The modification and extension of the strong equivalence principle

Abstract

In this paper, the strong equivalence principle is analyzed by the gravitational mechanism of etheric pressure, and the conclusion is drawn that an object at rest in a uniform gravitational field of a certain strength is equivalent to moving in a straight line in a uniform etheric space with a certain speed (not a certain acceleration). According to the etheric pressure gravitational mechanism, gravitational field is a scalar field (energy field or etheric field), and gravity is caused by the asymmetric density distribution of space energy (etheric), resulting in the asymmetric etheric pressure on the object at rest in space. According to this gravitational mechanism, if the gravitational field strength (energy density) of space is the same at every point, then objects in that space will not generate gravity. Therefore, a uniform gravitational field is not equivalent to a uniformly accelerated non-inertial system. The inequivalence between the uniform gravitational field and the uniformly accelerated non-inertial system is also reflected in: the object at rest in the gravitational field does not change in time, length, and mass, but the object at rest in the non-inertial system of accelerating motion (relative to the ether) has been slowing down in time, shortening in length, and increasing in mass; a charged particle at rest in a gravitational field does not radiate electromagnetic waves outward, but a charged particle at rest in a non-inertial system in accelerated motion (relative to the ether) will radiate electromagnetic waves outward continuously. The paper points out that the experimental fact of equivalence between gravity fields and velocity (rather than acceleration) in terms of time dilation has proven the equivalence between uniform gravity fields and inertial systems with uniform motion (rather than non-inertial systems with uniform acceleration). It further deduces that gravity fields are equivalent to velocity in terms of the increase in the inertial mass effect of objects, and gravity fields are equivalent to velocity in terms of the contraction effect of the electron orbit radius of atoms. The gravitational force experienced by a stationary object in a gravitational field with a gradient of field strength is equivalent to the inertial force experienced by the same object when it undergoes linear acceleration in the Ether space. The Ether (energy) field with a gradient of field strength generated by a fluid whose flow velocity decreases perpendicular to its motion is equivalent to the gravitational (energy) field with a gradient of field strength. Using these modified and extended equivalence principles, the author explains Newton’s bucket experiment, explains the physical mechanism of inertial force and inertial centrifugal force, explains the Casimir effect, and explains what reference system the flow rate of fluid in Bernoulli equation is relative to, and why the higher the flow rate is relative to the reference system, the lower the pressure.

Main article text

INTRODUCTION

The equivalence principle [1,2] is divided into weak equivalence principle and strong equivalence principle. The weak equivalence principle means that the observer cannot distinguish between the inertial force caused by acceleration and the gravitational force caused by the gravitational field acting on an object in a local area. The weak equivalence principle is derived from the fact that the gravitational mass is directly proportional to the inertial mass, a relationship first established by Galileo and Newton in a series of experiments. The strong equivalence principle states that a gravitational field at a point in a region of spacetime can be described by a locally accelerated reference frame with an equal acceleration (relative to a stationary observer), or that a uniform gravitational field is equivalent to a non-inertial reference frame with an equal acceleration. The strong equivalence principle cannot be deduced from the weak equivalence principle.

Since the principle of strong equivalence and the principle of general relativity are the two basic principles on which general relativity is based [1,2], relativity and quantum mechanics are regarded as the two pillars of modern physics. It can be seen that the modification and extension of the strong equivalence principle will have a great impact on physics.

General relativity, proposed by Albert Einstein in 1915, deals primarily with gravity and describes the large-scale structure of the universe. General relativity explains gravity as a geometric property of spacetime. Although general relativity has achieved great prestige, the following serious problems remain:

1. It is incompatible with quantum mechanics [3,4].

2. The gravitational problem of stars moving too fast around galaxies must be explained by the existence of “dark matter,” which has not yet been detected.

3. It cannot explain the formation and disappearance of supermassive black holes [5–7].

4. Black holes in general relativity [8] have singularities (points where the mass density tends to be infinitely large and the volume tends to be infinitely small)

5. General relativity does not reveal the physical mechanism of planetary perihelion precession [9,10]. The general relativity only obtains the calculation result which is consistent with the observed data of the perihelion precession of Mercury through the approximate solution of the equation, but does not give the physical mechanism of the perihelion precession. Otherwise, it should be possible to calculate the precession of all the planets, it should not require dark matter to explain stars moving too fast around galaxies and galaxies moving too fast around clusters of galaxies [5], and it should be possible to get a theory of black holes without singularities [5].

6. General relativity’s conclusion that gravitational redshift (the weaker the gravitational field, the longer the wavelength of light) is wrong. Based on the fact that time is faster with a weaker gravitational field and that time is proportional to radiosity [11], it is concluded that gravitational blue shift (the wavelength of light is shorter with a weaker gravitational field). However, experiments to verify the gravitational redshift of spectral lines cannot distinguish between gravitational redshift and gravitational blue shift [12].

7. General relativity does not explain why the inertial force is equivalent to gravity.

8. General relativity plus special relativity does not explain Newton’s bucket experiment [13].

In this paper, the problems of the strong equivalence principle of general relativity are analyzed, the strong equivalence principle is modified and extended, and the nature of space-time bending and gravitation is given by using a new ether mechanism. These modified and extended equivalence principles are used to explain Newton’s bucket experiment, explain the physical mechanism of inertial force and inertial centrifugal force, explain the Casimir effect, explain the flow rate of the fluid in the Bernoulli equation with respect to which reference frame and why the higher the flow rate with respect to the reference frame, the lower the pressure. Using these modified and extended equivalence principles, the fundamental reasons for the ability of aircraft wings to produce lift are also explained, and it is stated that: Although the space capsule is highly sealed, when the space capsule lifts off or returns to the earth, due to the speed of the space capsule relative to the earth and the strength of the gravitational field changes very fast, the etheric pressure in the space capsule will change rapidly, if the astronauts in the space capsule do not wear space suits, the rapid change of etheric pressure can endanger the lives of the astronauts.

MODIFICATION AND EXTENSION OF STRONG EQUIVALENCE PRINCIPLE

In “The Modification of Newton’s Gravitational Law and its Application in the Study of Dark Matter and Black Hole” [5], The author points out that the gravitational field is a scalar field (energy field), and gravity is caused by the asymmetric density distribution of space energy (ether), which leads to the asymmetric ether pressure on objects in space. For example, the reason why an object in the Earth’s gravitational field is gravitationally affected is that the strength of the gravitational field in space at each point on the surface of each mass block of the object is different (the stronger the gravitational field is the closer it is to the center of the earth), resulting in a gravitational force toward the center of the earth generated by the asymmetry of the etheric pressure on each block. The sum of the vectors of the gravitational force on all these small pieces of mass is the gravitational force on the object. According to this mechanism, if the gravitational field strength (energy density) of space is the same at every point, then objects in that space will not generate gravity. Since an object in uniform etheric (energy) density space moving with an acceleration a relative to the ether (such as a driver in a car moving with an acceleration a along the Earth’s surface) will experience an inertial force f=ma in the direction opposite to the acceleration. From the above analysis, it can be seen that the uniform gravitational field is not equivalent to the non-inertial system moving with uniform acceleration. The non-equivalence between uniform gravitational field and uniformly accelerated non-inertial system is also reflected in the following aspects:

1. An object at rest in a gravitational field does not change in time, length, or mass, but an object at rest in a non-inertial system that is accelerating (relative to the ether) is constantly slowing down in time, getting shorter in length, and getting larger in mass.

2. A charged particle at rest in a gravitational field does not radiate electromagnetic waves outward, but a charged particle at rest in a non-inertial system in accelerated motion (relative to the ether) will radiate electromagnetic waves outward continuously.

Since the stronger the gravitational field, the more energy the object in the gravitational field is bound by gravity, and the faster the object moves in the ether (such as along the Earth’s surface), the greater the kinetic energy of the object, we can infer the following modified equivalence principle: “An object in a uniform gravitational field of a certain intensity is exactly equivalent to moving uniformly in a straight line through a uniform ether at a certain speed.” In fact, on the time dilation effect of an object, the gravitational field is equivalent to uniform motion, that is:

(1) $$\text{t}={\text{t}}_0\sqrt{1-\frac{2\text{GM}}{{\text{c}}^2\text{r}}}\hspace{0.17em}$$

from General Relativity [1] is equivalent to

(2) $$\text{t}={\text{t}}_0\sqrt{1-\frac{{\text{v}}^2}{{\text{c}}^2}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}$$

from Special Relativity [14]. Because the equivalence of gravitational field and velocity (but not acceleration) on time dilation has been verified by numerous experiments, it can be regarded as a proof of the modified equivalence principle above. From the above modified equivalence principle, we may also predict or infer:

1. In the inertial mass change effect of the object, the gravitational field is equivalent to the velocity, that is [15],

   (3) $$\text{m}=\frac{{\text{m}}_0}{\sqrt{1-\frac{2\text{GM}}{{\text{c}}^2\text{r}}}}\hspace{0.17em}$$

   is equivalent to

   (4) $$\text{m}=\frac{{\text{m}}_0}{\sqrt{1-\frac{{\text{v}}^2}{{\text{c}}^2}}}$$

   In other words, the increase of the speed of the object relative to the ether will lead to the increase of the inertial mass of the object, and the increase of the strength of the gravitational field in the space where the object is located will also lead to the increase of the inertial mass of the object (for example, the same object is stationary at different heights above the Earth, the inertial mass is different, and the higher the altitude, the smaller the inertial mass).

2. On the effect of change of electron orbital radius of an atom [16] (Formula 5.31), the gravitational field is equivalent to the velocity, i.e.,

   (5) $${\text{r}}_{\text{a}}={\text{r}}_{\text{a}0}\sqrt{1-\frac{2\text{GM}}{{\text{c}}^2\text{r}}}$$

   is equivalent to

   (6) $${\text{r}}_{\text{a}}={\text{r}}_{\text{a}0}\sqrt{1-\frac{{\text{v}}^2}{{\text{c}}^2}}\hspace{0.17em}$$

   That is to say, an increase in the velocity of the object relative to the ether can lead to a decrease in the orbital radius of the atomic orbital electrons that constitute the object, and an increase in the strength of the gravitational field in the space where the object is located can also lead to a decrease in the orbital radius of the atomic orbital electrons that constitute the object (for example, the same object, stationary at different heights above the Earth, has different orbital radii of the atoms that constitute the object. The higher the altitude, the larger the orbit radius).

3. The force received by an object in a gravitational field with field intensity gradient is equivalent to the force received by the object accelerating in the ether, that is, the gravitational force is equivalent to the inertial force.

   When an object is in a gravitational field with a gradient of field intensity, the density of energy (ether) in the space the object is in increases with the increase of field intensity. Because the greater the density of space energy (ether), the smaller the pressure of space ether (the greater the negative pressure of space ether), so the atoms and molecules of the object will be subjected to a gravitational force caused by the asymmetric pressure of the ether, and the vector sum of the gravitational force of all atoms and molecules of the object is the gravitational force of the object.

   Because when an object accelerates in a straight line through the ether, it is subjected to a inertial force in the opposite direction of acceleration. Therefore, we suspect that when an object is accelerating in a straight line through the ether, an etheric density gradient will be formed inside the object, decreasing along the direction of acceleration. Because the greater the density of space energy (ether), the smaller the pressure of space ether (the greater the negative pressure of space ether), the atoms and molecules of the object will be subjected to an inertial force caused by the asymmetric pressure of the ether, and the vector sum of the inertial forces received by all atoms and molecules of the object is the inertial force received by the object.

4. Since objects moving in the ether with linear acceleration have the lowest density of ether (energy) in the head and the highest density in the tail. Therefore, we predict that the time of the head is faster than that of the tail, the shrinkage rate of the head is lower than that of the tail, and the density of the head is less than that of the tail.

   We can verify that the time of the head in the container is faster than that of the tail, and the density of the head is less than that of the tail, by using a cylindrical container filled with solution to accelerate in a straight line through the ether along the axis of the cylinder (for example, by placing the cylindrical container filled with solution parallel to the rocket in the lift-off).

5. The ether (energy) field with field gradient produced by a fluid whose velocity is decreasing in the direction perpendicular to the motion is equivalent to the gravitational (energy) field with field gradient.

In a fluid (liquid or gas) where the flow rate is decreasing in the direction perpendicular to the motion, the object is subjected to liquid (gas) pressure, and the direction of the liquid (gas) pressure is directed from the point of small velocity to the point of large velocity, that is, along the direction of the increasing field strength of the fluid velocity.

In a gravitational field with field intensity gradient, the object will be affected by gravity, and the direction of gravity is from the point of small gravitational field intensity to the point of large gravitational field intensity, that is, along the direction of increasing gravitational field intensity.

Because the greater the kinetic energy of the object, the higher the energy (ether) density of the local space in which the object is located, and the stronger the gravitational field of space, the higher the energy (ether) density of space. And because the higher the density of energy (ether) in space, the lower the pressure of ether in space. Thus, an etheric (energy) field with a field gradient produced by a fluid whose velocity (relative to the ether) is decreasing in the direction perpendicular to the motion is equivalent to a gravitational (energy) field with a field gradient.

DISCUSSIONS

1. Explanation of Newton’s bucket experiment [13]

   The Newton bucket experiment is an experiment conducted by Isaac Newton to prove the existence of absolute space. Newton described the experiment this way: “If a bucket is suspended by a long rope, and the bucket is rotated until the rope is tight, then water is poured into the bucket. For the moment, the water and the bucket are still. Then let go of the bucket, and it began to spin under the torque of the rope. At first, the bucket is rotating and the water in the bucket is not rotating with it, the water surface is flat. But as the bucket gradually transmits its motion to the water, the water also begins to spin, and the water gradually leaves the axis of rotation and rises along the wall of the bucket, making the surface of the water concave.”

   Explanation: According to the modified equivalence principle proposed in this paper, the greater the velocity of the fluid relative to the ether, the lower the ether pressure (the greater the negative ether pressure) in the space where the fluid is located. Because on the surface of the Earth, the ether layer of the Earth can be regarded as an absolute reference system [16], the greater the rotation speed of water in a bucket relative to the ether of the Earth, the lower the ether pressure. Due to the fact that the water in a rotating bucket rotates faster as it gets closer to the wall (relative to the Earth), a centrifugal force field is generated within the water in the rotating bucket, which extends along the rotation radius from the center of rotation to the distant point. Water molecules in this centrifugal force field are equivalent to those in a gravitational field with a gradient of field strength and will be subjected to a centrifugal force acting in a direction from a point with strong ether pressure to a point with weak ether pressure (i.e., along the rotation radius from the center of rotation to the distant point). Under the action of this centrifugal force, the water in the bucket gathers towards the wall, causing the surface of the water to concave.

2. How are inertial and Inertial centrifugal forces produced? Are they real forces?

   An object accelerating in a straight line relative to the ether forms an ether field with decreasing energy density along the direction of acceleration in the internal space of the object, and each particle forming the object will be subjected to an ether pressure, that is, inertial force, along the opposite direction of acceleration. When an object is rotating in the ether, because the particle farther away from the rotation axis moves faster relative to the ether, an ether field with increasing energy density is formed in the inner space of the rotating object starting from the rotation axis and pointing in the direction perpendicular to the rotation axis. Each particle forming the object is subjected to an etheric pressure, or inertial centrifugal force, pointing away in a direction perpendicular to the axis of rotation. From the above analysis, it can be seen that the inertial force and the inertial centrifugal force, like gravity, are essentially etheric pressure and are real forces.

3. The Explanation of Casimir Effect [17]

   The Casimir Effect is a phenomenon that occurs when two parallel metal plates are placed in a vacuum. When the distance between these two plates is close enough, an attractive force will be generated between them.

   Explanation: Due to the vibration of ions and electrons on the surface of the metal plate, the ether density of the space between the two metal plates is greater than the space outside the two metal plates. Therefore, the ether pressure of the space between the two metal plates is less than the space outside the two metal plates, so the attraction between the two metal plates is generated. Because the closer the two metal plates are, the larger the etheric density difference between the space between the two metal plates and the space outside the two metal plates, and the larger the etheric density difference between the space between the two metal plates and the space outside the two metal plates, the greater the attraction between the two metal plates. So, when the two metal plates are close enough together, there is a clear attraction between the two metal plates.

4. What reference system is the flow rate of the fluid in Bernoulli’s equation [18] relative to, and why is the pressure lower when the flow rate is higher relative to the reference system?

   Daniel Bernoulli proposed the “Bernoulli Equation” in 1726. Its essence is the conservation of mechanical energy of fluid. That is: kinetic energy + gravitational potential energy + pressure potential energy = constant. The most famous corollary of Bernoulli’s equation is that at equal altitudes, the higher the velocity, the lower the pressure. There is a very serious problem in Bernoulli’s equation, namely: what reference frame is the flow rate in the equation relative to?

   Explanation: According to the paper “The Modification of Special Relativity” [16], on the surface of the Earth, the ether layer of the Earth can be considered as an absolute reference system. Therefore, on Earth, the greater the velocity of a fluid relative to the Earth, the smaller its pressure will be. Because the space at a certain height of the Earth’s surface on the Earth can be regarded as the etheric layer moving with the earth, the motion relative to the Earth is the motion relative to the Earth’s etheric layer. According to the above modified equivalence principle, the faster the object moves in the ether, the higher the density of energy (ether) in the local space of the object, and the smaller the etheric pressure generated in the local space. Therefore, the greater the velocity of the fluid relative to the Earth, the lower the pressure of the fluid. It can be seen that on the earth, the pressure of water in the pipe is not related to the velocity of water in the pipe relative to the pipe, but to the velocity of water in the pipe relative to the earth. For example, if a straight pipe with the same diameter moves along the axis of the pipe in a still lake water, the pressure of the water in the pipe is independent of the velocity of the water in the pipe with respect to the pipe. However, for a pipe that is stationary relative to the earth, the pressure of the water in the pipe is related to the velocity of the water in the pipe relative to the pipe, and the faster the velocity, the lower the pressure.

   The hydrofoil craft can generate an upward lifting force when it moves in water because the hydrofoil forces the water above the hydrofoil to move faster relative to the Earth than the water below the hydrofoil.

   Similarly, when an airplane moves in the air, the wings can generate upward lift because the wings force the air above the wings to move faster relative to the Earth than the air below the wings.

   Why is it difficult for a plane to take off downwind? Because in the case of a plane taking off downwind, it is difficult for the wing to cause the air above the wing to travel faster relative to the Earth than the air below the wing, and the higher the wind speed, the harder it is. So it’s hard for a plane to take off downwind, and the higher the wind speed, the harder it is.

   Why do two high-speed trains traveling in opposite directions repel each other when they meet? Because of the attraction between the molecules, the surface of the train drags a layer of air along with it, and the farther away from the surface of the train, the faster the air layer moves relative to the train (and the slower it moves relative to the ground). When two trains meet, the air layer dragged by the two trains will rub against each other, causing the speed of the air layer relative to the ground to decrease. So the speed of the air between the two trains relative to the ground is less than the speed on the other side of the two trains. Therefore, the air pressure between the two trains is higher than on the other side of the two trains, and the two trains repel each other.

5. Why do astronauts in the capsule have to wear spacesuits during liftoff and return to Earth, but not in the fast-moving space station?

   Explanation: Although the space capsule is highly sealed, when the space capsule lifts off or returns to the earth, due to the speed of the space capsule relative to the earth and the strength of the gravitational field changes very fast [19], if the astronaut in the space capsule does not wear a space suit, the rapid change of etheric pressure can endanger the life of the astronaut. That’s why astronauts must wear spacesuits when they go up on rockets and return to Earth in re-entry capsules.

   In 1971, after the Soyuz 11 capsule returned to Earth, three astronauts were found dead when the hatch was opened [20]. How did the three astronauts die? The author believes that the fact that none of the three astronauts in the capsule were wearing spacesuits during their return to Earth contributed to their deaths. The author also suggest that the capsule’s tightness may not have been faulty, although the capsule is well sealed, but due to the severe slowdown of the capsule after entering the atmosphere, resulting in a rapid increase in etheric pressure (rapid decrease of negative etheric pressure) in the capsule. The rapid increase in etheric pressure in space leads to a rapid increase in hydraulic pressure inside the body. Because the astronauts did not wear spacesuits, the pressure difference between the body and the outside increased dramatically, resulting in the death of the astronauts.

   Because the space station orbits the Earth at a constant speed in a gravitational field of constant strength, the etheric pressure inside the space station is essentially constant. Although the space station moves quickly around the Earth, astronauts do not need to wear spacesuits inside the space station because the etheric pressure inside the space station is constant.

CONCLUSIONS

Through this study, we can draw the following conclusions: An object at rest in a uniform gravitational field of a certain intensity is equivalent to moving uniformly in a straight line in a uniform ether (energy) space at a certain speed; The gravitational force received by an object at rest in a gravitational field with a field gradient is equivalent to the inertial force received by the object in a linear acceleration motion in ether; The ether (energy) field with field gradient produced by a fluid whose velocity is decreasing in the direction perpendicular to the motion is equivalent to the gravitational (energy) field with field gradient.

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