Day 5 精读笔记 - Space and Time 概念梳理

1. nature is everywhere the cause of order.

— Aristotle, Physics VIII.1

While consistent with common human experience, Aristotle's principles were not based on controlled, quantitative experiments, so, while they account for many broad features of nature, they do not describe our universe in the precise, quantitative way now expected of science. Contemporaries of Aristotle like Aristarchus rejected these principles in favor of heliocentrism, but their ideas were not widely accepted. Aristotle's principles were difficult to disprove merely through casual everyday observation, but later development of the scientific method challenged his views with experiments and careful measurement, using increasingly advanced technology such as the telescope and vacuum pump.

2. Galileo proposed that a falling body would fall with a uniform acceleration, as long as the resistance of the medium through which it was falling remained negligible, or in the limiting case of its falling through a vacuum. He also derived the correct kinematical law for the distance travelled during a uniform acceleration starting from rest—namely, that it is proportional to the square of the elapsed time ( d ∝ t 2 ). Prior to Galileo, Nicole Oresme, in the 14th century, had derived the times-squared law for uniformly accelerated change, and Domingo de Soto had suggested in the 16th century that bodies falling through a homogeneous medium would be uniformly accelerated. Galileo expressed the time-squared law using geometrical constructions and mathematically precise words, adhering to the standards of the day. (It remained for others to re-express the law in algebraic terms).

He also concluded that objects retain their velocity in the absence of any impediments to their motion,[citation needed] thereby contradicting the generally accepted Aristotelian hypothesis that a body could only remain in so-called "violent", "unnatural", or "forced" motion so long as an agent of change (the "mover") continued to act on it. Philosophical ideas relating to inertia had been proposed by John Philoponus and Jean Buridan. Galileo stated: "Imagine any particle projected along a horizontal plane without friction; then we know, from what has been more fully explained in the preceding pages, that this particle will move along this same plane with a motion which is uniform and perpetual, provided the plane has no limits." This was incorporated into Newton's laws of motion (first law).

3. Newton's law of universal gravitation states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. (When Newton's book was presented in 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him; see the History section below.)

In modern language, the law states: Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them. The first test of Newton's theory of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. It took place 111 years after the publication of Newton's Principia and approximately 71 years after his death.

Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant.

Newton's law has since been superseded by Albert Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications. Relativity is required only when there is a need for extreme precision, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at very close distances (such as Mercury's orbit around the Sun).

4. Rømer's determination of the speed of light was the demonstration in 1676 that light has a finite speed, and so does not travel instantaneously. The discovery is usually attributed to Danish astronomer Ole Rømer (1644–1710), who was working at the Royal Observatory in Paris at the time.

By timing the eclipses of the Jupiter moon Io, Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter of Earth's orbit around the Sun. This would give light a velocity of about 220,000 kilometres per second in SI units, about 26% lower than the true value of 299,792 km/s.

Rømer's theory was controversial at the time he announced it, and he never convinced the director of the Paris Observatory, Giovanni Domenico Cassini, to fully accept it. However, it quickly gained support among other natural philosophers of the period, such as Christiaan Huygens and Isaac Newton. It was finally confirmed nearly two decades after Rømer's death, with the explanation in 1729 of stellar aberration by the English astronomer James Bradley.

5. The Michelson–Morley experiment was a scientific experiment to find the presence and properties of a substance called aether, a substance believed to fill empty space. The experiment was done by Albert Michelson and Edward Morley in 1887.

Since waves in water need something to move in (water) and sound waves do as well (air), it was believed that light also needed something to move in. Scientists in the 18th century named this substance "aether," after the Greek god of light. They believed that aether was all around us and that it also filled the vacuum of space. Michelson and Morley created this experiment to try and prove the theory that aether existed. They did this with a device called an interferometer.

The Earth travels very quickly (more than 100,000 km per hour) around the Sun. If aether exists, the Earth moving through it would cause a "wind" in the same way that there seems to be a wind outside a moving car. To a person in the car, the air outside the car would seem like a moving substance. In the same way, aether should seem like a moving substance to things on Earth.

The interferometer was designed to measure the speed and direction of the "aether wind" by measuring the difference between the speed of light traveling in different directions. It measured this difference by shining a beam of light into a mirror that was only partially coated in silver. Part of the beam would be reflected one way, and the rest would go the other. Those two parts would then be reflected back to where they were split apart, and recombined. By looking at interference patterns in the recombined beam of light, any changes in speed because of aether wind could be seen.

They found that there was in fact no substantial difference in the measurements. This was puzzling to the scientific community at the time, and led to the creation of various new theories to explain the result. The most important was Albert Einstein's special theory of relativity.

6. Albert Einstein, in his theory of special relativity, determined that the laws of physics are the same for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same no matter the speed at which an observer travels.

Space-time is a mathematical model that joins space and time into a single idea called a continuum. This four-dimensional continuum is known as Minkowski space.

Combining these two ideas helped cosmology to understand how the universe works on the big level (e.g. galaxies) and small level (e.g. atoms).

In non-relativistic classical mechanics, the use of Euclidean space instead of space-time is good, because time is treated as universal with a constant rate of passage which is independent of the state of motion of an observer.

But in a relativistic universe, time cannot be separated from the three dimensions of space. This is because the observed rate at which time passes depends on an object's velocity relative to the observer. Also, the strength of any gravitational field slows the passage of time for an object as seen by an observer outside the field.