be at the renormalization constant r _e Is located at the renormalization constant r _e The probability of the occurrence of the mathematical coordinate points outside the field source is lower, and the distribution of this frequency is a probability distribution, i.e., a wave function.

Then, the renormalization constant r in coulomb's law _e What is the physical meaning of? Any two-point charge q under singularity mechanics ₁ 、q ₂ What is again the physical meaning of the non-mathematical singularity distance R between?

We now give a number of specific application answers directly.

As mentioned above, we define the point charge q if it is a point under odd point mechanics ₁ 、q ₂ The motion state is changed under the action of an electric field, and the motion distance of the particle can adopt any two point charges q ₁ 、q ₂ The singular point distance between R-R + R _e From this we derive the singularity velocity concept under singularity mechanics, namely:

1. singular point average speed: during the time delta t, if the charge q is two points ₁ 、q ₂ The non-position superposition state displacement between the two is delta R, then the singular point displacement is R ═ delta R + R _e (or

) The ratio of the displacement of the singularity to the time at, i.e. the average speed V of the singularity of the charge at the time at, is then:

note that during the time Δ t, the charge q is charged at two points ₁ 、q ₂ When the non-position superposition state displacement between the two points is delta r is zero, the charges q of the two points are ₁ 、q ₂ The position between the two is in a superposition state, and the average speed V of the displacement of the superposition state is as follows:

in this case, the singular point average velocity V is an intrinsic motion in a superimposed state.

2. Singularity instantaneous speed: during dt times, if two points charge q ₁ 、q ₂ The non-position superposition state displacement between the two is dr, then the singular point displacement is R ═ Deltar + R _e (or

) Then, for circular motion, the ratio of the singularity displacement to the time dt, i.e. the singularity instantaneous velocity V of the charge of the point in the time dt, is:

note that when the charge q is two points ₁ 、q ₂ When the non-position superposition state displacement between the two points is delta r is zero, the charges q of the two points are ₁ 、q ₂ The position between the two is in a superposition state, and the instantaneous speed V of the displacement of the superposition state is as follows:

in this case, the singularity instantaneous velocity V and the spin angular velocity ω are intrinsic motions of a singularity.

3. Singularity instantaneous acceleration a:

4. for circular motion, centripetal acceleration at odd points a:

when r is equal to 0, the compound is,

5. newton's second law of motion under singularity mechanics:

L＝2πR＝2π(r+r _e )

when r is equal to 0, the compound is,

L＝2πR＝2πr _e

S＝πR ² ＝π(r+r _e ) ²

when r is equal to 0, the compound is,

S＝πR ² ＝πr _e ²

8. the formula for calculating the circle volume D under the singularity mechanics is as follows:

when r is equal to 0, the compound is,

9. a calculation formula of acting under the singularity mechanics:

if it is used

Then

10. Vacuum capacitance of parallel plate capacitor C:

wherein d is the distance between the inner surfaces of the two polar plates.

Under singularity mechanics, the Euler-Lagrangian equation for an object moving in a cardiac force field can be expressed as:

r in the above formula ₀ Is the renormalization constant of the centripetal force field.

Using Euler-Lagrangian equation, we can get

I.e. angular momentum

Is a conservative quantity.

We give the equations of motion for Euler-Lagrangian under singularity mechanics directly as follows:

the Gaussian theorem is used to derive the coulomb's law under the singularity mechanics.

The gaussian law (Gauss 'law) is also called gaussian flux theory (Gauss' flux theorem), or is called the divergence law, the gaussian-oerstroe-raydeschool formula, the austenite law, or the high-oerstroe formula.

In electrostatics, a relationship is shown between the sum of the charges in a closed curve and the integral of the electric flux of the generated electric field over the closed curve. Gauss' law indicates the relationship between the charge distribution within a closed curve and the generated electric field. Gauss's law in the case of electrostatic fields is analogous to the ampere's law applied to magnetic field, and both are concentrated in Maxwell's equations. Because of the mathematical similarity, gauss's law can also be applied to other physical quantities determined by the inverse square law, such as gravity or irradiance.

The gaussian theorem under singularity mechanics states that: the electric flux through a closed surface is proportional to the amount of charge enclosed by the closed surface under singularity mechanics, in other words: the area of the electric field intensity on a closed curved surface is proportional to the charge quantity enclosed by the closed curved surface under the singularity mechanics, namely:

we define the formula for the electric field of a point charge derived from gaussian theorem under the force of singularity, in the case where the volume of the point charge q1, q2 … qi … cannot be zero:

the potential U of the point charge under the singularity mechanics is as follows:

the physical meaning of the electric field strength E in the above formula is: when we test the electric field intensity with the test charge, the point charge to be tested is still stored even if the distance r between the test charge and the particle is 0In practice, the point charge volume is very small but cannot be zero, and the radius of the point charge is r _e The surface area of the point charge is 4 pi r _e ² Is covered by 4 pi r _e ² The electric quantity of the point charge enclosed therein is q, and the surface area is 4 π r _e ² The electric flux on the sphere is still a finite constant and cannot be infinite. Therefore, we use r + r _e As the upper limit boundary of the integration calculation, zero is used as the lower limit boundary of the integration calculation. That is, the distance between the point charge and the test charge is r + r under the singularity mechanics _e It is no longer r in the prior knowledge, even if r is 0, there is still an r between the point charge and the test charge _e Is constant distance.

The above analytical calculations with respect to the gaussian theorem apply equally to gravitational fields of the law of universal gravitation.

In magnetostatics, the Biot-Savart Law (English: Biot-Savart Law) describes the magnetic field excited by an electric current element at an arbitrary point P in space. Biot-savart law is expressed as follows:

the magnitude of the magnetic induction intensity dB generated by the current element Idl at a certain point P in space is in direct proportion to the magnitude of the current element Idl, in direct proportion to the sine of an included angle between a position vector of the current element Idl to the point P and the current element Idl, and in inverse proportion to the square of the distance r from the current element Idl to the point P.

μ ₀ Is a vacuum magnetic conductivity;

the prior biot-savart law has a clear defect that the magnetic induction dB tends to infinity under the condition that the distance between the current element Idl and the point P tends to be zero, but the conclusion is obviously inconsistent with the fact that the point P cannot generate infinite magnetic induction dB even at the origin of the current element Idl. In fact, even if the distance between the current elements Idl and the point P tends to zero, the magnetic induction dB tends to be a constant only, and never infinite, in other words, even at the origin where the individual electrons constituting the electron current are located, the magnetic induction dB at that location tends to be a constant only, and never infinite. Therefore, from the experiment, the existing biot-savart law needs to be renormalized to avoid the magnetic induction dB from appearing infinite, and the modified biot-savart law can be expressed as follows:

the magnitude of magnetic induction dB generated by the current element Idl at a certain point P in space is in direct proportion to the magnitude of the current element Idl, the sine of an included angle between a position vector of the current element Idl from the point P and the current element Idl, and the sum of the distance r from the current element Idl to the point P and a distance correction constant r _b Is inversely proportional to the square of (d):

in the formula r _b Is the distance correction constant of the biot-savart law.

It should be noted that, after obtaining sufficient accurate and sufficient experimental data, it is possible to find the distance correction constant r by calculating by interpolating the experimental data _b The two modified Biao-Saval laws are not constant but variable, which shows that the formulas of the two modified Biao-Saval laws are not matched, and at this time, the expression of the Biao-Saval law is adjusted continuously according to the specific condition until the distance correction constant r is calculated according to experimental data _b The expression of the magnetic field strength at this time is the magnetic field strength calculation formula which is most consistent with the actual state and is more accurate as far as a constant is approached.

It is to be noted that the distance correction constant r of the biot-savart law _b The specific numerical value of (a) is not known at present. Therefore, it is necessary to obtain the distance correction constant r in the biot-savart law through experimental measurement _b The specific numerical value of (1).

We directly give the maxwell equations under singularity mechanics as follows:

(Ampere Loop Law under singularity mechanics)

(Faraday's law of electromagnetic induction under singularity mechanics)

(Gauss's law of electric field under singularity mechanics)

(Gauss's law of magnetic field under singularity mechanics)

In the formula r _e Is the renormalization constant of the electric field, r _b The specific values for the renormalization constants of the magnetic field are experimentally derived. Note that r as a field source _e And r _b Independently of the charge, i.e. photons moving at the speed of light may also have their own r _m 、r _e And r _b 。

From the definition of the current, J ═ ρ v, we can see that:

the wave zone refers to the spatial extent of the distance from the radiation source that greatly exceeds the linearity of the radiation system and its radiation wavelength. In a certain local small area of the wave zone, the electromagnetic wave can be regarded as a plane wave, and in the wave zone, the electromagnetic radiation of the radiation system can be determined by the retardation vector a.

If the origin of coordinates is chosen within the limited range of the radiation system, i.e. very small compared to the radiation wavelength, then the retardation vector a of the field in singularity mechanics in the wave zone is:

wherein R + R _e The sagittal diameter to the observed point of the field; r + R _e ＝|R+r _e |；

r′+r _e The radial of the radiation system volume element dV' to the field;

to facilitate understanding of the renormalization constants in coulomb's law, we review the relevant knowledge in the acoustic rationale. It is well known that in the basic theory of acoustics, if the potential function

And other physical quantities characterizing the wave characteristics of a medium in which the medium is fluctuating are related only to the distance r from a point in time and space, called the wave center, such a longitudinal wave being called a longitudinal spherical wave. In isotropic homogeneous media, the waves excited by a point source are spherical waves. By point source is meant a point-like vibrating body whose linearity can be regarded as very small.

In singularity mechanics, we use the singularity distance R ═ R + R ₀ Instead of r, the wave equation of the longitudinal spherical wave is:

when the distance r is 0, the wave equation of the longitudinal spherical wave in the singularity mechanics becomes:

in singularity mechanics, the general solution form of the wave equation for longitudinal spherical waves of formula (a) is:

where c is the wave velocity of the longitudinal spherical wave, f1 and f2 are arbitrary functions,

is a potential function of the diverging spherical wave,

is a potential function of a spherical wave converging toward the center, r ₀ Is a renormalization constant of the longitudinal spherical wave.

When the distance r is 0, i.e. at a point source, the general solution form of the wave equation of an longitudinal spherical wave in singularity mechanics is:

the wave surface of the spherical wave is a group of concentric spherical surfaces, and the equation of the divergent spherical sine wave under the singularity mechanics is as follows:

where k is the wave vector, α is the initial phase of the wave source vibration, r is the distance from the wave source, A ₀ For the amplitude of each particle vibration at a distance r equal to 1, r ₀ Is the renormalization constant of a diverging spherical sine wave, renormalization constant r ₀ It needs to be measured experimentally.

At a point source, the equation for a diverging spherical sine wave under singularity mechanics is:

the exponential form of the spherical wave equation under singularity mechanics is:

wherein A is the complex amplitude of the wave,

wherein the potential function

The wave equation is satisfied at all positions including r-0:

at a point source, the exponential form of the spherical wave equation under singularity mechanics is:

through the above description of the related knowledge in the acoustic basic theory, it is helpful for us to understand the physical meaning of the renormalization constant of the longitudinal spherical wave, i.e. the renormalization constant r of the longitudinal spherical wave ₀ Corresponding is a potential function at the point source

The state of (1). Obviously, the potential function at any real point source

It cannot be infinite, which indirectly demonstrates that in coulomb's law, the two point charges q ₁ 、q ₂ With a distance of zero, two point charges q ₁ 、q ₂ Electric field force F between ₁₂ It is unlikely to be infinite and a renormalization process is required to avoid infinite unreasonable values.

An expression of the Schrodinger equation in the electrostatic field under singularity mechanics is directly given as follows:

in the formula r _e Is the renormalization constant of the electrostatic field.

In the singularity mechanics, the "particle" of the electric field property is the "field source" of the electric field, and also includes the "extended electric field source" part outside the field source, so in the singularity mechanics, the "particle" can have the state of the position under different mathematical points at the same time, and this state is called the superimposed state. In other words, the renormalization constant r _e It is possible to let them have different (under mathematical points) states at the same time, such a measurement will let you randomly get one of them when you look for one of them with the measurement to define the position of the "particle" of the force field property, and the wave function of the system in the superimposed state collapses randomly into one of them when you measure it.

For example, the mathematical point coordinates of the field source of the electric field of the electrons may be at the same time at its renormalization constant r _e At different places within. If you really measure the exact location of one of the mathematical points, you measure that is its renormalization constant r _m One of the specific locations within, as to which mathematical coordinate point is specific, is completely random. The measurement will have some results that occur more frequently and some that occur less frequently, the highest occurring should be at the renormalization constant r _e Is located at the renormalization constant r _e The probability of the occurrence of the mathematical coordinate points outside the field source is lower, and the distribution of this frequency is a probability distribution, i.e., a wave function.

Note that the renormalization constant r is obtained based on experiments _e Unlike conventional distances, if Schrodinger's equation is described by coordinate points of a coordinate system, due to the renormalization constant r _e Not a mathematical point but a length of space that is not detachable for mathematical processing, and therefore has a renormalization constant r _e Is changed by using a coordinate systemIn other mathematical processes, difficulties may be encountered. A possible solution is to first renormalize the constant r before performing the mathematical derivation _e Withdrawing from the formula, and normalizing constant r after mathematical derivation _e Reinserted into the formula.

The wave function of a beam of free electrons under the singularity mechanics is directly given as follows:

this fluctuation has a real, physical imaginary component, i.e. the part a located inside the field source is the real, physical imaginary component.

The wave function of electrons in hydrogen atoms in the ground state under the singularity mechanics is given directly below:

an expression of a hydrogen atom Schrodinger equation in a spherical polar coordinate system under singular point mechanics is directly given as follows:

r in the above formula _e Is the renormalization constant under coulomb's law.

The expression of the hydrogen atom Schrodinger equation in the spherical polar coordinate system under the singularity mechanics also helps us to deeply understand the physical meaning of the renormalization constant. By solving the hydrogen atom Schrodinger equation in the spherical polar coordinate system under the singularity mechanics, the renormalization constant r under the Coulomb's law can be solved _e The specific numerical values of (a) are theoretically calculated.

It should be noted that, in the schrodinger equation expression under singular point mechanics, there is a special solution in singular point mechanics, that is, when r is equal to 0.

If the experiment proves that

Then all of the above R ═ R + R _e All are replaced by

An expression of Schrodinger equation in a magnetic field under singular point mechanics is directly given below:

in the formula r _b Is the renormalization constant of the magnetic field.

Note that the renormalization constant r is obtained based on experiments _b Unlike conventional distances, if Schrodinger's equation is described by coordinate points of a coordinate system, due to the renormalization constant r _b Not a mathematical point but a length which cannot be disassembled for mathematical treatment, and therefore has a renormalization constant r _b The formula (2) may encounter some difficulties in the mathematical process of transformation using a coordinate system. A possible solution is to first renormalize the constant r before performing the mathematical derivation _b Withdrawing from the formula, and repeating the normalization constant r after the mathematical derivation is completed _b Reinserted into the formula.

In the following, we directly give an expression of schrodinger equation in a gravitational field under singular point mechanics:

in the formula r _m Is the renormalization constant of the gravitational field.

Again, the experimentally derived renormalization constant r is emphasized _m Unlike conventional distances, if the positional relationship is described by coordinate points of a coordinate system, the renormalization constant r is used _m Not a mathematical point but a length of space that is not detachable for mathematical processing, and therefore has a renormalization constant r _m The formula (2) may encounter some difficulties in mathematical processing of transformation using a coordinate system. A possible solution is to first renormalize the constant r before performing the mathematical derivation _m Withdrawing from the formula, and normalizing constant r after the mathematical derivation is completed _m Reinserted into the formula.

We now give the expression of the de broglie relation in the electric field under singularity mechanics directly:

we directly give the expression of the de broglie relation in magnetic field under singularity mechanics as follows:

we directly give the expression of the de broglie relation in the gravitational field under singularity mechanics as follows:

it should be noted that the momentum of a particle with mass m under singularity mechanics is related to the field properties of the effect to which the particle is subjected, whereas the intrinsic meaning of λ reflecting the particle's volatility under singularity mechanics is what is reasonably inferred to be that the wavelength λ of a particle should be related to the "negative length" dimension present in the field source, which needs to be expressed in imaginary coordinates.

We directly give the expression of the uncertainty relation for heisenberg in the electric field under singularity mechanics as follows:

we directly give the expression of the uncertainty relation for heisenberg in magnetic field under singularity mechanics as follows:

we directly give the expression of the uncertainty relation for heisenberg in the force field under singularity mechanics as follows:

the real particles exist on the premise that the volume of the particles cannot be zero, so that the inaccuracy relation of the Heisenberg under the singularity mechanics is actually corrected based on experimental data to solve the problem that the volume of the real particles cannot be zero. That is, the traditional mathematical point has no volume and does not occupy the actual space, and the real particle has a volume and occupies the actual space, so that if the position of the real particle is not measured and located by the "precise" mathematical point, the measured data is definitely not unique, that is, the position of the particle can be located by using a plurality of mathematical point coordinates, and the coordinate points are all correct to locate the position of the real particle with volume, which constitutes the so-called "mismeasurement", because we can not really describe the position of the real particle with only one mathematical point coordinate, and the unique position determined by us cannot be unique.

Schrodinger equation for arbitrary particles under singularity mechanics

Quantum theory is now considered by most to be involved in the statistical interpretation of this equation. That is, Schrodinger equation describes the state of a particle as a function of time, if the microscopic particle is in the state at time t ═ 0

If the state at any time t is known, the state can be determined in principle from this equation

Order to

Obtaining stationary Schrodinger equation under singularity mechanics

In the formula r ₀ Is the renormalization constant of the field effect.

We now give the expression of schwarcil Metric (Schwarschild Metric) under singularity mechanics directly:

the solution of the Schwarzkyo metric under the singularity mechanics is as follows:

r in the above formula _m Is the renormalization constant under the law of universal gravitation, G is the universal gravitation constant, and M is the mass of the celestial body.

Thus, the visual radius r of the Schwarzschiff's black hole under singularity mechanics _s Comprises the following steps:

visual radius r of Schwarzschiff's black hole under the above-mentioned singularity mechanics _s The mathematical expression of (A) undoubtedly helps us to understand the matter of renormalization constant more deeplyThe theory means.

Visual radius r of black hole from Schwarzschiff's solution under singularity mechanics _s The mathematical expression of (A) shows that the mass of one particle is only 2GM-c ² r _m The black hole can be formed only when the mass is more than or equal to 0, namely the mass of the black hole meets the following relation:

if this condition is not met, r _s The value of (d) will be negative.

The following is a mathematical expression for the generalized relativistic clockwork effect under singularity mechanics:

when r is 0, the mathematical expression of the generalized relativistic slowness effect under singularity mechanics is:

the mathematical expression for the scaling effect of generalized relativity under singularity mechanics is:

that is to say

When r is 0, the mathematical expression for the generalized relativistic scaling effect under singularity mechanics is:

if the experiment proves that

Then all of the above R ═ R + R _m All change to

The mathematical expression for the scale-down effect of the narrow relativity theory under the singularity mechanics in the gravitational field is given directly below:

wherein L ₀ Is the ruler length in the stationary frame of reference, and the renormalization constant Xm is a constant that is invariant.

The mathematical expression for the clockslow effect of the narrow relativity theory under the singularity mechanics in the gravitational field is given directly below:

wherein Δ t ₀ Is a time interval in a stationary frame of reference, r _m And/c is a zero time constant under the singularity mechanics, G is a universal gravitation constant, and c is the speed of light.

The mathematical expression for the scaling effect of the narrow relativity theory under the singularity mechanics in the electrostatic field is given directly below:

wherein L ₀ Is the ruler length in the stationary frame of reference.

In singularity mechanics, when the distance r between two particles is 0, there is also a renormalization constant r due to the particles themselves ₀ In the presence of particles having a superimposable size constant, we can "imagine" the magnifying glass in which the particles are locatedThe position of (a) is enlarged to "infinity", thus a new space is provided for us to analyze the enlarged particles. In the new space generated by the 'imagination' amplification, a new three-dimensional space coordinate system can be established, the coordinate axes of the three-dimensional space coordinate system can be represented by imaginary numbers, the corresponding wave function psi is also a wave function of imaginary nature in the new three-dimensional space coordinate system, the imaginary three-dimensional space coordinate system is completely different from the real three-dimensional space coordinate system familiar to human beings, in the imaginary three-dimensional space coordinate system, the form of a substance can be changed, namely, a basic particle with static mass observed in the real three-dimensional space coordinate system space can be changed into a field substance without static mass and moving at the speed of light when observed in the imaginary three-dimensional space coordinate system, and the change of the form of the substance is the observation effect brought by the point where the basic particle is amplified to infinity.

Then we observe where the elementary particles with static mass are seen in the real three-dimensional space coordinate system space, of course, the wave function Ψ in the schrodinger equation expression under singularity mechanics is such a function, both in the real three-dimensional space coordinate system and in the imaginary three-dimensional space coordinate system.

The wave function Ψ is a function that exists in a real three-dimensional space coordinate system and also exists in an imaginary three-dimensional space coordinate system.

The wave function Ψ of the elementary particle in the real three-dimensional space coordinate system expresses the particle property in the real three-dimensional space coordinate system, and the wave function Ψ of the elementary particle in the real three-dimensional space coordinate system expresses the wave property in the imaginary three-dimensional space coordinate system.

If we do the spatial variation process of enlarging the basic particles in the imaginary three-dimensional space coordinate system to infinity, a new space will also appear to let us analyze the enlarged particles in the imaginary three-dimensional space coordinate system. In the new space generated by 'imagination' amplification, a new three-dimensional space coordinate system can be established, the coordinate axes of the three-dimensional space coordinate system can be represented by a super-imaginary number, the corresponding wave function psi is also a wave function with super-imaginary nature in the new three-dimensional space coordinate system, the super-imaginary three-dimensional space coordinate system is completely different from the real three-dimensional space coordinate system familiar to human beings in space, and the form of a substance in the super-imaginary three-dimensional space coordinate system can be continuously changed.

As described above, the fundamental particle with a static mass observed in the real three-dimensional space coordinate system space becomes a field substance without a static mass and moving at the speed of light when observed in the imaginary three-dimensional space coordinate system, and the change of the substance form is the observation effect brought by the point where the fundamental particle is amplified to infinity.

The basic particles with static mass observed in the virtual three-dimensional space coordinate system space become virtual particles when observed in the real three-dimensional space coordinate system, namely, the basic particles cannot be observed at all. This change in material morphology is an observed effect brought about by the nature of the imaginary three-dimensional space coordinate system. However, when observing the basic particle with static mass in the space of the imaginary three-dimensional space coordinate system in the super-imaginary three-dimensional space coordinate system, the basic particle becomes a field substance without static mass and moving at the speed of light, and the change of the substance form is also the observation effect brought by amplifying the point of the basic particle to infinity.

We can also use the "imagination" minifier to reduce the universe space where we are located to "infinitesimal" so that a new space can appear, suppose we enter the new three-dimensional space and generate a new three-dimensional space coordinate system in the new space which is "imagination", the coordinate axes of the three-dimensional space coordinate system can be represented by the super real number, the corresponding wave function Ψ is also a wave function with super real number property in the new three-dimensional space coordinate system, the super real three-dimensional space coordinate system is completely different from the real three-dimensional space coordinate system which is familiar to our human beings, in the super real three-dimensional space coordinate system, the form of the substance can be changed, that is, the basic particles with static mass observed in the real three-dimensional space coordinate system space, when observed in the real super three-dimensional space coordinate system, it will resemble a virtual particle, i.e. it is not observed at all. This change in material morphology is an observed effect brought about by the properties of the hyper-real three-dimensional space coordinate system. When field substances moving at the speed of light in the real three-dimensional space coordinate system space are observed in the real three-dimensional space coordinate system, the field substances are found to be basic particles with static mass, and the change of the substance form is also an observation effect brought by the fact that the space of the real three-dimensional space coordinate system is reduced to infinity.

It should be noted that the real three-dimensional space coordinate system can also be reduced to "infinity" by "imagining" the reduction mirror, and then the generated real three-dimensional space coordinate system is the real three-dimensional space coordinate system, and thus, in the loop direction, there can be an infinite number of new real three-dimensional space coordinate systems. The super-imaginary three-dimensional space coordinate system can also amplify one point in the super-imaginary three-dimensional space coordinate system to be infinite through the imagination magnifier, and then the super-imaginary three-dimensional space coordinate system is generated, and the circulation is downward, so that an infinite number of new imaginary three-dimensional space coordinate systems can be provided. A real 'particle' in a certain space coordinate system can exist in all three-dimensional space coordinate systems, but the existing form is changed, and in the three-dimensional space coordinate systems with different properties, the particle has material forms with different properties.

Then, we observe where the basic particles with static mass are seen in the real three-dimensional space coordinate system space, and certainly, in the ultra-real three-dimensional space coordinate system and also in the imaginary three-dimensional space coordinate system, the wave function Ψ in the schrodinger equation expression under singularity mechanics is also such a function.

The wave function Ψ is a function that exists in the hypercritical three-dimensional space coordinate system and also exists in the imaginary three-dimensional space coordinate system.

If the wave function Ψ of the basic particle in the three-dimensional space coordinate system is represented as being particle in the three-dimensional space coordinate system, the wave function Ψ of the basic particle in the three-dimensional space coordinate system is represented as being wave in the three-dimensional space coordinate system.

As is well known, in order to describe the motion of one object, another object is usually selected as a reference object, and in order to describe the law of relative motion between the objects conveniently, we should select an object which interacts with or moves relative to the described object as much as possible as a reference system. We specify as the relative frame of reference the object chosen as the reference for which there is an interaction or relative motion with the object being described, the state of motion of the object chosen as the reference can be arbitrary.

When describing the relative motion between objects with a relative frame of reference, the following law can be obtained:

in the formula m ₁ And m ₂ Masses of two objects respectively interacting, F ₁₂ Is the interaction force between two interacting objects, a ₁₂ Acceleration, F, possessed by relative movement between two bodies interacting with each other ₁ Is a mass of m ₁ Is subjected to an external force of an object, F ₂ Is a mass of m ₂ Subject to external forces. The law of motion expressed by the above mathematical expression we refer to as the law of relative motion.

Next, we analyze the law of motion of a black hole interacting with another object using the law of relative motion.

Let the mass of the black hole 1 be m ₁ Mass of the object 2 is m ₂ Assuming that only mutual gravitational force exists between the two, neglecting other external force, and based on the law of universal gravitational force under the singularity mechanics:

and the law of relative motion, one can derive:

the acceleration of the relative motion between the two is obtained by arranging:

let the object 2 be at a singular point distance R from the origin of the black hole, i.e. R + R from the black hole _m Gravitational potential energy of the object 2

The relative energy of the relative movement velocity V of the object 2 to be separated from the black hole 1

Is greater than gravitational potential energy

Taking the exact equivalence of the two as a critical value, we can get:

substituting the related known data into the above formula, and solving the equation to obtain the singular point distance r + r of the object 2 from the origin of the black hole _m The departure speed V and the singular point distance r + r from the origin of the black hole _m The relationship between the two is under a critical value, and the relationship can help us to qualitatively understand the renormalization constant r in the law of universal gravitation _m The physical meaning of (1).

The experiment shows that the electron has spin motion, and the spin motion of the electron can be calculated and analyzed by using a circumference calculation formula under the singularity mechanics, namely the spin motion of the electron is the rotation motion of the electron under the condition that r is 0, and according to an area calculation formula under the singularity mechanics, the spin area S of the electron is as follows:

under singularity mechanics, the perimeter L of the electron spin is:

then setting the electron as a stable circular standing wave, namely the electron performs the surrounding motion of spin in an imaginary three-dimensional space coordinate system, the perimeter of the spin is the wavelength lambda, and then, the radius r of the spin of the electron is obtained _b Comprises the following steps:

and the current intensity of the electron spin I ═ ve, so we can calculate the magnetic moment μ of the electron spin _s :

Radius r of electron spin in the above calculation _b Comprises the following steps:

it is possible that the values associated with the renormalization constants in the biot-savart law can be used as a reference in the analysis of the experimental data of the present invention.

First illuminance law: when illuminated with a point source, the illumination E on the surface of an object perpendicular to the light is proportional to the intensity I of the light emitted by the source and inversely proportional to the square of the distance R from the illuminated surface to the source. Namely:

similar to the law of universal gravitation, the first law of illuminance as known has the obvious drawback that the illuminance E tends to infinity in the case where the distance R from the illuminated surface to the light source tends to zero, but this is clearly not true, i.e. the illuminance E cannot be infinity when the distance R from the illuminated surface to the light source is zero. In fact, even if the distance R from the illuminated surface to the light source is zero, the illuminance E tends to be constant and never infinite. Therefore, it is necessary to perform renormalization processing on the existing first law of illuminance from the beginning of experiments to avoid the situation that the illuminance E is infinite, for this reason, a constant can be inserted into the denominator term of the first law of illuminance, the basic principle of the insertion is to make the illuminance E not infinite under the condition that the distance R from the illuminated surface to the light source tends to be zero according to the first law of illuminance, and the corrected first law of illuminance, namely the first law of illuminance under the singularity mechanics, can be expressed as follows:

when illuminated with a point light source, the illumination E on the surface of the object perpendicular to the light is proportional to the intensity I of the light emitted by the light source, plus a distance correction constant X to the distance R from the illuminated surface to the light source _i Is inversely proportional to the square of. Namely:

in the formula r _i Is a distance correction constant of a first law of illumination under the singularity mechanics.

Lannay-Jones potential (Lennard-Jones potential), also known as the L-J potential, 6-12 potential, or 12-6 potential, is a relatively simple mathematical model used to model the interaction potential between two electrically neutral molecules or atoms. Was first proposed by the mathematician john lan-jones in 1924. It is widely used because of its simple analytical form, and is especially accurate for describing the intermolecular interaction of inert gases.

The Lanna-Jones potential energy takes a two-body distance as a unique variable and comprises two parameters, and the Lanna-Jones potential energy form under the singularity mechanics is directly given as follows:

in the formula r ₀ Is the renormalization constant of the Lanna-Jones potential, ε is the depth of the potential energy well, and σ is the two-body distance at which the interaction potential is exactly zero. In practical applications, the epsilon and sigma parameters are often determined by fitting known experimental data or accurate quantum computation results.

Physically speaking, the first term

It can be considered that the second term corresponds to the action of two bodies mainly repelling each other at a close distance

Corresponding to the action of the two bodies which are predominantly attracted to each other (e.g. by van der waals forces) at a distance.

The two body forces corresponding to the Lanna-Jones potential are:

B. preparing a device for measuring the constant of universal gravitation;

E. according to the formula of the corrected law of universal gravitation

F ₁₂ ＝G m ₁ m ₂ /(r+r _m ) ² (21)

F1＝G m ₁ m ₂ /(R1+r _m ) ² (22)

F2＝G m ₁ m ₂ /(R2+r _m ) ² (23)

the two equations of formula (22) and formula (23) are simplified to obtain:

F1/F2＝(R2+r _m ) ² /(R1+r _m ) ² (24)

As a further improvement of the present invention, the field strength Ee of the gravitational field of the electron at the field source is calculated by using the modified law of universal gravitation, i.e. the law of universal gravitation under singularity mechanics, as follows:

Ee＝C me/r _m (11)

wherein C is the corrected universal gravitation constant C, r _m Is the renormalization constant in the law of universal gravitation, me is the mass of the electron.

As a further improvement of the present invention, the field intensity E of the gravitational field of the black hole at the field source is calculated by using the modified law of universal gravitation, i.e. the law of universal gravitation under singularity mechanics:

E＝C M/r _m (12)

As a further improvement of the invention, the universal gravitation F when the distance between the pi meson and other hadrons is zero is calculated by utilizing the corrected universal gravitation law, namely the universal gravitation law under the singularity mechanics _π The size of (A) is as follows:

F _π ＝C M _π M/r _m (13)

As a further improvement of the present invention, the above-mentioned device for measuring the gravitational constant is a cavendian torsion balance, and the two objects with mass m1 and m2 are solid spherical bodies made of metal respectively.

Claims

1. The method for renormalizing the law of universal gravitation based on experimental data is characterized by comprising the following steps: the method comprises the following steps:

B. preparing a device for measuring the constant of universal gravitation;

E. according to the formula of the corrected law of universal gravitation

F ₁₂ ＝G m ₁ m ₂ /(r+r _m ) ² (21)

F1＝G m ₁ m ₂ /(R1+r _m ) ² (22)

F2＝G m ₁ m ₂ /(R2+r _m ) ² (23)

the two equations of formula (22) and formula (23) are simplified to obtain:

F1/F2＝(R2+r _m ) ² /(R1+r _m ) ² (24)

2. The method for renormalizing the law of universal gravitation based on experimental data as claimed in claim 1, characterized in that: and calculating the field intensity Ee of the gravitational field of the electron at the field source by using the corrected universal gravitation law as follows:

Ee＝C me/r _m (11)

3. The method for renormalizing the law of universal gravitation based on experimental data as claimed in claim 1, characterized in that: and calculating the field intensity E of the gravitational field of the black hole at the field source by using the corrected universal gravitation law as follows:

E＝C M/r _m (12)

4. The method for renormalizing the law of universal gravitation based on experimental data as claimed in claim 1, characterized in that: calculating the universal gravitation F when the distance between the pi meson and other hadrons is zero by using the corrected universal gravitation law _π The size of (A) is as follows:

F _π ＝C M _π M/r _m (13)

5. Method for renormalizing the law of universal gravitation on the basis of experimental data according to any one of claims 1 to 4, characterized in that: the device for measuring the universal gravitation constant is a Kavindesi torsion balance, and the two objects with the mass m1 and the mass m2 are solid spherical bodies made of metal respectively.