The mechanical motion of a particle shows that the position of the particle changes with time. The position of particles is relative to a reference system. Reference frame refers to selecting a three-dimensional, undeformed object (rigid body) or a group of objects as a reference body, selecting three intersecting lines with different planes as a frame on the reference body, and adding a clock fixedly connected with the reference body. In other words, the reference frame includes a reference body, a frame and a clock. Traditionally, we simply refer to the frame of reference as the frame of reference. In order to quantitatively describe the motion of an object, we need to establish a coordinate system in the reference system. Cartesian coordinates and polar coordinates are the two most commonly used coordinate forms.
Newton called the reference system of uniform linear motion inertial reference system. 1905, Einstein proposed in his paper that all inertial reference frames are equivalent, that is, all physical laws are equally applicable in inertial reference frames and have the same form. Einstein's point of view is correct, because people can't find out the difference between this frame of reference and the static frame of reference in any inertial frame of reference by any physical law (that is, they don't refer to objects outside this frame of reference). It was on this basis that Einstein established the special theory of relativity.
So, what if we are in a non-inertial frame of reference? The movement of non-inertial reference frame has a certain acceleration, but this acceleration can be regarded as a kind of gravity (also called universal gravitation). For example, when we are in an elevator, when the elevator accelerates or decelerates, we feel a little light and the weight seems to be reduced. We don't look at the reference objects outside in the elevator, and we don't know whether the elevator is accelerating or decelerating. We just feel that gravity is changing.
According to Newton's point of view, absolute motion is relative to an absolutely stationary frame of reference. In other words, there is an absolutely still space in nature, that is, absolute space. According to the modern viewpoint, absolute space has no objective meaning. In order to explain the contradiction between J.C. Maxwell's electromagnetic theory and the relativity principle in Newtonian mechanics, physicists in the19th century assumed that the space was filled with the massless and flowing elastic medium "ether" and electromagnetic waves were regarded as the vibration of "ether". A frame of reference that is stationary relative to the ether represents an absolutely stationary frame of reference. Electromagnetic phenomena in this frame of reference has special properties, which leads to the argument that inertial coordinate system is not equivalent to describing electromagnetic phenomena. The famous experimental results published by A.A. Michelson and E.W. Morey in 1887 show that the "ether" effect cannot be detected. Since then, other experiments have also shown that the static frame of reference can not be found. Therefore, an Einstein pointed out that there is no absolute stillness at all.
Einstein put forward two basic hypotheses of special relativity in his famous paper Electrodynamics of Moving Objects published in 1905, namely, the principle of relativity and the constant speed of light. These two hypotheses are the basis of special relativity, and many phenomena that cannot be explained by Newtonian mechanics can be accurately described by special relativity. Einstein's theory of relativity points out that the laws of physics, including mechanics, electrodynamics and optics, are the same in all inertial reference systems. That is to say, the inertial coordinate system is equal to describing physical phenomena. Without a special absolutely static reference system, absolute space is meaningless.
inertial frame of reference
The reference system for establishing the law of inertia is referred to as inertial system for short. The relativity principle of classical mechanics points out that all mechanical laws are the same in a reference frame with uniform motion without rotation. An observer moving in a straight line at a uniform speed in a sealed cockpit cannot judge whether the cockpit is stationary or moving at a uniform speed relative to the star through internal mechanical experiments. He can only know if he looks out of the window, but he still can't tell whether the cockpit is moving or the stars are moving. On the other hand, this mechanical equivalence of the reference frame does not hold true for any moving reference frame. In the bumpy train and the train running at a constant speed, the mechanical movement does not follow the same law. When accurately writing the equation of motion relative to the earth, we must consider the rotation of the earth. A reference system is called inertial reference system or Galileo reference system if a free particle does not accelerate in it. All reference systems that do not accelerate and do not rotate with each other are inertial reference systems.
Judging whether a particular reference frame is an inertial system depends on how accurate the measurement of the tiny acceleration effect of this reference frame is. In general engineering dynamics on the ground, because the angular velocity of the earth's rotation is very small and the centripetal grip force of a point on the ground is very small, the coordinate system fixedly connected with the earth can be used as the inertial reference system. In some problems that must consider the earth's rotation, such as studying the drift of gyro instruments, the earth's central coordinate system can be used as an approximate inertial reference system, whose origin coincides with the center of the earth and its axis points to the identified star. In astronomy, the ecliptic coordinate system or the galactic coordinate system is used as the inertial reference system. The centripetal acceleration at a point on the equator on the earth's surface is 3.4cm/s 2, the centripetal acceleration around the sun is 0.6cm/s 2, and the centripetal acceleration around the center of the Milky Way galaxy is about 3x 10-8cm/s 2. From the above data, we can see the approximate degree of the selected inertial reference system.
Non-inertial inspection department
The reference system of accelerating or rotating inertial reference system, referred to as non-inertial system.
The non-inertial system moving with constant acceleration α is called the accelerated motion reference system. In this frame of reference, a stationary object must have a force F=mα. In the gravitational field, all objects are affected by gravity, so the objects in the gravitational field with static inertial system are also affected by gravity. If there is another non-inertial system, its acceleration to the inertial system is the same as the acceleration generated by this gravity, then the observer in this non-inertial system will not feel the gravitational field and will not know that he has accelerated motion. This is Einstein's "elevator", which shows that the gravitational field and the non-inertial system are equivalent.
The rotating reference system of inertial reference system is called rotating reference system. Assuming that the inertial system is stationary, the rigid body motion fixedly connected with the rotating reference system is the motion of the rotating reference system to the inertial system.
Frame of Reference and Equivalence Principle
The equality of inertial mass and gravitational mass is generally called equivalence principle. This principle leads to a conclusion: an inertial reference system with gravitational field and another non-inertial reference system with accelerated motion are equivalent, that is, internal physical experiments cannot distinguish these two reference systems, which is Einstein's equivalence principle. Take Einstein's "elevator" for example. If the elevator is stationary in the uniform gravitational field of 1g, and moves upward at the acceleration of 9.865,438+0m/s 2 in free space, the same internal physical experiment results are the same in the above two cases because the inertial mass and gravitational mass are equal. The observer inside can think that the elevator is static and there is a gravitational field in the car; It can also be considered that the car has no gravitational field, but the elevator moves upward at an acceleration of 9.8 1 m/s 2.
The equivalence of inertial mass and gravitational mass leads to another situation. If an object falls freely in a uniform gravitational field, the inertial force and gravity are balanced because the inertial mass and gravitational mass are equal. Therefore, the non-rotating reference frame fixed with the free falling body in the uniform gravitational field is equivalent to the inertial reference frame in the free space. In the spacecraft flying around the earth, the balance between gravity and centrifugal inertia force causes the phenomenon of "weightlessness".
The equality of inertial mass and gravitational mass is often called weak equivalence principle, and Einstein's equivalence principle is called strong equivalence principle. The principle of equivalence is the basis of general relativity.