particles

• everything is changing including atoms
• protons attract electrons till the atoms get close then the electrons repel
• everything behaves this way even animals like us
• but there is more
• particles over time are heading to a balanced state called entropy
• wolfram for 50 years has worked on a computational proof for entropy
• society avoids this topic because it is not comfortable we prefer to live in denial
• people tell me this is negative but I think avoidance and denial is more negative
• similar to the matrix neo takes the red pill
• some people want the blue pill to keep eating steak and looking at girls in red dresses
• read on at your egos peril

Dirac

The Dirac equation is a relativistic wave equation that describes the behavior of spin-1/2 massive particles, such as electrons and protons. It is one of the cornerstones of quantum mechanics and quantum field theory.

$$ (i\hbar\gamma^{\mu}\partial_{\mu} - mc)\psi = 0 $$

where:

• $\psi$: Dirac spinor
• $\gamma^{\mu}$: Dirac gamma matrices
• $\partial_{\mu}$: Four-gradient
• $m$: Mass of the particle
• $\hbar$: Reduced Planck's constant
• $c$: Speed of light

Dirac Sea

Dirac introduced the concept of the Dirac sea to explain the negative energy solutions of the Dirac equation. He postulated that all negative energy states are filled with electrons, forming a sea. A hole in this sea, created by exciting an electron to a positive energy state, behaves like a positron, the antiparticle of the electron.

Quantum Field Theory

Dirac's work laid the foundation for quantum field theory, which describes the interactions of particles and fields. It is the basis for understanding fundamental forces like electromagnetism, the weak force, and the strong force.

richard feynman

• said something to the effect:
• everything is atoms
• protons attract electrons till the atoms get close then the electrons repel
• everything behaves this way even animals like us

Feynman's Fundamental Computations

Path Integral Formulation

Feynman's path integral formulation provides a powerful way to calculate quantum mechanical amplitudes. It involves summing over all possible paths a particle can take between two points in spacetime.

$$ \langle x_f, t_f | x_i, t_i \rangle = \int \mathcal{D}x(t) e^{iS[x(t)]/\hbar} $$

where:

• $\langle x_f, t_f | x_i, t_i \rangle$: Amplitude for a particle to go from $(x_i, t_i)$ to $(x_f, t_f)$
• $\mathcal{D}x(t)$: Functional integral over all paths $x(t)$
• $S[x(t)]$: Action of the path $x(t)$

Quantum Electrodynamics (QED)

Feynman made significant contributions to the development of QED, which describes the interaction between light and matter. He introduced Feynman diagrams, a graphical representation of particle interactions, to visualize and calculate quantum processes.

Other Contributions

Feynman also made important contributions to many other areas of physics, including:

• Statistical mechanics
• Nanotechnology
• Quantum computing
• Particle physics

His work has had a profound impact on our understanding of the physical world.

shunryu suzuki

• adds to feynman
• everything is changing

robot prompts

• beware I am having the corporate robot answer these questions for now
• my reference for particles is the book stella marris alicia says something like we have no definition of a particle
• we don't know what we're talking about and that makes us uncomfortable
• even the best physicists cannot do more than speculate on how energy exists it cannot be created or destroyed but it is here
• so what are the rules?

make a markdown table
put it inside a code block
list the 

shells

• as cormac mccarthy would say: what are the rules for these shells?

Shell Number (n)	Maximum Electrons (2n²)	Subshells	Examples
1	2	1s	Hydrogen (H), Helium (He)
2	8	2s, 2p	Lithium (Li), Oxygen (O), Neon (Ne)
3	18	3s, 3p, 3d	Sodium (Na), Argon (Ar), Potassium (K)
4	32	4s, 4p, 4d, 4f	Calcium (Ca), Krypton (Kr)

Shell Number (n)	Approximate Average Radius (pm)	Description
1	53	1s shell, closest to the nucleus (hydrogen atom)
2	106	2s/2p shell, further from the nucleus
3	159	3s/3p/3d shell, even further
4	212	4s/4p/4d/4f shell, larger yet
5	265	5s/5p/5d/5f shell, further distance

• theories behind these shell rules

Theory/Concept	Confidence Level (%)	Notes
Quantum Mechanics	95%	Extensive experimental validation; foundational to modern physics.
Atomic Structure	90%	Supported by spectroscopy and chemical behavior observations.
Pauli Exclusion Principle	95%	Consistently observed in atomic and subatomic systems.
Electron Shell Model	90%	Validated through experiments and explains periodic trends.
Quantum Entanglement	85%	Supported by experiments but still an area of active research.
Wave-Particle Duality	90%	Well-supported by experimental evidence, though conceptual complexities exist.
Uncertainty Principle	90%	Confirmed by numerous experiments; fundamental to quantum mechanics.

The concept of electron shell radii and their behavior in atoms is grounded in several key theories and principles in quantum mechanics and atomic physics. Here are some of the popular theories and models that help explain the radii of electron shells:

1. Bohr Model

• Overview: Proposed by Niels Bohr in 1913, the Bohr model was one of the first to provide a clear understanding of atomic structure. It introduced the idea of quantized energy levels for electrons orbiting the nucleus.
• Key Concepts:
• Electrons occupy fixed orbits (shells) around the nucleus.
• The radius of each orbit is quantized and depends on the principal quantum number ( n ). The formula for the radius of the nth orbit is given by: [ r_n = \frac{n^2 \hbar^2}{k e^2 m_e} ] where ( \hbar ) is the reduced Planck's constant, ( k ) is Coulomb's constant, ( e ) is the charge of the electron, and ( m_e ) is the mass of the electron.
• Limitations: While successful in explaining hydrogen's spectral lines, the Bohr model doesn't account for electron-electron interactions in multi-electron atoms and fails with more complex atoms.

2. Quantum Mechanical Model

• Overview: This model emerged from the development of quantum mechanics and replaced the Bohr model as a more accurate representation of atomic structure.
• Key Concepts:
• Electrons are described by wave functions, which provide a probability distribution of finding an electron in a given region of space (orbitals).
• The Schrödinger equation is used to calculate the allowed energy levels and corresponding wave functions for electrons in atoms.
• The average radius of electron shells is derived from these wave functions and varies with quantum numbers.

3. Heisenberg Uncertainty Principle

• Overview: Proposed by Werner Heisenberg in 1927, this principle states that the position and momentum of a particle cannot both be precisely determined at the same time.
• Key Concepts:
• The uncertainty principle implies that electrons do not have fixed paths or orbits but instead exist in a probabilistic cloud around the nucleus.
• This concept leads to the understanding that the radius of electron shells is not a precise distance but rather an average or expected value based on probability distributions.

4. Electron Shielding and Penetration

• Overview: In multi-electron atoms, electron shielding and penetration affect the effective nuclear charge experienced by outer electrons.
• Key Concepts:
• Inner electrons shield outer electrons from the full charge of the nucleus, effectively altering the average radius of the outer shells.
• This phenomenon can be modeled using quantum mechanics to predict how the radius of electron shells varies with electron configurations.

5. Quantum Numbers

• Overview: The quantum numbers (principal ( n ), azimuthal ( l ), magnetic ( m_l ), and spin ( m_s )) describe the properties and behavior of electrons in atoms.
• Key Concepts:
• The principal quantum number ( n ) directly influences the energy level and size of the electron shell. Higher ( n ) values correspond to larger radii.
• The shape of the orbitals (determined by ( l )) also plays a role in understanding electron distribution around the nucleus.

Conclusion

The radius of electron shells is a complex topic that integrates multiple theories and principles from quantum mechanics and atomic physics. While the Bohr model laid the groundwork for understanding atomic structure, the quantum mechanical model, along with concepts like the uncertainty principle and electron shielding, provides a more comprehensive view of the behavior and distribution of electrons in atoms.

smallest visible

• we observe symptoms of particle theories
• we can see the nucleus of an atom
• we cannot see protons or neutrons or electrons

Feature	Electron Microscope	Atomic Force Microscope
Imaging method	Electron beam	Mechanical probe
Resolution	Higher (can resolve individual atoms)	Lower (can resolve features on the nanometer scale)
Sample preparation	Requires vacuum conditions and often thin sections	Can image samples in air or liquid
Applications	Biology, materials science, nanotechnology	Biology, materials science, surface chemistry

Rank	Particle	Description
1	Quark	The smallest known particle that makes up protons and neutrons.
2	Lepton	A type of fundamental particle that includes electrons, neutrinos, and muons.
3	Photon	A particle of light that carries electromagnetic force.
4	Gluon	A particle that carries the strong nuclear force that holds protons and neutrons together.
5	W boson	A particle that carries the weak nuclear force responsible for radioactive decay.
6	Z boson	A particle that carries the weak nuclear force and is responsible for the mass of particles.
7	Higgs boson	A particle that gives mass to other particles.

Number	Range	Rules or Specs
1	1-2	Alkali Metals
2	2-3	Alkaline Earth Metals
3	3-12	Transition Metals
4	13	Boron Group
5	14	Carbon Group
6	15	Nitrogen Group
7	16	Oxygen Group
8	17	Halogens
9	18	Noble Gases
10	57-71	Lanthanides
11	89-103	Actinides

periodic table computations

Computation	Description
Atomic Number	The number of protons in an atom's nucleus, uniquely identifying an element.
Electron Configuration	The arrangement of electrons in an atom's energy levels, determining its chemical properties.
Atomic Mass	The average mass of an atom of an element, considering isotopes.
Ionization Energy	The energy required to remove an electron from an atom, influencing reactivity.
Electron Affinity	The energy change when an electron is added to an atom, indicating its tendency to gain electrons.
Electronegativity	The ability of an atom to attract electrons in a chemical bond, determining bond polarity.
Periodic Trends	Patterns in properties across the periodic table, such as atomic size, ionization energy, and electronegativity.
Quantum Mechanics	The underlying theory describing the behavior of electrons in atoms, leading to the periodic table's structure.
Isotopes	Atoms of the same element with different numbers of neutrons, affecting atomic mass and stability.
Radioactivity	The spontaneous decay of unstable atomic nuclei, leading to the formation of new elements.

tools

Full Name	Shorthand
Mass spectrometer	MS
Inductively coupled plasma mass spectrometer	ICP-MS
X-ray fluorescence spectrometer	XRF
Atomic absorption spectrometer	AAS
Atomic emission spectrometer	AES
Neutron activation analysis	NAA

einstein

Einstein's Fundamental Computations

Special Relativity

• Mass-Energy Equivalence: $$ E = mc^2 $$
• Time Dilation: $$ t' = \frac{t}{\sqrt{1 - \frac{v^2}{c2}}} $$
• Length Contraction: $$ L' = L\sqrt{1 - \frac{v^2}{c2}} $$

General Relativity

• Einstein Field Equations: $$ R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu} $$
• Geodesic Equation: $$ \frac{d^2x\mu}{d\tau^2} + \Gamma^{\mu_{\alpha\beta}\frac{dx}\alpha}{d\tau}\frac{dx^\beta}{d\tau} = 0 $$

Einstein's work revolutionized our understanding of gravity, space, and time. His theories have had a profound impact on modern physics and cosmology.