A physics book draft

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1About the book and its approach

1.1The approach of this book?

I am trying to justify physics. I am trying to answer "How do we know (that atoms exist, etc.)?"

I am trying to construct a coherent narrative that will enable me to understand physics. This narrative is not necessarily chronological.

Both theory and experiment are important, and should be balanced.

1.2The order of the contents of this book: The dependency graph of physical concepts?

The contents of this book are ordered ascending by knowability.

It may be beneficial to compare the sequence in this book against the sequence in other books, such as "The Feynman lectures on physics"¹, and "University physics"².

The format "A: B, C, D" means that A depends on B, C, and D, and thus B, C, and D should precede A.

Mass: Weight. Because weight is directly perceptible by people who grow up on Earth.

Electrochemistry: Electrostatics.

Thermionic emission: Two-charge electricity.

Electrodynamics: Electrochemistry, Battery.

Cathode rays: Thermionic emission, Electrodynamics.

Electrons: Thermionic emission.

Atomic theory: Molecules, Electrochemistry. Because electrochemistry is the only known way to isolate many chemical elements.

Electromagnetism: Mechanics. Because understanding electric force and magnetic force obviously requires understanding force.

Electromagnetism: Magnetostatics, electrodynamics.

Energy: Work.

Crystals: Atomic theory.

Davisson–Germer experiment: Crystals.

Quantum mechanics: light polarization, Franck–Hertz experiment, Davisson–Germer experiment.

Electromagnetic waves: Fields.

Black-body radiation: Photoelectric effect. Contrary to history, and contrary to some physics textbooks³, we can use hindsight to avoid Planck's toil?

Relativity: Simultaneity, synchronization.

1.3Rant about the ideal education system?

In lower education, there should not be a math class, a physics class, a chemistry class, and a biology class; there should be only one science class. Students may benefit more from learning those subjects concurrently than from learning them in isolation.

By philosophy, I mean applied philosophy, especially applied epistemology and applied ontology. By "applied", I mean using English words with their everyday meanings, and going only as far as can be tested with the scientific method. We assume that everyday logic holds in the world. We assume that our senses are good enough for some scientific experiments. We interpret the word "to know something" and "to understand something" to mean "to have a useful internal mental model about something".

Here I try to follow Vladimir Arnold's advice in his essay "On teaching mathematics"⁴. Particularly motivating is his comment "Mathematics is the part of physics where experiments are cheap."

How to read the book: Mentally visualize what is evoked by the text. Read a sentence, then visualize that sentence you have just read, and then do the same thing with the next sentence, and so on.

This book should be read strictly sequentially, because understanding later parts requires understanding earlier parts. If you already know a part, you can skim it, or scan it, or glance at it, or read it quickly, just to make sure.

1.4Rant about typical books?

The problem with typical books is that they merely feed us with macronutrients such as information, and not nourish us with micronutrients such as epistemology. Those books are are nutritionally unbalanced. They feed but they don't nourish. They inform but they don't inspire.

(Really?)

Susan Fowler recommended⁵ these books for quantum mechanics: Griffiths's "Introduction to quantum mechanics" [1] and Sakurai's "Modern quantum mechanics" [3]. She recommends these books for quantum field theories: Anthony Zee's "Quantum field theory in a nutshell" [4]. Unfortunately none of them suited my wants; otherwise I would not have written this book.

1.5Rant about ancient philosophers?

(Can we really blame our ancestors for this? We have hindsight; they did not.)

Perhaps the biggest misfortune of the ancient philosophers is that they thought too much and experimented too little. Sometimes they guessed right, but most of the times their guesses were nonsensical or even misleading. If we could go back in time and told them to balance their theorizing and experimentation, perhaps we would have the technology to live forever by the 21st century.

But we should be wary of being too wary, lest we become the polar opposite of those ancient philosophers; we do not want to think too little and experiment too much. A balance is vital. Hypotheses should be testable, and experiments should be insightful. Hypotheses should lead us to the next experiments, and experiments should lead us to the next hypotheses.

But surely people have been experimenting since humans existed?⁶ Also, those ancient people had to invent engineering before they could do the experiments?

The science-engineering cycle: Science enables engineering to build more advanced instruments which enable more advanced experiments which enable more advanced science. After scientists find a new theory, engineers make more advanced instruments. It is getting harder to make more advanced instruments. The scale is exponential. Going from 10 nanometers to 1 nanometer is much harder than going from 10 millimeters to 1 millimeter.

Science began to take off when we began asking Nature directly instead of guessing the answers. Experiment is the language of Nature. To do an experiment is to ask Nature about a piece of truth. Nature tells the same truth to everyone who asks the same question. The only condition is that we speak Nature's language: experiments. Perhaps our lives will take off too, when we realize that we don't know, and we ask people questions instead of guessing the answers.

However, perhaps we have to cut our ancestors some slack. We have the benefit of hindsight.

Indeed, if I am able to write this book only in several years, it is because the toil of our ancestors that we do not repeat. They planted and nurtured the tree of knowledge; I am merely harvesting the fruits. It is only by the theories that I do not ponder and the experiments that I do not perform, that I am able to write this book in less than a few thousand years.

1.6Dividing physics by scale

We can divide physics into several parts, depending on whether the object of study is manipulable by human hands:

• physics of small objects, for objects that are too small for the human hand, such as atoms;
• physics of medium objects, for objects that are about the size of the human hand; and
• physics of large objects, for objects that are too large for the human hand, such as celestial objects.

Basically, the physics of large objects is the part of physics that does not require the theory of atoms in order to be understood.

The physics of medium objects is easy to experiment with and verify, and thus should motivate us to dive deeper into physics. Hence it comes early in this book.

1.7TODO Title of this book: what should it be?

• Physics: How do we know?
• Modern physics from scratch, Quantum physics from scratch, Relativity from scratch
• Learn quantum physics in X hours, Learn relativity in X hours
• Handbook of amateur physicists
• Reasonable physics
• Justifiable physics; Justifying natural knowledge; Physics with justification
• A holistic approach to learning natural science, ordered by knowability; Learning natural science with emphasis on epistemology; An epistemological physics text book
• Understanding physics; Understandable physics; Physics with understanding
• Physics with conviction; Physics with confidence
• (something else?)

2? Mathematical modeling

What is the minimum number of parameters needed to model a physical system? How many parameters are required to capture the aspects we are interested in?

A physical theory is a combination of a mathematical model and a philosophical justification.

"How do we measure something" is an epistemological question.

The marriage between physics and mathematics has been so intimate and fruitful that it is impossible to do any significant physics in the 21st century without mathematics.

3— Part — The physics of medium objects

4Matter, properties, and measurement

4.1Ontology: Classes, instances, and properties

"Water" is a class, a category, a concept, an idea, an abstract object. The liquid thing in my drinking bottle is a concrete object that is an instance of the "water" concept.

We will sometimes conflate a concept and its instances.

Class property and instance property. Example of class property: all water is clear. Example of instance property: this bucket of water weighs 1 kg.

More properties of matter will be discussed in the "Analytical chemistry" section.

4.2Properties: How we know what something is

Pretend that we were our ancestors who did not know much chemistry.

How do we identify something? By its properties. We assume that if two things have the same properties, then they are the same thing.⁷ For example, in 1000 BC, if something looks like water, tastes like water, flows like water, weighs like water, then it probably is really water. What is water? Water is whatever that we define to have the properties of water: clear liquid at room conditions, weighing 1 kg per liter, boiling at 100 deg C at sea level, and so on. We name such thing "water".

First, we define "water" as whatever that is flowing in the nearest river. Then we take some of that water, and experiment to find its properties, such as its color, taste, boiling point, and so on. Then we declare that everything else that has those properties is also water.

4.3Properties of an object: How do we know?

We know a thing's properties through our senses and reasoning.

We don't know all properties of water, but we know some properties to distinguish water from non-water in everyday life.

How do we know that something is water? If it is liquid, and it comes in large amount from the sky or a river, then it is very likely water. But that is just a caveman heuristic, not a scientific test. The real answer was only found in the 18th century. Cavendish 1781 mixed "inflammable air" and "dephlogiscated air" into one container, created an electric spark inside the container with an electrostatic machine, and observed the formation of water.⁸⁹¹⁰ Back then the term "hydrogen" and "oxygen" had not been invented. Terms like "inflammable air" suggest that people back then thought that air everywhere is the same on Earth, and there is a recipe for turning common air into "inflammable air".

Thus, the next question is, "What properties are there?"

The properties of matter may be classified into two kinds: physical properties¹¹ and chemical properties¹², depending on whether the property involves chemical reactions.¹³

Some examples of properties that are simple to observe: color, weight, density, odor, taste, feel, texture, phase (solid or liquid).

Early analytical chemistry relies on appearance and measurements: If it's red and it's found on the ground, we call it "copper".

Analytical chemistry¹⁴ tries to answer "How do we know what something is?" And we answered "By its properties." Thus, analytical chemistry tries to answer the question "What properties are there, especially, what chemical properties are there?"

Static properties: color, phase.

Dynamic properties: reactions with other things. For example, it is a property of salt to dissolve in water. Conversely, it is a property of water to dissolve salt.

One property alone may be insufficient to identify substances. For example, both water and sulfuric acid is a clear liquid. If we rely on color alone, we may accidentally drink the wrong liquid.

4.4Database/record of properties: Where is it?

Where is our cumulative knowledge of matter stored?

It is vital to have a record of things, their properties, and their chemical reactions ("chemical recipes"). Such information was kept in books and libraries. In the 21st century, we have computers.

Wikipedia has some properties for some chemical substances.

Also see:

https://en.wikipedia.org/wiki/Chemical_database

4.5TODO What?

Substance S is something that has color C, density D, phase P at room temperature at sea level, reacts with substance T to produce substance U, and so on. That is, substance S is whatever that has all the supposed properties of substance S.

One way is by density. For example, the density of water is one kilogram per liter, so if there is one liter of liquid that weighs two kilograms, then it may be contaminated water, or not water at all.

How do we know that two similar substances are the same substance? All metals look shiny. How do we tell apart silver from platinum?

A molecule?

"Chemical analysis" or "analytical chemistry"? How do we know what something is, what is in it, what it is made of? By a collection of classical tests¹⁵. But there is some risk of false positive/negative.

More sophisticated tests¹⁶¹⁷?

An observable property is a property that we can perceive with our senses. We will only deal with properties that can be known by experiment.

4.6Properties: Can we know all of them?

To distinguish between two substances, we only have to find one property in which they differ. However, to show that two substances are identical, we have to show that all their properties are the same. But if we cannot know all properties, then we cannot know whether two substances are identical, but we can still hold strong beliefs.

4.7Weight: How do we measure it?

Weight is what a weight scale¹⁸ measures.

One handful of iron is heavier than one handful of water. Thus we say that iron is more dense and more heavy than water. Thus one liter of iron contains more matter than one liter of water does.

4.8Mass: How do we measure it?

The mass of a thing is the amount of matter in that thing.

Tacit assumption: Things are made of a finite amount of matter.

• Water is made of water matter.
• Iron is made of iron matter.
• X is made of X matter, etc.

An object's mass can be measured indirectly by applying a controlled force to it and measuring its acceleration.

4.9Density: How do we measure it?

The average density is inferred by dividing the inferred mass and the measured volume.

• Define: Density is mass per volume.
• Observe: Mass is not weight.
  • Jump around while measuring the weight of something.
  • The weight scale glitches.
• Assume: The mass of \( n \) copies of X is \( n \) times the mass of X.
  • Problems
    • What do we mean by a copy of X? An instance of X?
    • Tacit assumption: Copies of a thing are made of the same kind of matter.
    • Tacit assumption: Things of the same type behave in the same way.
  • Observe: The weight of \( n \) copies of X is \( n \) times the weight of X.
  • Assume: Weight is proportional to mass.
• History of measurement?¹⁹

4.10Volume: How do we measure it?

Volume is amount of space occupied.

• Tacit assumption: Space exists.
• Tacit assumption: Space can be occupied.

Volume is what volume meter measures. Here is one way of measuring volume:

• Submerge the thing completely into a bucket full of water.
• The volume of that thing is the amount of water that spills.

But what if the thing is not solid, or absorbs water, or reacts with water?

5TODO (Replace emphasis from math to epistemology)

5.1Field?

Does a gravitational field have material existence? Is gravitational field physical or mathematical? A gravitational field describes the gravitational force that a unit point mass would experience. Note the counterfactual. The verb describes implies that the subject (a gravitational field) is abstract.

At first I think matter changes spacetime around it, and we call this change "field". But Quantum Field Theory seems to imply that the fields are real, and matter seems to be our limited perception of the fields.

We think that a matter establishes an associated gravitational field.

Einstein's E = mc2 is about that gravity affects both energy and mass.

A Lagrangian tells how a system interchanges potential energy and kinetic energy?

We can use continuum mechanics.

QFT is basically a mathematical model of motion, like Newton's theory, but with fewer simplifying assumptions. Theoretical physics advances by removing simplifying assumptions.

Lagrangian and Hamiltonian are mathematical things. Do they have physical meaning?

5.2Gases?

The gas flows according to the pressure difference.

Imagine a room full of gas. We are interested in modeling the flow of such gas.

We assume that a part of gas can always be split into smaller parts.

Let \( P(x) \) be the pressure at point \(x\).

Defining "pressure at a point" requires rejecting the theory of atoms. It is surprising that a model that violates the theory of atoms is so accurate at describing the motions of things that consist of atoms. Why does this assumption not invalidate the model?

5.3What

https://www.quora.com/What-is-the-most-misunderstood-thing-in-physics

See "You can never actually fall into a black hole."

5.4Statics?

5.4.1What

²⁰

Thermodynamics began as a theory of steam engines.

Volume is how much space something occupies.

Density is weight per volume.

5.4.2Archimedes's principle of buoyancy

²¹²²

Put a solid into a container full of liquid.

The volume of the spilled part of the liquid is equal to the volume of the submerged part of the solid.

Equal are the weight of the object and the buoyant force on the object. (???)

5.4.3Pascal's law of fluid pressure transmission

Blaise Pascal 1647

Pascal's law: Incompressible fluid spreads pressure evenly.

\( P = \rho g h \)

Appreciating Pascal's barrel demonstration:

Counterintuitive: The hydrostatic pressure does not depend on how much fluid. It depends on how deep.²³

5.4.4Zeroth law of thermodynamics: How do we test it?

Put hot iron into cold water. Eventually both become equally warm.

Zeroth law of thermodynamics: Heat never spontaneously flows from cold to hot.

5.4.5Unstructured content

TODO Pendulum

A pendulum is a bob hung on a string.

Conservation of mechanical energy: A released pendulum comes back to the same height.

TODO Interplay between potential and kinetic energy: Galileo's interrupted pendulum

TODO Vacuum

Boyle showed that objects of different masses fall with the same acceleration.

TODO Toricelli manometer

TODO von Guericke, Magdeburg

TODO Boyle

TODO Pascal

Boyle's experiments

TODO Lavoisier's law of conservation of mass

5.4.6Understanding energy

Conservation of energy

Kinetic energy

Kinetic energy is \( \frac{1}{2} m |v|^2 \) which can also be written as \( |p|^2 / (2m) \). This is explained by energy conservation and work by a constant force \(F\) that accelerates an initially resting mass. \(F = ma\) and \(s = \frac{1}{2}at^2\) and \( W = Fs \) and \( v = at \) therefore \( W = E_k = \frac{1}{2} m(at)^2 = \frac{1}{2}mv^2 \).

5.4.7Understanding heat

Heat capacity

Black’s principle: When two liquids are mixed, the heat released by one equals the heat absorbed by the other. ???

??? If \(m_1\) amount of water at temperature \(T_1\) is mixed with \(m_2\) amount of water at temperature \(T_2\), then the result, after equilibrium, is \(m_1+m_2\) amount of water at temperature \(\frac{m_1 T_1 + m_2 T_2}{m_1+m_2}\).

Specific heat

Latent heat

5.4.8Understanding thermodynamic process and cycle?

Isobaric? Isochoric? Adiabatic? Expansion of gas? Work done by a gas?

Carnot engine?

Thermodynamic efficiency?

5.4.9Understanding the laws of thermodynamics

²⁴²⁵

5.4.10Working with simple machines

²⁶

Lever

Wheel and axle

Pulley

Tilted plane

Wedge

Screw

TODO: Modern machine theory: Kinematic chains

5.5Relating velocities, tangent lines, and derivatives

There are several ways of understanding \(f'(x)\) (the derivative of \(f\) at \(x\)):

Average velocity and the secant line

Let there be an object.

Let \(x(t) : V^2\) be a vector that describes its position at time \(t : \Real\).

The average velocity of that object in the time interval \([t,t+\Delta t]\) is \[\frac{x(t+\Delta t) - x(t)}{\Delta t}.\]

If at time \(t_1\) its position is \(x_1\) and at time \(t_2\) its position is \(x_2\), then its average velocity in the time interval between \(t_1\) and \(t_2\) is \((x_2 - x_1) / (t_2 - t_1)\).

A secant line of $f$ is a line that passes \((x_1,f(x_1))\) and \((x_2,f(x_2))\). Think of average velocity.

Instantaneous velocity and the tangent line

If the position of an object at time \(t\) is \(x(t)\), then its instantaneous velocity at time \(t\) is \(v(t) = (d(x))(t)\). The velocity function is the derivative of the position function.

The term instantaneous velocity is often shortened to just velocity.

The unqualified velocity means instantaneous velocity.

A car's speedometer measures its instantaneous speed.

Derivative is about rate of change: how fast a function changes value, how big is the change in output compared to the change in input.

Consider a function \(f : \Real \to \Real\). If the input is \(x\), then the output is \(f(x)\). If you change the input by \(\dd{x}\), the output changes by \(\dd{y}\). Formally, \(f(x+\dd{x}) = f(x)+\dd{y}\).

A tangent line of \(f\) at $x$ is what the secant line converges to if both \(x_1\) and \(x_2\) converge to \(x\). Think of instantaneous velocity.

Understanding the derivative as the slope of the tangent line

The derivative of \(f\) at $x$ is the slope of the tangent line of \(f\) at \(x\). Reminder: The line \(y = mx + c\) has slope \(m\).

5.6Mechanics?

2017-12-18 05:29:06.343592295 +0700

Mechanics is a theory of motion.

Reading: The science of mechanics by Ernst Mach. Historical evolution. The principles of statics. The principles of dynamics.

5.7Mechanical system

A mechanical system is a set of objects \( \{ M_1,\ldots,M_n \} \) and forces \( \{ F_1,\ldots,F_n \} \). Each \(F_k\) is an expression. With Newton's laws, we can turn such mechanical system into \(n\) equations, each of the form \( F_k = m_k \cdot d(d(x_k)) \) for \(k\) from 1 to \(n\).

One way of describing the motion of an object is by modeling time as a real number \( t \), and modeling the position as a function of time \( x : \Real \to \Real^n \). Thus, at time \( t \), the object is at \( x(t) \).

5.8Potential energy

²⁷

Wikipedia "potential energy": Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.

5.9Field as gradient of potential

(This requires multivariate calculus.)

5.10More complex cases?

So far everything has been constant. Now we shall consider the case where they change with time.

Let \(g\) be a vector. For understanding phase space, we will consider the motion of a point mass \(M\) influenced by a uniform gravitational field \( G(x) = g \).

The acceleration will be \( a(t) = g \). The velocity can be obtained by integrating \( a \). The position and acceleration are related by the equation \( a = d(d(x)) \). In Newtonian dynamics, if we know \( x(0) \), \( v(0) \), and all the forces acting on a body, then we can calculate the trajectory (all past and future position and velocity) of that body.

Let \( F(t) \) be the force acting on \(M\) (that is, the sum of all forces acting on \(M\)) at time \(t\). Let \( x(t) \) be the position of \( M \) at time \(t\). Let \( v(t) \) be the velocity of \( M \) at time \(t\). Let \( a(t) \) be the acceleration of \( M \) at time \(t\). Then \( a = d(v) \) and \( v = d(x) \). Let \( p : \Real \to \Real^n \). Let \( p(t) \) be the momentum of \( M \) at time \( t \). Then \( F = d(p) \).

Newton's laws of motion:²⁸

First law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force. Second law: In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: \( F = d \ p \). Let \( p : T \to M \cdot V \). Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Andrew Motte's 1729 English translation of Newton's 1726 third edition of Philosophiae naturalis principia mathematica uses English words and geometry; the modern statement uses algebra.

Newton's law of universal gravitation:²⁹

Force carrier³⁰

³¹

³²

Shell theorem

Newton's laws of motion imply Kepler's laws of planetary motion.

6TODO Light, and its geometry?

6.1How do we know that light travels in a straight line?

From the shape of shadows and reflections.

We know that light travels in a straight line, from comparing the shape of an object and its shadow.

The image in a mirror has the same shape as the original thing, but the left and right are swapped. This is consistent with the hypothesis that light travels at a straight line.

Mirrors reflect light in a similar way that walls reflect rolling balls. The ball is reflected because momentum is conserved?

Let A be a point passed by a light ray some time before it hits the front of a mirror.

Let B be a point where the ray hits the front of the mirror.

Let C be a point where the ray is found some time after it has hit the front of the mirror.

Let D be a point in front of the mirror such that BD is perpendicular to the mirror.

Then the angle ABD (the angle of incidence) is equal to the angle DBC (the angle of reflection).³³³⁴

An observer would not be able to tell any difference between whether a ray of light came from somewhere else and is reflected by the mirror, and whether the ray of light originated from the mirror and is emitted by the mirror itself. We may as well reason that the incident ray of light is first absorbed by the mirror and then the mirror emits another ray of light in a certain direction.

6.2How do we know that a line is straight?

We know that a line is straight, if we cannot shorten the line any further without moving the endpoints.

We can also define "straight" as the way light moves in a free space. We can define that a line is straight if it is possible for light to have a trajectory of such shape in free space.

A line is a one-dimensional thing.

A line connects point P to point Q iff one end of the line is P and the other end of the line is Q.

For short lines, we can see with our eyes whether it is practically straight.

The distance between two points is the length of the shortest line connecting them.

A line connecting two points is straight iff that line is the shortest line connecting those points. When we travel on Earth without ever turning, we think we are traveling in a straight line, but after about 40,000 km we will arrive at where we departed from. Someone far enough in the sky will see that we are traveling in a great circle. If you find it hard to imagine the size of the Earth, just imagine that you were an ant-sized human on a tennis ball.

A geodesic is a straight line?

6.3How do we measure how much light is there?

Darkness is the absence of light.

Daytime is lit. Nighttime is dark. But a cave is always dark, regardless of what time it is outside.

Objects have different brightnesses.

Light can be blocked by matter.

6.4If light is a wave, how do we measure its speed and wavelength?

In 1675, Ole Rømer calculated the speed of light, based on the moons of Jupiter, but its verification requires the alignment of some celestial bodies, which cannot be procured at will.³⁵³⁶

The wavelength can be measured indirectly with a formula that involves the size of the pattern in a diffraction grating.^3738394041

6.5The cavity studied by Planck?

Cavity: opaque box with a small hole. Rays of light enter the box through the hole at various angles. Because the box is enclosed, there is very little chance that a ray of light can enter the box and leave it without hitting any walls. A ray of light entering the box through the hole hits a wall, is reflected, hits another wall, and so on, many times, and is eventually absorbed. If it is probable that a ray is absorbed every time it hits a wall, then it is even more probable that such ray is absorbed when it hits walls many times. Thus the hole appears black from outside.

German "der Hohlraum" is cognate of English "the hole-room"?

6.6Light-matter interaction

Reflect, absorb, diffract.

How do we know whether a thing absorbs light?

Shine some light onto it.

How do we know when an electron absorbs light?

How do we know that light is polarized?

How do we measure the polarization of light? How do we polarize light?

Light-electron interaction?

Light is electromagnetic wave with electric-field component and magnetic-field component.

The electric-field component of light influences a free electron.⁴²

6.7Is light matter?

If light were matter, then shining some light on an object would move the object.

But a ball hitting a wall does not seem to move the wall. Does it mean that the ball is not matter? Or does the wall indeed move, only by a very little distance?

Shining some light on an object does move the object.⁴³⁴⁴ It's just that we require a huge amount of light.

But light does not have the properties of matter: Light does not have a boiling point?

What are the properties of light? "The primary properties of visible light are […]"⁴⁵

6.8Obvious things: fire, light, and heat

• Observe: Fire.
  • WP:Control of fire by early humans
    • Infer: The first human encounter of fire is accidental.
      • Assume: There existed a time when no human had encountered fire.
      • Possible scenarios:
        • Someone encountered a plant burning due to lightning or volcanism.
        • Someone focused sunlight onto leaf using natural glass, out of pure curiosity.
          • Not implausible, but isn't this less likely than accidental discovery of fire due to lightning or volcanism?
    • Quora: How did humanity find out how to make fire?
    • acsh.org: How And When Did Humans Discover Fire?
    • sapiens.org: Who Started the First Fire?
    • WP:Fire making
      • "Fire occurs naturally as a result of volcanic activity, meteorites, and lightning strikes."
        • WP:Wildfire
• Define: To burn something is to put it in fire.
• Define: Something is burning if it is exhibiting fire.
• Define: Flame.
• What is the difference between WP:Flame and WP:Fire?
• Define: Heat
  • Heat is what we feel with our skin near a fire.
  • We feel more heat as we approach a fire.
• Define: Light.
• Define: Shadow.
• Infer: Light travels in straight line.
  • Observe: The shape of the shadow.
  • Observe: two fires, two shadows.
    • Stand between two fires.
    • Observe: two shadows of you.
  • Observe: Light can be blocked. (Experiment using two hands and a fire.)
• Infer: Heat behaves like light.
  • Observe: Heat can be blocked. (Experiment using two hands and a fire.)
• Observe: Water boils and evaporates when heated.

7TODO Oscillations, waves, and differential equations

7.1Oscillations

An oscillation can be modeled by a periodic function such as \( f(t) = f(t+p) \) where \( p \) is the period.

An ideal oscillation exactly repeats after one period.

Here are some examples of simple oscillation. A spring will oscillate if it is suddenly released after being pulled a little from its resting position. A pendulum will oscillate if it is suddenly released after being pulled from its resting position.

What does "moving energy" mean? Earlier we said that energy is a mathematical concept and not a physical reality.

The oscillation of a spring can be modeled by a differential equation. We assume that the restoring force is \( F(x) = - k x \). Then, force is the rate of change of momentum, then substitute… (TODO)

7.2Waves

Imagine that we are holding an end of a taut rope whose other end is tied to a pole. We write \( h(x,t) \) to mean the amplitude (the vertical displacement) of the point at the rope at horizontal distance \(x\) from our hand at time \(t\). Thus \( h(0,t) \) is the vertical displacement of our hands at time \(t\). We assume that the wave propagates at constant velocity \(v\). Thus, after a duration \(dt\) has elapsed, the wavefront at \(x\) at time \(t\) has moved to \(x + v \cdot dt\): We write this \( h(x + v \cdot dt, t + dt) = h(x, t) \), which can be rearranged to \( h(x, t) = h(0, t - x / v) \). If we want to easily know how the rest of the rope behaves given our hand motion, we can rearrange the equation to \( h(x, t + x / v) = h(0, t) \). The amplitudes are simply the "echoes" of our hand motion. Each point moves imitating our hand motion, but that point's motion is delayed proportionally to its distance from our hand.

When we throw a stone into a pool of water, the disturbance travels as an expanding circle. This implies that the disturbance propagates equally in all directions. We say that water is an isotropic medium.

7.3What is a wave, oscillation, undulation, vibration?

One wave happens every time water slaps the beach. Thus waves are countable.

We see ripples when we throw a stone into a body of water. Ripples are waves?

We see oscillation when we disturb a spring (the spiral thing, not the water source).

A wave is a pattern of motion. A wave does not exist objectively. We see waves. We use the word "wave" to refer to some repetitive motions.

"Wave moves energy without moving matter"⁴⁶ But matter is congealed energy⁴⁷? But energy is only a mathematical artifact, an unreal quantity.

7.4What causes a wave?

A wave is caused by a restoring force⁴⁸, a force that goes against a thing's displacement. This force tends to restore a thing to its resting position.

Wave happens because the propagation medium has inertia that laggedly opposes the forces acting on it.

A wave is a propagating oscillation, a contagious oscillation?

Must a wave always be caused by a restoring force? Must a restoring force exist wherever we see a wave?

What do we mean by "force"? Do we mean Newtonian "force", or do we mean "cause"?

https://philosophy.stackexchange.com/questions/25003/what-is-the-philosophical-origin-of-waves

http://www.informationphilosopher.com/introduction/physics/wave-particle_duality.html

7.5What is the difference between these: wave, undulation, oscillation, resonance?

7.6Sine waves

A sine wave is the motion of an ideal spring that is oscillating naturally after released from an initial strain.

A sine wave is approximated by a pendulum with long rope and small swing angle.

A sine function is a function such that its displacement and its acceleration have equal magnitudes but opposite directions.

A sine function \(x\) is a solution of \( d(d(x)) = -x \).

7.7Dropping a pebble into a pond

Imagine looking down on a pond from bird's-eye view, and gently dropping a pebble into the pond.

The pebble displaces a volume of water around it. The displaced volume of water displaces other nearby volumes of water, and so on.

7.8Diffraction

Outsource to Wikipedia⁴⁹⁵⁰?

It seems that justifing the Huygens–Fresnel principle⁵¹ requires fluid dynamics.

Single-slit diffraction

Calculate the pattern spacing depending on propagation medium characteristics, slit size, slit spacing, and the distance between slit and screen.

Kirchhoff's diffraction formula⁵²?

Young's double-slit experiment

7.9Wavefront, reflection, and diffraction

A point disturbance such as a pebble dropped into the pond causes an expanding circle wavefront on the surface. This speed in which this circle expands is the speed of the propagation of disturbances in water.

An obstacle reflects the sector of the wavefront that hits it.

8— Part — The bridge between medium and small

Electrochemistry, statistical physics (mechanics, thermodynamics)?

In this part, we try to justify the existence of small objects.

9Gaining knowledge of small things by indirect observations and inferences

9.1Mindsets

The physics of small objects is not intuitive. Everything is inferred indirectly. It requires a lot of abductive reasoning.

We can only manipulate medium-sized objects, due to the limitation of our senses. Everything else, we can only infer, indirectly, by transduction through experimental apparatuses into something of medium size.

9.2Reasoning with deduction, induction, and abduction

Deduction is the use of syllogism?

Induction is generalization from examples. The difficulty is in finding examples diverse enough to represent most possibilities. Example: We saw that there are ten white swans. Thus we infer that all swans are white. (Then we find a black swan.)

Abduction is finding the best explanation for a surprising evidence. Example: We observe that the road is wet everywhere. We abduce the hypothetical explanation that it may have rained a few hours ago. Another example: We cannot find the scissors at home; they are not at the usual location. We abduce that it must be due to our siblings.

We cannot live without deduction, but we cannot live with only deduction either.

Reddit has a summary⁵³ of deduction and induction.

9.3Sensor galore, sensor design mindset, transduction/apparatus mindset

Voltage is measured with volt-meter, amperage is measured with ampere-meter, ohmage is measured with ohm-meter, pressure is measured with pressure-meter, temperature is measured with temperature-meter, X is measured with X-meter, and so on.

How do we know X => How do we detect X => How do we measure X => How do we design an apparatus for measuring X?

How do we translate a microscopic phenomenon into something macroscopic that we can perceive directly with our senses.

For example: electroscope => electrometer.

For example:

• How do we detect electric current? By observing the corrosion of the metal electrodes of an electrochemical cell.
• How do we measure electric current? By measuring the rate of the corrosion above.

How do we measure the magnitude of X?

How do we measure the direction of X?

9.4Calculus, scale invariance, and naïve abstract miniaturization

By using calculus, we assume that a thing can always be scaled down into an ever-smaller version of it that behaves exactly the same, only smaller.

We often assume scale invariance⁵⁴.

How can an assumption so wrong produce a model so right?

9.5Reductionism and emergent behavior

Reductionism: The macroscopic properties of matter emerge from the microscopic properties. Every macroscopic phenomenon can be explained in terms of what is happening microscopically.

10Electricity

10.1Electricity: What is it?

"[C]ertain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers"⁵⁵

We say that such rubbed amber exhibits electricity.

Thus electricity is the interaction of electric charges.

However, these things might be easier to find in a 21st-century city:

• Glass (instead of amber).
• Silk or wool (instead of cat fur).
• Pieces of paper (instead of feather).

If two things attract each other after they are rubbed against each other, then they exhibit electricity?

Triboelectricity: charging by friction.

How do we measure how much charged an object is? "The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer."⁵⁶ By measuring the deflection of the leaf of an electroscope⁵⁷, by exploiting electrostatic induction. A problem is that touching the electrometer discharges the object.

We assume that charge is a property of matter.

To charge a thing is to make it exhibit electricity.

10.2Electric charges

10.2.1Two kinds of charges: How do we know?

Two kinds of charges, vitreous (Latinate English for "glassy") and resinous (a resin is a solid secreted by an injured tree⁵⁸⁵⁹). Those terms go back to Charles du Fay's discoveries⁶⁰ in 1733⁶¹. Two similarly charged things repel each other. Two differently charged things attract each other.

Positive charge is defined as the charge left on glass after being rubbed with silk. "It is arbitrary which polarity is called positive and which is called negative."⁶²

10.2.2Charging: How do we do it?

• Rubbing
  • Triboelectric effect and triboelectric series⁶³
  • frictional machines, Otto von Guericke, 1663⁶⁴
• Influencing
  • Electrostatic induction⁶⁵
  • Let A be a charged thing.
  • Let B be an uncharged thing.
  • Putting A near B charges B.
  • Putting A away from B uncharges B.
• Touching
  • Let A be a charged thing.
  • Let B be an uncharged thing.
  • If A and B touch, then B becomes charged.
  • If A and B are separated after touching, then B is still charged.
  • Assume: This doesn't work if B is a metal?
  • Observe: Two things equalizes their electric charge when they touch?
• Conduction
  • Let A be a charged thing.
  • Let B be an uncharged thing.
  • Let C be a piece of iron.
  • Let C touch both A and B, but without A touching B directly.
  • Remove C.
  • Verify that B is now charged.
  • Assume: This still holds if the iron in C is replaced with any other metal.
  • Define: Iron is a conductor.
  • Assume: Every metal is a conductor.
  • Define: Everything is either a conductor or an isolator.
  • Assume: An isolator is a thing that can be charged by rubbing.
• Observe:
  • Rub glass G with silk S.
  • Rub glass H with silk T.
  • The glasses repel each other (G-H).
  • The silks repel each other (S-T).
  • A glass and a silk attract each other (G-S, G-T, H-S, H-T).
  • Define: A rubbed glass is vitreously charged.
    • "Vitreous" is a Latinate word that means "glassy".
    • Wiktionary:vitreous
      • 1733, WP:Charles François de Cisternay du Fay
  • Define: A thing is resinously charged iff it is charged but not vitreously.
  • Phys. SE 266246: How did physicists know that there are two kind of charges?
• Superseded theories
  • WP:Fluid theory of electricity

10.2.3Electric potential: How do we measure it?

• Assume: An electrometer measures the strength of electricity exhibited by a thing.
  • Assume: The strength of electricity exhibited by a rubbed amber can be measured by the amount of paper it can pull.
  • WP:Electrometer
  • How do we know whether a thing is charged, if we don't care about the exact amount of charge?
    • WP:Electroscope
      • WP:Versorium
• What?
  • Coulomb's torsion balance
    • WP:Coulomb's law
      • \( F = k \cdot q_1 \cdot q_2 / r^2 \)

10.2.4Metal?

• Observe: Rubbing a piece of iron doesn't charge it?
• Observe: Electric charge can be stored.
• Observe: Electric charge can be unloaded.
• Phys. SE 23572: How does an object regains its neutrality after being charged by rubbing?

• todo:
  • Conductors and isolators
  • Infer: Metal and electricity
    • Observe: Iron doesn't exhibit electricity after being rubbed.
    • Observe: Iron exhibits electricity by influence.
  • WP:Electrical conductor
    • https://www.quora.com/Why-do-conductors-not-produce-static-electricity
    • https://www.scientificamerican.com/article/static-science-how-well-do-different-materials-make-static-electricity/
    • https://www.reddit.com/r/askscience/comments/2ujpw8/why_does_metal_eg_a_metal_slide_not_produce_static/
  • Capacitor
  • WP:Leyden jar

10.2.5Storage of charges: How do we know?

How do we know that charges can be stored? By connecting von Guericke's friction machine⁶⁶ to Leyden jars⁶⁷, and then discharging the jars.

How do we know that an electric catfish is electric? By connecting it to Leyden jars, and then discharging the jars.

How do we know that lightning is electric discharge? By connecting it to Leyden jars, and then discharging the jars.

How do we know that there is an electrical discharge? By observing an electrical spark.

Lots of people were shocked in the process of understanding electricity.⁶⁸

10.2.6Charges: How do we measure them?

How do we know how much charge is in an object? Coulomb's torsion balance experiment. Inverse-square law.

10.2.7Electrical potential: How do we measure it?

By the deflection of the leaf of an electrometer, provided that the deflection is small.

10.2.8Lightning rod: How to avoid being shocked at office

That cold-dry-air electric zap when touching certain metallic surfaces at the office.

Simple solution: Hold the metal part of a key with your bare hand, and touch the key to the zappy office metal object, but don't touch the zappy object with your hands directly.

It is also how a lightning rod works. The pointed metal end bleeds the charge? What does it mean? See also the video⁶⁹.⁷⁰

10.2.9How do pointed edges (like nails) bleed electric charges?

10.3Electric currents

10.3.1Currents: How do we know?

What is electric current?

Electric current is whatever that comes into being when we connect the terminals of a Voltaic pile.

We know that there is an electric current if we see that the metal electrodes are corroding.

Electric current is the flow of electric fluid?

How do we know that an electric current is a flow of electric charge?

How do we know that the Voltaic pile drives electricity flow in the wire connected to its ends?

Before the electron was discovered, electricity was thought of as a fluid.⁷¹

"Current causes several observable effects, which historically were the means of recognising its presence."⁷²

• electrolysis of water

Current measurement: galvanometer vs ammeter: What?⁷³⁷⁴⁷⁵

How do we know the magnitude of the current?

By the rate of corrosion of the electrodes of an electrochemical cell. For example, in a zinc-copper cell.

Detour: Justification of electric current requires chemistry:

• http://www.need.org/Files/curriculum/infobook/Elec3I.pdf
• http://practicalphysics.org/electric-charge-and-current-short-history.html
• https://en.wikipedia.org/wiki/Electric_current

10.3.2How was the battery invented before the concept of currents was invented?

From an article⁷⁶ and another article⁷⁷.

Galvani, Volta, animal limbs, and metals.

Volta found that using two different kinds of metals twitches the frog legs more than using only one kind of metal.

They would not have known; electrochemistry was not yet known. Galvani experimented with frog legs in 1791, and died in 1798. Galvanometers did not exist before 1820.⁷⁸⁷⁹

Volta discovered bimetal⁸⁰ electricity, Volta invented the Voltaic pile for bioelectricity, not for electrochemistry. Moreover, Volta's idea of current was the obsolete "contact tension" theory.

"1778 – Volta discovered that the electrical potential (we now often call this the voltage) in a capacitor is directly proportional to electrical charge."⁸¹

From Italian Wikipedia⁸²:

• Nel 1778 nella lettera a de Saussure Sulla capacità dei conduttori elettrici ("On the capacity of electrical conductors") […]
• Nel 1780 inventa il "condensatore di elettricità", apparecchio che serve a ricevere, accumulare, condensare in sé e rendere visibile anche le più deboli quantità di elettricità.

Volta's condenser electrometer⁸³⁸⁴⁸⁵ is an apparatus for measuring electric charges too weak for straw electrometers⁸⁶ to measure.

In the study of "animal electricity", many frogs were harmed.⁸⁷ But finally "Alessandro Volta showed that the frog was not necessary. […] Earlier Volta had established the law of capacitance […] with force-based detectors"⁸⁸ How? What is the details? This "force-based detector" is probably Volta's condenser electrometer.

How did Volta measure current? He did not? He measured potentials?

In Volta's time, the concept of electric current had not yet been invented, let alone the apparatus to measure such current.⁸⁹

"Volta did not set out to invent the battery. His experiments in this area were actually performed to show the claims of [Luigi Galvani] were wrong."⁹⁰

Volta tried various pairs of metals, and arranged his results into the electrochemical series, for the metals known in his time.

How do we know that something is electrified, besides by touching it and shocking ourselves?

"If the column contains about twenty of these couples of metal, it will be capable of giving to the fingers several small shocks."⁹¹ Is about 30 volts DC high enough to be felt by a human?

"The battery Volta invented gave chemists a very powerful new method to study substances."⁹²

"In 1802, Humphry Davy had what was then, the most powerful electrical battery in the world at the Royal Institution."⁹³

11Electricity and magnetism

11.1Magnetism: What is it?

It has been known for a long time that two pieces of lodestone attract or repel each other. This phenomenon was then named magnetism.

• Define: WP:Lodestone.
• Define: A magnet is a piece of lodestone.
• Magnetism
  • Observe: Two magnets attract or repel each other.
  • Observe: A magnet and a piece of iron attract each other.
  • …
  • todo: Magnetic pole
  • Infer: The Earth is a magnet.
    • Observe: Every resting magnetic needle near you points to the same direction (except if you're at the Earth's magnetic poles).
    • Observe: The Earth has magnetic poles.
      • WP:North Magnetic Pole, expeditions
      • WP:South Magnetic Pole, expeditions
      • Observe: They are moving.
        • WP:Polar drift
  • WP:Magnetism, history
  • WP:De Magnete (1600)

11.2Ferromagnetism: Distinguishing between electricity and magnetism

How do we distinguish between electricity and magnetism?

By the following experiment, which goes back to 1600, in Gilbert's "De Magnete" Book 2.⁹⁴

Four things are required:

• a piece of amber rubbed to charge it,
• a piece of magnetic lodestone,
• a piece of metal, and
• and a piece of paper.

Then, we observe that the rubbed amber attracts both metal and paper, but the lodestone attracts only metal and does not attract paper.

"[T]he English scientist William Gilbert wrote De Magnete, in which he made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber."⁹⁵

William Gilbert (1544–1603) distinguished the lodestone effect (magnetism) from the amber effect (electricity).⁹⁶

"Electric" means "like amber⁹⁷".

11.3TODO Deflection of magnetic needles by electric current

Electrical current in a wire deflects nearby magnetic needles.⁹⁸

12Light, and electromagnetic waves

12.1How do we know that light is electromagnetic wave?

They have the same speed, but is that sufficient to convince a skeptic?

We know that light behaves like an electromagnetic wave, from the speed of light, and the wave behavior of light. But that's all; how do we know that it is it?

12.2How do we split a beam of light?

How does a beam splitter work?

13TODO Extract from chemistry text books

https://openstax.org/details/books/chemistry-2e

14Elements

14.1Substances, mixtures, and elements: How do we know?

What is a mixture? How do we know that something is a mixture?

• If we have just created the mixture ourselves, then we know that it is a mixture.
• If something has the same properties as a mixture we created earlier, then it is a mixture.
• If a thing can be separated into several things with different chemical properties, then it is a mixture.

Each constituent of a mixture has a unique set of properties.

The properties of a mixture may greatly differ from the properties of its constituents.

If we mix sand and salt, the result is a mixture of sand and salt. If we shake the mixture, the result is still a mixture of sand and salt.

What are the properties of a mixture?

What is the relationship between a mixture and its constituents?

The mass of a mixture is the sum of the mass of its constituents: The result of mixing 1 kg salt and 2 kg water is 3 kg mixture of salt water.

Mixing is easier than separation. It is easier to mix things into a mixture than to separate a mixture into its constituents.

An element is a thing that is not a mixture.

How do we know that something is an element?

If we cannot separate a substance into several constituents, how do we know whether we have reached a limit of Nature or we have merely reached a limit of our instruments?

How do we know that a thing consists of exactly one kind of chemical element?

We know that something is an element by being unable to separate the thing into several constituents with different properties.

14.2How did the concept of "chemical element" evolve?

• WP:Chemical element, history
  • 1661, Robert Boyle, "corpuscularism"
    • WP:Corpuscularianism
      • WP:Chemical revolution
  • https://www.sciencehistory.org/historical-profile/robert-boyle
    • "In his experiments Boyle made many important observations, including that of the weight gain by metals when they are heated to become calxes."
      • Calcination, calx, phlogiston, oxygen
        • WP:Calx "is a substance formed from an ore or mineral that has been heated."
        • [WP:Calcination] is "heating to high temperatures in air or oxygen" (IUPAC).
        • Wiktionary:calx
          • "(archaic) The substance which remains after a metal or mineral has been thoroughly burnt, seen as being the essential substance left after the expulsion of phlogiston."
        • Observe: Burning copper in air produces copper calx (copper oxide).
        • http://chemed.chem.purdue.edu/demos/main_pages/9.9.html
        • WP:Phlogiston theory
          • 1667
          • "[…] from the Ancient Greek φλογιστόν phlogistón (burning up), from φλόξ phlóx (flame)"
          • How was it superseded?
            • Invalidated by experiment:
              • "some metals gained mass when they burned, even though they were supposed to have lost phlogiston."
            • Replaced by Lavoisier's oxygen theory in the 1780s
              • "[…] combustion requires a gas that has mass (oxygen) and could be measured by means of weighing closed vessels."

14.3How were the first known elements isolated/produced/extracted/purified?

15TODO Gases

15.1How do we know that gases expand to fill their containers?

By manipulating a colored gas such as nitrogen dioxide in a transparent container with a piston, or in a gas syringe, such as in this video⁹⁹.

There are some colored gases¹⁰⁰, but all of those examples are hazardous gases.

15.2How do measure how much gas is in a container?

The same way we measure everything else: We weigh the empty container, then we fill the container, then we weigh the filled container, and then the difference is the weight of the content, assuming that the content does not react with the container.

15.3Gay–Lussac's observation of the relative volumes of gas-only reactions?

Avogadro 1811 http://ricerca.mat.uniroma3.it/ipparco/pagine/deposito/archivio/avogadro.pdf

M. Gay-Lussac has shown in an interesting Memoir (M´emoires de la Soci´et´e d’Arcueil, Tome II.) that gases always unite in a very simple proportion by volume, and that when the result of the union is a gas, its volume also is very simply related to those of its components. […]

15.4Pressure: How do we measure it?

By barometers?

15.5Vessel?

• Require: closed vessel
  • Which "vessel" is meant?
    • "Vessel" might mean "bowl". (WP:Vessel, Wiktionary:vessel)
    • WP:Pressure vessel, history (1495, Leonardo da Vinci, or earlier)

15.6Ideal gases: What are the assumptions?

How do we know that \( P \cdot V = n \cdot R \cdot T \)?¹⁰¹

• "as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law." (Clapeyron 1834)
• "It can also be derived from the microscopic kinetic theory" (Kronig 1856 & Clausius 1857)

If we press the piston, the gas shrink. We know that the gas pressure increases, because the more we press it, the more it resists our press.

There are two options for verifying Boyle's law:

• One can manipulate the pressure, and measure the volume.
• One can manipulate the volume, and measure the pressure.

Manipulate the pressure, and measure the volume. A 1 kg piston, a container, a gas, and some 1-kg weights. Put one 1-kg weight on the piston, record the gas's volume. Put two 1-kg weights on the piston, record the gas's volume.

Manipulate the volume, and measure the pressure. See video¹⁰².

Let there be a container of gas with pressure \(P_1\) and volume \(V_1\). Let this gas expand or shrink without changing its temperature so that its pressure becomes \(P_2\) and its volume becomes \(V_2\). Then, Boyle's law: \( P_1 V_1 = P_2 V_2 \).

Other gas laws?^103104105 Charles's law? Dalton's law?¹⁰⁶

Kinetic energy of one mole of gas is \( \frac{3}{2} RT \)?

Statistical thermodynamics: kinetic theory of gases?

15.7Kinetic theory of gases?

"in which several simplifying assumptions are made, chief among which are that the molecules, or atoms, of the gas are point masses, possessing mass but no significant volume, and undergo only elastic collisions with each other and the sides of the container in which both linear momentum and kinetic energy are conserved."¹⁰⁷ How do we test it?

15.8Acids

How did people know? Did they taste it? Did they really put sulfuric acid, albeit dilute, in their mouth?

15.9Hydrogen gas

<2019-07-15> https://en.wikipedia.org/wiki/Hydrogen#History

In 1671, Robert Boyle discovered and described the reaction between iron filings and dilute acids, which results in the production of hydrogen gas.[63][64] In 1766, Henry Cavendish was the first to recognize hydrogen gas as a discrete substance, by naming the gas from a metal-acid reaction "inflammable air". He speculated that "inflammable air" was in fact identical to the hypothetical substance called "phlogiston"[65][66] and further finding in 1781 that the gas produces water when burned. He is usually given credit for the discovery of hydrogen as an element.[4][5] In 1783, Antoine Lavoisier gave the element the name hydrogen (from the Greek ὑδρο- hydro meaning "water" and -γενής genes meaning "creator")[6] when he and Laplace reproduced Cavendish's finding that water is produced when hydrogen is burned.[5]

"Hydrogen" was coined to mean "inflammable air" (Lavoisier 1783).

15.10Diatomic molecules?

How do we know that hydrogen gas is diatomic, helium gas is monatomic, etc.?

The bridge: Mole Avogadro 1 faraday How do we know how many protons in an atom?

Dalton assumed that all elements were monatomic, that is, that water was HO, not H2O.¹⁰⁸

Water is two part hydrogen and one part oxygen (Gay-Lussac & von Humboldt, 1805).

15.11Avogadro's law: How do we know?

How do we know how many gas molecules are in a gas container?

<2019-07-15> https://en.wikipedia.org/wiki/Johann_Josef_Loschmidt

[Loschmidt's] method allowed the size of any gas molecules to be related to measurable phenomena, and hence to determine how many molecules are present in a given volume of gas. This latter quantity is now known as the Loschmidt constant in his honour, and its modern value is 2.69×1019 molecules per cubic centimetre at standard temperature and pressure (STP).[7]

"[U]nder the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules." "The law is approximately valid for real gases at sufficiently low pressures and high temperatures."¹⁰⁹

How did Avogadro get his law? "The derivation of Avogadro's law follows directly from the ideal gas law […]"¹¹⁰

How did Avogadro get his number? What does it mean?

How do we know that 1 mole of any gas = 22.4 liters at STP? Does it really hold for all gases at STP?

https://www.scientificamerican.com/article/how-was-avogadros-number/

15.12Gases?

¹¹¹¹¹²

A gas is …

Pressure is measured by a manometer.

In statics, the volume of a gas is the volume of its container. Statics assumes that a gas fills its container evenly.

Temperature is measured by a thermometer. The unit of temperature is kelvin (K).

% ? Gas and piston at equilibrium: Gas and a piston with weight \(F\).

15.13Boltzmann's constant?

¹¹³ Boltzmann’s constant relates the average kinetic energy of particles in a gas and the temperature of the gas?

¹¹⁴ The gas constant (molar gas constant, universal gas constant, ideal gas constant)?

15.14Entropy: How do we measure it?

16TODO Mineralogy and metallurgy

16.1Minerals: How are they distributed on Earth?

• Mineral distribution hypothesis?
  • Assume:
    • The Earth was once a hot liquid.
    • The surface cooled down and solidified.
  • Infer:
    • Denser minerals should sink towards the core of Earth.
    • As we dig deeper, the Earth should be more dense.
• Where do minerals come from?
  • "Minerals are concentrated by igneous, sedimentary and metamorphic processes"
  • WP:Structure of the Earth

16.2Metals: How do we know?

A guess, as in Spongebob Squarepants season 3 episode 54 ("Ugh")^115116117: It is plausible that, some time after the first humans (or perhaps hominids) discovered fire, they curiously tried to burn everything, and one of those things is a mineral found in a cave or somewhere on the surface of Earth.

What are metals? Here are some of their properties. They shine under sunlight. They heat up easily when exposed to sunlight or fire. They don't burn, unlike dry leaf or wood that burn.

The first metal worked by humans is probably copper, probably since around 9000 BC¹¹⁸¹¹⁹, because copper is found on the surface of the Earth.¹²⁰¹²¹

Why is copper readily found on the surface of the Earth?

Copper-Stone Age comes before Bronze Age.¹²²

Iron?^{123124125126127}

Bronze is an alloy¹²⁸ of 88% copper and 12% tin.¹²⁹

16.3Metals: How do we extract them from Earth?

A rock is a hard thing.

To mine is to extract mineral.

An ore is a rock that contains metal.¹³⁰ For example, an iron ore is a rock that contains iron, and a copper ore is a rock that contains copper.

Ore is synonym for mineral ("from Latin 'minera' ('ore')"¹³¹).

"A mineral is a naturally occurring chemical compound"¹³²

Mineralogy?¹³³¹³⁴

To smelt is to extract metal from ore. Burning an ore produces metal?

"The first metal to be smelted in the ancient Middle East was probably copper (by 5000 BCE), followed by tin, lead, and silver."¹³⁵

The heat source used for smelting was charcoal, which is made by heating wood without air.¹³⁶

What is the difference between charcoal, ash¹³⁷, and soot¹³⁸?

16.4Hard vs tough

<2019-07-16> https://en.wikipedia.org/wiki/Metallurgy#Heat_treatment

There is a balance between hardness and toughness in any steel; the harder the steel, the less tough or impact-resistant it is, and the more impact-resistant it is, the less hard it is. Tempering relieves stresses in the metal that were caused by the hardening process; tempering makes the metal less hard while making it better able to sustain impacts without breaking.

17Analytical chemistry in the era of Voltaic piles

17.1Chemical analysis is like "twenty questions"

An analyte¹³⁹ is what is being analyzed.

Chemical analysis is like "twenty questions"¹⁴⁰.

1. Is it solid at room temperature?
2. Does it dissolve in water?
3. Does it react with sulfuric acid?
4. Does it react with nitric acid?
5. (and so on)

I'm sure there is already an expert system for this.

Natural science is like playing "twenty questions"¹⁴¹ with Nature.

Atom-themed twenty questions is trivial, because we can just binary-search the answer like this:

1. Does its nucleus have less than 64 protons?
2. Does its nucleus have less than 32 protons?
3. Does its nucleus have less than 48 protons?
4. Does its nucleus have less than 56 protons?
5. (and so on)

17.2Reactions: How we know they happen

What is a chemical reaction?

There is a reaction between two solids. See video¹⁴².

17.3Anodes, cathodes, anions, cations

"An anode is an electrode through which the conventional current enters into a polarized electrical device. This contrasts with a cathode, an electrode through which conventional current leaves an electrical device."¹⁴³

Origin: 1834 Whewell and Faraday?¹⁴⁴

The syllables are an-ions and cat-ions.

17.4Electrolysis of water

Electrolysis of water produces two kinds of gases in 2:1 proportion of mass. (What year?)

People did not know the exact number of atoms, but they know the proportion of mass.

Two parts hydrogen, one part oyxgen.

1789 Deiman & van Troostwijk, electrostatic machine; 1800 Nicholson & Carlisle, with Voltaic pile;¹⁴⁵

18Electrons

18.1Electrons: How do we know they exist?

Crookes tube?¹⁴⁶

18.2Electrons: How do we know they exist?

By the electric field they cause?

How do we know in a thermionic emission, it is indeed electrons that are emitted?

Thomson's cathode ray experiment?¹⁴⁷¹⁴⁸

Requirements:

• battery, electrochemistry, for high voltage
• Daltonian atomic theory (How did they know that hydrogen is the lightest atom?)
• vacuum pump
• thermionic emission

How do we know the charge of an electron? Millikan's oil drop experiment?

How do we know that electricity is due to electrons?

18.3Thermionic emission: Hot objects leak negative charges

How did people think of thermionic emission before they invented the concept of electrons?

We infer thermionic emission, because negatively-charged metals lose their charges when heated to red-hot: A negatively-charged red-hot iron sphere leaks its negative charge (into the surrounding air), but such sphere does not leak charges if it is positively charged.¹⁴⁹¹⁵⁰ Thus only negative charges leak out of heated objects, and positive charges do not.

18.4Electric fields: How do we measure them?

We cannot? We can only measure the voltage difference between two points?

18.5Digression: Can we get a positively-charged metal by cooling after thermionic emission?

We heat a metal, so that it emits electrons.

We keep it hot, until it emits no more electrons.

Then we cool it down. My hypothesis is that the cool metal should now be positively charged.

19TODO Spectroscopy, atomic electron transitions, atomic emission spectrums?

Where does this fit in the narrative?

TODO Extract history

https://en.wikipedia.org/wiki/History_of_spectroscopy

https://www.chemteam.info/Electrons/Spectrum-History.html

http://galileo.phys.virginia.edu/classes/252/spectra.html

https://en.wikipedia.org/wiki/Spectral_line

https://en.wikipedia.org/wiki/Atomic_electron_transition

https://en.wikipedia.org/wiki/Excited_state

https://en.wikipedia.org/wiki/Fluorescence

https://en.wikipedia.org/wiki/Phosphorescence

20TODO Photons

20.1TODO Photoelectric effect

20.2TODO Photovoltaic?

20.3TODO How do we detect a single photon?

• https://physics.stackexchange.com/questions/102313/how-does-one-detect-a-single-photon
• https://perg.phys.ksu.edu/vqmorig/tutorials/online/wave_part/Single%20Photons.html

21TODO Existence of small objects

21.1? Particles and waves

How do we know whether something is a particle or a wave?

What is a particle?

What is a wave?

Photons and electrons are neither particle nor wave. It is a categorical impossibility, a logical contradiction, for something to be both particle and wave.

21.1.1What do we mean by "light is a wave"?

If we say "light is a wave", then we are saying that light has no objective (material) existence. Also, what is the restoring force of this wave?

The sea has waves, but the sea is not the waves.

If we say "light behaves like a wave", then, what does it mean for an objective thing to behave like a subjective thing?

The people who thought about the luminiferous aether¹⁵¹ must have thought about this.

If the aether does not exist, then light is not a wave.

Light is electromagnetic radiation. A disturbance in the electromagnetic field?

We must distinguish between physical wave and mathematical wave.

Light is not a physical wave, but we sometimes think of light as a mathematical wave.

A wave both propagate in a medium and may diffract. Light may diffract but propagates in vacuum?

We thought light was a wave. It is not. Neither is it a particle. It behaves like wave under certain circumstances, and it behaves like particle under certain circumstances, but it is neither a particle or a wave.

21.1.2How do we know whether there is light?

In order to see something, we have to direct our eyes toward that thing, and the surrounding has to be bright enough. We can see things in broad daylight, but we cannot see things in a cave even though it is daytime outside, but we can bring fire with us into the cave and then we can see things again. We can also light a fire, and then we can see things even though it is nighttime. The light from the sun and the light from the fire has the same nature in that they both help us see; they only have different quantities of light.

21.1.3Can light diffract?

What do we mean by light?

Can light be detected?

Is light whatever a light detector detects? A light detector affects the light.

21.1.4Wave-particle duality is category error

Wave is abstract; particle is concrete. A thing cannot be both abstract and concrete.

Wave is a kind of repetitive motion. Particle is a small thing.

Wave is abstract, subjective, mental, conceptual, and has no objective existence. What objectively exists is the particles and their interactions.

21.2Quantum mechanics?

If quantum mechanics is the answer, what is the question?

What problem does quantum mechanics solve?

Which simplifying assumptions of classical mechanics are removed by quantum mechanics?

21.3? Davisson–Germer experiment

What is the details of the Davisson–Germer experiment, "in which electrons, scattered by the surface of a crystal of nickel metal, displayed a diffraction pattern"¹⁵²?

21.4Observables?

"In systems governed by classical mechanics, it is a real-valued function on the set of all possible system states. In quantum physics, it is an operator, or gauge, where the property of the system state can be determined by some sequence of physical operations."¹⁵³ Why is that so? What is the motivation?

21.5Quantum statics?

What is the quantum analog of the classical statics? What is the quantum analog of Archimedes's law of the lever?

Quantum statics should be simpler, because it should not require calculus.

21.6Teaching quantum mechanics: How should we introduce quantum mechanics?

Experiments must guide us because our everyday intuition breaks down.

State-space formalism of classical mechanics? By quantizing Hamiltonian mechanics?

Sakurai 2011 [3] begins with Stern–Gerlach experiment¹⁵⁴, but that book is not for beginners. Classical mechanics predicts that the collisions form a line, but reality gives us two clusters instead of a line.

Electromagnetism is required to understand the Stern–Gerlach experiment. What is a magnetic moment?

[2]

21.7Brownian-motion view of quantum-mechanical indeterminacy?

Photons are like Brown's pollens in Einstein's Brownian motion paper. Pollens jiggle because they are hit by water particles much smaller than the pollens.

Hypothesis: Material particles (such as electrons) appear to have indeterminate position because they are hit by ether particles much smaller than the material particles.

What about non-localities (entanglements)?

But this is fundamentally different. A pollen always has a position at each point in time. A quantum particle does not have a position until it is measured. (The orthodox interpretation as described by Griffiths 2015 [1])

21.8Quantum Venn diagram paradox

• Three polarizers.
  • Bell's Theorem: The Quantum Venn Diagram Paradox https://www.youtube.com/watch?v=zcqZHYo7ONs
    • It is surprising that adding a third filter increases brightness. We think that a filter should only decrease, not increase brightness.

21.9The meaning of probability?

If something is possible (that is, if something has non-zero probability), will it eventually happen?

There is a non-zero probability that a black hole appearing out of nowhere kills us all. Will it happen? Is it happening in a parallel universe?

21.10Philosophy of quantum mechanics?

21.10.1Which one of these are ontologically justified?

• Matter can behave as a wave or a particle?
  • In what way?
• Matter is both a wave and a particle?
  • Refutation?
    • A water wave is not water.
      • Wave is the name we give to periodic motion.
        • We can perceive a wave because we can interact with the constituents of the wave.
          • If light is a wave, then light should have constituents.
• Observe: double-slit experiment: shooting electrons through two slits.
  • de Broglie hypothesis relates the momentum and wavelength.
• Observe: quantum tunneling.
  • How do we explain quantum tunneling without probabilities?
  • How does QFT explain electron tunneling?
• How does QFT (quantum field theory) describe an electron?
  • https://www.symmetrymagazine.org/article/july-2013/real-talk-everything-is-made-of-fields
  • http://www.quantum-field-theory.net/electron-look-like/
• 2013 "Particles, Fields and The Future of Physics - A Lecture by Sean Carroll" https://www.youtube.com/watch?v=gEKSpZPByD0
  • lecture for public audience
  • 30:40
    • The mass of a particle is the energy required to get the corresponding quantum field to vibrate.
    • There is a field for every type of particle. There is an electron field, there is a photon field, and so on.
    • Particle interaction is the coupling between different fields.
• QED (quantum electrodynamics) http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/qed.html
  • Feynman diagram is one way of teaching QED.

21.10.2What is a wave?

• A water wave does not require the water to flow.

21.10.3Path to understanding quantum mechanics?

• Electrons fired toward a screen behind two slits show interference pattern.
• Hydrogen absorption/emission spectrum
• https://en.m.wikipedia.org/wiki/Planck%27s_law
• A small hole on a closed box approximates a black body. The hole looks black from outside. Heating the box changes the hole's color.
• What is a concrete example of a potential barrier?

21.10.4Double-slit experiments?

• How do we detect electrons? https://en.wikipedia.org/wiki/Electron_capture_detector
• What is used to detect electrons in the double slit experiment? https://www.reddit.com/r/askscience/comments/3ebcw6/what_is_used_to_detect_electrons_in_the_double/
• https://physics.stackexchange.com/questions/364312/how-does-the-electron-detector-detect-electrons-dbl-slit "How Do We Know Protons, Electrons, and Quarks really Exist?"
• https://www.nsta.org/publications/news/story.aspx?id=51054
• How do we know electrons exist? https://www.quora.com/How-do-we-know-electrons-exist
• Unread
  • https://en.wikipedia.org/wiki/Matter_wave
  • 2017 article "On the self-interference in electron scattering: Copenhagen, Bohmian and geometrical interpretations of quantum mechanics" https://arxiv.org/abs/1710.02583
  • I don't understand the question enough to determine why it is downvoted. "Can the intensity distribution behind edges and slits be explained by the interaction with the surface electrons of the edges?" https://physics.stackexchange.com/questions/158105/can-the-intensity-distribution-behind-edges-and-slits-be-explaint-by-the-interac
  • https://www.reddit.com/r/Physics/comments/4ugmc7/can_someone_explain_the_double_slit_experiment/
    • 2013 article "Controlled double-slit electron diffraction" http://iopscience.iop.org/article/10.1088/1367-2630/15/3/033018/meta
  • Variation of double slit experiments?
    • Double slit with nuclear decay?
    • Double slit with tracers? (What is a tracer?)
  • What is an atom and how do we know? https://www.youtube.com/watch?v=LhveTGblGHY
  • Variations, modifications, and expansions
    • https://noetic.org/research/projects/next-generation-double-slit

1. Quantum eraser?

2. Afshar experiment?

   • http://steve-patterson.com/quantum-physics-abuse-reason/
     • Afshar experiment
     • Weak measurement
   • How do we know where an electron is? How do we measure the position of an electron? How do we measure the momentum/energy of an electron?

21.11Probability arises from basic physical laws?

• https://www.theatlantic.com/science/archive/2018/11/science-full-mavericks-like-my-grandfather-was-his-physics-theory-right/574573/
• https://www.researchers.one/article/2018-10-6

21.12Obtaining wave equation

Can we model the double-slit experiment as classical wave diffraction, and then interpret the square of wave function as probability density, a la Born?

21.13TODO Does not belong here?

21.13.1Reformulations?

https://www.quora.com/Has-an-attempt-ever-been-made-to-reformulate-quantum-mechanics-in-a-space-other-than-Hilbert-space

21.13.2What?

Why is it hard to convert between matter and energy? What does QFT say? (Related: Why isn't everything homemadeable?)

How do we know where an electron is? How do we measure the position of an electron?

How do we measure the velocity of an electron?

21.13.3Intro to QFT?

An Introduction to Quantum Field Theory Mrinal Dasgupta http://hepwww.rl.ac.uk/hepsummerschool/Dasgupta%2008%20Intro%20to%20QFT.pdf

A Very Short Introduction to Quantum Field Theory A. W. Stetz http://physics.oregonstate.edu/~stetza/COURSES/ph654/ShortBook.pdf

21.13.4Do these theories have practical applications?

Physics and monads¹⁵⁵. From Abdullah. How much background knowledge do we need to understand that?

Baez seems to say that quantum mechanics is a special case of classical mechanics, whereas we usually think the other way, that classical mechanics is a special case of quantum mechanics.

21.14TODO Statistical thermodynamics, for the Franck–Hertz experiment?

21.15TODO Polarization of light, for quantum mechanics

21.16TODO Diffraction crystallography

<2019-07-16> http://scarc.library.oregonstate.edu/coll/pauling/bond/narrative/page9.html

Until 1912, when Max Theodor Felix von Laue, a German physicist, discovered a roundabout way of seeing the unseeable. He did it by shooting a beam of x-rays at crystals and then analyzing the way the atoms in the crystal reflected the x-rays. The resulting "diffraction pattern" could be seen by developing a piece of photographic film placed near the crystal. By analyzing the pattern created by the scattered x-rays — a process requiring very complex mathematical calculations — researchers could painstakingly work out, at least for simple crystals, the distances and angles between the atoms that comprised them. Once the basic crystal unit involved more than a handful of atoms, however, the patterns became too complex to analyze directly.

For the Davisson–Germer experiment.

Crystallography¹⁵⁶

A crystal is a solid with regular structure.¹⁵⁷¹⁵⁸

How do we know whether a solid has a regular structure?

How does a liquid solidify when cooled?

21.16.1Crystals: How do we know their internal arrangements?

What does Bragg's equation model? How do we test it?

21.16.2Crystals: How do we make them?

A crystal (a crystalline solid) is formed by slowly cooling a liquid?

How do we make diffraction gratings small enough for electrons? "[…], the periodic crystal structure serves as a type of three-dimensional diffraction grating."¹⁵⁹¹⁶⁰

22TODO Fields

22.1Fields: How do we know?

A field assigns something to each point in space. The gravitational field assigns to each point a gravitational force per unit mass.

A field is modeled by a multivariate function (a function that takes several variables). The variables can be grouped into a vector. This gives the impression that the function takes one big vector instead of several scattered real numbers.

A scalar field is a field that gives a scalar.

A vector field is a field that gives a vector.

A field \(f\) is uniform iff \(f(x)\) is the same for all \(x\).

How do we know whether fields are real or just a mathematical abstraction?

22.2Can we reverse-compute the density that causes a field?

Given a mass density scalar field, we can compute the resulting gravity vector field.

Can we do the inverse? Given a gravity vector field, can we compute what mass density scalar field would give rise to that?

Divide the space into small cubes v0 v₁ …. Let xk be a point anywhere in cube v_k. \( g(x) = sum_k rho(x_k) v_k \).

How do we know which is real: the gravity field or the mass density?

23Electromagnetism

Electromagnetism unifies optics, electricity, and magnetism.

23.1How do we know that electricity and magnetism is the "same" phenomenon?

What do we mean by "same"?

Electric current deflects magnets (Ørsted 1???)¹⁶¹. Two electrified wires electric current running in the same direction, attract each other (Ampère ????)¹⁶². (Do we get the signs/directions right?)

Then?

23.2How do we know that magnetism is caused by electrons looping?

Now we think in reverse: Given the shape of the magnetic field of a magnetic dipole (such as a small bar magnet), what is the shape of the electric current that produces the magnetic field with the same shape? It's a loop! That is, a wire that forms one circle! Thus, perhaps the magneticity of a stone is caused by a concert of aligned electrons orbiting in tiny loops? Tiny loops of electric current acting in concert. Each electron is racing alone in its own circuit. Is this picture correct?

The word "spin" suggests that an electron is a ball that rotates in an axis, but "Our concept of spin must also be adjusted to fit with the discoveries of the 20th century."¹⁶³

23.3Given an electron's motion, how do we infer its electromagnetic disturbance?

Suppose that an electron has position \( x(t) \) at time \( t \). What is the travelling electromagnetic disturbance caused by the electron?

23.4Alpha, beta, and gamma radiation: How do we distinguish them?

By a magnet. Alpha radiation bends one way, beta radiation bends the other way, and gamma radiation goes straight through. See video¹⁶⁴.

23.5Electromagnetic energy?

Nick Lucid's explanation of Poynting vectors and electromagnetic energy "Energy doesn't FLOW the way you THINK! (Electrodynamics)"¹⁶⁵ The charges are not "energy carriers".

23.6TODO Reorganize?

23.6.1TODO Electric motor and generator?

• Reversibility between motor and generator
  • Input electricity, output mechanicity.
  • Input mechanicity, output electricity.
• https://en.wikipedia.org/wiki/Homopolar_motor
• https://en.wikipedia.org/wiki/Homopolar_generator
• https://en.wikipedia.org/wiki/Electric_motor
• https://en.wikipedia.org/wiki/Electric_generator
• https://en.wikipedia.org/wiki/Electromagnetic_induction
• https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction
• https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law
• https://en.wikipedia.org/wiki/Lenz%27s_law

23.6.2TODO History of electromagnetism?

• WP:History of electromagnetic theory
• WP:Timeline of electromagnetism and classical optics

24Gases and statistics

24.1Statistical thinking

Statistics is about seeing the forest and ignoring the trees.

Statistics is about gaining knowledge about the population at the cost of losing knowledge about the individual.

To appreciate the relevance of statistics, consider a box of gas with 1 billion particles. It is impractical to model that by 1 billion equations of motion. However, we can still say something useful, because statistics allows us to summarize the gas. With statistics, we can talk about macroscopic behavior, but we can't talk about individual particles; we get the summary but we sacrifice the details. Now we can talk about the distribution of the velocity of the particles, such as 50% of the particles are slower than something; but now we cannot say anything about the individual particles.

Statistical physics is macro-physics. The idea is we consider a statistics of the system. We look at the big picture instead of looking at each particle. There are many particles. We cannot say anything about one particle. What is an example of statistical ensemble?

24.2Gas model

We think of a gas in a container as a collection of many tiny balls with negligible mass moving around freely according to Newton's laws of motion.

We ignore gravity?

24.3What

https://en.wikipedia.org/wiki/Temperature TODO paraphrase this Wikipedia text: Based on the historical development of the kinetic theory of gases, temperature is proportional to the average kinetic energy of the random motions of the constituent microscopic particles

https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution

Statistical mechanics explains thermodynamics.

https://en.wikipedia.org/wiki/Thermodynamics

mole is

Chemistry?

Entropy?

Canonical ensemble?

Statistical ensemble?

http://demonstrations.wolfram.com/BoseEinsteinFermiDiracAndMaxwellBoltzmannStatistics/

24.4Getting used to probability and statistics

Exercise (Discrete probability): Roll a fair six-faced die once. What is the probability of getting the three-dotted face?

Answer: 3/6.

Exercise (Joint probability of independent events): Roll a fair six-faced die three times. What is the probability of getting the three-dotted face three times?

Answer: \((3/6) \times (3/6) \times (3/6)\).

A distribution of a set \(\Omega\) describes how members of \(\Omega\) are distributed. Let \(f\) be the density of that distribution. Then \(f(x)\) describes the tendency of values to gather around \(x\)? Values tend to gather near the peaks of \(f\).

24.5What/how is Maxwell–Boltzmann distribution?

Maxwell distribution is a chi-distribution with 3 degrees of freedom. What?

24.6Using the Maxwell–Boltzmann distribution of speed (for what?)

An example question that statistical physics (statistical mechanics) can answer is "What is the probability of finding a particle with a given speed?" For example, see the probability density function of the Maxwell–Boltzmann distribution.

Don't remember the equation. To be a physicist, you don't need to remember this; you can always go to Wikipedia or open a book. The important thing is that you know what it means and what it's useful for. The density of Maxwell–Boltzmann distribution is \(f(v)\). The number \(\int_A f\) describes the probability of finding a particle whose speed is in the set (the range) \(A\). Let that sink for a moment, especially if you aren't yet comfortable with probability theory. The density of Maxwell–Boltzmann distribution is ???

\[\begin{align*} f(v) = \parenthesize{ \frac{m}{2\pi k T} }^{3/2} 4 \pi v^2 \exp \parenthesize{ - \frac{mv^2}{2kT} } \end{align*} \]

Who got that? How?

24.7Central limit theorem

Let there be many random variables, independent. Then, their sum tends to be normally distributed, even if the random variables themselves are not normally distributed.¹⁶⁶

The sum of normally-distributed random variables tends to be normally distributed.

24.8Concordances

Griffiths' quantum mechanics book [1] introduces practical statistics-and-probability.

24.9Temperature and radiation

Why does a heated iron glow?

Why does a body radiate when heated?

Does a heated gas glow? Heated solid iron glows. Heated liquid iron glows too. Does a heated gaseous iron also glow?

A solid is not absolutely motionless. There is a lot of micromotions. The atoms are vibrating.

Why is a solid thing solid?

What is temperature? A measure of how cold or hot something is. Zero degree Celsius is the temperature at which water solidifies into ice at sea level.

Why does matter expand when heated?

Thermometers exploit the expansion of heated matter. What we actually measure is the length of the thermometer. The heat is measured indirectly.

Microscopically, what is temperature? "For an ideal gas, temperature is proportional to the average kinetic energy of the random microscopic motions of the constituent microscopic particles."¹⁶⁷

What is the relationship between temperature and radiation?

Does a colliding electron emit photon?

25— Part — The physics of small objects

26Motion of small objects

26.1How do we know that an electron moves?

By the change of its position.

26.2How do we measure an electron's position?

How do we measure an electron's position?

Can we do it in the same way we detect large objects? By shining some light on them, and sensing the reflected light that reaches a light detector?

Some ideas:

• by the change of its electric field,
• by electron-photon interaction¹⁶⁸,
• by electron scattering¹⁶⁹?
• by strobing (repeatedly and quickly flashing) the object with light?¹⁷⁰

We can know the movement of an electron, but can we know its motion?

What does it even mean to measure an electron's position?

Do electrons reflect light?¹⁷¹¹⁷²

Hint?¹⁷³

Bombard it with photons?

What is the wavelength of the photons used to bombard the electron?

Can we analogize a photon-electron collision as billiard ball collision?

If there is an electron known to be roughly somewhere in a region of space, how do we find where exactly that electron is?

To understand physics, it is essential to understand the details of the experiments.

26.3How do we measure the polarization of a photon?

Interesting simple quantum-mechanical experiments with polarization filters¹⁷⁴

26.4TODO How do we know that a current is a flow of electrons?

27TODO Functionals; motion

27.1Brachistochrone problem?

Why did some fine 17th-century gentlemen concern themselves with problems that had no apparent practical applications, such as the brachistochrone problem¹⁷⁵? What benefits were there, besides personal satisfaction?

When Lagrange formulated his mechanics, the concept of potential energy had not yet been invented?

27.2Moving from force-based thinking to energy-based thinking

We thought \( F(t) = -g \) and thus \( a(t) = -g/m \) and \( v(t) = - gt / m \) and \( x(t) = - gt^2 / (2m) \). We think about the forces, figure out the accelerations, integrate them to get the velocities, and integrate them to get the positions.

How does Hamiltonian mechanics explain a ball falling near the ground? \( P = mgh \). \( K = \frac{1}{2}mv^2 \). The state of the system is \( (h, mv) \). The operator is \( P(h, mv) = mgh \) and \( K(h, mv) = \frac{1}{2}mv^2 \). \( P + K = \text{constant} \) which means that \( \pdv{P}{h} = 0 \) and \( \pdv{K}{v} = 0 \).

28TODO Groups? Symmetries?

Unread:

• On the wonderfulness of Noether's theorems, 100 years later, and Routh reduction

Pieces of the story:

• Wu experiment¹⁷⁶, parity violation

28.1What is left and right?

• We can define left and right absolutely due to parity violation.
• WP:Wu experiment
  • WP:Parity, violation
• Phys. SE 18729: absolute defintion of the right (i. e. not left) direction

29TODO Reorganize?

29.1Philosophy?

29.1.1Truth is a continuum (not binary true-and-false).

(Why are we saying this?)

29.1.2Epistemology (how we know)

We assume that there are three sources of knowledge:

• observation (the senses)
• definition (fiat, agreement between speakers of the same language)
• inference (logic, rules of thought)

29.1.3Theoretical physics advances by discovering and removing simplifying assumptions

What does Thomas Kuhn say?

A problem with physics: too many unjustified tacit assumptions?

Every scientific revolution invalidates some tacit assumptions?

Physics is mathematics + engineering + philosophy.

• If we skip the mathematics, we can't measure.
• If we skip the engineering, we can't experiment.
• If we skip the philosophy, we can't progress.
  • We will make unjustified tacit assumptions.

(TODO avoid linking without summarizing)

• WP:Tacit assumption
• Tacit assumptions or Implicit assumptions (if they are flawed) leads to paradoxical paradigm and scientific crisis
• How to expose insidious tacit assumptions, which sidetrack scientific progress into wrong path (leading to scientific crisis), if not exposed?
• 1975, article, paywall, "Tacit Assumptions in Fundamental Particle Physics"
  • unpaywalled

29.1.4What

Which one makes sense: "There is space between two things." "Things exist in space." "This thing requires/occupies/takes space." Operational definitions: Space is whatever rulers measure. Time is whatever timers measure.

Search "ontology of energy"

https://en.wikipedia.org/wiki/Philosophy_of_physics

Time is the sequence of events. Time is an ordering of events. Time is whatever a timer measures.

29.2Fluid

How do we think of a fluid?

29.2.1Statics

A continuous ever-divisible fluid. A density field. The symbol \(\rho(x)\) represents the density of the fluid at point \(x\). The product \(\rho(x) ~ dV\) represents the mass of a small part of the fluid at volume \(V\) containing the point \(x\).

29.2.2Dynamics

The symbol \(\rho(x,t)\) represents the density of the fluid at point \(x\) at time \(t\).

But we can use spacetime coordinates: We let \(x\) be four-dimensional, and we write \(\rho(x)\).

29.3Physics

Physics should not be separated from philosophy, mathematics, and engineering.

29.4Philosophy of physics

• The epistemology (how-do-we-know) of physics is the scientific method.

  • WP:Scientific method
  • WP:Hypothetico-deductive model

  • If theory and experiment disagree, experiment wins.

    • Unless the experiment is faulty.

  • Are there alternatives?

• The ontology?

  • Something is defined by its properties?
  • Something is defined by its behaviors (relation to others)?
  • WP:Intrinsic and extrinsic properties
• WP:Philosophy of physics

• WP:Philosophy of science

  • WP:Demarcation problem: What is science? What isn't?

29.5Ontology

• an attempt

  • undefined terms

    • touch

  • A matter is something we can touch.

    • The air is also a matter because we can feel it with our sense of touch.

    • Problem: subjective definition

      • What about people without sense of touch?

        • WP:Anaphia
        • WP:Hypoesthesia

    • Is there a definition that doesn't depend on our senses?

      • Is such definition even possible?

        • Should "matter" be undefined?

          • Is physics about explaining our perceptions?

    • A matter is something that exists?

      • But how do we know that it exists if not from our senses?

        • Is there a teapot orbiting the sun?

          • WP:Russell's teapot

            • How do we prove non-existence?

              • Do we have to?

                • Yes?

                  • Who claims, proves.

                    • If you claim that someone raped you, you have to prove it.

                    • Problem?

                      • If you claim that someone has never raped you, you have to prove it.

                        • But how?

                          • Let there be three people X, Y, Z.
                          • Z (probably a judge in a court) doesn't know either X or Y.

                          • How does X prove, to Z, that Y has never raped X?

                            • There are things that are true but unprovable?

                              • Is God true but unprovable (if there is a coherent definition of "God")?

                        • This can be used as a joke?

                          • X: "Hey, do you know? Y has never raped me, but I can't prove it."
                          • Z: "So, what are you suggesting?"

                      • How do we prove that Y has never transferred anything to X's bank account?

                        • We assume that the bank is honest and maintains correct records.

                          • Why should Z accept this assumption?

                            • Should Z still accept this assumption if X owned the bank?
                        • The bank record is finite.

                        • Then we only need to check exhaustively whether there is anything from Y in the records.

                      • How do we prove that there isn't a teapot orbiting the sun?

                        • We can't visit every point in space.
                        • We can't exhaustive-check the entire Universe.
                        • We can't.

                        • But we can say that it's implausible.

                          • Why? How?
                          • What if there is really a teapot-shaped space rock orbiting the sun?
                      • How do you prove that two people have never met before?

                      • How to prove libel?

                        • Suppose:

                          • X did rape Y.
                          • Y claims that X raped Y, but can't prove it.

                        • Then can X countersue Y with libel?

                    • If you claim that God exists, you have to prove it.
                    • If you claim that God doesn't exist, you also have to prove it.
                    • If you don't claim that God exists or not, then you don't have to prove anything.

                    • If you believe something, then you don't have to prove anything to others, as long as you don't claim it before them.

                      • Our belief is a claim we make before ourselves. If we can prove it, good for us. If we can't prove it, it's our problem.
                      • But, spreading a belief is making a claim before others. It has to be proven.

• concepts

  • mass, acceleration, force

    • Mass is resistance to force.

      • Isn't this definition circular?

        • Force accelerates mass.
    • Mass is the amount of matter.
    • WP:Mass
    • WP:Matter

29.6Theoretical physics

• Unifying quantum mechanics and general relativity?

  • Unifying quantum mechanics and special relativity

    • WP:Quantum electrodynamics

      • "is the first theory where full agreement between quantum mechanics and special relativity is achieved"

  • Hamiltonian mechanics in Minkowski spacetime?

• Undigested

  • The changing concept of matter in H. Weyl's thought, 1918-1930
  • Introducing Groups into Quantum Theory (1926 – 1930)
  • Bob Coecke, categorical quantum mechanics
  • Why John von Neumann did not Like the Hilbert Space formalism of quantum mechanics (and what he liked instead)
  • What are the von Neumann–Dirac axioms?

  • quark fusion

    • Scientists Accidentally Discovered Quark Fusion, Could It Be the Future of Energy?

• WP:Entropic force

  • http://entropicai.blogspot.co.id/2017/06/fractal-optimising-first-paper.html

• A crystal is a repeating structure.

  • A time crystal or space-time crystal is a structure that repeats in time, as well as in space. (WP: Time crystal)

• Futurism

  • Interesting idea: harnessing energy from spinning black hole ergosphere, and making a black hole bomb. Penrose process. kurzgesagt video
  • https://en.wikipedia.org/wiki/Stellar_engine
  • https://en.wikipedia.org/wiki/Astronomical_engineering
  • https://en.wikipedia.org/wiki/Megascale_engineering
  • https://en.wikipedia.org/wiki/Kardashev_scale

29.7Nuclear energy

• Is there any way to convert nuclear energy into electrical energy without going through heat and turbines?
• Nuclear recycling

29.8Undigested information fragments

• ECAT, LENR (low-energy nuclear reaction), cold fusion

  • http://ecat.com/
  • http://e-catworld.com/what-is-the-e-cat/

• nuclear fusion

  • http://news.mit.edu/2015/small-modular-efficient-fusion-plant-0810
  • http://www.lockheedmartin.com/us/products/compact-fusion.html

• DC-powered home

  • Different sockets in addition to AC sockets.
  • http://www.mnn.com/green-tech/research-innovations/stories/the-home-of-tomorrow-will-run-on-direct-current

• Given a bomb power in kiloton TNT, find the detonation altitude that maximizes destruction. See the blast curve.

  • WP: Blast damage
  • 
  • WP:NUKEMAP

• computers

  • Photonic Chips Will Change Computing Forever… If We Can Get Them Right

• lasers

  • jellyfish for polariton lasers Jellyfish Lasers Are Revolutionizing Quantum Physics

• chemistry

  • This is not an introduction to computational chemistry: A Guide to Molecular Mechanics and Quantum Chemical Calculations, 2003, Warren J. Hehre

• nuclear

  • Isotope vs nuclide https://en.m.wikipedia.org/wiki/Isotope

29.9engineering

• How to save 51 billion lives for 68 cents with simple Engineering

  • Some constraints are good for creativity.

29.10space

• This Massive Asteroid Is Headed for Earth…. What Now?
• WP: rockoon (rocket-balloon)

29.11Other external resources

• Overview

  • WP:Physics
  • WP:Outline of physics
  • WP:Portal:Physics
  • YT:The Map of Physics
• YT:minutephysics user
• YT:GraduatePhysics channel
• YT:CrashCourse Physics playlist for AP Physics 1 and 2

• YT:For the Love of Physics - Walter Lewin - May 16, 2011

  • around 35:40

    • Cloud is white due to Mie scattering.
    • Sky is blue due to Rayleigh scattering.
    • Scattering depends on particle size.

• Will We Ever Time Travel? Scientists Say 'No' Based on This New Discovery

  • This youtube video title needs to be declickbaited. What new discovery?

29.12Philosophy?

• https://en.wikipedia.org/wiki/Problem_of_induction

29.13Simulation hypothesis

• WP:Simulation hypothesis

  • section: testing the hypothesis physically

• Is the Universe a simulation? Testing the simulation hypothesis

  • How do we find out if we are in a simulation?

    • https://www.technologyreview.com/s/429561/the-measurement-that-would-reveal-the-universe-as-a-computer-simulation/
    • Look for numerical errors in the Universe. [UniNumError] https://arxiv.org/abs/1210.1847
      • 2012 article "Constraints on the Universe as a Numerical Simulation"
  • http://www.washington.edu/news/2012/12/10/do-we-live-in-a-computer-simulation-uw-researchers-say-idea-can-be-tested/
  • http://www.huffingtonpost.co.uk/2012/12/12/physicists-universe-simulation-test-university-of-washington-matrix_n_2282745.html
  • anisotropy of space?

29.14Theoretical?

• YT:The more general uncertainty principle, beyond quantum
• https://en.wikipedia.org/wiki/Amplituhedron
• https://en.wikipedia.org/wiki/Theoretical_physics
• https://en.wikipedia.org/wiki/Protoscience
• https://en.wikipedia.org/wiki/Pseudoscience
• https://newrepublic.com/article/118655/theoretical-phyisicist-explains-why-science-not-about-certainty

• Free electron can't absorb photon

  • https://physics.stackexchange.com/questions/225522/free-electron-cant-absorb-a-photon
  • https://www.quora.com/If-photons-can-be-absorbed-by-electrons-why-can-photons-not-be-absorbed-by-free-electrons

• theoretical physics meta-research

  • https://www.kth.se/en/sci/phd/programs/physics/forskning/aktuell-forskning-inom-teoretisk-fysik-1.76843
  • https://www.quora.com/What-are-some-of-the-best-Physics-blogs
  • https://blog.feedspot.com/physics_blogs/

29.15High-energy physics information system

• https://inspirehep.net/

29.16Unchecked physical theories? Non-mainstream? Suspicious? Not yet mainstream or will never be mainstream?

• http://www.unifiedphysics.com/

29.17What?

• 2018 quantum entanglement size record: trillions of atoms? https://www.youtube.com/watch?v=LAvfPof1ySI

• Getting started

  • physics expository works https://physics.stackexchange.com/questions/194300/physics-journals-that-focus-on-expository-work

• Keeping up with recent research

  • "Newly published articles in physics" http://www.scholarpedia.org/article/Encyclopedia:Physics

• Finding literature

  • PhysNet
  • PhysNet PhysDoc: Physics Documents Worldwide

29.18Colors

29.18.1We don't see the objects themselves. We see only the light arriving at our eyes.

29.18.2What

https://en.wikipedia.org/wiki/Color_of_chemicals

Red is a color category, not a color. What?

https://www.quora.com/What-is-the-difference-between-polychromatic-and-monochromatic-light

Chroma vs color

"Color Perception" http://hyperphysics.phy-astr.gsu.edu/hbase/vision/colper.html

Trichromatic vision Three kinds of cone cells Tristimulus Young–Helmholtz trichromatic theory https://en.wikipedia.org/wiki/Trichromacy https://en.wikipedia.org/wiki/Young%E2%80%93Helmholtz_theory https://en.wikipedia.org/wiki/Tristimulus_colorimeter

https://biology.stackexchange.com/questions/58759/can-human-perception-differentiate-between-monochromatic-and-polychromatic-light

29.18.3Understanding metamerism is the key to understanding color perception.

https://en.wikipedia.org/wiki/Metamerism_(color) Purple vs violet https://en.wikipedia.org/wiki/Purple History of color theory Television https://en.wikipedia.org/wiki/Color_vision

https://www.hunterlab.com/blog/color-measurement-2/understanding-tristimulus-values-taking-guesswork-color-measurement-instrumentation/

https://en.wikipedia.org/wiki/CIE_1931_color_space

"The CIE 1931 color spaces were the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision."

https://en.wikipedia.org/wiki/CIE_1931_color_space#Meaning_of_X,_Y_and_Z

29.18.4Newton's prism splits sunlight into spectrum?

29.18.5Good question about the meaning of the wavelength of a photon

https://physics.stackexchange.com/questions/267034/what-exactly-is-meant-by-the-wavelength-of-a-photon

29.18.6Colors?

• What is color?
  • https://en.wikipedia.org/wiki/Color
• monochrome vs polychrome
• subjective color vs objective color
• What is the difference between the purple that is red-blue mixture and the purple that is monochromatic purple laser?
• Why is red+blue+green light = white, but red+blue+green ink = something dark?
  • https://en.wikipedia.org/wiki/Additive_color
  • https://en.wikipedia.org/wiki/Subtractive_color
• Shaded checkerboard color optical illusion.
• "Why aren't there printers that use red-green-blue ink cartridges?" https://graphicdesign.stackexchange.com/questions/108620/why-arent-there-printers-that-use-red-green-blue-ink-cartridges
• Mary's room https://en.wikipedia.org/wiki/Knowledge_argument
  • We aren't going down this rabbit hole for now.

How do we predict the color of a solid from its electron configuration?

29.19Unread

• Ampere's experiments
  • Ampère's Experiments
  • http://www.larouchepub.com/eiw/public/1992/eirv19n20-19920515/eirv19n20-19920515_030-the_ampere_crucial_experiments.pdf
• https://newrepublic.com/article/118655/theoretical-phyisicist-explains-why-science-not-about-certainty
• Reddit: In quantum physic's 'observer effect', what qualifies as an 'observer'?

29.20Are these real?

http://fisika.fst.unair.ac.id/theory/

29.21Humans, science, technology, ethics

29.21.1On ignorance

In the 18th century, occasionally, steam boilers and coal mines exploded, killing tens of people.

Then nuclear power plants exploded.

What if a Dyson sphere exploded?

29.22What

29.22.1Philosophy

• Some branches of philosophy

  • Epistemology (how do we know?)
  • Ontology (what exists?)
  • Ethics (morality; what should be?)

• Epistemology

  • There are two kinds of knowledge: prior and posterior.

    • Prior (before-the-fact) knowledge is obtained by inferring theorems from axioms through the rules of logic.
    • Posterior (after-the-fact) knowledge is obtained by observation from the real world through the physical senses.
  • WP:a priori and a posteriori
  • WP:Epistemology
  • WP:Empiricism
  • WP:Experimentalism
  • WP:Occam's razor
  • In physics, we know things from experiments and inference.
  • https://en.wikipedia.org/wiki/Scientific_method

  • [wenning2009scientific] explains scientific epistemology (about 15 pages).

    • http://www2.phy.ilstu.edu/pte/publications/scientific_epistemology.pdf

  • What does "to know" mean?

    • Some possibilities

      • To know an object is to be familiar with that object.
      • To know an object is to be able to use that object.

• Ontology

  • Measurabilism

    • A thing exists if and only if it can be measured.

    • WP:Mike Alder, Newton's flaming laser sword

      • "What cannot be settled by experiment is not worth debating."
  • WP:Ontology
  • Ontology defines objects, their properties, and their relationships?
  • "Object" is another word for "thing"?

  • Entity is distinguishable object.

    • An entity has identity.
    • An entity can be distinguished from other entities.

  • An Ontology for Engineering Mathematics

• Thoughts

  • If our past is better than our present, then we have failed.

• How to study philosophy without wasting time?

  • Phil. SE 21292: Do some continental philosophers deliberately obfuscate their writing? Why?
  • WP:Pseudophilosophy
  • WP:Sophist

  • philosophy vs science

    • HSM SE 2608: Why and when did some areas separate themselves from philosophy and some not?

      • When Did Science and Philosophy Separate Into Different Fields of Study?

        • Quora: Where and why did scientists and philosophers branch out, and what is the significance of philosophy in the field of science?

    • Quora: Why are the sciences separate from philosophy?

• Ungrouped

  • What is the difference: egoism, egotism, individualism?

• Ethics

  • question group

    • Is it good to force someone to do something even if such forcing makes the world better off?
    • Is it good to make a few people worse off to make many people better off?
    • Which should we value more: individual liberty or collective good?

  • test your morality online

    • test your moral parsimony

  • For the sake of logical consistency

    • Amorality

      • Everyone does whatever they want.
      • The only reason for not doing something is fear?
      • Is amorality the only consistent moral system?
      • Intention doesn't matter.
      • Intention doesn't change the morality of a situation.

      • amoral vs immoral

        • amorality = absence of morality
        • immorality = what majority thinks bad
      • WP:Amorality
      • WP:Immorality

      • WP:Moral nihilism

        • What's the difference?

    • What is this position named?

      • Something is morally right iff the majority says so.

  • WP:Evolution of morality

• How do I avoid forgetting things?

  • Make forgetting impossible.

    • Everything has its place.
    • This doesn't apply to dementia.

• pointing out 21th century unwisdom

  • Adam Ruins Everything - Why Weddings Are A Total Rip-Off

    • "Despite your family's wishes, weddings are pointless and expensive displays of wealth."
• "It is sometimes said, common sense is very rare." (François-Marie Arouet a.k.a. Voltaire (1694–1778) in "Philosophical Dictionary" (1767))
• too long, need summary: How to Pick a Career (That Actually Fits You)

• chubbyemu

  • this kid thinks he knows everything: "Successful people feel gratitude. Unsuccessful people feel entitlement."
  • You Can't Be Whatever You Want To Be
• The philosophy of Stoicism - Massimo Pigliucci

• Machiavelli is misunderstood.

  • Misunderstood Machiavelli
  • Have we got Machiavelli all wrong?
• WP:Paradox of hedonism

• Is forcing moral?

  • Is it good, to give people something they did not ask for?
  • Is it good, to force people to do something that betters them but unwanted by them?
• Is it good, to give people something they did not ask for?
• Does morality depend on intention or outcome?

• Why do young people (below 30 years old) have impractical expectations?

  • Because their frontal cortex hasn't fully developed?

• Ontology, hierarchy, knowledge organization

  • WP:Porphyrian tree

    • Ontology in Computer Science
• What is the difference between data, information, belief, knowledge, wisdom?
• WP:First principle

• Pop material

  • https://www.whatisitliketobeaphilosopher.com/

    • Biographical interviews.
• Science and Popper's falsifiability?

• Knowledge is a tower.

  • It is built from the bottom upward.
  • Concepts stand on other concepts.

  • The bottom of that tower is everything we know from our senses?

    • Or is it logic?

• Abductive reasoning?

  • We know Y from experiment.
  • Find a theory X that explains Y.

• Linguistics?

  • What is a question?

    • What are its answers?
    • https://plato.stanford.edu/entries/questions/

  • How do we answer "What is X"?

    • Semantics of the copula ("be")?
    • Depends on the language?
    • WP:Semantics of logic?
    • "X is Y" means "X is another word for Y".

    • "X is a Y" means "X is an instance of Y".

      • X a special kind of Y
      • There exists Z such that "X is a Y that Z"

    • "X is a Y that Z" means that every X is an instance of Y that satisfies Z.

• Distraction

  • How do we justify knowledge?

    • How do we justify knowledge from observation?

      • Philo. SE 15463: Why distrust our senses?

    • How do we justify knowledge from inference?

      • Why does logic work? Why is Nature logical?
      • WP:Syllogism
      • WP:Modus ponens
      • WP:Deductive reasoning
      • Philo. SE 22103: How to justify the use of logic?
  • WP:Epistemology

  • SEP:Epistemology

• Definition of "selfish"? Does intention matter?

29.22.2Is mass absolute? Is charge absolute?

Position is relative. Spacetime is relative.

Is the mass of a thing (the amount of matter in that thing) the same in all frames of reference?

Is the electric charge of a thing the same in all frames of reference?

https://en.wikipedia.org/wiki/Charge_invariance

29.22.3Rebooting human knowledge after mass destruction

• How do we reboot human knowledge from zero?

  • There are some ways in which everything might be destroyed:

    • the next world war
    • the next big space object impact

  • We must survive.

    • Find, gather, and follow the survivalists.

      • WP:Survivalism

    • We must drink.

      • Settle near a clean river.

    • We must eat.

      • Forage.

        • Hunt some game/meat.
        • Gather edible plants.
        • https://www.reddit.com/r/AskHistorians/comments/2zsm4z/how_often_did_prehistoric_man_eat_meat/
        • WP:Optimal foraging theory
        • WP:Foraging

      • How do we forage with less effort?

        • Weapon. Sharp edges.
        • Fire. Cooking.
        • Husbandry. Raise. Farm. Ranch. Agriculture. Crops.
    • Try to restore some of the Internet (Google, Wikipedia) before the survivalists die???

29.23Nuclear fusion

29.23.1Magnetic confinement

Given the desired radius of confinement, how strong is the required magnetic field (and therefore the electric current)?

29.24TODO was: Numbers and arithmetics

How much physics can we understand with only arithmetics and experiments?

29.24.1Heat, air conditioning

I want to cool down the air in my room from 33 deg C to 27 deg C. How strong should my air conditioner be? This can be calculated by simple tables, experimentation, and arithmetics.

What is 1 BTU?

Where should I put my fan?

29.24.2Cooking

How much salt should I put in my food? In my experiment and taste, I use one teaspoon of salt per three people per eating, with the assumption that one teaspoon of salt means that the salt makes a flat surface on the teaspoon, not a mound. Thus, if I am cooking for myself, I usually put in a third of a teaspoon of salt.

29.25Materials engineering

29.25.1What

How do we know stress and strain curves? What curves? https://en.wikipedia.org/wiki/Universal_testing_machine

Construction:

How do I build a house that won't kill me if it collapses?

29.25.2What is the cheapest metal?

<2019-07-12> Aluminum at $0.82/lb.¹⁷⁷

29.25.3What material should I use?

Consult Ashby's "Material selection in mechanical design"?¹⁷⁸

29.26Some chemistry ideas about carbon dioxide

Break the bonds with electric arc, producing carbon and oxygen.

CO2 -> … -> C + O2

Carbonatate¹⁷⁹ calcium oxide:¹⁸⁰

CaO + CO2 -> … -> CaCO3

29.27Principles vs laws

A principle is a-priori. It comes from thought.

A law is a-posteriori. It comes from observations/experiments.

But some principles can be experimentally tested. Einstein's principle of equivalence. Fermat's principle of least time.

But these laws don't seem to follow the pattern: Metcalfe's law (of network effect), Say's law (in economics)?

29.28Thermochemistry

There seem to be two kinds of substances:

• Substances that are broken down by heat: wood, etc.
• Substances whose formation requires heat: metal, sulfuric acid.

It seems to me that substances formed by heat are more dangerous. It seems that such substances somehow absorb some of the heat used to form it, and store that heat as its internal energy.

29.29Interesting things Linus Pauling said about Harvard in 1929

<2019-07-16> http://scarc.library.oregonstate.edu/coll/pauling/bond/narrative/page19.html

[In 1929, Pauling] was twenty-eight years old and flattered by the attention, but he also found things – some big, some little – he did not like [about Harvard]. Whereas Caltech was becoming famous for allowing researchers a free hand to develop their own unique approaches to science, at Harvard, Pauling found, subdisciplines such as organic chemistry and physical chemistry had ossified into separate fiefdoms. There was a sense of backbiting and politicking and a hoarding of talent he did not like. A product of the egalitarian American West, Pauling also received his first taste of eastern class snobbery. "Here was a society where there were a lot of important people who were important just because of birth. They had money and stature not based on their own abilities," he remembered. "I thought I would be a sort of second-class citizen at Harvard."

30TODO Discard?

30.1What is the difference between physics and chemistry?

Compare physical chemistry¹⁸¹ and chemical physics¹⁸².

Usually, in English, "physical chemistry" should mean "chemistry with some physics", that is, primarily chemistry, but with occasional excursions to physics.

"Physical chemistry, in contrast to chemical physics, is predominantly (but not always) a macroscopic or supra-molecular science […]"¹⁸³

"[…] Nonetheless, the distinction between the two fields is vague, and workers often practice in both fields during the course of their research."¹⁸⁴

In short, not much.

30.2Why cannot a broken solid be restored just by bringing the pieces close together?

A solid thing can be broken into two pieces, but merely bringing the pieces close together does not restore the thing into the state before it was broken, whereas water in a bucket can be divided into two buckets and then poured back into one bucket without any significant difference besides making some undulations that eventually subside. Why is that?

30.3Why, at STP, is hydrogen gaseous, is lithium solid, and is radon gaseous?

Why is there no apparent relationship between the mass of an element and the phase of a homogenous mixture?

• Radon atom is much heavier compared to hydrogen atom.
• Intermolecular interaction?
• Why different elements have different boiling points?
• periodic table https://ptable.com/

30.4Predicting chemical reactions?

• 2011 "Learning to Predict Chemical Reactions" https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3193800/

How do we make something? Synthetic chemistry?¹⁸⁵

• Ontology:
  • atom
  • molecule
  • electron
  • nucleus
  • orbital

30.5Unsorted, mostly chemistry

• WP:Electrolysis
• Electrochemical cell
  • Reduction-oxidation (redox) reaction
    • WP:Electric battery
      • WP:Electrochemical cell
        • WP:Voltaic pile
          • Alessandro Volta (1745–1827)
            • WP:History of the battery

Unread?

• 2016, "Theories of matter"
• http://www.edu.pe.ca/queencharlotte/homework/mmorrison/9science/matter/section2_1.pdf
• WP:Chemistry, history
• WP:History of chemistry
• WP:Three-age system
• Define: Natural means not man-made.
• Define: Rust.
• Assume: Rust occurs naturally.
• Observe: Rust becomes iron when burned?
• WP:Potash, history of production
  • WP:Leaching

What?

• Define: Glass is transparent (see-through) solid.
  • WP:History of glass
• Why is the symbol Na read "sodium" in English?
  • Quora: Who renamed Natrium and Kalium to Sodium and Potassium? Why?
    • Because people are too proud of themselves?
      • WP:Not invented here
      • WP:Law of triviality: "members of an organisation give disproportionate weight to trivial issues"
• Observe: Water dissolves salt.
  • Solution of salt in water?
  • Mixture of water matter and salt matter?
• WP:Fick's laws of diffusion, Adolf Fick, 1855
  • WP:Adolf Eugen Fick (1829–1901)

30.6? Proto-physics

<2019-02-12> (Change of opinion.)

There is no need to rediscover everything in the way our ancestors did. We have hindsight. We should exploit the full benefit of hindsight. But we should not trivialize the toil of our ancestors.

(End of change of opinion.)

Let's begin with very "wrong" ideas; we're "cheating" with our hindsight that our ancestors did not have. We will revise knowledge as we go. We will become less "wrong".

We might will never be 0% wrong. But knowledge does not have to be 100% correct in order to be useful.

30.6.1Chemistry

• Observe: A burning leaf stops burning if it's enclosed.
• Observe: Food spoils. Food goes rancid.
• Phys. SE 259021: How do flames neutralize a static charge?

30.6.2What

• WP:Buoyancy
• Observe: Salt conducts electricity?

30.6.3What

• Formal Physics
  • 2012, article, "Physics and proof theory"
• Unread
  • WP:History of science
  • Experiments
    • https://www.explainthatstuff.com/great-physics-experiments.html
    • https://www.quora.com/What-are-some-of-the-most-important-experiments-in-physics
    • https://www.telegraph.co.uk/news/science/science-news/3341042/Top-ten-greatest-experiments.html
    • https://www.space.com/36307-5-most-ingenious-experiments.html
    • https://explorable.com/physics-experiments
    • https://en.wikipedia.org/wiki/List_of_experiments#Physics
    • https://en.wikipedia.org/wiki/Experimental_physics#Famous_experiments
    • de Sitter's Observations - Intro to Physics
• Scientific theory
  • https://en.wikipedia.org/wiki/Scientific_theory#Unification
  • https://en.wikipedia.org/wiki/Superseded_scientific_theories#Physics
• 1999, book, Roberto Torretti, "The philosophy of physics"
• Quora: Will the theories of relativity and quantum mechanics merge? With what result?
• https://en.wikipedia.org/wiki/Scientific_Revolution
• Define: Sundial.
  • WP:Sundial
  • WP:Analemma; solar analemma = figure eight pattern of the sun on the sky across the year

30.7Biology

• How do we cure death?
• How do we live forever?
• Why do we age?
• Why don't limbs regrow after amputation?
• How do we reverse-engineer the genetic code?

• If we want to live forever, then which should we bet on: biology or artificial intelligence?

  • What is digital "immortality"?

    • You teach computers your thoughts. Then they mimic you. People can interact with "you" through computers. Then "you" would be digitally "immortal". But you'll still die. "You" is the machine's model of you.
    • It's like hiring someone to imitate you for life.

    • Is it legit?

      • Wikipedia: Digital immortality

  • Can we reach immortality by replacing all organs (except the brain) with artificial organs?

• Does fasting help someone heal from a disease?

  • Hypothesis: it might help healing because when you not don't eat, your body's immune system can focus on fighting the disease.
  • Hypothesis: it might worsen the disease because your body doesn't get enough nutrient to fight the disease.
  • Hypothesis: it might have no effect.

• bacteriophage might help us fight antibiotic-resistant bacteria

  • kurzgezagt video
  • seeker video
• wings at first evolved to help climb steep angles (trees) The Origin of Flight–What Use is Half a Wing? - HHMI BioInteractive Video
• CRISPR is a gene editing technology WP: CRISPR
• Toxin, venom, poison, what's the difference?

• Undigested

  • Opinion: Biology is the new physics (to be revolutionized by math)
  • https://design.tutsplus.com/articles/human-anatomy-fundamentals-advanced-body-proportions--vector-19869

• AeroFarms (Newark, New Jersey) uses no soil and 95% less water

  • large-scale hydroponics?
• WHY Exercise is so Underrated (Brain Power & Movement Link)
• Mutated Plastic-Munching Enzyme Accidentally Created During Lab Experiment

• Anatomy

  • Bones & Joints of the Shoulder
  • Hip range of motion

  • Where are the sinuses?

    • http://www.cancerresearchuk.org/about-cancer/nasal-sinus-cancer/about

    • choana: connection between nose and mouth

      • https://en.wikipedia.org/wiki/Posterior_nasal_apertures
• WP:TOFI (thin outside fat inside)
• 2018, How Long Do You Remain Conscious If Your Head Is Chopped Off? A few seconds, around 15 seconds.
• 2018, This Unorthodox Procedure Makes Short People A Foot Taller Distraction osteogenesis. Breaking the leg bones. Undesirable side effects.

• Why don't we throw away our trash to volcanos?

  • https://www.reddit.com/r/explainlikeimfive/comments/2suzan/eli5_why_dont_we_dump_our_trash_in_volcanos/

    • Local incineration is cheaper.
  • https://www.quora.com/Ecology-Why-not-dump-garbage-into-a-volcano

  • https://www.popsci.com/why-dont-we-just-throw-all-our-garbage-into-volcanos

• https://en.wikipedia.org/wiki/Marshall_Warren_Nirenberg

  • some experiments in molecular biology
• Teenage dolphins getting high, recreational drug use, pufferfish, neurotoxin

• Neuro-parasitogy of the Jewel Wasp and its Zombie Cockroach Host

  • Ampulex compressa, Periplaneta americana

    • https://en.wikipedia.org/wiki/Alien_(creature_in_Alien_franchise)
• Is nattokinase real? https://www.healthyhabits.com/hh_news/warfarin-rat-poison-riches/
• 2018, article, Melatonin: Much More Than You Wanted To Know

• proper posture animations

  • https://www.youtube.com/watch?v=eb4rKCM3BKM
  • https://www.youtube.com/watch?v=6SkKPgKX_gY
  • https://www.youtube.com/watch?v=n78PS4zq3D8

• animals that photosynthesize

  • https://www.nationalgeographic.com/animals/2018/07/solar-powered-photosynthetic-sea-slugs-in-decline-news/

• Reversing global warming

  • Reversing desertification

    • How to green the world's deserts and reverse climate change | Allan Savory

      • Use livestock to mimick natural predators to make livestock move around.

  • We might be able to use Tali Sharot's TEDx talk to reduce global warming (the way the electric company manipulates her into using less electricity).

• "How to build synthetic DNA and send it across the internet - Dan Gibson", youtube

  • https://en.wikipedia.org/wiki/Gibson_assembly
• https://www.boredpanda.com/chinese-family-before-and-after-6-month-weight-loss-results-fan/
• Your Skin Cells Could Make a Baby, Will This Be the End of Infertility?

• falling asleep quickly

  • A secret military technique could help you fall asleep in 2 minutes - Business Insider

    • Relax all muscles
    • Think "don't think"

30.8TODO Astronomy

30.8.1Reading sky map to find celestial objects

• Other names: star chart, star map, sky map
• WP:Celestial sphere
• The sky looks as if it were projected to a spherical screen?
• If a space object is far enough, it will look as if it were fixed in the sky.

• Suppose you found something in the sky. How do you tell your friends where that thing is? How do you tell them where to look at in the sky?

  • Use equatorial coordinate system: Right ascension, Declination, and Epoch

    • Example: Alpha Centauri A. (WP)

      • Right ascension 14 h 39 m 35.06311 s
      • Declination -60 deg 50 min 15.0992 sec
      • Epoch J2000

    • WP:Epoch

      • J2000 is the Gregorian date 2000-01-01 12:00 TT (terrestrial time).
• https://en.wikipedia.org/wiki/Celestial_coordinate_system
• https://en.wikipedia.org/wiki/Star_chart

• Equatorial coordinate system

How to read star chart?

What are equatorial coordinates?

30.8.2Distance

• https://en.wikipedia.org/wiki/Parsec

• 1 au (astronomical unit) is roughly the distance between the Sun and the Earth.

  • 1 au is about 150 million km.
  • 1 au is about 6 light minutes.

• 1 ly is 1 light year.

  • It's a unit of length, not time.

    • A light year is the distance traveled by light in one year.
• Parsec is also a unit of length.
• 1 pc is about 3.26 ly.

30.8.3Objects, ontology, hierarchy?

• planet

• https://en.wikipedia.org/wiki/Stellar_evolution

  • star

    • "A star is a luminous sphere of plasma held together by its own gravity."
    • Every star begins from collapsing clouds of gas and dust?

    • A star is a self-sustaining fusion nuclear reactor.

      • WP:Stellar nucleosynthesis
    • protostar
    • main-sequence star
    • supernova
    • brown dwarf

    • white dwarf

  • solar system

    • "sol" is Latin word for "sun"
  • galaxy
  • nebula

  • constellation (con + stella)

    • "stella" is Latin word for "star"
    • "constellation" means "bunch of stars"
  • satellite
  • moon
  • comet
  • asteroid
  • black hole

30.8.4Related fields of study?

• https://en.wikipedia.org/wiki/Cosmology
• https://en.wikipedia.org/wiki/Cosmogony

30.8.5When does gravity exceed electrostatic repulsion?

• https://physics.stackexchange.com/questions/13971/minimum-number-of-atoms-in-star
• http://www.jgiesen.de/astro/stars/star.htm

30.9Niels Henrik Abel: The unluckiest mathematician ever?

• Abel sent an important paper to Gauss, but Gauss discarded "without a glance what he believed to be the worthless work of a crank".
• Abel gave an important paper to Cauchy, but Cauchy misplaced it.
• Abel, 28 years old, died, after waiting four years for a professorship, only for the offer to arrive two days after his death.

<2019-07-17> (all emphasis mine) http://scienceworld.wolfram.com/biography/Abel.html

Abel sent a paper on the unsolvability of the quintic equation to Gauss, who proceeded to discard without a glance what he believed to be the worthless work of a crank.

(The unsolvability of the quintic equation is what Abel is perhaps most famous for today.)

Abel then traveled to Paris, where he gave an important paper […]. However, Cauchy proceeded to misplace the manuscript.

In Berlin, Abel met and was befriended by August Crelle […]

However, an offer of a professorship in Berlin was not forthcoming for four years, by which time it was too late. A letter from Crelle arrived two days after Abel's death, informing his that he had been offered professorship at the University of Berlin.

Galois also died young.

---

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