Take the supermarket to the apocalypse

Chapter 460 Dimensional Space
Generally, to determine the size of an object, its shape and dimensions are known.

For a cuboid, if its length, width and height are known, its volume can be calculated by using the formula of Euclidean geometry. As long as its up-down, left-right and front-back distances are known relative to another static reference object of negligible size, it can also be calculated by using the Euclidean geometry formula to calculate its volume. A few miles of geometry will suffice.

It is not enough to describe the instantaneous position of a moving object, but also need to know the instantaneous velocity and acceleration.Thus, the concepts of three-dimensional space coordinate system and one-dimensional time coordinate can be abstracted.The nature and law of motion of an object are closely related to the space coordinate system and time coordinates used to measure.In order to determine the inertial system, L. Newton abstracted the concepts of three absolute spaces and one absolute time.Absolute space satisfies three-dimensional Euclidean geometry, absolute time flows uniformly, and their nature is independent of any specific objects and their motions in it.An inertial system is a coordinate system in which an object that is stationary or moving in a straight line at a uniform speed relative to absolute space is the reference object.

In classical mechanics, any object satisfies the Galilean transformation between the space coordinates and time coordinates of different inertial coordinate systems.Under this group of transformations, position and velocity are relative; space length, time interval, and acceleration of moving objects are absolute or constant.Simultaneity in time measurement is also invariant; it is invariant whether two events occur simultaneously with respect to some inertial frame of reference.Two events that occur simultaneously relative to a certain inertial frame of reference, and two events that occur simultaneously relative to a certain inertial frame of reference must also be simultaneous relative to other inertial frames of reference, which is called the absoluteness of simultaneity.All the laws of Newtonian mechanics, including the law of universal gravitation, are invariant under Galileo transformation.This point can be abstracted as Galileo's principle of relativity; the laws of mechanics remain unchanged under the transformation of the inertial frame of reference.At the same time, invariance is closely related to conservation laws.The time translation invariance of a moving object under Galileo transformation corresponds to the energy conservation of the object; the space translation and space rotation invariance under Galileo transformation correspond to the momentum conservation and angular momentum conservation of the object.

If absolute space exists, the motion of an object relative to absolute space should be measurable.This is equivalent to requiring that some laws of mechanical motion should contain absolute velocity.However, there is no absolute speed in the laws of science.In other words, the correctness of the scientific laws of the last days does not require the existence of absolute space.

According to this type of transformation, the length of the ruler and the time interval (that is, the speed of the clock) are not constant; the ruler moving at high speed is shorter than the ruler at rest, and the clock moving at high speed is slower than the clock at rest.

Simultaneity is no longer constant (or absolute); two events that occur simultaneously in one inertial frame of reference do not occur simultaneously in another high-speed moving inertial frame of reference.

In special relativity, the speed of light is an invariant, so the time-space interval (referred to as space-time interval) is also an invariant; between some inertial systems, in addition to the conservation of energy and momentum corresponding to the invariance of time translation and space translation, There is also time-space translation invariance; thus, there is an energy-momentum conservation law.According to this conservation law, the mass-energy relationship can be derived.This relationship is extremely fundamental in atomic and nuclear physics.

The special principle of relativity requires that all physical laws have the same form with respect to an inertial frame of reference.However, incorporating the law of gravity into this requirement does not correspond to observational facts.

According to the general theory of relativity, if the inertial force or gravitational interaction between objects is considered, there is no large-scale inertial frame of reference, only a local inertial frame exists at any point in time and space; between local inertial frames at different points in time and space, through inertia force or gravitational connection.The space-time with inertial force is still the straight four-dimensional Minkowski space-time.

The space-time in which the gravitational field exists is no longer straight, but is the four-dimensional curved space-time, and its geometric properties are described by the four-dimensional Riemannian geometry with sign difference in the metric.The degree of curvature of spacetime is determined by the energy-momentum tensor of matter (object or field) and its motion in it, through the gravitational field equation.

In general relativity, time-space is no longer just a "stage" for objects or field motions, curved time-space itself is a gravitational field.The time-space properties that characterize gravity are closely related to the properties of objects and fields moving in it.

On the one hand, the energy-momentum of the motion of objects and fields is used as the source of the gravitational field, and the strength of the gravitational field is determined by the field equation, that is, the degree of curvature of space-time; on the other hand, the geometric properties of curved space-time also determine the objects and fields moving in it the nature of the movement.

For example, the sun is the source of the gravitational field, its mass makes the space-time where the sun is located bend, and the degree of curvature represents the strength of the sun's gravitational field.The trajectory of Mercury, which is the closest to the sun, is most affected, and the light of stars passing the edge of the sun will also be deflected, and so on.

Not long after the general theory of relativity was proposed, astronomical observations showed that the theoretical calculations of the general theory of relativity were consistent with the observation results.

The understanding of space and time has always been closely related to the understanding of the universe.Modern cosmology is based on cosmological principles and Einstein's gravitational field equations.

According to the principle of cosmology, the universe as a whole evolves in time, that is, there is an arrow of time, and it is uniform and isotropic in space.

The spatial position and momentum, time and energy of the system described by quantum mechanics cannot be precisely measured at the same time, they satisfy the uncertainty relationship; classical orbits no longer have precise meaning, etc. How to understand quantum mechanics and the essence of measurement has always been debated.In the apocalypse, research on quantum entanglement, quantum teleportation, and quantum information also brings new problems and challenges to important concepts such as causality and localization that are closely related to time and space.

The combination of quantum mechanics and special relativity leads to quantum electrodynamics, quantum field theory, electroweak unified model, and the standard model including quantum chromodynamics describing the strong interaction. Although it has achieved great success, it also brings some challenges problems.While profoundly changing some important concepts about time-space, it also brings some principle issues.

For example, the vacuum is not empty, there is zero-point energy and vacuum fluctuations, which greatly changed the understanding of the vacuum in physics.

On this basis, the perturbation theory calculation of quantum electrodynamics can give a result that is in close agreement with the experiment, but this perturbation expansion is unreasonable.The mechanism of symmetry breaking makes the weakly acting intermediate boson gain mass, but the vacuum expectation value of the Higgs field and the aforementioned zero-point energy are in a certain sense equivalent to the constant maturity of the universe, but their values ​​are lower than those of astronomical observations. The cosmological constant is tens to more than 100 orders of magnitude larger.

(End of this chapter)