Quantum Physics Notes

"Not only is the Universe stranger than we think, it is stranger than we can think."
- Werner Heisenberg
References
Quantum Physics Notes
1900 - Planck's Constant
Karl Ernst Ludwig Max Planck
Planck proposed that energy (e), could only exist in discrete packets known as Quanta (plural of Quantum, from the Latin, Quantus, meaning 'how much'). These Quanta were proportional to the frequency (v) of light by a universal constant he called h, so…
e = hv

This solved a serious nagging problem known as the Ultraviolet Catastrophe. By using his mathematical solution, now known as Planck's Law of Blackbody Radiation, he solved the problem completely, but he did not understand why it should work. His clever mathematical solution however turned out to be the Cornerstone of all of Quantum Mechanics. By using Planck's Constant & the concept of Quanta, everything began to fall into place.

R =
2πc2h
λ 5 ( e (hc ⁄ λkT)  - 1)
Planck's Law of Blackbody Radiation

When frequency is expressed in radians per second (angular frequency) instead of cycles per second, it is useful to incorporate into the Planck Constant. The result is called the Reduced Planck Constant or H-Bar, written as . It is a very, very, small number equal to:

ħ = 1.054571596 x 10-34 kg m2 ⁄ s
ℏ   Planck Units   ℏ
Planck Units, a.k.a. Natural Units are a set of Units of Measurement defined solely in terms of Universal Natural Constants. They are established by setting the Speed of Light, Time, Length, etc. equal to ONE UNIT. This is the ultimate Natural World, non-arbitrary, measurement system. For those who study the quantum world it greatly simplifies calculating solutions to problems.

Reduced Planck's Constant     ħ = 1.054571596 x 10-34 kg m2 ⁄ s

The Planck Length (Lp) is the Smallest Measurement of Length that has any real meaning in our universe. It is about 10-20 the size of a proton. It derives directly from Planck's Constant and tells us about the actual 'fabric' of our universe. Imagine our universe as a giant TV screen with the Planck Length representing the size of each pixel. What is happening BETWEEN the pixels has no meaning.

Planck Length = 1.6 x 10-35 m

Planck Time (tp) is the Smallest Measurement of Time. Planck Time is defined as the time required for a Photon moving at the Speed of Light (c) to cross a distance of one Planck Length.

Planck Time = 5.39 x 10-44 seconds

Since this is the Smallest Division of Time that has ANY meaning, we can only say that our universe came into existence when its age was One Planck Duration (10-43 seconds) after the Big Bang.

Planck Temperature = 1.417 x 1032 °K

The Planck Temperature (Tp) is the Highest Temperature theoretically possible for matter, most likely occurring at One Planck Duration (10-43 seconds) after the Big Bang singularity.

1905 - Special Relativity
Albert Einstein
Einstein proposed two basic principles that apply for all Inertial (Non-accelerating) systems.

1. The speed of light (c) is the same for all observers.
2. The Laws of Physics remain constant in all such systems.

From these two basic principles it directly follows that all events in the universe (spacetime) must be considered relative to each other. Events were related to each other by a factor known as The Lorentz Transform Factor γ = 1/√(1- v²⁄c²). Special Relativity did away with any universal or absolute reference system. Also from this Principle can be derived the famous equivalence of matter to energy:

e = mc²

Speed of Light in a Vacuum:     c = 299,792,458 m ⁄ s
The Lorentz Transform Factor:     γ = 1 ⁄ √(1- v²⁄c²)

1913 - Atomic Structure
Niels Henrik David Bohr
Bohr proposed the theory that describes the postion of electrons in an atom. Since the nucleus of an atom is massive, its position is well defined, however since the mass of an electron is so small, its position must be defined by an 'Electron Cloud' of probability. These Probabilistic Regions or 'Clouds' exist in different energy levels defined by the first Quantum Number N and also take on different shapes as defined by their 2nd Quantum Number L. In addition, each Orbital State has Sub-Orbital states s, p, d, f (named by Bohr as Sharp, Principal, Diffuse, and Fundamental). Some examples are:

1915 - Equivalence Principle → General Theory of Relativity
Albert Einstein

Gravity ≡ Acceleration
Einstein postulated that the effects of gravity are indistinguishable from the effects of acceleration. His 'Equivalency Thought Experiment' explained his reasoning. The forces acting upon someone who is in a Space Ship in deep space that is accelerated constantly is Equivalent to the forces acting upon someone in a similar stationary box on Earth, which is only being acting upon by gravity. Therefore: Gravity ≡ Acceleration.

In the Space-Ship light always bends down towards the accelerating force. This leads to the conclusion that light must also bend in any gravitational field. BRILLIANT ! This in turn leads to the conclusion that space must be curved in any gravitational field since light always takes the shortest path. These brilliant conclusions lead to Einstein developing his General Theory of Relativity. As a test, the theory correctly predicted the apparent shift of the planet Mercury during the Total Solar Eclipse of 1919.

1924 - Wave ⁄ Particle Duality of Matter
Louis de Broglie
In his 1924 PhD thesis Louis de Broglie hypothesized that all matter has wave properties. He postulated that electrons zipping around a nucleus should be thought of as waves instead of particles. The electrons as waves certainly cannot destructively interfere with themselves or they would quickly self-annihilate. Therefore, each electron's frequency (λ = h ⁄ mv) could only be allowed at unique quantized orbits. This reinforced electron shell theory and for this he won the Nobel Prize for Physics in 1929.

Wave ~ Particle Duality
Louis de Broglie's theory can also be applied to the 'Particle In A Box' thought experiment. Consider a single sub-atomic particle bouncing about inside a box. Ever so slowly we reduce the size of the box. As the box becomes smaller and smaller we know the position of the particle with ever more precision. Classically, if we reduce the size of the box down to the size of the particle itself, then we would know its exact position. This should work, right? BUT NO! Since the Particle has BOTH Particle AND Wave Descriptions, as the box gets smaller the Particle's Wave component becomes more and more important. When the box reaches a certain very small limit the Particle's wave description actually extends 'beyond the box' and the particle can no longer be considered as being 'inside the box'. It appears to have tunneled through the barriers and is suddenly outside the box.
1925 - Pauli Exclusion Principle
Wolfgang Ernst Pauli
For any of the electrons in an atom their quantum numbers must be different. This prevents any two electrons from simultaneously having the same quantum numbers N, L, & M and helps explain how electrons occupy certain probabilistic regions around the nucleus.
N = size of the orbital (1, 2, …)
L = shape of the orbital (spheroid, teardrop, torus, etc.)
M = momentum of the electron, which includes it's spin value
1925 - Probability Wave Equation
A Wave Packet
Erwin Rudolf Josef Alexander Schrödinger
Schrödinger derived a partial differential equation using the variables of space, momentum, particle spin, and time that describes how any system changes with time. It accurately predicts the Probability Amplitude of the position and momentum for sub-atomic as well as macro systems. This was a major leap forward towards understanding the effect known as Quantum Tunneling. This suggested that particles could sometimes be thought of as Wave Packets, spread out over SpaceTime. The Schrödinger Equation (general case):

𝑖 ħ ∂t Ψ = Ĥ Ψ
1927 - Heisenberg Uncertainty Principle and The Ideal Oscillator
Werner Karl Heisenberg
Heisenberg proposed that the POSITION and MOMENTUM of any particle are COMPLEMENTARY properties. The more you pinpoint the POSITION, the less you know about the MOMENTUM, and vice-versa. Their product can only be more than a very small number (Planck's Constant). This is a Basic Law of Physics and is independent of the ability of ANY aparatus to measure. This Fundamental Priciple is used to accurately explain many quantum effects and forces us to use Laws of Probabilities at sub-atomic levels. Among the possibilities introduced is Quantum Tunneling ⬇.

Heisenberg Uncertainty Principle:   Δx Δp ≥
2

Heisenberg also brilliantly suggested discarding the electron orbital description of the atom, and instead treating the entire Atom as an Ideal Oscillator - without visualizing the exact internal mechanics and just focusing upon measureable quantities. As such it's Total Energy H would oscillate as a function of the Observables A with respect to time t, according to the following formula:

d
dt
A(t) =
i
[H, A(t)] + (
∂A
∂t
) H

Where H is the Hamiltonian (an operator representing the total energy of a system), and A are Observables (physical properties that can be measured).

1928 - The Dirac Equation
Paul Adrien Maurice Dirac
Arguably the Most Important Physicist of the 20th Century and probably the least known even though he was on a par with Sir Isaac Newton. Dirac derived an equation that was both Mathematically Beautiful and powerful beyond even his dreams. Dirac worked on deriving the equation for 3 full years, finally presenting it in 1928. It seamlessly combines all the aspects of Quantum Physics with Einstein's Theory of General Relativity and among other things Predicted the Existence of Anti-Matter for the very first time.
βm 2 + c n=1 3 αnpn Ψ (x,t)  =  i ℏ 
∂Ψ (x,t)
———
∂t
Dirac's Original 1928 Equation
Where:
Ψ = Ψ(x, t) is the Wave Function for an electron of rest mass m with spacetime coordinates x, t. The variables p1, p2, p3 are the components of the momentum operator in the Schrödinger equation. Also, c is the speed of light, and is Planck's constant divided by 2π. The fundamental physical constants and c represent special relativity and quantum mechanics. α and β are 4 x 4 Matrices of the superposition of a spin-up electron, a spin-down electron, a spin-up positron, and a spin-down positron. Dirac's Equation theorizes Anti-Matter 4 years before the positron was discovered!

Using Planck (Natural) Units, where ℏ = c = 1, the Dirac Equation can be re-written two ways, so:

γμ ( 𝑖∂μ - eAμ ) 𝛹 = m𝛹

( 𝑖∂⃒ - 𝑚) 𝛹 = 𝛰
1935 - Schrödinger's Cat
Erwin Rudolf Josef Alexander Schrödinger
Schrödinger's Cat is a thought experiment, first presented in 1935, to help scientists understand in our everyday world what was happening in the odd quantum world. In this experiment a live cat is enclosed in a sealed box with no windows for one hour. Inside the box is a vial of poison and an apparatus to break the vial, triggered by the decay of a small amount of radioactive material with a half-life of one hour. The vial will be broken at some random time killing the cat. Schrödinger suggested that until we open the box and actually LOOK the Copenhagen Interpretation of quantum mechanics implies that the cat is BOTH alive and dead. It's fate is ONLY known when we look, and the quantum superposition collapses into only one possibility.

1948 - Feynman Diagrams
Richard Phillips Feynman
Electron - Positron Annihilation
Feynman was a brilliant theoretical physicist who developed a theory of sub-atomic particle interactions that came to be known as Quantum ElectroDynamics (QED). In 1948 he presented his theory to the world's top physicists through the use of his special graphics known as Feynman Diagrams that boiled down the complex mathematics into simple drawings.

Time is shown along the bottom axis. Antiparticles are shown as moving backwards through time. i.e. a Positron p+ is an Electron e- moving backwards in time!

Shown here is an Electron e- meeting it's antiparticle the Positron p+. Their mutual annihilation generates a Photon (gamma wave 𝛾 ), which soon decays into a Quark (q) and an Anti-Quark (q̄) pair. The Anti-Quark (q̄) then expels a Gluon (g) which is a Force carrier.

1955 - Quantum Foam
John Archibald Wheeler

Quantum Foam
Process
The Energy (E) and also the Time (t) accuracy of any system is limited by Plank's constant.
ΔE Δt ≥ ħ
Wheeler postulated that spacetime was very turbulent on small scales below the Planck Length. At these extremely small scales he suggested that Energy could be 'borrowed' from the universe and then almost instantly 'repaid'. Doing so would briefly generate particles and anti-particles, that would almost instantly self-annihilate. The time (t) duration would be extremely short. The shorter the time scale the more energetic can be the particle pairs. Since Einstein's General Theory of Relativity states that energy can curve spacetime, on these extremely small scales, below the Planck Length, space makes a significant departure from its smooth macro appearance resulting in what he called a 'Quantum Foam' seething with activity. This 'Foam' is impossible to observe directly.

As Δt→ 0 , ΔE→ ∞      E ⇒ photon + e- + e+ ⇒ E
1958 - Black Holes
David Ritz Finkelstein
Einstein's General Releativity predicts that mass curves spacetime. Taken to the extreme, there are sufficiently compact masses whose gravity is so strong that no particle or light ray entering the region can ever escape from it. The boundary of this region from which no escape is possible is called the Event Horizon. The Event Horizon's Radius was worked out by Karl Schwarzschild in 1916 purely from General Relativity, but it's interpretation was not suggested until 1958 by Finkelstein. The Schwarzschild Radius (Rs) is porportional to the Black Hole's total mass (M), the Universal Gravitational constant (G), and inversely by the speed of light (c) squared so:

Rs =
2GM

Crossing the event horizon seals the fate of any object crossing it, but has no locally detectable features other than tidal gravitational effects. An object approaching an event horizon would appear to an outsider however, to slow down and gradually fade out to infra-red as it comes under the effects of Relativity.
1974 - Hawking Radiation
Stephen William Hawking
Quantum Foam           Hawking Radiation
In 1974 Stephen Hawking provided a theoretical argument combining Einstein's General Theory of Relativity, the Schwarzschild Radius prediction, and Wheeler's Quantum Foam Theory. Hawking reasoned that at the event horizon of a Black Hole it might be possible for the randum fluctuations of spacetime to create pairs of objects, from which, one of the pair might proceed towards the Black Hole and the other one might proceed away from the Black Hole with enough energy to escape from the Event Horizon. These pairs would not be able to re-unite and Black Holes should therefore appear to radiate the extra particles and associated photons. This effect is known as Hawking Radiation.

Counter to intuition, the Black hole losses mass equivalent to the Energy of the Radiation, since e = mc². Over vast stretches of time the Black Hole would eventually radiate away all of it's mass and evaporate. I.E. if we stand back and view an individual Black Hole in deep space, then as it radiates energy its mass must decrease over time.

Sub-Atomic Particles
The Photon
T he Photon (γ) is considered to be the quantum of light. Also known as a Gamma Wave, it has zero rest mass and ALWAYS moves at the speed of light (c) in a vacuum. The speed of light is given the symbol c, from the Latin, celeritas (speed). A Photon can even exhibit wave interference with itself. The Photon can carry information, e.g. thermal information, doppler information, radio waves, microwaves, etc. A Photon carries Energy (E) porportional to its frequency (v) according to the Planck-Einstein Relation:

E = hv
v = frequency in Hertz (Hz) = cycles ⁄ sec
h = Planck's Constant = 6.626 x 10-34 Joule·sec
ℏ = Reduced Planck's Constant (h-bar) = h ⁄ 2π

speed of light:     c = 299,792,458 m ⁄ s   (186,000 mph)

Niels Bohr worked out that a Photon was absorbed or emitted when an electron transitions between two energy levels in an atom. This is given by the energy difference:

ΔE = hv
The Electron
T he Electron (e-) was first discovered in 1897. Electron (from the Latin, electrum and the Greek, ēlektron) are the ancient names for amber. Amber of course has the ability to create a significant static charge. The Electron is a Lepton (from the Greek, leptós, 'tiny') and the main carrier of electric charge in the universe. It has an extremely small mass but carries a full -1 Charge. It also has what physicists call s Spin of + ½. Spin is a measure of an Elementary Particle's Angular Momentum (as if it were spinning) but Elementary Particles do not literally "spin". High energy Electrons, especially those used in experiments, are known as Beta Particles (β-). Electrons exhibit Wave ~ Particle Duality, i.e. they can be described as BOTH a Wave AND Particle. The Heisenberg Uncertainty Principle describes their complementary Position & Momentum properties.
Δx Δp ≥
2

T he Electron's Anti-Particle is the Positron (e+, β+). When Particles combine with their Anti-Particles they mutually annihilate and generate high energy Photons according to Einstein's famous equivalency E=mc2. Some physicists have theorized that a Positron is actually an Electron moving Backwards in Time.

Quarks
up
+2/3
down
-1/3
charm
+2/3
strange
-1/3
top
+2/3
bottom
-1/3
Q uarks are tiny theoretical entities that are used to explain the properties of Sub-Atomic Particles. In Particle Reactors, like SLAC at Stanford University, physicists analyze hundreds of complex sub-atomic particles, observing their paths and their decay sequences. Quarks never exist alone by themselves but rather always combine in ways that make up all the varieties of matter about which we know. Quarks all have fractional electric charges of either +2/3 or -1/3. All Quarks have a + 1/2 Spin.

G luons are the exchange Particles that carry the Strong Nuclear Force which binds Quarks together inside the Nucleus. If one were to somehow 'stretch' two Quarks apart this Strong Nuclear Force would snap like a rubber band and the released energy of the separation E=mc2 would create two more Quarks, one for each of the separated Quarks. There would then be two Quark pairs.

A s with other Elementary Particles there are also Anti-Quarks with opposite charges than their counterparts. These Anti-Quarks combine to make up the Anti-Particles like Anti-Neutrons and Anti-Protons.

QuarkChargeAnti-QuarkCharge
Up (u)+2/3Anti-Up (ū)-2/3
Down (d)-1/3Anti-Down (d̄)+1/3
Charm (c)+2/3Anti-Charm (c̄)-2/3
Strange (s)-1/3Anti-Strange (s̄)+1/3
Top (t)+2/3Anti-Top (t̄)-2/3
Bottom (b)-1/3Anti-Bottom (b̄)+1/3

✓  FYI, a bar   over a particle symbol indicates an Anti-Particle, e.g. ū d̄.
The Proton
T he Proton (P+) was first discovered in 1866. Proton is from the Greek word for first. They define each element. The number of Protons in the atomic nucleaus is unique to each Element and is known as the Element's Atomic Number. Protons carry a Charge of +1 and a + ½ Spin. Protons are known as Hadrons (from the Greek, hadrós, 'thick') and are 1836 times as massive as the Electron. High energy Helium nuclei (2 Protons + 2 Neutrons) are known as Alpha Particles (α, He2+).

Protons are composed of 3 Quarks - two 'Up Quarks' (u) and one 'Down Quark' (d). Quarks have fractional electric charges: Up Quarks (u) +2/3 and Down Quarks (d) -1/3. Combined they give the Proton a +1 Charge. Quarks CANNOT exist seperately.

Proton:   u (+2/3) + u (+2/3) + d (-1/3) = +1 Charge

T he Proton's Anti-Particle is the Anti-Proton () (pronounced p-bar). Anti-Protons are composed of 3 Quarks different from the Proton - two 'Anti-Up Quarks' (ū) and one 'Anti-Down Quark' (d̄). The Anti-Quark charges are: Anti-Up Quarks (ū) -2/3 and Anti-Down Quarks (d̄) +1/3. Combined they give the Anti-Proton a Charge -1.

Anti-Proton:   ū (-2/3) + ū (-2/3) + d̄ (+1/3) = -1 Charge
P ROTONS ARE STABLE. Their decay is only theoretical. Despite significant experimental effort in all the world's particle accelerators, NO Proton Decay has ever been observed. Theoretically, if one would decay, it would decay into a Positron p+ and a Neutral Pion π o. The Proton's half-life is calculated to be at least 1.67 x 1034 years, which is on the order of 1024 times the current age of our universe!
The Neutron
T he Neutron (N0) was first discovered in 1932. They exist in the atomic nucleus of every Element except Hydrogen. Neutrons have No Charge but do have a + ½ Spin. Neutrons are grouped as Baryons (from the Greek, barýs, 'heavy') and are 1838 times as massive as the Electron. Neutrons and Protons are bound together in the atomic nucleus with the Strong Nuclear Force. Neutrons are required for the atomic nucleus to remain stable. When there are more Neutrons than Protons in the atomic nucleus the atom is said to be an Isotope of the Element. Some Elements have many Isotopes and some none, but when there are excessive amounts of Neutrons in the nucleus the atom can become unstable and release Neutrons over time. Such Elements are then called Radioactive. Their decay is measured by Half-Life, i.e. the amount of time required for Half of the Isotopes to spontaneously decay and eject Neutrons.

Neutrons are composed of 3 Quarks - two 'Down Quarks' (d) and one 'Up Quark' (u). In the Neutron therefore we have: 1 Up Quark (u) +2/3 and 2 Down Quarks (d) -1/3. Combined they give the Neutron a Zero Charge.

Neutron:   u (+2/3) + d (-1/3) + d (-1/3) = 0 Charge

T he Neutron's Anti-Particle is the Anti-Neutron () (pronounced n-bar). Anti-Neutrons are composed of 3 Quarks different from the Neutron - one 'Anti-Up Quark' (ū) and two 'Anti-Down Quarks' (d̄). The Anti-Quark charges are: Anti-Up Quark (ū) +2/3 and Anti-Down Quarks (d̄) -1/3. Combined they give the Anti-Neutron a Zero Charge.

Anti-Neutron:   ū (-2/3) + d̄ (+1/3) + d̄ (+1/3) = 0 Charge
💪   The Strong Nuclear Force   💪
A tomic Nuclei are composed of Protons P+ and Neutrons No held together by The Strong Nuclear Force. This Attractive Force acts like a 'glue' or 'net' and binds the nucleus together. But it only extends for an extremely short distance, on the order of a just a few Proton diameters. It just barely manages to overwhelm the strong Repulsive Electro-Magnetic Force (EM) caused by having positively charged Protons so extremely close together. Neutrons in the nucleus spread apart the Protons just enough to reduce their EM Repulsion and so, stabilize the nucleus. But it is a balancing act and juggling too many vibrating, energetic 'balls' can occasionally lead to instability.

B ismuth, with 83 Protons in the Nucleus, is considered to be the heaviest stable element. All nuclei with more than 83 protons are unstable to varying degrees and The Strong Nuclear Force of Attracion progressively loses out against the EM Repulsive Force. This results in Proton(s) or Alpha Particle(s) (a Helium Nucleus with 2 Protons & 2 Neutrons) being violently ejected and then immediately repulsed by the enormous collection of positive charges. The Atomic nucleus is radioactive and decays.

Two Protons Trying to Separate
but held by Strong Nuclear Force
A lso The Heisenberg Uncertainty Principle explains that the decay of a nucleus is a probabalistic event and cannot be predicted. It can however be measured as the Half-Life of the nucleus. The Protons in the nucleus are susceptible to the effects of Quantum Tunneling and can sometimes for a split second actually 'exist' just outside the bounds of The Strong Nuclear Force. When this happens they are violently repulsed by the EM Force and Zoom away.
The Pions (π)
P ions are a group of particles, intermediate in size between the Electrons & Protons, but still possessing full integer charges. They are 273 times as massive as the Electron and were first discovered in particle accelerators as by-products of particle collisions. All Pions are composed of a Quark and an Anti-Quark. They are very UNstable, existing for only about 26 nano-seconds (2.6 x 10-8 seconds). Pions (π) have Zero Spin.

π+ Pions are composed of TWO Quarks - one 'Up Quark' (u) and one 'Anti-Down Quark' (d̄).

π- Pions are composed of TWO Quarks - one 'Anti-Up Quark' (ū) and one 'Down Quark' (d).

one 'Up Quark' (u) + one 'Anti-Up Quark' (ū)
OR
one 'Down Quark' (d) + one 'Anti-Down Quark' (d̄)
πo Neutral Pions are composed of TWO Quarks, like so …
π+ Pion:   u (+2/3) + d̄ (+1/3) = +1 Charge

π- Pion:   ū (-2/3)  +  d (-1/3) = -1 Charge

πo Pion:   u (+2/3)  + ū (-2/3) = 0 Charge

πo Pion:   d (-1/3)   + d̄ (+1/3) = 0 Charge
π+
Up + Anti-Down
π-
Anti-Up + Down
The Muon (μ)
T he Muon (aka Mu Meson) is a particle, slightly less massive than a Pion, but still possessing a full -1 charge. The Muon is 207 times as massive as the Electron. They were first discovered in 1936 in particle accelerator cloud chambers as a decay-product of Pions. Muons are NOT however composed of any smaller particles. They are their own particle. Muons are very UNstable and exist for only 22 nano-seconds (2.2 x 10-8 seconds). All Muons (μ-) have a +½ Spin. There is also an Antimuon (μ̄) which has a +1 charge.

W hen a Muon decays (in 2.2 x 10-8 seconds), they decay into neutrinos (𝜐) and an Electron. Here is the usual Muon decay process (a.k.a. Michel Decay) of a Muon (μ-) from a Pion (π-).

Neutrinos (𝜐)
N eutrinos (𝜐) are elusive, practically massless, sub-atomic particles, moving at very near the speed of light. They possess zero charge and react with only Gravity and the Weak Nuclear Force. Neutrinos 𝜐 are created in nuclear reactions. There are 3 theoretical types; the Electron Neutrino 𝜐e, the Muon Neutrino 𝜐μ, and the Tau Neutrino 𝜐τ. They all have a + ½ spin. Trillions of Neutrinos are ejected every second from the nuclear reactions taking place within our Sun. They pass through the Sun's interior and then through us and the Earth as if we are not even here. They could easily pass through a light year's thickness of matter without being disturbed. It was only in 1956 that we finally detected one directly, and even then, only a super high energy Neutrino 𝜐e. There is no known process to detect low energy Neutrinos.
Standard Model of Fundamental Particles
~ Fermions ~
These 3 Create All The Elements
~ Bosons ~
Force-Information Carriers
- 1
e
electron
+ 2/3
u
up quark
- 1/3
d
down quark
0
g
gluon
0
γ
photon
Leptons
+1/2 Spin
Quarks
+1/2 Spin
Gauge Bosons
+1 Spin
Sub-Atomic Particles Reference Table
Particle Symbol Charge Spin Components
Electrone-- 1+ 1/2Fundamental Particle
Positronp++ 1+ 1/2Anti Particle of Electron
ProtonP++ 1+ 1/2* Fundamental Particle:   u(+2/3) + u(+2/3) + d(-1/3)
Anti-ProtonP-- 1+ 1/2* Anti Particle:   ū(-2/3) + ū(-2/3) + d̄(+1/3)
Neutronno0+ 1/2* Fundamental Particle:   u(+2/3) + d(-2/3) + d(-1/3)
Anti-Neutrono0+ 1/2* Anti Particle:   ū(-2/3) + d̄(+1/3) + d̄(+1/3)
Pion (Pi Meson)π++ 1+ 1/2** Decay Particle: u(+2/3) + d̄(+1/3)
Pion (Pi Meson)π-- 1+ 1/2** Decay Particle: ū(-2/3) + d(-1/3)
Pion (Pi Meson)πo0+ 1/2** Decay Particle: u(+2/3) + ū(-2/3) OR d(-1/3) + d̄(+1/3)
Muon (Mu Meson)μ-- 1+ 1/2Anti Particle: μ̄ (+1), Decays into: e- + 𝜐̄e + 𝜐μ
Tauon (Tau Lepton)τ-- 1+ 1/2Anti Particle: τ̄ (+1)
Neutrino (Electron)𝜐e0+ 1/2Anti Particle: 𝜐̄e
Neutrino (Muon)𝜐μ0+ 1/2Anti Particle: 𝜐̄μ
Neutrino (Tau)𝜐τ0+ 1/2Anti Particle: 𝜐̄τ
Gluong0+ 1Fundamental Force Carrier
Photonγ0+ 1Fundamental Particle of Light
Up Quarku+ 2/3+ 1/2Fundamental Particle, ↺ Antiparticle: ū (-2/3 charge)
Down Quarkd- 1/3+ 1/2Fundamental Particle, ↺ Antiparticle: d̄ (+1/3 charge)
Charm Quarkc+ 2/3+ 1/2Fundamental Particle, ↺ Antiparticle: c̄ (-2/3 charge)
Strange Quarks- 1/3+ 1/2Fundamental Particle, ↺ Antiparticle: s̄ (+1/3 charge)
Top Quarkt+ 2/3+ 1/2Fundamental Particle, ↺ Antiparticle: t̄ (-2/3 charge)
Bottom Quarkb- 1/3+ 1/2Fundamental Particle, ↺ Antiparticle: b̄ (+1/3 charge)
* Quarks in Protons and Neutrons must align so that two of the three + 1/2 spins cancel each other and leave a net spin of + 1/2

** Pions (Pi Mesons) only exist for 26 nanoseconds

Quantum Effects

||   Double Slit Experiment   ||
T he DOUBLE-SLIT EXPERIMENT is considered to be the most important experiment in all of Quantum Physics. Its odd behavior can only be explained by discarding what you think you know about how things work in the universe.

A device fires INDIVIDUAL electrons at a barrier with two slits. On the other side is a collecting wall. Each electron can ONLY go through one slit or the other. We would expect to see two groups of electron 'hits' on the wall, but instead we see a spread out INTERFERENCE PATTERN of hits. What the…?

Interference patterns would only occur if the electron PARTICLES were acting like WAVES. How can this be? Even when the electrons are fired ONE-AT-A-TIME we still get the same results.

IT GETS WORSE !! If we just MEASURE which slit of the two the electron actually goes through, the interference pattern disappears! Now, if we leave the "spying apparatus" there but leave the room and turn it off - the interference pattern RETURNS! WHY would our LOOKING make any difference? Why does the electron care if we peeked?

Quantum Tunneling
Q uantum Tunneling arises from the Heisenberg Uncertainty Principle which puts limits on just how finely we can pinpoint a small object. The smaller the object, the less certain we are of its position. Schrödinger suggested that an object's location is actually a Probability that drops off quickly with distance. However, when a small object is very, very close to a barrier (physical or energy), it still has a probability (however slight) of actually BEING on the other side.

F or only one particle, there is an overwhelming probability it is exactly where we think it is (at X1), but if we consider a great many particles, there is a good chance that a few of them might actually BE on the other side of the barrier (at X2) as if they somehow mysteriously tunneled through. This is known as Quantum Tunneling. It affects how the sun shines, how genes mutate, how life evolves, how touch screens work, and much more.

🌞 How The Sun Shines 🌞
I t is because of Quantum Tunneling that our sun can shine at all. Our sun, like any star, releases energy when Hydrogen fuses into Helium. But in order to fuse Hydrogen into Helium the sun should be about 100 TIMES HOTTER than it is, so how can this be happening? The answer is Probability. There is a slight chance (very very slight) that even the non-energetic Hydrogen atoms can fuse into Helium anyway (by tunneling across an energy barrier). Only the tiniest percentage due so however, but the sun has SO MUCH HYDROGEN that this is happening all the time.

T he sun is now about half-way through it's main sequence life expectancy of approximately 9 billion years. Each second the sun fuses about 600 million tons of Hydrogen into Helium. Do not worry, there is a LOT of Hydrogen left, so don't re-schedule your weekend plans. When the Hydrogen is all used up the sun will begin to fuse Helium into heavier elements with ever-decreasing energy generation. Hydrogen → Helium → Carbon → Neon → Oxygen → Silicon → Iron. The final product of this fusion process will be the creation of Iron atoms which are extremely stable. After that, no more energy can be generated by fusion. However, the sun's immense gravitation WILL be used to create a few more heavier elements (like Silver, Gold, Uranium, etc.) although that process does not create energy but instead consumes it.

📱 Touchscreen Technology 📱
Normal State of Nano-Particles
Compressed State of Nano-Particles

The Basics
Atoms have a negative electron cloud surrounding a positive nucleus. This electron cloud prevents the atoms from coming too close together (like charges repel).

How It Works
In a polymer film composed of a grid of nano-particles there is a natural energy barrier (electrical resistance) between the particles. By applying finger pressure to the film the nano-particles are moved closer together. A TINY change in the distance between these nano-particles creates a HUGE change in the amount of quantum tunneling between them. In fact, for each Angström Å (10-8 cm), the nano-particles are moved closer together the quantum tunneling increases by a factor of 10!

Simple finger touches can actually lower the localized resistance of the nano-particles on the order of a Trillion Times, from 1012 Ω → 1 Ω. This change can easily be detected by an electronic circuit and the input sent to a computer processor.

🥶 Absolute Zero 🥶
A bsolute Zero is the Theoretical thermodynamic bottom limit where there is NO heat (i.e. zero motion). It is defined as 0° K (Kelvin) which corresponds to -273.15° C or -459.67° F. When matter nears Absolute Zero it exhibits very exotic behavior. Theoretically at Absolute Zero even Sub-Atomic Particles stop vibrating and Electrons are freed from their bonds with the nucleus. The Electrical resistence, measured in ohms, drops to almost zero (Ω → 0 ) and the material becomes Super-Conductive.

🤝 Quantum Entanglement 🤝
Q uantum Entanglement is a most fascinating aspect of Quantum Physics. Two particles are selected that are known to have opposite properties such as two Paired-Electrons with opposite Spins. The Electrons are then separated by an enormous distance, even light years. As soon as we measure the Spin Property of one, we instantly know the Spin Property of the other. This would seem to contradict the Law of Faster than Light Information Transfer which is forbiddenby by the Theory of Relativity. Einstein had great difficulty with this problem calling it, " Spooky action at a distance."

E  instein's approach was to think about the problem as if the two Entangled Particles were like a pair of gloves, one Left-handed and one Right-handed. Put them in seperate boxes so that you do not know which is which. If you separate the boxes even by an enormous distance, as soon as you look into one box, you Instantly know what is in the other box. Is this Faster than Light Travel of Information? I think not. No magic. No hocus-pocus.

W e have learned that we cannot describe the Quantum State of Individual Pieces. Instead, we can only describe the Quantum State of a System as a whole. Entanglement can occur when measuring Position, Momentum, Spin, or Polarization. Until a measurement is made the Quantum State cannot be determined.

Physics Definitions & Formulas
Definitions
Velocity
Velocity (v) is the change () of position (x) per unit time (t)
v =
x
t
Acceleration
Acceleration (a) is the change () of velocity (v) per unit time (t)
  which is also:
The change () of position (x) per unit time, per unit time ()
a =
v
t
=
x
Momentum
Momentum (ρ) is the product of mass (m) and velocity(v). It is a VECTOR quantity, i.e. it has direction and value. We define it with the greek letter, rho (ρ).
ρ = mv
Gravity
 Newton's Law of Universal Gravitaion 
F = G
m1 m2
————
r 2
G = Gravitational Constant (Big G)
G = 6.67408·10-11 m3 kg-1 s-2

g = Earth standard gravitional acceleration (small g) = 9.80665 m ⁄ s2 = 32.174 ft ⁄ s2

Gal = Galileo, unit useful in measuring tiny changes in small g (mGal = milli Gal = 10-3 Gal)
Gal = 1 cm ⁄ s2 = 0.01 m ⁄ s2 = 0.0328 ft ⁄ s2

Newton's Second Law of Motion
The Force on an object is equal to its Mass (m) times its Acceleration (a)
F = ma

Kinetic Energy
Kinetic Energy (Ek) is equal to one-half the Mass (m) times the velocity squared (). It is a SCALAR quantity, i.e. it is a Quantity without a direction.
Ek = ½mv²

Potential Energy
Potential Energy (Ep) is the stored up energy of an object in a system with some kind of restoring force.
Formulas for Ep can take different forms depending upon the system(s) involved. Here are a few…

Entropy
The Second Law of Thermodynamics states that in any CLOSED system the total Entropy will either remain constant or increase. Any CLOSED system will tend towards disorder and randomness and NOT towards orderliness. Entropy is a measure of a system's DISORDER. This has profound ramifications:

Einstein's Mass-Energy Relationship
e = mc²

Heisenberg Uncertainty Principle
x p ≥ ℏ
E t ≥ ℏ

Lorentz Transform Factor
1 ⁄ (1- v²/c²) 

Wheeler's Quantum Foam Prediction
from E t ≥ ℏ , as t → 0 , E → ∞   ∴     E ⇒ e- + p+ ⇒ E

Planck's Constant
= 1.054571596 x 10-34 kg m2 s-1

Boltzmann Constant
k = 1.38964852 x 10-23 kg m2 s-2 K-1

Imaginary Number ( i )
i = -1 
i² = -1

Euler's Formula
e π i = -1

Ratio of Diameter of a Circle to its Circumference ( π )
π = 3.14159265358…

Natural Logarithm - ( loge )
ln (e) = -1
e = 2.718281828459045…

The Golden Ratio
φ - 1 = 1φ
φ  = 1.6180339887… (Golden Ratio)
1φ = .6180339887… (Inverse Golden Ratio)

⛵   Reynold's Number   ⛵
Reynold's Number ( Re )
Re =
ρvL
———
μ
=
vL
———
ν
where:
ρ is the density of the fluid (kg ⁄ m3)
v is the velocity of the fluid with respect to the object (m ⁄ s)
L is the characteristic linear dimension (m)
μ is the dynamic viscosity of the fluid (N·s ⁄ m2   or   kg ⁄ m·s)
ν is the kinematic viscosity of the fluid (m2 ⁄ s)

Re < 1,000 (Laminar Flow)
Re > 2,000 (Turbulent Flow)

[Reynold's Number, Side Note]
In Modeling tests for airplanes and ships the Reynold's Number must be maintained.

Laminar Flow in Ship Modeling…
For a 1/30 scale model, the flow of water past the model must also be reduced by 30 (ν constant)
For instance:
A 60 foot long boat modeled to a 2 foot long model (1/30), then
Its real world speed of 20 knots (34 ft/sec) must also be modeled by 1/30 to 0.67 knots (1.13 ft/sec)

⚡   Electricity   ⚡
E lectricity is the flow or effective flow of Electrons, usually through a Conductor, like metals or water. Insulators like plastics and rubber present great Resistance to the flow of Electrons. Semi-conductors use special exotic materials like germanium and provide a very limited flow of Electrons.

V (volts) - Voltage is the Potential of Electricity to flow
I (amperes) - Amperage is the measure of How Much Electricity flows, aka Current
R (ohms) - Resistance is a measure of How Much Resistance to Electric flow
Hz (hertz) - Frequency, expressed as cycles per second
W (watt) - Measurement of Electric Power
kW (kilowatt) - 1,000 watts of Electric Power

OHMS's LAW is the relationship between the first three.

V = I x R
T here are two types of Electron Flow, Direct Current (DC) and Alternating Current (AC). Direct Current flows from a Voltage Source like a battery to a Ground source like the Earth. Alternating Current flows one direction and then reverses direction many times per second. Alternating Current is usually provided to homes with a Frequency of 50-60 Hz and in one of two Voltages, 120 volt or 240 volt, with typical Amperages of 50 Amps. FYI, only the United States uses 120 volts. The entire rest of the planet uses 240 volts.

A  s a practical reference, a house circuit of 120 volts powering a 1200 watt microwave oven (or 12 light bulbs of 100 watts each) uses 10 amps of current. Most home circuit breakers are rated for 12 or 15 Amps.

W = I x V
or
V = W ÷ I

LED  light bulbs use only about 15% of the energy of incandescent bulbs. This is because LED bulb's brightness peak in the visible light section of the spectrum whereas incandescant bulbs peak in the InfraRed part of the spectrum. Incandescent bulbs use 7 times more energy to produce the same amount of visible light as an LED. The extra energy produces heat NOT light. Go LED ASAP

60w Incandescent ≡ 8w LED
The Electromagnetic Spectrum
L ight quanta are known as Photons, which move at the speed of light in a vacuum. Photons can also be described by their Electromagnetic wave characteristics. Visible light is only a tiny range of the entire spectrum. However there are other species on this planet that can see Infra Red, Ultra Violet, and even Polarized Light. Please explore these external links.
⟵   The Visible Light Section   ⟶

An Electric Current generates a Magnetic Field (e.g. Electromagnet)
Conversely …
A moving Magnetic Field generates an Electric Current (e.g. Generator)

LONGER Wavelegths = LOWER Frequency & LOWER Energy

Radio Waves (10 m +)
Microwaves (1 cm - 1 m)
Infra Red (IR) (1 μm - 1 mm)

Visible Light ( R O Y G B I V ) (400 nm - 700 nm)

Ultra Violet (UV) (10 nm - 400 nm)
X Rays (1 Å - 10 nm)
Gamma Rays (10-4 Å - 1 Å)

SHORTER Wavelegths = HIGHER Frequency & HIGHER Energy

Reference
1m = 103mm = 106μm = 109nm = 1010 Å
1 Å = 10-10 meters
Physical Constants
ConstantValuePlanck Units
cSpeed of Light in a Vacuum299,792,458 m s-11
hPlanck's Constant6.626 x 10-34 kg m² s-1
Reduced Planck's Constant h1.055 x 10-34 kg m² s-11
GNewton's Gravitationl Constant6.674 x 10-11 m³ kg-1 s-21
meElectron Mass9.109 x 10-31 kg
mpProton Mass1.672 x 10-27 kg
kBoltzman Constant1.381 x 10-23 J K-11
LpPlanck Length1.600 x 10-35 m1
tpPlanck Time5.39 x 10-44 s1
TpPlanck Temperature1.417 x 1032 °K1
JJoule1 Watt s-1 (1 kg m² s-2)