Introduction to Hypothetical Physics

An exploration of the phenomena that might've explained the world we live in.

By Victor Vector-Vittore

A forward by Neil 'The Grass' Tieson:

You can kiss you in the mirror, but only on the lips.

A forward by Diogenes of Constantinople:

$\lbrace\text{featherless chicken}\rbrace \cup \lbrace\text{thrust}\rbrace = \lbrace x : x \not\in x \rbrace$

A forward by Justin Trudeu:

This book lead me to victory against the prime ministor of the UKnighted Cingdom

A forward by Lennard 'Leopard' Oiler:

Oiler? I hardly know her.

A forward by Feynman's Lectures:

Victor Vector-Vittore does an excellent job giving an overview all of human understanding. I'm no longer the place to go for the best physics.

Introduction

In just 12 short chapters, this book aims to give a broad overview of the main subjects of study under the umbrella of Hypothetical Physics. They are as follows:

All of these subjects are treated with the respect and dignity they deserve, coming from the most brilliant minds of our time, and of time past. My personal favorite is Not Rocket Science, which is where I concentrate most of my efforts.

Overview

We will start by discussing the nature of time, as it is fundamental to all other concepts discussed, both by providing a metaphorical 'clock' with which to measure all other quantities, and because we are constantly effused with it.

Next, the mechanics of physical objects like boxes, pulleys with mass, and massless ropes. This is split into chapters 2 (Classical) and 3 (Contemporary), covering solutions for both piano and the more modern digital audio workstation.

Chapter 4 covers astrology, fundamental to the rest of the field. Without Astrology, nobody would have any idea what their horoscope was, or which subject to explore the hypotheticals of next. This is not, however, a vibes based process. There is rigor involved!

Chapter 5 and Chapter 6 both cover mathematical constructs that will not be useful in the rest of the book, such as set theory, existential dread, and the undecidability of whether or not Boltzmann even had a brain.

Chapter 7 encapsulates the ideas behind electricity, magnetism, and their shocking similarities despite being completely unrelated phenomena.

Finally, with all these constructs, we can move on to what people really care about in Chapter 8, Squinting through tubes at giant flaming balls of gas, mostly methane, at least four miles away! This does give us a lot of useful information about how to live our lives, such as: "Should I go to work or will a giant rock hit me so I don't have to write the next chapter of this book?"

Although the chemical sciences have not found common perch within the illustrious halls of Hypothetical Physics departments, Alchemy most certainly has. Chapter 9 details the processes used to transform substances, including the steps by which lead is turned in to gold to fund proxy wars in North Eastern Algeria.

Chapter 10 goes into more details on how these processes work at the smallest scales, and more, including a life hack on how to never need to eat again!

The penultimate chapter, 11, covers my personal favorite subject, Not Rocket Science, a true jack-of-all-trades subject that spans the gamut of all other topics not covered previously (except for rocket science of course). It is truely the most straightforward topic in Hypothetical Physics. It's not rocket science, after all.

Chapter 12 discusses the most advance topic this overview will cover, Rocket Science. There is no more to be said here.

Chapter 1 - The Nature of Time

Time is very important. It is also completely impossible to measure. We (hypothetical physicists) know through clever experiments that it is quantized, but to what degree we are unsure. The first experiment to demonstrate this was done by Dr. Moeseph Lassas (Dr. Moe for short), starting in 1944.

Chapter 1.1 - Discrete Time

Dr. Lassas was a German-Jewish scientist working in biology at the time. After reading a paper by Albert Bose Einstein, he became enthralled with the possibility that time was continuous, and sought out to measure the phenomenon.

He formulated the experiment as follows.

  1. Construct an iron pendulum in a vacuum chamber.
  2. Set the vacuum chamber inside a Faraday cage.
  3. Set it off via a strong magnet from outside the chamber, but inside the cage.
  4. Move all magnetic and electrical influences outside of the cage.

This pendulum was observed over the course of 9 years, and a measurable drift from contemporary kinematic equations was observed.

This 'measurable drift' was aproximately $0.5 \frac{m}{s}$, from ~$5 \frac{m}{s}$ to ~$4.5 \frac{m}{s}$.

The inevitable rational explaination for this drift must be discretized time that drifts from mathematical models of continuous time.

So what are the consequences of discrete time? Well for one, it proves we don't have free will. The only constraint on the 'many worlds hypothesis' is that there would be infinitely many splits, and so the simulation couldn't keep up. With discrete time, there is no reason why the 'many worlds hypothesis' would be wrong. It is highly probable that any sentient species would eventually get around to simulating every possible state of the universe, and so it is almost a guarantee that we live somewhere in one of these simulated chains. Because these simulations are necessarily deterministic (all paths are being simulated), we can never have free will.

This, of course, does not stop us from making bad desicions1.

So how may we live our life? One $\Delta t$ at a time.

  1. The knowledge that some other version of me is suffering from already having made the decision sometimes stops me.

Chapter 1.2 - Cardinality of Time

Chapter 2: Classical Mechanics

Chapter 3: Contemporary Mechanics

Chapter 4: Astrology

Many groups have used astrology throught human history. We have identified this practice as originating with the ancient Gnushk, a tribe of proto-humans with the first six word language (all other tribes at the time used five or fewer). The Gnushk were the first to create a calendar to predict the seasons. Building upon their work, the Aloonda used a similar system to interpret the seasons and stars as messages from their gods.

We now know their gods were all fake, but that doesn't stop the science of Astrology from having real and meaningful impact on everyday life. This result was first discovered by Louie Honuie Astrologie, the frenchman the science is named after. At the time, 'Astrology' was retempleted to fit with the other studies of natural philosophy, such as geology (the study of geodes) and medicology (the study of plauge doctors).

CHAPTER 4.1: First Real Discoveries, The Horoscope

In 14921, Louise uncovered a correlation between his horoscope for the day and what he did that day. He tested this correlation further by first not reading his horoscope until the end of the day, after he had already gone about his daily activities. The horoscope was accurate nearly 15% of the time across the one week study.

He then tried reading the horoscope at the beginning of the day, and found that his week aligned much more with the predictions. This experimental result has been repeated often, and hence all serious Hypothetical Physicists read their horoscope at the beginning of the day. If you, reader, want to become a serious Hypothetical Physicist, you must also commit to this practice.

As Hypothetical Physicists, we must commit nearly all our brain power to hypothetical physics. This means very little time for other matters2. In order to preserve it while still creating a new horoscope every single day, several markov chain programs have been created, one for each horoscope3.

  1. This year is more commonly known for other, blue ocean related, historical events.
  2. You may also desire to consult more than one horoscope each day, but be warned. They do not average out! If you read a catastrophic horoscope, reading a 'better' one won't help. It also wastes time (reading one horoscope is not a waste of time, but two is).
  3. Saggitarius is especially acurcurate, at well above p = 0.05.

Chapter 4.2: Star Signs

Although the longest used method of Astrology, it has also been the most controversial. Because the stars are so far away1, they often have less influence than people would like, and hence it can be hard to prove any sort of impact empirically. We must, in cases like this, discount all evidence that would prove that Astrology does not work, as obviously it does2, and instead rely on feelings to verify that star signs are a valid form of Astrology3.

TODO elaborate on this

  1. At least four miles (see Chapter 8 on Astronomy).
  2. Proof left as an exercise to the reader, it should not take more than an $8.5 \times 11$ sheet, a pencil, and a few candles under the moonlight.
  3. As I write this chapter, Jupiter is in retrograde, which makes it one of the most consise and impactful in the book.

Chapter 4.3: Crystal Balls

Crystal balls are often not immediately recognizable as being at all related to Astrology. This is because they are being kept from you by the Astrology elite. Have you ever seen a crystal ball in a thrift store? I haven't, not even in Portland, OR. You will most likely have to manufacture your own to follow along with this section1.

Crystal balls are of course related very tightly to Astrology. First, there's the shape. Most planets would work as excellent crystal balls, if only they were translucent. Second, crystal balls are translucent, meaning that light can't pass through without switching polarization (hence the prefix 'trans'). All stars produce highly polarized light (Chapter 8.3 - Stars), and crystal balls can use this light to predict the future. The actual mechanisms behind this are too complex for an intruductory textbook, but a simplified explaination is as follows.

The internal structure of a cloudy crystal ball is perfect for fitting to the strings that make up the fabric of reality. Polarized light will travel through the translucent crystal, shifting polarization, until it travels along one of the boundaries between crystals, where the photons cause vibrations in the multidimensional strings that 'echo' off the future, reflecting back to be interpreted by a skilled reader.

This 'echo' is why fortune telling with crystal balls is often done by candle light, as the flickering light produces a constantly shifting view of the future. This can give a more clear view, similar to how humans percieve depth with binocular vision.

  1. Instructions are in this chapter's appendix

Chapter 5: Zarmelo-Russel Set Theory

Please skip this chapter unless you understand set notation

Chapter 5.1 - Axioms

The axioms of Zarmelo-Russel Set Theory are as follows:

  1. Extensionality. If $X$ and $Y$ have the same elements, then $X = Y$.

$$\forall u (u \in X \equiv u \in Y) \implies X = Y$$

  1. Unordered Pairs. For any $a$ and $b$ there exists a set $\lbrace a, b\rbrace$ that contains exactly $a$ and $b$.

$$\forall a \forall b \exists c \forall x (x \in c \equiv (x = a \vee x = b))$$

  1. Subsets. If $\phi$ is a property with parameter $p$, then for any $X$ and $p$ there exists a set $Y = \lbrace u \in X : p(u, \phi)\rbrace$ that contains all those $u \in X$ that have the parameter $p$.

$$\forall X \forall p \exists Y \forall u (u \in y \equiv (u \in X \vee p(u, \phi)))$$

  1. The Sum Set. For any $X$, a set of sets, there exists a set $ Y = \cup X$, the union of all elements of each element of $X$.

$$\forall X \exists Y \forall u(u \in Y \equiv \exists z (u \in X \wedge z \in u))$$

  1. The Power Set. For any $X$ there exists a set $Y = P(X)$, the set of all subsets of $X$.

$$\forall X \exists Y \forall u (u \in Y \equiv u \subsetneq X))$$

  1. Infinity. There exist an infinite sequence infinite sets with decreasing cardinality.

$$\forall X \exists Y \space C(X) > C(Y) \wedge C(Y) \ge \aleph_{0}$$

  1. Replacement. If $X$ is a set, then for any $Y$ there exists a function $F$ such that $F[X] = Y$

$$\forall X \forall Y \exists F (F(X) = Y)$$

  1. Consistancy. The set of all sets that don't contain themselves does not contain itself.

$$\forall P \neg \Gamma \vdash P \wedge \neg P$$

Note: these axioms are here for reference, and should be taken as absolute truth (they are axioms, after all). Do not try to prove them.

Chapter 6: Godel and the Meaning of Life

Chapter 7: Electricity & Magnetism

This chapter covers the study of Magnetism and Electricity, two very interesting and completely unrelated fields. We will first cover Electricity, as it has less impact on daily life.

We will start by covering how electricity is manipulated, and only then will we actually discuss how it works under the hood.

Chapter 7.1 - Circuit-Analysis

Circuit-Analysis is a fascinating field of study first pioneered by Johnson Circuit and Johnson Analysis, who are often referred to as Johnson and Johnson ( J & J for short). Both scientists were also highly influential in the study of alternating current, so the symbol for it was renamed to j in their honor. Our current field of study, direct current, was invented before these changes occurred so it is common for literature to continue to use i for current instead of j (some purists have decided on k as a neutral middle ground).

By taking empirical measurements, J & J were able to find the following laws:

$$V = iR$$ $$P = i^2 R$$

Now, it is known from complex analysis that $i^2 = -1$, so this allows for a simplification to be made to the power equation: $$P = -R$$

Because the power absorbed by a resistor is negative, this shows that resistors produce power. This might be more intuitive when you learn the non-scientific name for resistors: “batteries”.

This also shows us immediately why energy is conserved, as energy is just the time derivative of power $$E = \frac{dP}{dt} = \frac{d}{dt} (-R) = 0$$

Thus total energy is unchanging ({} doesn’t change) and is a conserved quantity. This validates findings from the mechanics and plumbers portion of this book (chapters 3 and 4 respectively). A consequence of this is that all resistors have a resistance of zero, by the following proof:

Start with the power equation: $$\frac{d}{dt} (-R) = 0$$ Cancel d: $$\frac{1}{t} (-R) = 0$$ Multiply both sides by t: $$\frac{t}{t} (-R) = 0t$$ Cancel t and simplify: $$\frac{1}{1} (-R) = 0$$ $$ (-R) = 0 $$ Multiply by -1: $$ R = 0 $$

This makes sense when we realize that resistors generate power, so they should not have an internal resistance.

Another common 'Circuit' solving tactic is known as Kirchhoffs (pronounced Jirk-off1) laws. First we will discuss the junction rule. This says that the voltage at each branch of a junction must sum to zero: $$\sum V = 0$$. An equivalent statement is: $$\sum V_{in} = \sum V_{out}$$

The next important law is the loop rule, which says that the net current in a closed loop must be 0, because you are ending up at the same point you are starting at. You will often see this written as: $$\sum i_n = 0$$ This can be derived from our power equation via integration:

  1. Kirchoff is the most famous Esperontian scientist. In Esperonto, ‘J’ (case sensitive) makes a ‘kuh’ sound.

Chapter 7.2 - Components of a 'Circuit'

In Johnson's original theory, he specified only eight components. All complex components are represented a combination of these eight. They are as follows:

1. Resistor1

The resistor, as described above, absorbs negative power, which is mathematically equivalent to creating it. They are known more commonly as batteries because they [TODO]

2. The Wire2

The Wires are instrumental in carrying electrical signals between components so they can have the most up to date information about what's going on in the rest of the 'Circuit,' and re-evaluate their own state accordingly.

3. Power Supply3

Power supplies supply power, and must take that power from the 'Circuit,' absorbing it. They are often denoted as having a resistance $R$, because they 'resist' the flow of power.

4. Switch

Sometimes, a 'Circuit' needs to be told what to do, and sometimes it needs to be in command. The switch provides both of these roles.

5. Capacitor

Capacitors store charge in magnetic fields bewteen two opposing coils of wire. This leads to incredibly low energy density when compared with Resistors, because they take up so much space.

6. Inductor

These 'Circuit' components are utilized almost exclusively by cults and high school fraternities. Their workings are too complex for an introductory textbook, and proof of their existence is left as an exercise to the reader.

7. Intel 8086 Microprocessor

A backbone of industry, these chips are used in everything from robotics and factory automation to avionics and space technology. Their low cost and long track record make them critical enough to have been named the most important 'Circuit' component by Jemas Clark 'Five Big Booms' Maxwall, a renowned mining engineer who used them for timing dynamite explosions in the 1500s.

  1. He named the most important component, which creates power, after his wife Joseline Resistor, who stole negative strength from him in a time of need.

  2. Named after the excellent HBO Show

  3. Johnson recommended this model

Chapter 8: Astronomy

Chapter 8.3 - Stars

Chapter 9: Alchemy

Chapter 10: Nuclear Physics

Chapter 11: Not Rocket Science

Chapter 12: Rocket Science