- Introduction.
- The process of law unification from Newton to Maxwell to Einstein
- Overview of Special and General Relativity
- E=mc² : Equation indicating that mass can be converted into energy
- Comparison of Electromagnetic Force and Gravity: Differences in Scale
- Field theory: from direct interaction to interaction via fields
- New Perspectives Brought by the Theory of Relativity
Introduction.
I was interested in Einstein’s theory of relativity, but had never read it before, so I started with a very introductory reading book. It was biting and explained in a way that I could understand if I understood middle school and high school physics levels.
I would need a college-level physics course to understand the details accurately, but as someone who wanted to get a general idea, I found the book very helpful.
The following is a memorandum of the parts that impressed me.
The process of law unification from Newton to Maxwell to Einstein
It can be said that the development of physics has been a step toward unifying a wide variety of laws.
Newton: Unified laws of motion
Integrate the results of Galileo and Kepler
- Newton unified the laws of motion, and the laws of conservation of mass, momentum, and energy, into a theory of “universal gravitation.
Concept of Absolute Space
- The idea that objects move and change within space, but that space itself is permanently unchanging. → This idea of absolute space was later overturned by the theory of relativity.
Maxwell: unifying the laws of electricity and magnetism as electromagnetism
Integration of electricity and magnetism
- Developed a theory that unifies electricity and magnetism. Example: Electromagnetic waves travel at the speed of light while alternately generating electric and magnetic fields.
Elucidating the Nature of Light
- He showed that light is also a type of electromagnetic wave, a phenomenon transmitted by the interaction of electric and magnetic fields.
Einstein: Unification of space-time, mass and energy
- Special Theory of Relativity: Unifies the laws of motion (Newtonian mechanics) and electromagnetism (Maxwell’s equations) to create a new theory of motion based on the principle of light speed invariance.
- General relativity: unifies time and space as space-time and interprets gravity as a geometric distortion of space-time
- As a result, the laws of conservation of mass, momentum, and energy expressed in Newtonian mechanics were combined into a single equation: conservation of energy and momentum.
Overview of Special and General Relativity
Special Theory of Relativity: A theory that holds true in inertial systems
Principle of light speed invariance: the speed of light c is always constant regardless of the speed of motion of the observer.
In Newtonian mechanics, it was assumed that the velocity depends on the observer’s state of motion (the law of addition of relative velocities holds), but the experimental results showed that the speed of light does not change depending on the observer’s state of motion.
In order to resolve the above contradiction between Newtonian mechanics and Maxwellian electromagnetism, Einstein assumed the principle that “the speed of light is constant regardless of its state of motion (velocity) as long as the observer is in constant velocity linear motion, ” and introduced the principle of relativity, on which he showed that both time and space are relative .
- Relativity of time and space: time is not absolute; it stretches and shrinks according to the speed of the observer in motion (time delay). The length of space also changes in response to the observer (length contraction).
- Relation between mass and energy: The famous equation E=mc2 shows that mass and energy are equivalent (derived from the principle of light speed invariance and the laws of conservation of mass and momentum). This makes it possible to explain the energy generation mechanism of fusion and fission.
General Relativity: Theory valid for any system including gravity
- Gravity = distortion of space-time: massive objects distort space-time around them, and this distortion affects the motion of other objects. This is the essence of gravity.
- Light is also affected by gravity: light also bends its path due to space-time distortion (gravitational lensing effect).
- Free fall and equivalence principle: The theory is based on the principle that free fall in a gravitational field is indistinguishable from an inertial system.
Under the influence of a non-inertial system or a gravitational field, the path of light may appear to be bent because of the change in the observer’s state of motion and the nature of space. The speed of light, however, remains constant. To explain this phenomenon, Einstein’s general theory of relativity explained gravity as a distortion of “space (spacetime)” itself.
Light tries to take the “shortest path” through space (spacetime) distorted by the inertial system, resulting in a curvilinear path.
The novelty lies in the fact that light bends because of the distortion of space itself, and in the fact that light is redefined as simply traveling the shortest possible path within that distorted space.
E=mc² : Equation indicating that mass can be converted into energy
Energy-mass equivalence: denotes the amount of energy E if the mass m were completely converted into energy.
Relativity and Energy
Einstein derived the following two important facts through his theory of special relativity
Kinetic and static energy
- In classical mechanics, energy was limited to “kinetic energy: K=1/2mv2”. The kinetic energy is proportional to mass and to the square of the speed of motion. This classical equation for kinetic energy applies exactly at low speeds (very slow compared to the speed of light), but special relativity corrections are required when the speed approaches the speed of light.
- However, relativity has shown that objects not in motion also have energy. This energy is “rest energy” and its equation is E=mc2 .
The senses seem to believe that matter in motion has energy, but it is hard to believe that matter at rest also has energy, but in fact mass exists as a condensed form of energy.
However, in order to actually utilize the rest energy E=mc2, a physical process that causes a mass loss is necessary, which requires a very large amount of energy. Therefore, it is difficult to realize the existence of rest energy in our daily life, because we rarely feel it directly like kinetic energy or potential energy.
Equivalence of mass and energy
- The theory of relativity showed that the mass m of an object and its energy E are essentially the same thing. This “mass-energy equivalence” can now explain energy production in nuclear reactions and astrophysics.
- Impact on daily life: The principles of nuclear power and nuclear weapons are based on this formula.
For example, at the center of the sun, four hydrogen nuclei (protons) fuse to form a helium nucleus, but in this process, there is a difference in mass (mass defect) before and after the reaction. This mass loss is converted into energy by E=mc2.
Comparison of Electromagnetic Force and Gravity: Differences in Scale
- Electromagnetic force: a force between electric charges that is very strong compared to gravity. Can be observed as easily as lifting a hair by electrostatic force.
- Gravity: Force acting between objects having mass. However, it is very weak. When global masses come together, they finally form an observable gravitational field.
- Gravitational wave: A phenomenon in which the accelerated motion of a mass causes a distortion of the surrounding space-time to propagate at the speed of light. They are caused by fluctuations in an extremely strong gravitational field, such as collisions between black holes, and can be captured by instruments on Earth (such as LIGO).
Field theory: from direct interaction to interaction via fields
In Newtonian mechanics, objects appeared to exert forces “directly” on each other, but Maxwell and Einstein’s theory considers that forces are transmitted through fields.
| Conventional direct interaction model | model based on field theory |
| Objects interact directly with each other | Objects interact through fields |
| Mechanism of force transmission unknown | The field explains the mechanism of force transmission. |
| Cannot explain the remote action of gravity and electromagnetic forces | Remote action can be explained in place |
The field concept was also incorporated into quantum mechanics and a unified framework was established as “quantum field theory. Not only electromagnetic and gravitational fields, but also fundamental particles of matter (electrons and quarks) are described as fields.
If we use the analogy of human relationships, it is like a person’s (material) behavior changes the “environment” of the workplace, home, etc., and the changed environment changes the behavior and personality of other people. For example, like a stressful workplace changes the behavior and performance of the people there.
New Perspectives Brought by the Theory of Relativity
Einstein’s theory revolutionized the framework of physics and gave new perspectives on
- Time and space are not absolutes; they change depending on the observer and the situation.
- Gravity is not just a “force” but a property of space-time itself.
- Energy and mass are essentially the same thing and are deeply involved in the energy cycle of the universe.
These theoretical innovations have been applied to many areas of modern physics, including black holes and the expansion of the universe
