list of bridge derivations for Physics

[bhpayne]

Look for derivations that bridge two topics. See

• https://en.wikipedia.org/wiki/Outline_of_physics#Branches_of_physics
• https://en.wikiversity.org/wiki/High_school_physics
• https://en.wikipedia.org/wiki/Category:Equations_of_physics
• https://physics.info/equations/

[bhpayne]

Using the list of topics from https://en.wikipedia.org/wiki/Outline_of_physics#Branches_of_physics

prompt for Gemini 2.0 Flash Thinking Experimental, https://aistudio.google.com/prompts

In mathematical Physics a derivation is comprised of steps and equations.

Given the following list of topics in Physics, for every pair of combination for two topics, is there a derivation that bridges the two topics?
If there is, name the pair of topics and provide a short summary of the derivation.

Astronomy - studies the universe beyond Earth, including its formation and development, and the evolution, physics, chemistry, meteorology, and motion of celestial objects (such as galaxies, planets, etc.) and phenomena that originate outside the atmosphere of Earth (such as the cosmic background radiation).
Astrodynamics - application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft.
Astrometry - the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies.
Astrophysics - the study of the physical aspects of celestial objects
Celestial mechanics - the branch of theoretical astronomy that deals with the calculation of the motions of celestial objects such as planets.
Extragalactic astronomy - the branch of astronomy concerned with objects outside our own Milky Way Galaxy
Galactic astronomy - the study of our own Milky Way galaxy and all its contents.
Physical cosmology - the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution.
Planetary science - the scientific study of planets (including Earth), moons, and planetary systems, in particular those of the Solar System and the processes that form them.
Stellar astronomy - natural science that deals with the study of celestial objects (such as stars, planets, comets, nebulae, star clusters, and galaxies) and phenomena that originate outside the atmosphere of Earth (such as cosmic background radiation)
Atmospheric physics - the study of the application of physics to the atmosphere
Atomic, molecular, and optical physics - the study of how matter and light interact
Optics - the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it.
Biophysics - interdisciplinary science that uses the methods of physics to study biological systems
Neurophysics - branch of biophysics dealing with the nervous system.
Polymer physics - field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation and polymerization of polymers and monomers respectively.
Quantum biology - application of quantum mechanics to biological phenomenon.
Chemical physics - the branch of physics that studies chemical processes from physics.
Computational physics - study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists.
Condensed matter physics - the study of the physical properties of condensed phases of matter.
Electricity - the study of electrical phenomena.
Electromagnetism - branch of science concerned with the forces that occur between electrically charged particles.
Geophysics - the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods
Magnetism - the study of physical phenomena that are mediated by magnetic field.
Mathematical physics - application of mathematics to problems in physics and the development of mathematical methods for such applications and the formulation of physical theories.
Mechanics - the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.
Aerodynamics - study of the motion of air.
Biomechanics - the study of the structure and function of biological systems such as humans, animals, plants, organs, and cells using the methods of mechanics.
Classical mechanics - one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces.
Kinematics - branch of classical mechanics that describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion.[6][7][8]
Homeokinetics - the physics of complex, self-organizing systems
Continuum mechanics - the branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
Dynamics - the study of the causes of motion and changes in motion
Fluid mechanics - the study of fluids and the forces on them.
Fluid statics - study of fluids at rest
Fluid kinematics - study of fluids in motion
Fluid dynamics - study of the effect of forces on fluid motion
Statics - the branch of mechanics concerned with the analysis of loads (force, torque/moment) on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity.
Medical Physics - the branch of physics that deals with the application of physics in medicine - such as imaging exams (NMR, PET scans, and so on), radiotherapy and nuclear medicine.
Statistical mechanics - the branch of physics which studies any physical system that has a large number of degrees of freedom.
Thermodynamics - the branch of physical science concerned with heat and its relation to other forms of energy and work.
Nuclear physics - field of physics that studies the building blocks and interactions of atomic nuclei.
Particle physics - the branch of physics that studies the properties and interactions of the fundamental constituents of matter and energy.
Psychophysics - quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they affect.
Plasma physics - the study of plasma, a state of matter similar to gas in which a certain portion of the particles are ionized.
Quantum physics - branch of physics dealing with physical phenomena where the action is on the order of the Planck constant.
Quantum field theory - the application of quantum theory to the study of fields (systems with infinite degrees of freedom).
Quantum information theory - the study of the information-processing capabilities afforded by quantum mechanics.
Quantum foundations - the discipline focusing in understanding the counterintuitive aspects of the theory, including trying to find physical principles underlying them, and proposing generalisations of quantum theory.
Quantum gravity - the search for an account of gravitation fully compatible with quantum theory.
Relativity - theory of physics which describes the relationship between space and time.
General Relativity - a geometric, non-quantum theory of gravitation.
Special Relativity - a theory that describes the propagation of matter and light at high speeds.
Agrophysics - the study of physics applied to agroecosystems
Soil physics - the study of soil physical properties and processes.
Cryogenics - cryogenics is the study of the production of very low temperature (below −150 °C, −238 °F or 123 K) and the behavior of materials at those temperatures.
Econophysics - interdisciplinary research field, applying theories and methods originally developed by physicists to solve problems in economics
Materials physics - use of physics to describe materials in many different ways such as force, heat, light, and mechanics.
Vehicle dynamics - dynamics of vehicles, here assumed to be ground vehicles.
Philosophy of physics - deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists.

thoughts

Here's a thinking process to arrive at the solution:

1. Understand the Task: The core task is to identify pairs of physics topics from the provided list and determine if a derivation exists that connects them. If a derivation exists, provide a short summary.

2. Initial Approach - Pairwise Comparison (Brute Force): The most straightforward approach is to consider every possible pair of topics. Since there are a lot of topics, this will be lengthy but systematic. We can iterate through the list, taking one topic as the first element of the pair, and then iterate through the rest of the list (to avoid duplicates and pairs like "Topic A - Topic A").

3. For Each Pair, Ask "Is there a Derivation?": For each pair of topics, the key question is: "Can we derive concepts or results in one topic using principles and equations from the other topic?". This requires some basic knowledge of physics and how these topics relate. If unsure, it's best to err on the side of "yes, there's a connection, let's see if we can summarize it." It's better to give a potentially weak derivation than to miss a valid one.

4. Brainstorm Derivations (or Connections): For each pair, think about fundamental concepts. Are there overlapping areas? Does one topic build upon the principles of another? Think about equations, laws, and models that are shared or used to bridge the topics. Consider if one topic is a special case of another, or if one topic provides the foundational principles for the other.

5. Summarize the Derivation (if possible): Once a connection is identified, try to summarize the derivation in a short, concise way. Focus on the key steps or principles involved. Avoid overly technical details, as the request is for a summary. The summary should highlight how concepts from the first topic are used to arrive at concepts in the second topic.

6. Example Walkthrough (Astronomy & Astrodynamics):

   • Pair: Astronomy - Astrodynamics
   • Connection? Astrodynamics studies spacecraft motion in space. Astronomy studies celestial bodies and their motions. Spacecraft move through space governed by gravitational forces from celestial bodies. Yes, there's a connection.
   • Derivation Idea: Start with Newton's Law of Universal Gravitation (from mechanics, foundational to astronomy). Apply it to spacecraft motion. Derive orbital mechanics equations (Keplerian orbits, etc.). These are core to astrodynamics.
   • Summary: "Yes. Derivation of Orbital Mechanics: Starting from Newton's Law of Universal Gravitation (from Astronomy/Celestial Mechanics), we can derive the equations of motion for spacecraft. These equations form the basis of astrodynamics, allowing us to predict and control spacecraft trajectories."

7. Example Walkthrough (Astrophysics & Atomic, Molecular, and Optical Physics):

   • Pair: Astrophysics - Atomic, Molecular, and Optical Physics
   • Connection? Astrophysics studies celestial objects. How do we learn about their composition, temperature, etc.? Through the light they emit. Light interacts with atoms and molecules. Atomic/Molecular physics studies these interactions. Yes, strong connection.
   • Derivation Idea: Atoms and molecules emit and absorb light at specific wavelengths (atomic/molecular spectra). Astrophysicists analyze the spectra of stars and galaxies to determine their composition, temperature, velocity, etc.
   • Summary: "Yes. Derivation of Stellar Composition: Using the principles of atomic and molecular physics, specifically the study of atomic and molecular spectra, astrophysicists can analyze the light emitted by stars and other celestial objects to determine their chemical composition, temperature, and other physical properties."

8. Example Walkthrough (Classical Mechanics & Quantum Mechanics):

   • Pair: Classical Mechanics - Quantum Mechanics
   • Connection? Quantum Mechanics is a more fundamental theory than Classical Mechanics. Classical Mechanics is often seen as an approximation of Quantum Mechanics at macroscopic scales or high energies. However, there isn't a direct derivation of quantum mechanics from classical mechanics in the sense of a series of logical steps. It's more of a paradigm shift.
   • Derivation Idea (loosely interpreted): Think about the limitations of classical mechanics at atomic scales. Blackbody radiation, photoelectric effect, atomic spectra – classical physics fails to explain these. These failures motivate the development of quantum mechanics. The correspondence principle suggests a link – quantum mechanics should reduce to classical mechanics in certain limits.
   • Summary (needs to be nuanced): "Yes, in a way, through the historical development and the Correspondence Principle: The limitations of classical mechanics in explaining phenomena at the atomic level (like blackbody radiation and atomic spectra) led to the development of quantum mechanics. The Correspondence Principle suggests that quantum mechanics should reproduce classical mechanics in the macroscopic limit." (This summary acknowledges it's not a direct derivation but a historical and conceptual link).

9. Handle "No Derivation" Cases (Carefully): Some pairs might seem less directly connected. For example, "Astronomy - Polymer Physics." It's harder to see a direct derivation. However, polymers could exist in space (though perhaps less commonly studied in astronomy itself, maybe in planetary science contexts). It's better to look for indirect connections or areas where principles might be applied, even if not a "derivation" in the strict mathematical physics sense. If truly no clear connection, acknowledge that a direct derivation isn't obvious, but applications might exist. (In this case, polymer physics is less likely to have a direct derivation in astronomy in its core sense but polymers might be studied in meteorites or planetary atmospheres, which are related to astronomy). For the most part, many physics topics are interconnected, even if the derivations are sometimes conceptual or historical rather than purely mathematical.

10. Organize and Refine: After going through many pairs, organize the results. Ensure summaries are concise and accurately reflect the derivation or connection. Review for clarity and completeness. Check if any obvious pairs were missed. Consider if any summaries could be improved for better clarity and precision.

By following this process of pairwise comparison, brainstorming connections, and summarizing derivations (even loose ones), we can systematically address the prompt and generate a comprehensive list of topic pairs and their connecting derivations. The key is to interpret "derivation" broadly enough to capture conceptual and historical links, while still focusing on how principles from one area inform or contribute to another.

response

Okay, let's systematically go through the provided list of physics topics and consider pairs to see if derivations bridge them. This will be a lengthy process, but we'll try to be concise in our summaries.

General Approach: For each pair, we'll consider if fundamental principles, equations, or methodologies from one topic are used to derive or explain phenomena in the other. If a derivation exists, we'll describe it briefly. If the connection is more of application or related study, we'll note that as well.

Let's go through the topics roughly in order of the list provided:

Astronomy & ...

• Astronomy - Astrodynamics: Yes. Derivation of Orbital Mechanics: Starting from Newton's Law of Universal Gravitation (from Astronomy/Celestial Mechanics), we can derive the equations of motion for spacecraft. These equations form the basis of astrodynamics, allowing us to predict and control spacecraft trajectories.

• Astronomy - Astrometry: Yes. Derivation of Parallax and Distance Measurement: Astrometry provides precise measurements of stellar positions. Using the geometric principles of parallax (derived from basic geometry and our understanding of Earth's orbit – astronomical observations), we can derive distances to nearby stars.

• Astronomy - Astrophysics: Yes. Astrophysics uses physical laws to explain astronomical observations. For example, deriving stellar structure equations (pressure balance, energy transport, etc.) from fundamental physics (gravity, thermodynamics, nuclear physics) allows us to understand stars, which are the primary objects of study in astronomy.

• Astronomy - Celestial mechanics: Yes. Celestial mechanics is a core part of Astronomy. Derivation of Planetary Orbits: Starting from Newton's Laws of Motion and Law of Universal Gravitation, we can derive Kepler's Laws of Planetary Motion, which describe the orbits of planets – a central topic in both celestial mechanics and astronomy.

• Astronomy - Extragalactic astronomy: Yes. Extragalactic astronomy applies the principles and derivations of astronomy and astrophysics to objects outside our galaxy. For example, deriving distances to galaxies using standard candles (like Cepheid variables, understood through stellar astrophysics) is a derivation bridging these fields.

• Astronomy - Galactic astronomy: Yes. Galactic astronomy is also a specialized area within astronomy. Derivation of Galactic Rotation Curves: By applying Newtonian mechanics and the concept of gravity to the distribution of mass within our galaxy (studied in galactic astronomy), we can derive rotation curves, which reveal the presence of dark matter.

• Astronomy - Physical cosmology: Yes. Physical cosmology builds heavily on astronomy. Derivation of the Friedmann Equations: Starting from General Relativity (a physical theory), and applying it to a homogeneous and isotropic universe (an assumption based on astronomical observations at large scales), we derive the Friedmann equations, which describe the expansion of the universe – a fundamental concept in physical cosmology.

• Astronomy - Planetary science: Yes. Planetary science is a subfield of astronomy focusing on planets. Derivation of Planetary Atmosphere Models: Using principles of fluid mechanics, thermodynamics, and atmospheric physics (and astronomical observations of planetary atmospheres), we can derive models of planetary atmospheres, including temperature profiles, wind patterns, etc.

• Astronomy - Stellar astronomy: Yes. Stellar astronomy is a major branch of astronomy. Derivation of Stellar Evolution: Using principles of nuclear physics, thermodynamics, and fluid mechanics, we can derive models of stellar evolution, describing how stars are born, live, and die – a core topic in stellar astronomy.

• Astronomy - Atmospheric physics: Yes. While atmospheric physics primarily focuses on Earth's atmosphere, the principles are broadly applicable. Derivation of Atmospheric Radiative Transfer: The principles of radiative transfer (how light interacts with matter, from atmospheric physics) are crucial for understanding planetary atmospheres observed in astronomy.

• Astronomy - Atomic, molecular, and optical physics: Yes. Derivation of Spectral Lines: The study of atomic and molecular physics is fundamental to interpreting astronomical observations. Deriving the wavelengths of spectral lines for different elements and molecules is crucial for determining the composition, temperature, and velocity of astronomical objects.

• Astronomy - Optics: Yes. Optics is essential for astronomical observation. Derivation of Telescope Resolution: Using the principles of wave optics (diffraction), we can derive the theoretical resolution limit of telescopes, which is critical for designing and using astronomical instruments.

• Astronomy - Biophysics, Neurophysics, Polymer physics, Quantum biology, Chemical physics, Computational physics, Condensed matter physics, Electricity, Electromagnetism, Geophysics, Magnetism, Mathematical physics, Mechanics, Aerodynamics, Biomechanics, Classical mechanics, Kinematics, Homeokinetics, Continuum mechanics, Dynamics, Fluid mechanics, Fluid statics, Fluid kinematics, Fluid dynamics, Statics, Medical Physics, Statistical mechanics, Thermodynamics, Nuclear physics, Particle physics, Psychophysics, Plasma physics, Quantum physics, Quantum field theory, Quantum information theory, Quantum foundations, Quantum gravity, Relativity, General Relativity, Special Relativity, Agrophysics, Soil physics, Cryogenics, Econophysics, Materials physics, Vehicle dynamics, Philosophy of physics:

  For many of these, the connection is less about direct "derivation" from Astronomy to these topics, but rather the application of these topics to Astronomy or areas related to space exploration. For example:

  • Electromagnetism: Crucial for understanding electromagnetic radiation from space, magnetic fields in planets and stars.
  • Plasma Physics: Essential for understanding the solar wind, interstellar medium, and astrophysical jets.
  • Fluid Mechanics: Used to model gas dynamics in accretion disks, stellar atmospheres, nebulae.
  • Thermodynamics: Fundamental to understanding stellar interiors, planetary atmospheres, and the early universe.
  • Nuclear Physics: Essential for understanding stellar energy generation and nucleosynthesis.
  • Computational Physics: Used extensively in astrophysical simulations (galaxy formation, stellar evolution, etc.).
  • Relativity: Crucial for cosmology and for understanding strong gravitational fields near black holes and neutron stars.
  • Materials Physics & Cryogenics: Relevant for designing spacecraft components and instruments that operate in extreme space environments.

  While direct derivations from Astronomy are less common for these, the application of these principles to explain astronomical phenomena is extensive. It's more about using these fields as tools within astronomy and astrophysics. We can say there are applications and connections, but not always a clear "derivation" in the sense of starting from astronomical principles and deriving principles in these other fields.

Astrodynamics & ...

• Astrodynamics - Astrometry: Yes. Astrometry provides the precise positions needed for astrodynamics. Derivation of Orbital Parameters from Astrometric Data: Using astrometric measurements of a celestial object (planet, asteroid, spacecraft), and applying orbital mechanics (astrodynamics), we can derive the orbital parameters (semi-major axis, eccentricity, inclination, etc.) of that object.

• Astrodynamics - Astrophysics: Yes. Astrophysical forces (radiation pressure, stellar winds, gravitational perturbations from multiple bodies) can affect spacecraft trajectories. Derivation of Perturbed Orbits: By incorporating astrophysical forces into the equations of motion from astrodynamics, we can derive models for perturbed orbits, which are more realistic for long-duration space missions.

• Astrodynamics - Celestial mechanics: Yes. Celestial mechanics is the theoretical foundation of astrodynamics. Derivation of Orbital Maneuvers: Using the principles of celestial mechanics (energy and momentum conservation, orbital equations), we can derive equations for orbital maneuvers (Hohmann transfer, gravity assist, etc.) used in astrodynamics to change spacecraft orbits.

• Astrodynamics - Computational physics: Yes. Astrodynamics heavily relies on numerical simulations. Derivation of Numerical Orbit Propagation Algorithms: Computational physics provides the numerical methods (e.g., Runge-Kutta methods) used to solve the differential equations of motion in astrodynamics for orbit propagation and mission planning.

• Astrodynamics - Classical mechanics: Yes. Classical mechanics is the fundamental theory underlying astrodynamics. Derivation of the Two-Body Problem Solution: Starting from Newton's Laws of Motion and Gravity (classical mechanics), we derive the analytical solution for the two-body problem, which is the basis for understanding spacecraft orbits in astrodynamics.

• Astrodynamics - Dynamics: Yes. Dynamics is the study of motion and forces. Astrodynamics is an application of dynamics to spacecraft motion. The derivations in astrodynamics are inherently dynamics derivations.

• Astrodynamics - Fluid mechanics: Potentially Indirect. For atmospheric entry of spacecraft or aerobraking, fluid mechanics (aerodynamics) becomes important. Derivation of Aerodynamic Forces on Spacecraft: Using principles of fluid mechanics, we can derive equations for aerodynamic forces (drag, lift) acting on spacecraft during atmospheric entry, which are crucial for trajectory design in these phases.

• Astrodynamics - Mathematical physics: Yes. Astrodynamics is a field where mathematical physics is directly applied. Many derivations in astrodynamics involve setting up and solving differential equations using mathematical techniques.

• Astrodynamics - Mechanics: Yes. Mechanics is the overarching field; astrodynamics is a subfield of mechanics.

• Astrodynamics - Special Relativity/General Relativity: Yes, for high precision or strong gravity. For very precise orbit calculations or missions near strong gravitational fields (e.g., near the Sun or black holes), relativistic corrections are needed. Derivation of Relativistic Orbital Effects: Using General Relativity, we can derive corrections to Newtonian orbits, such as the precession of Mercury's perihelion, or relativistic effects on spacecraft trajectories in strong gravitational fields.

• Astrodynamics - Vehicle dynamics: Yes. Astrodynamics is a specialized area of vehicle dynamics focusing on space vehicles.

Astrometry & ...

• Astrometry - Optics: Yes. Optics is crucial for astrometric instruments. Derivation of Instrument Calibration Methods: Understanding the optical properties of telescopes and instruments allows us to derive calibration methods in astrometry to correct for optical aberrations and atmospheric distortions, leading to more accurate position measurements.

• Astrometry - Mathematical physics, Computational physics, Statistical mechanics: Yes. Astrometry relies heavily on statistical methods for data analysis and error estimation. Derivation of Statistical Error Analysis in Astrometry: Statistical mechanics provides the framework for understanding and quantifying uncertainties in astrometric measurements. Computational physics is used to implement complex data reduction and analysis pipelines.

Astrophysics & ...

• Astrophysics - Atomic, molecular, and optical physics: Yes. Already mentioned the derivation of stellar composition using spectral lines. This is a core bridge.

• Astrophysics - Condensed matter physics: Potentially. For understanding the interiors of planets, white dwarfs, and neutron stars, condensed matter physics is relevant. Derivation of Equations of State for Dense Matter: Condensed matter physics provides equations of state (pressure as a function of density and temperature) for matter at extreme densities found in astrophysical objects, which are essential for modeling these objects.

• Astrophysics - Electromagnetism: Yes. Astrophysical plasmas, magnetic fields, and radiation are governed by electromagnetism. Derivation of Synchrotron Radiation Spectrum: Using electromagnetism, we can derive the spectrum of synchrotron radiation emitted by relativistic electrons spiraling in magnetic fields, a crucial process in many astrophysical environments (jets, supernova remnants).

• Astrophysics - Fluid mechanics & Plasma physics: Yes. Astrophysical flows are often fluid flows, sometimes plasmas. Derivation of Magnetohydrodynamic (MHD) Equations: Combining fluid mechanics and electromagnetism, we derive the MHD equations, which describe the dynamics of conducting fluids (plasmas) in magnetic fields, essential for understanding solar flares, accretion disks, and astrophysical jets.

• Astrophysics - Nuclear physics & Particle physics: Yes. Stellar energy generation, nucleosynthesis, cosmic rays involve nuclear and particle physics. Derivation of Nuclear Reaction Rates in Stars: Nuclear physics provides the reaction rates for nuclear fusion processes in stars, which are used to calculate stellar energy generation and elemental abundances.

• Astrophysics - Quantum physics & Statistical mechanics: Yes. Quantum mechanics is needed for atomic and molecular spectra, and statistical mechanics is crucial for thermodynamics and understanding large ensembles of particles in astrophysical systems. Derivation of the Planck Blackbody Spectrum: Using quantum mechanics and statistical mechanics, we derive Planck's law for blackbody radiation, which describes the spectrum of thermal radiation and is fundamental to understanding the radiation from stars and other astrophysical objects.

• Astrophysics - Thermodynamics: Yes. Thermodynamics is essential for understanding energy transport and equilibrium in stars, planets, and galaxies. Derivation of Stellar Structure Equations (Hydrostatic Equilibrium, Energy Transport): Thermodynamics provides the principles of energy transport (radiation, convection, conduction) and equations of state that are used in deriving stellar structure equations.

• Astrophysics - General Relativity: Yes. For strong gravity environments and cosmology. Derivation of Black Hole Solutions: General Relativity is used to derive solutions for black holes (Schwarzschild metric, Kerr metric), which are important astrophysical objects.

Celestial Mechanics & ...

• Celestial mechanics - Classical mechanics: Yes. Celestial mechanics is a branch of classical mechanics.

• Celestial mechanics - Mathematical physics, Computational physics: Yes. Celestial mechanics relies heavily on mathematical formulations and numerical solutions.

Extragalactic Astronomy & ... , Galactic Astronomy & ..., Physical Cosmology & ..., Planetary Science & ..., Stellar Astronomy & ...

These are all specialized branches of Astronomy and Astrophysics. The derivations that bridge them to other fields are largely the same as those already mentioned for Astronomy and Astrophysics, just applied to more specific contexts (galaxies, the universe as a whole, planets, stars).

Atmospheric Physics & ...

• Atmospheric physics - Fluid mechanics, Thermodynamics, Optics, Electromagnetism: Yes. Atmospheric physics is built on these foundations.

  • Fluid Mechanics: Derivation of Atmospheric Circulation Models: Using fluid mechanics, we can derive models of global atmospheric circulation patterns (Hadley cells, jet streams).
  • Thermodynamics: Derivation of Atmospheric Temperature Profiles: Using thermodynamics, we can derive models for how temperature varies with altitude in the atmosphere.
  • Optics: Derivation of Atmospheric Scattering and Absorption: Using optics, we can derive models for how sunlight is scattered and absorbed by the atmosphere, explaining phenomena like the blue sky and sunsets.
  • Electromagnetism: Derivation of Ionospheric Plasma Behavior: Using electromagnetism and plasma physics, we can model the behavior of the ionosphere.

• Atmospheric physics - Geophysics: Yes. Atmospheric physics is a subfield of geophysics, specifically focusing on the atmosphere.

Atomic, Molecular, and Optical Physics & ...

• Atomic, molecular, and optical physics - Quantum physics, Electromagnetism, Thermodynamics, Statistical mechanics, Optics: Yes. These are foundational to AMO physics.
  • Quantum Physics & Electromagnetism: Derivation of Atomic Spectra: Quantum mechanics and electromagnetism are used to derive the energy levels and spectral lines of atoms and molecules.
  • Statistical Mechanics & Thermodynamics: Derivation of Thermal Radiation from Atoms/Molecules: Statistical mechanics and thermodynamics are used to describe the thermal distribution of atomic and molecular energy levels and the resulting thermal radiation.
  • Optics: Derivation of Refractive Index and Dispersion: AMO physics helps explain the macroscopic optical properties of materials like refractive index and dispersion based on the interaction of light with atoms and molecules.

Optics & ...

• Optics - Electromagnetism, Quantum physics, Mathematical physics: Yes.
  • Electromagnetism: Derivation of Wave Equations for Light: Optics is ultimately derived from Maxwell's equations of electromagnetism, which describe light as electromagnetic waves.
  • Quantum Physics: Derivation of Photon Nature of Light: Quantum physics explains the particle nature of light (photons) and phenomena like the photoelectric effect.
  • Mathematical Physics: Optics heavily relies on mathematical formulations, especially wave equations and Fourier optics.

Biophysics, Neurophysics, Polymer physics, Quantum biology, Chemical physics & ...

These are all interdisciplinary fields that apply physics principles to other areas. The derivations often go from fundamental physics to these fields.

• Biophysics - Mechanics, Statistical mechanics, Thermodynamics, Fluid mechanics, Electromagnetism, Quantum physics, Mathematical physics: Yes. Biophysics applies all these.

  • Mechanics & Fluid mechanics & Biomechanics: Derivation of Biomechanical Models of Movement: Classical mechanics and fluid mechanics are used to derive models of animal locomotion, muscle mechanics, blood flow, etc. (Biomechanics is a subfield).
  • Statistical mechanics & Thermodynamics: Derivation of Biomolecular Thermodynamics: Statistical mechanics and thermodynamics are used to understand protein folding, enzyme kinetics, membrane properties, etc.
  • Electromagnetism: Derivation of Membrane Potentials: Electromagnetism is used to understand the electrical properties of cell membranes and nerve impulses.
  • Quantum Physics & Quantum Biology: Derivation of Quantum Effects in Biological Systems: Quantum mechanics is being explored to understand phenomena like photosynthesis, enzyme catalysis, and bird navigation (Quantum biology is a developing field).
  • Mathematical Physics: Mathematical modeling is crucial in biophysics.

• Neurophysics - Biophysics, Electricity, Electromagnetism, Statistical mechanics, Mathematical physics: Yes. Neurophysics is a branch of biophysics focused on the nervous system.

• Polymer physics - Statistical mechanics, Thermodynamics, Condensed matter physics, Mechanics: Yes.

  • Statistical Mechanics & Thermodynamics: Derivation of Polymer Chain Statistics: Statistical mechanics and thermodynamics are used to derive models for the conformation and behavior of polymer chains (e.g., random walk models, Flory-Huggins theory).
  • Mechanics & Continuum mechanics: Derivation of Polymer Mechanical Properties: Mechanics and continuum mechanics are used to understand the elastic, viscoelastic, and plastic properties of polymers.

• Quantum biology - Quantum physics, Biophysics, Chemical physics, Statistical mechanics: Yes. Quantum biology is a very interdisciplinary field.

• Chemical physics - Quantum physics, Statistical mechanics, Thermodynamics, Electromagnetism: Yes. Chemical physics bridges physics and chemistry.

  • Quantum Physics: Derivation of Molecular Electronic Structure: Quantum mechanics is used to derive the electronic structure of molecules (quantum chemistry).
  • Statistical Mechanics & Thermodynamics: Derivation of Reaction Rates and Equilibria: Statistical mechanics and thermodynamics are used to understand chemical reaction rates and chemical equilibria.

Computational physics & ...

• Computational physics - Mathematical physics, Mechanics, Electromagnetism, Quantum physics, Fluid mechanics, Statistical mechanics, Thermodynamics, ... (all other physics fields that can be modeled): Yes. Computational physics is a methodology that applies to all areas of physics where numerical solutions are needed. It's not a field with its own fundamental derivations in the same way, but it implements derivations from other fields numerically.

Condensed matter physics & ...

• Condensed matter physics - Quantum physics, Statistical mechanics, Electromagnetism, Thermodynamics, Mechanics, Mathematical physics, Cryogenics, Materials physics: Yes. Condensed matter physics is built upon these.
  • Quantum physics, Statistical mechanics, Electromagnetism: Derivation of Electronic Band Structure in Solids: Quantum mechanics, statistical mechanics, and electromagnetism are used to derive the electronic band structure of solids, which explains their electrical and optical properties.
  • Statistical mechanics & Thermodynamics: Derivation of Phase Transitions: Statistical mechanics and thermodynamics are used to understand phase transitions in materials (solid-liquid-gas, magnetic transitions).
  • Mechanics & Continuum mechanics: Derivation of Elastic Properties of Solids: Mechanics and continuum mechanics are used to understand the elastic and mechanical properties of solids.

Electricity & Electromagnetism & Magnetism & ...

• Electricity - Electromagnetism: Yes. Electricity is a part of electromagnetism.
• Magnetism - Electromagnetism: Yes. Magnetism is a part of electromagnetism.
• Electromagnetism - Classical mechanics, Quantum physics, Relativity, Optics, Plasma physics, Mathematical physics: Yes.
  • Classical mechanics: Derivation of Lorentz Force Law: Electromagnetism and classical mechanics are combined to derive the Lorentz force law, which describes the force on a charged particle in electric and magnetic fields.
  • Quantum physics: Derivation of Quantum Electrodynamics (QED): Quantum physics is used to quantize electromagnetism, leading to Quantum Electrodynamics, the quantum theory of light and matter interactions.
  • Relativity: Electromagnetism is consistent with Special Relativity. Derivation of Relativistic Transformations of Electric and Magnetic Fields: Special Relativity is needed to understand how electric and magnetic fields transform between different inertial frames.
  • Optics: Derivation of Wave Nature of Light from Maxwell's Equations: Maxwell's equations of electromagnetism are used to derive the wave equation for electromagnetic waves, which is the basis of classical optics.
  • Plasma physics: Electromagnetic forces are crucial in plasma physics.

Geophysics & ...

• Geophysics - Mechanics, Fluid mechanics, Thermodynamics, Electromagnetism, Seismology (part of mechanics), Atmospheric physics, Soil physics, Cryogenics, Mathematical physics, Computational physics: Yes. Geophysics applies all these to the Earth.
  • Mechanics & Continuum mechanics: Derivation of Earthquake Wave Propagation: Mechanics and continuum mechanics are used to model the propagation of seismic waves through the Earth.
  • Fluid mechanics & Thermodynamics: Derivation of Mantle Convection Models: Fluid mechanics and thermodynamics are used to model mantle convection, which drives plate tectonics.
  • Electromagnetism & Magnetism: Derivation of Geomagnetic Field Models: Electromagnetism and magnetism are used to understand the Earth's magnetic field and its generation in the core.

Mathematical physics & ...

• Mathematical physics - all other fields of physics: Yes. Mathematical physics provides the mathematical tools and formalisms used in all other areas of physics. It's not a field with its own specific phenomena, but rather the language and framework for expressing and solving problems in physics.

Mechanics & ...

• Mechanics - Classical mechanics, Kinematics, Dynamics, Statics, Continuum mechanics, Fluid mechanics, Aerodynamics, Biomechanics, Vehicle dynamics, Homeokinetics, Relativity, Quantum physics, Statistical mechanics, Thermodynamics, Mathematical physics, Computational physics: Yes. Mechanics is a very broad field, and the other listed topics are either branches of mechanics or use mechanics as a foundation.

Aerodynamics & ...

• Aerodynamics - Fluid mechanics, Mechanics, Thermodynamics, Computational physics, Vehicle dynamics: Yes. Aerodynamics is a branch of fluid mechanics focusing on air flow, especially around objects.

Biomechanics & ...

• Biomechanics - Mechanics, Fluid mechanics, Biomechanics, Biophysics, Medical Physics, Homeokinetics: Yes. Biomechanics is an application of mechanics to biological systems.

Classical mechanics & ...

• Classical mechanics - Kinematics, Dynamics, Statics, Continuum mechanics, Fluid mechanics, Celestial mechanics, Astrodynamics, Aerodynamics, Biomechanics, Vehicle dynamics, Statistical mechanics, Thermodynamics, Mathematical physics, Computational physics: Yes. Classical mechanics is a foundational theory with many branches and applications.

Kinematics & Dynamics & Statics & Continuum mechanics & Fluid mechanics & Fluid statics & Fluid kinematics & Fluid dynamics & Homeokinetics & ...

These are all branches within Mechanics and Fluid Mechanics. Derivations connect them based on the hierarchical structure of these fields. For example, fluid dynamics builds upon fluid kinematics and fluid statics, which are derived from more general principles of continuum mechanics and mechanics.

Medical Physics & ...

• Medical Physics - Physics (broadly), Nuclear physics, Electromagnetism, Optics, Acoustics (mechanics), Thermodynamics, Mathematical physics, Computational physics, Biophysics: Yes. Medical Physics applies physics principles to medicine.

Statistical mechanics & ...

• Statistical mechanics - Thermodynamics, Quantum physics, Condensed matter physics, Polymer physics, Chemical physics, Biophysics, Astrophysics, Cosmology, Mathematical physics, Computational physics: Yes. Statistical mechanics provides the microscopic foundation for thermodynamics and is used in many areas dealing with large systems.

Thermodynamics & ...

• Thermodynamics - Statistical mechanics, Fluid mechanics, Atmospheric physics, Astrophysics, Cosmology, Chemical physics, Materials physics, Cryogenics, Mathematical physics, Computational physics: Yes. Thermodynamics is a fundamental theory with broad applications.

Nuclear physics & ...

• Nuclear physics - Quantum physics, Particle physics, Astrophysics, Medical Physics, Materials physics, Mathematical physics, Computational physics: Yes. Nuclear physics is built on quantum physics and particle physics and has applications in astrophysics, medicine, and materials.

Particle physics & ...

• Particle physics - Quantum physics, Relativity, Quantum field theory, Mathematical physics, Computational physics, Astrophysics, Cosmology: Yes. Particle physics is a fundamental field built on quantum physics and relativity and has connections to astrophysics and cosmology.

Psychophysics & ...

• Psychophysics - Physics (stimuli), Physiology (sensations), Statistical mechanics (data analysis), Mathematical physics (modeling): Yes. Psychophysics quantitatively relates physical stimuli to psychological sensations. It uses physics to define stimuli and statistical methods for analysis.

Plasma physics & ...

• Plasma physics - Electromagnetism, Fluid mechanics, Statistical mechanics, Thermodynamics, Atomic physics, Astrophysics, Cosmology, Fusion research (applied physics): Yes. Plasma physics is built upon electromagnetism, fluid mechanics, and thermodynamics and has applications in astrophysics and fusion.

Quantum physics & ...

• Quantum physics - Classical mechanics (correspondence principle), Electromagnetism, Statistical mechanics, Thermodynamics, Condensed matter physics, Atomic physics, Molecular physics, Nuclear physics, Particle physics, Quantum field theory, Quantum information theory, Quantum foundations, Quantum gravity, Relativity (Quantum Field Theory in Curved Spacetime, Quantum Gravity attempts), Optics, Chemical physics, Biophysics, Mathematical physics, Computational physics: Yes. Quantum physics is a fundamental theory underpinning many areas of physics.

Quantum field theory & ...

• Quantum field theory - Quantum physics, Special Relativity, Particle physics, Condensed matter physics, Mathematical physics, Computational physics, Quantum gravity (as a potential future QFT of gravity), Cosmology: Yes. Quantum field theory is a framework combining quantum mechanics and special relativity, crucial for particle physics and with applications in condensed matter physics and cosmology.

Quantum information theory & ...

• Quantum information theory - Quantum physics, Information theory (mathematics/computer science), Mathematical physics, Computational physics, Quantum foundations: Yes. Quantum information theory is an interdisciplinary field using quantum mechanics for information processing.

Quantum foundations & ...

• Quantum foundations - Quantum physics, Philosophy of physics, Mathematical physics, Quantum information theory, Quantum gravity: Yes. Quantum foundations is concerned with the interpretation and conceptual basis of quantum mechanics.

Quantum gravity & ...

• Quantum gravity - Quantum physics, General Relativity, Particle physics, Cosmology, Quantum field theory, Mathematical physics, Philosophy of physics: Yes. Quantum gravity is a theoretical endeavor to unify quantum mechanics and general relativity.

Relativity (Special & General) & ...

• Relativity - Classical mechanics (limit), Electromagnetism (consistent with Special Relativity), Thermodynamics, Astrophysics, Cosmology, Particle physics, Quantum field theory, Quantum gravity, Mathematical physics, Computational physics: Yes. Relativity is a fundamental theory with broad implications.

Agrophysics & Soil physics & ...

• Agrophysics - Physics (broadly), Soil physics, Fluid mechanics (water flow in soil), Thermodynamics (heat transfer in soil/plants), Optics (light interaction with plants), Biomechanics (plant mechanics), Mathematical physics, Computational physics, Biophysics: Yes. Agrophysics applies physics to agricultural systems.
• Soil physics - Fluid mechanics, Thermodynamics, Mechanics, Materials physics, Agrophysics, Geophysics, Mathematical physics, Computational physics: Yes. Soil physics applies physics to soil properties and processes.

Cryogenics & ...

• Cryogenics - Thermodynamics, Statistical mechanics, Condensed matter physics, Materials physics, Fluid mechanics (cryogenic fluids), Superconductivity (condensed matter), Quantum physics (low-temperature phenomena), Mathematical physics, Computational physics: Yes. Cryogenics is about low-temperature physics and technology.

Econophysics & ...

• Econophysics - Statistical mechanics, Complex systems, Mathematical physics, Computational physics, Economics (application domain): Yes. Econophysics applies physics methods (especially from statistical mechanics and complex systems) to economic systems.

Materials physics & ...

• Materials physics - Condensed matter physics, Thermodynamics, Statistical mechanics, Quantum physics, Mechanics, Electromagnetism, Optics, Cryogenics, Chemical physics, Mathematical physics, Computational physics: Yes. Materials physics uses physics to study and design materials.

Vehicle dynamics & ...

• Vehicle dynamics - Mechanics, Classical mechanics, Dynamics, Aerodynamics (for aircraft/cars), Fluid mechanics (for ships), Astrodynamics (for spacecraft), Control theory (engineering), Mathematical physics, Computational physics: Yes. Vehicle dynamics is a branch of mechanics focusing on the motion of vehicles.

Philosophy of physics & ...

• Philosophy of physics - all of physics, logic, philosophy of science, epistemology, metaphysics: Yes. Philosophy of physics deals with the conceptual foundations, interpretations, and implications of physics theories.

Summary of Approach:

For almost every pair, we can find a derivation or at least a strong connection where principles from one topic are used to explain or model phenomena in the other. In some cases, it's a direct mathematical derivation. In others, it's about applying the principles of one field as tools in another. The interconnectedness of physics is very strong. The few cases where "derivation" is less direct are often where one field is a methodology (like computational physics or mathematical physics) or an application domain (like medical physics or agrophysics) for more fundamental physics principles. Even in those cases, there are derivations involved in applying the fundamental principles to the specific domain.