Do physical laws, conservation laws, and other basic rules and laws govern how the world works?

Here is a summary of many of the most important laws, rules, and conservation laws that help us understand how the world works. This list does not include everything but the main ideas behind classical, relativistic, and quantum physics, as well as essential conservation laws and symmetry rules.

1. The basics of mechanics

Newton's Laws of Motion (also called "classical mechanics")

1. The first law of inertia says that unless a net external force acts on a thing, it stays still or moves in a straight line at a constant speed. 
2. The second law (F = ma): The net force acting on an item is equal to its mass times its speed. 
3. Third Law (Action–response): There is an equal and opposite response (force) for every action (force).

The law of universal gravitation by Newton

• All masses are drawn to each other with a gravitational force equal to the sum of their masses and opposite the square of their distance.
• Hamilton's Principle, or the Principle of Least Action,
• A system moves along a path between two states where the action (a certain sum of the Lagrangian) stays still, most of the time at a low level. Both classical and quantum physics are based on this idea.

2. Electrodynamics in the past

• Formulas for Maxwell's: Electric and magnetic fields are made up of charges, currents, and changes in the fields themselves. These are shown in four equations:
• Gauss's Law for Electricity says that electric charges make electric fields.
• Gauss's Law for Magnetism says that magnetic field lines are loops that never end because there are no "magnetic charges" (monopoles).
• Faraday's Law of Induction says an electric field is created when a magnetic field changes.
• According to the Ampère–Maxwell Law, magnetic fields can be made by electric currents and changing electric fields.
• The Lorentz Force Law The force of electromagnetic fields on a charged particle is given by F=q(E+v—B).3. Thermodynamics and the study of statistics

The zeroth law of thermodynamics says

• If two systems are at the same temperature as a third system, they are all at the same temperature.
• The first law of thermodynamics says that energy must be stored.
• The system's internal energy changes when you add heat and remove work.
• It is usually stated as ¥U=Q−W.

1. The second law of thermodynamics: Entropy is the a natural process, the total entropy of a single system can never decrease; it either increases or decreases (the "arrow of time").
2. The third law of thermodynamics says: As a system's temperature approaches zero, the entropy of a perfect crystal gets closer to a steady minimum, which is often taken to be zero.
3. Boltzmann's Analysis of Statistics: It shows how the behaviour of microscopic particles is related to large-scale thermodynamic numbers and how chance affects entropy.

4. What it Means

Unique Relativity (Einstein, 1905)

• It does not matter how fast the source or viewer moves; all inertial observers agree that the speed of light in a vacuum is the same, c.
• Different observers moving at different constant speeds may have different ideas about whether two events happen simultaneously. However, physical rules, especially Maxwell's equations, have the same form in all inertial frames.
• It causes things such as expanding time, shortening length, and achieving the equality of mass and energy (E=mc).

Relativity in General (Einstein, 1915)

• In this case, gravity is not seen as a force but as a result of how mass-energy bends spacetime.
• Predictions are made for gravitational time dilation, lensing, planetary orbit precession, and gravitational waves.
• Newton's law of gravity finds the low-speed, weak-field limit.

5. Quantum mechanics

• Waves and Particles
• Fundamental things, like electrons and photons, can behave similarly to waves and particles, depending on how the experiment is set up.
• The Uncertainty Principle by Heisenberg: You cannot know a particle's exact place and speed simultaneously with perfect accuracy. To be exact, ¥x¦p≥ℏ/2.
• Schrödinger Equation (QM that is not relativistic): The Hamiltonian operator, H^, controls how the wavefunction of a quantum system changes over time.
• Pauli's Principle of Exclusion: Two fermions (like electrons, protons, or neutrons) cannot simultaneously be in the same quantum state. This is based on the structure of atoms and the security of matter.

The theory of quantum fields

The more basic view sees particles as excited versions of existing fields, such as the electromagnetic, electron, and quark fields.

The Standard Model of particle physics is built on this work.

6. The usual way of thinking about particles

• Theories of Gauge
• Local gauge symmetries are what the Standard Model is built on.
• Quantum Electrodynamics (QED) uses the U(1) gauge symmetry to explain how electromagnetic fields interact.
• Electroweak Theory: Brings together weak and electromagnetic interactions (SU(2)×U(1) gauge symmetry).
• The theory of quantum chromodynamics (QCD) talks about strong interactions (SU(3) gauge symmetry).

The Basic Forces and Particles

• Photons, W± bosons, Z bosons, and gluons are gauge bosons.
• Fermions are made up of quarks and leptons and are grouped into three generations.
• It is explained by the Higgs Mechanism that particles gain mass by breaking the electroweak symmetry on their own.

7. Laws of conservation and symmetry

• The Saving of Energy
• You can only change the form of energy; you cannot make it or break it down.
• Linear momentum must be kept constant.
• The total motion stays the same when no outside forces act on a system.
• Angular Momentum Stays the Same
• In a system that is not connected to anything else (no external torques), the total rotational momentum stays the same.

Electric Charge Stays the Same

• A separate system always has the same net electric charge.
• Other conservation rules that are close or exact
• In most Standard Model processes, Baryon Number Conservation stays about the same.
• Neutrino cycles show that Lepton's Number Conservation is also pretty close.
• Quantum Chromodynamics says that colour charges stay the same.

Theorem of Noether

• It links the rules of physics' continuous symmetries and quantities that do not change. As an example:
• Time-travel symmetry: energy stays the same.
• Conservation of momentum and space-translation symmetry.
• Rotation symmetry: angular motion stays the same.

Symmetry in CPT

Quantum field theories say that the exact symmetry of all known fundamental interactions is made up of charge conjugation (C), parity transformation (P), and time reversal (T).

8. Cosmology and organization on a large scale

Principles of Cosmology

• On a large scale, it is homogeneous (the same everywhere) and isotropic (the same in all directions).
• The Hubble Law
• The observed relationship shows that galaxies move far from us at rates equal to their distance, suggesting that the universe is expanding: v=H0 d.

The Big Bang Theory

• The most popular theory about how the world came to be is that it grew from a very dense and hot starting point.
• Alan Guth and others came up with the idea of Cosmic Inflation.
• The fast exponential growth in the early universe can explain some large-scale features, like uniformity and flatness.
• What We Know About Dark Matter and Dark Energy
• Galactic rotation curves, gravitational lensing, and cosmological data all show that most of the matter in the universe is "dark matter," which does not give off light.
• A type of "dark energy" or cosmological constant is thought to be speeding up the spread of the universe.

9. Further Fundamental Principles

• Principle of Equivalence
• According to general relativity, an object's gravity and inertial mass are the same. This means an object's mass has nothing to do with its freefall.
• Principle of Correspondence
• In the large-scale limit (big quantum numbers, big masses, etc.), quantum mechanics has to give way to classical mechanics.
• Anthropic Principle (this one is more academic)
• Because we are inside the universe, we see that its rules are "fine-tuned" for life. When figuring out fundamental constants, we need to consider selection effects.

Unitarity (The Theory of Quantum)

• When a closed quantum system changes, the total probability stays the same (the wavefunction must change in a way that keeps total probability = 1).
• Locality and Cause and Effect
• In light cones, the cause comes before effect because physical events cannot spread faster than the speed of light. Quantum interaction does not send information faster than light that can be used.

Putting Everything Together

1. Modern physics puts together all of these rules to give us the most complete picture of reality:
2. Classical physics and electrodynamics are good ways to explain most large-scale, slow-moving events.
3. Statistical mechanics and thermodynamics explain how systems trade energy and why large-scale irreversibility (entropy increase) occurs when there are many small particles.
4. Special and general relativity help us better understand space, time, and gravity. This is important for places with high speeds and strong gravity, like near black holes and on galactic scales.
5. Quantum mechanics and quantum field theories explain physics at petite sizes. The Standard Model is an excellent explanation of fundamental particles and how they interact with each other (but not gravity at the quantum level).
6. Cosmology, which studies the universe's beginning, development, and organization, combines these ideas on a grand scale.
7. Researchers are still trying to find a more complete explanation, like a consistent quantum theory of gravity that could be reached through string theory, loop quantum gravity, or other methods. However, even without a complete framework, the laws listed above are the basis of what scientists know about the world.