# Einstein solved Newton’s question

Does it really come from an apple tree?

This is a story that all Chinese people know: One day in the summer of 1666, Newton stayed in his hometown, which was Woolthorpe Manor in Grantham, Lincolnshire, England, which has now become a famous Newton House. The year before, in 1665, 22-year-old Newton received a bachelor’s degree from Cambridge University. At that time, Newton’s talents were first revealed, and when he was about to make his own voice in the academic world of Cambridge, a plague broke out in London. Newton had to leave Cambridge and returned to the country. However, his life in the country was very fulfilling-his orchard became a place for him to think about math and physics. This was destined to be an extraordinary day. When Newton was sitting under the apple tree thinking, an apple hit him on the head. So a well-known question appeared in Newton’s mind, why did Apple fall into the ground? The answer is also known to everyone, this is because there is universal gravitation! It was like an apple hitting the ground, leading Newton to think ahead and independently think about the theory of universal gravitation.
Is this really the case?

no. Newton said: “If I see farther than others, it’s because I stand on the shoulders of giants.” The law of gravity can be discovered because Newton “stands on” several “giants”. Shoulders.

One of the most important “giants” is the German astronomer Johannes Kepler. Kepler was originally an assistant to the Danish astronomer Tycho Brahe, but after only less than a year in this assistant position, Tycho died. Kepler was very fortunate to obtain accurate data from Tycho’s astronomical observations for more than 20 years. He studied these data carefully, discovered the phenomenon of planets moving along elliptical orbits, and proposed the three laws of planetary motion (ie, Kepler’s three laws), which summarized the laws of planetary orbits observed at that time.
But the question is, why do these planets orbit the stars? Is force at work? If it is a force, what force is it, how is this force calculated, and what law does it have? It can be said that it was the discovery of Kepler’s three major laws that led to the conjecture of universal gravitation between objects, and Newton directly derived the law of universal gravitation from Kepler’s three major laws-any object has a mutual attraction force. The magnitude of this force is directly proportional to the mass of each object, and inversely proportional to the square of the distance between them.
The discovery of universal gravitation was one of the greatest achievements of natural science in the 17th century. Only after the emergence of the law of universal gravitation, did people formally base the study of the motion of celestial bodies on the basis of mechanical theory, thus creating celestial mechanics.
Distant and weak gravitation

In 1687, Newton officially published the law of universal gravitation in the book “The Mathematical Principles of Natural Philosophy”-the formula of universal gravitation is F=GMm/r2 (G is the constant of gravitation, M and m are the masses of two objects, and r is the weight of the two objects. distance). But what is the value of the gravitational constant G, Newton himself does not know. Ordinarily, as long as the masses of two objects are measured, the distance between the two objects is measured, and the gravitational force between the objects is measured, this constant can be measured by substituting it into the universal gravitation formula. But the fact is that this is a work that is as difficult as a Nobel Prize work.

The reason is that gravitation is too small. The mass of celestial bodies is very large, and the gravitational force generated between them is also relatively large. We can know the magnitude of gravitational force through the orbit of the celestial body. But to know the constant of gravitation, you have to know the mass of celestial bodies. However, in the past, people could not know the mass of huge celestial bodies, and even the mass of the earth was not clear. It wasn’t until 1798 that the British physicist Cavendish used his own improved torsion to convert gravity into the deflection angle of reflected light, and then calculated the value of the gravitational constant.
How small is gravity? From a macro perspective, people can easily overcome the gravitational pull of an object as large as the earth (5.965×1024 kg) on ​​the human body-we can easily walk, climb stairs, and climb mountains. The gravitational force between ordinary objects is even more trivial. For example, when two iron balls with a diameter of 1 meter are close together, the gravitational force is only 1.11×10-3 Newtons, which is equivalent to the weight of a small drop of water of 0.113 grams. From a microscopic point of view, the gravitational force between two protons is only 1/(1.235×1036) of the electromagnetic force between them, and the gravitational force of the proton by the earth is only as great as the electromagnetic force of a weak electric field of 1000 volts/meter. 1/(9.761×109). Therefore, when studying the interaction between particles or the movement of particles in electron microscopes and accelerators, the role of gravitation is not considered. For a long time, the gravitational force has been so weak that it has puzzled the theoretical physics community.

Judging from the law of universal gravitation, although gravitation is small, it is everywhere. All things are affected by gravitation, and gravitation exists in all spaces. There is universal gravitation between any two objects, no matter how far apart they are, even if they are separated by trillions of light years, although the gravitation between them is close to 0, it will not be absolutely zero. From this perspective, any object in the universe is subject to the gravitational force given to it by the entire universe.
The flaws of Newtonian gravitation

Newton’s law of universal gravitation not only successfully explained and predicted the trajectories of many planets and their satellites, but also explained many phenomena such as tides caused by gravity. In addition, the law of universal gravitation has even helped scientists discover unknown planets, such as Neptune, the eighth largest planet in the solar system that is farthest from the sun. In 1845, French astronomer Le Verrier was working on the theory of Uranus’ orbit. He noticed that the orbit of Uranus was a little abnormal-Uranus’s orbit deviated from the orbit predicted by the law of universal gravitation, and its actual elliptical orbit around the sun was more outward. . Le Verrier vaguely felt that there might be an unknown celestial body affecting the movement of Uranus. He used 18 observations of Uranus and applied the law of universal gravitation to solve 33 equations to calculate the effect on Uranus on August 31, 1846. Perturbation (perturbation refers to the deviation of the orbit due to the attraction of other celestial bodies or the influence of other factors when a celestial body moves around another celestial body) the orbit and mass of an unknown planet, and its position is predicted. On September 18, 1846, according to the position predicted by Le Verrier, the German astronomer Galle observed the star, Neptune, which was not on the chart at that time, in just one and a half hours.

The result of handling the problem of Uranus perturbation is encouraging. It not only gave people an unexpected gain, but also strengthened the correctness of Newton’s law of universal gravitation once again, making this theory even more popular. However, not all the mysteries of motion in the space world can be so easily revealed by the law of universal gravitation. Soon, when applying the law of universal gravitation, scientists encountered a huge trouble-from Mercury’s precession at perihelion. Precession refers to a phenomenon in which a self-rotating object is subjected to external force to cause its rotation axis to rotate around a certain center. All planets have precession. In 1859, Le Verrier discovered that the observed value of Mercury’s precession when it was at perihelion was 38″ faster per century than the theoretical value calculated according to Newton’s law. He speculated that this might be caused by the attraction of a planet closer to the sun than Mercury. But After years of diligent search, the planet under speculation has never been seen. People have tried to explain this deviation with many theories, but they have all failed, so people began to doubt whether Newton’s law of universal gravitation has any shortcomings, or is there Insurmountable difficulties.

The law of universal gravitation has not only encountered problems in actual observation, but also encountered difficulties in theory. The first difficulty is the action over distance. According to the law of gravitation, two objects that are infinitely far apart can generate gravitation, and this gravitation does not involve time, which means that the propagation of gravitation does not require time. We know that even if the electromagnetic field can be transmitted to a long distance, its propagation is in accordance with a certain time law. The effect of distance is difficult to be understood by people. Even Newton himself thought it was a very absurd thing, but he really couldn’t think of a better theory. The second difficulty is the contradiction between the law of universal gravitation and the special theory of relativity published by Einstein in 1905. “Narrow sense” means that this theory is only applicable to inertial reference systems, and the core equation of the theory is the Lorentz transformation. Special relativity predicts some new effects (relativity effects) that Newtonian classical physics does not have, such as time expansion, length contraction, lateral Doppler effect, mass-velocity relationship, mass-energy relationship, etc. According to the requirements of the special theory of relativity, all laws of physics should conform to the principle of special relativity, and the mathematical form remains unchanged under the Lorentz transformation. For example, F=ma, no matter what coordinates the object is in, even if the mass of the object changes with the speed according to the Lorentz transformation, the formula itself will not change. But the law of universal gravitation has changed its form under different coordinates, and it has an irreconcilable conflict with the special theory of relativity. Moreover, the special theory of relativity holds that the speed of light is the limit speed in the universe, which is also in contradiction with the ultra-distance effect of universal gravitation.
Gravity in Einstein’s eyes

Ten years after the special theory of relativity was proposed, Einstein completely independently introduced the general theory of relativity, which shocked the world once again and proved the greatness of the greatest scientist of the 20th century. General relativity has carried out a new interpretation of universal gravitation and made up for the insufficiency of Newton’s law of universal gravitation.
The general theory of relativity believes that the essence of universal gravitation is space-time bending, and mass (or energy) is the cause of space-time bending. Therefore, in general relativity, the force of “gravity” does not exist. The reason why two objects are attracted to each other is because of the equivalent effect caused by the motion of the objects in the curved space. In other words, it is the orbital motion of celestial bodies, which makes people mistakenly believe that celestial bodies attract each other. Why do celestial bodies in space exhibit the current movement? According to Newton’s first law: any object must maintain a uniform linear motion or a static state until the external force forces it to change its state of motion. We conclude that the trajectory of a moving object that is not subject to external force is always in a straight line. In general relativity, planets in space are not subject to external forces, but they have mass and bend space. In a curved space, they still try to keep moving in a straight line, which is the origin of their elliptical trajectory.

Gravity compresses space-time

But can we just say that Newton’s law of universal gravitation is wrong? In most cases, Newton’s law of gravity is still very accurate and very practical. It’s just that we have encountered bottlenecks in small issues, such as the inability to explain the precession of Mercury’s perihelion, and the incompatibility with the special theory of relativity. These problems are perfectly solved by the general theory of relativity. It can be said that both general relativity and the law of gravitation are correct. Compared with the law of universal gravitation, the result calculated by general relativity is closer to the actual measured value. To some extent, the law of universal gravitation is just an approximate theory of general relativity in the weak gravitational field. But the law of universal gravitation has a huge advantage: the calculation is simple. Because the formulas of general relativity are abnormal and difficult to understand, it will cause inconvenience whether they are used in large quantities in learning or in application, so the law of universal gravitation is more widely used than general relativity.