um ## Tags - Topics: [[landing/docs/Contents/Exobrain/Topics/Science|Science]] [[Mathematics|Mathematics]] - Additional: ## Significance - Allowing to predict, control, design and explain any physical system, which is all systems in reality. ## Definitions - [[Mathematics]] constrained by physical reality. ## Technical summaries - Equations describing physical systems. ## Main resources - [Physics - Wikipedia](https://en.wikipedia.org/wiki/Physics) <iframe src="https://en.wikipedia.org/wiki/Physics" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> - Stanford [Leonard Susskind The Theoretical Minimum Course](https://theoreticalminimum.com/courses) and other university lectures linked in the various pages of subfields - Hardest way to learn physics: [geometry of physics in nLab](https://ncatlab.org/nlab/show/geometry+of+physics) - [Classical Mechanics: John R. Taylor: 9781891389221: Amazon.com: Books](https://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X) - [best physics books - Hledat Googlem](https://www.google.com/search?q=best+physics+books&sca_esv=e14f95cbc2b145ff&sca_upv=1&sxsrf=ADLYWIKtFzCIMux6n-YEJCoeYSSUEq5ASA%3A1727604729394&ei=-Sf5ZvzZF8Dn7_UPxuSD2QI&ved=0ahUKEwi8utSR9eeIAxXA87sIHUbyICsQ4dUDCA8&uact=5&oq=best+physics+books&gs_lp=Egxnd3Mtd2l6LXNlcnAiEmJlc3QgcGh5c2ljcyBib29rczIFEAAYgAQyBRAAGIAEMgsQABiABBiRAhiKBTIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgARI_UdQuzlY50ZwAngBkAEAmAF-oAHPC6oBAzkuNrgBA8gBAPgBAZgCEaAClg3CAgoQABiwAxjWBBhHwgINEAAYgAQYsAMYQxiKBcICDhAAGLADGOQCGNYE2AEBwgITEC4YgAQYsAMYQxjIAxiKBdgBAcICChAjGIAEGCcYigXCAgsQLhiABBjRAxjHAcICChAAGIAEGBQYhwKYAwCIBgGQBhO6BgYIARABGAmSBwQ2LjExoAewXg&sclient=gws-wiz-serp) - [Search | MIT OpenCourseWare | Free Online Course Materials](https://ocw.mit.edu/search/) ## Landscapes - [Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics) <iframe src="https://en.wikipedia.org/wiki/Outline_of_physics" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> - [The Map of Physics - YouTube](https://www.youtube.com/watch?v=ZihywtixUYo) <iframe title="The Map of Physics" src="https://www.youtube.com/embed/ZihywtixUYo?feature=oembed" height="113" width="200" allowfullscreen="" allow="fullscreen" style="aspect-ratio: 1.76991 / 1; width: 100%; height: 100%;"></iframe> - [[Mathematical physics]] - By domain - [[Classical mechanics]] - [[Fluid mechanics]] - [[Field theory]] - [[Electromagnetism]] - [[Optics]] - [[Theory of relativity]] - [[Special relativity]] - [[General relativity]] - [[Quantum mechanics]] - [[Statistical mechanics]] - [[Thermodynamics]] - [[Non-equilibrium statistical mechanics]] - [[Non-equilibrium thermodynamics]] - [[Dynamical systems theory]] - [[Information theory]] - Unity - [[Relativistic quantum mechanics]] - [[Quantum field theory]] - [[Standard Model of Particle Physics]] - [[Quantum electrodynamics]] - [[Quantum chromodynamics]] - [[Quantum statistical mechanics]] - [[Quantum field statistical mechanics]] - [[Quantum information theory]] - [[Loop Quantum Gravity]] - [[String theory]] - [[M Theory]] - [[Causal sets]] - [[Cosmology]] - [[Interdisciplinarity]] - [[Biophysics]] - [[Neurophysics]] - [[Technology]] - [[Computing]] - [[Quantum computing]] - [[Thermodynamic computing]] - [[Artificial Intelligence]] - [[Quantum machine learning]] - [[Thermodynamic AI]] - [[Power generation]] - [[Black hole]] - [[Interpretations of quantum mechanics]] - [[Artificial Intelligence x Physics]] #### Fundamental equations of the universe [X](https://x.com/skdh/status/1847616858398089303) [[Images/71ede449f0921c12dfd2b4686b47b940_MD5.jpeg|Open: Pasted image 20241022020353.png]] ![[Images/71ede449f0921c12dfd2b4686b47b940_MD5.jpeg]] [[Images/16c21171fb1dff8faafcc146b896f06e_MD5.jpeg|Open: Pasted image 20241006100449.png]] ![[Images/16c21171fb1dff8faafcc146b896f06e_MD5.jpeg]] - [[Standard Model of Particle Physics#Lagrangian]] ![[Standard Model of Particle Physics#Lagrangian]] ## Deep dives - [[Natural science#Structure of reality from first principles]] ![[Natural science#Structure of reality from first principles]] - [List of unsolved problems in physics - Wikipedia](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics) - <iframe src="https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> - [Every Thing in Space - YouTube](https://www.youtube.com/watch?v=uniGQrGLEoI) - [The Map of Black Holes | Black Holes Explained - YouTube](https://www.youtube.com/watch?v=Wf0uxjWGwPk) - [physics in nLab](https://ncatlab.org/nlab/show/physics) ## Resources Stanford: classical mechanics, quantum mechanics, statistical mechanics, cosmology, particle physics, string theory https://theoreticalminimum.com/ MIT: classical mechanics https://www.youtube.com/playlist?list=PLyQSN7X0ro203puVhQsmCj9qhlFQ-As8e https://www.youtube.com/playlist?list=PLUl4u3cNGP61qDex7XslwNJ-xxxEFzMNV electricity and magnetism electromagnetism https://www.youtube.com/playlist?list=PLyQSN7X0ro2314mKyUiOILaOC2hk6Pc3j https://www.youtube.com/playlist?list=PLmNMkuCOhP2sGhvByEAq2LAS2QMFDPQM- quantum physics https://www.youtube.com/playlist?list=PLUl4u3cNGP61-9PEhRognw5vryrSEVLPr https://www.youtube.com/playlist?list=PLUl4u3cNGP60cspQn3N9dYRPiyVWDd80G https://www.youtube.com/playlist?list=PLUl4u3cNGP60QlYNsy52fctVBOlk-4lYx https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L vibration and waves https://www.youtube.com/playlist?list=PLUl4u3cNGP61R5sPDPKVfcFlu95wSs2Kx https://www.youtube.com/playlist?list=PLyQSN7X0ro22WeXM2QCKJm2NP_xHpGV89 https://www.youtube.com/playlist?list=PLUl4u3cNGP62JTiv0epD_FMmUV6Y7wMv_ history of 20th century https://www.youtube.com/playlist?list=PLUl4u3cNGP63bAfjGas3TuA4ZCPUtN6Xf general relativity https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx special relativity https://www.youtube.com/playlist?list=PLUl4u3cNGP61Zc3rR6wVM0kpsiyIq0fk8 nuclear and particle physics https://www.youtube.com/playlist?list=PLUl4u3cNGP60Do91PdN978llIsvjKW0au relativistic quantum field theory https://www.youtube.com/playlist?list=PLUl4u3cNGP61AV6bhf4mB3tCyWQrI_uU5 statistical mechanics https://www.youtube.com/playlist?list=PLUl4u3cNGP60gl3fdUTKRrt5t_GPx2sRg https://www.youtube.com/playlist?list=PLUl4u3cNGP63HkEHvYaNJiO0UCUmY0Ts7 atomic nucelar and optical physics https://www.youtube.com/playlist?list=PLUl4u3cNGP62FPGcyFJkzhqq9c5cHCK32 https://www.youtube.com/playlist?list=PLUl4u3cNGP62uOSArqLf4vNLiZtgIRm1K nuclear engineering https://www.youtube.com/playlist?list=PLUl4u3cNGP61FVzAxBP09w2FMQgknTOqu solid state physics https://www.youtube.com/playlist?list=PLcxQMvk7OdDN2B2M9tLwr9bnsjEIIxZLl experimental physics https://www.youtube.com/playlist?list=PLUl4u3cNGP6393Jj6WMmNd1_pOs0UDq2R physics experiments https://www.youtube.com/playlist?list=PL7145A9AA4BAF35FC thermodynamics of materials https://www.youtube.com/playlist?list=PLUl4u3cNGP61g-yRbJz4ghFPJLiok1HxX thermodynamics and kinetics https://www.youtube.com/playlist?list=PLA62087102CC93765 early universe https://www.youtube.com/playlist?list=PLUl4u3cNGP61Bf9I0WDDriuDqEnywoxra physical chemistry https://www.youtube.com/playlist?list=PLUl4u3cNGP62RsEHXe48Imi9-87FzQaJg optics https://www.youtube.com/playlist?list=PLEA084AC2DD3CEC09 thermodynamics https://www.youtube.com/playlist?list=PLF6C6594F42ECEE0D cosmology https://www.youtube.com/playlist?list=PL4BUyFYOFtUZIUtcSDo6vm4HPxS9aZmHC engineering dynamics https://www.youtube.com/playlist?list=PLUl4u3cNGP62esZEwffjMAsEMW_YArxYC string theory and holographic duality https://www.youtube.com/playlist?list=PLUl4u3cNGP633VWvZh23bP6dG80gW34SU plasma diagnostics https://www.youtube.com/playlist?list=PLUl4u3cNGP61wK-NwYKZMuABl_eHBmhu4 nuclear physics https://www.youtube.com/playlist?list=PLOarn8QL6W_LOBTvWwLac5VCxJpkiHa-e black holes https://www.youtube.com/playlist?list=PL5CA9864EFB258E8A yale electromagnetism https://www.youtube.com/playlist?list=PLB1A0BF14EB31C3BE Physics Sean Carroll [The Biggest Ideas in the Universe! - YouTube](https://www.youtube.com/playlist?list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX) [An Elegant Structural Overview of Modern Theoretical Physics - YouTube](https://www.youtube.com/watch?v=2bi5G6plWCI) An Elegant Structural Overview of Modern Theoretical Physics Nonequilibrium thermodynamics, nonequilibrium statistical mechanics [Non-equilibrium statistical physics - YouTube](https://www.youtube.com/playlist?list=PL04QVxpjcnjjoN7xfc7Vy63uUSkDlOYiU) [Fluctuations in Nonequilibrium Systems: Theory and Applications - YouTube](https://www.youtube.com/playlist?list=PL04QVxpjcnjgmUoD6tlO_0YT1k5GYgQWi) [Nonequilibrium Stat Mechanics - YouTube](https://www.youtube.com/playlist?list=PLCVqYvWXt6ZM3Sh5qbN2SAWABpinU6smE) [nonequilibrium - YouTube](https://www.youtube.com/playlist?list=PLrbFeBstDbRLw9kwTqJJsD490YcPEU8x8) [Nonequilibrium - YouTube](https://www.youtube.com/playlist?list=PLsdMv0E_Hm4bavLh1nm12XvjHwlekZ-WZ) [Statistical Mechanics 1 (Equilibrium & Non-equilibrium) - YouTube](https://www.youtube.com/playlist?list=PLv64M6nvmocsPYna-WHr0mX8dSp_OEgVV) [Non Equilibrium Stat Mech - YouTube](https://www.youtube.com/playlist?list=PLXi9EP7hqH1aFw8_-kf-h70zSIXUARLNH) [School on Emergent Phenomena in Non-Equilibrium Quantum Many-Body Systems - YouTube](https://www.youtube.com/playlist?list=PLg0_ydgtbHGGQM_VDY9562kPfFHCn_C_z) [Non-Equilibrium Thermodynamics (NET) - YouTube](https://www.youtube.com/playlist?list=PLMi1tmgJbrSINVKIVjLLqkARXsixSftqf) [Physics - Nonequilibrium Statistical Mechanics - YouTube](https://www.youtube.com/playlist?list=PLbMVogVj5nJQqNx0ElSk3Ip04Ofg7B22W) [How_to_learn_Physics_from_the_ground_up/README.md at main · joaocarvalhoopen/How_to_learn_Physics_from_the_ground_up · GitHub](https://github.com/joaocarvalhoopen/How_to_learn_Physics_from_the_ground_up/blob/main/README.md) [GitHub - llSourcell/Learn_Physics_in_2_Months: This is the curriculum for "Learn Physics in 2 Months" by Siraj Raval on Youtube](https://github.com/llSourcell/Learn_Physics_in_2_Months) [GitHub - comp-physics/awesome-numerics: Resources for learning about numerical methods.](https://github.com/comp-physics/awesome-numerics) [GitHub - Hridoy-31/physics-video-courses: List of Physics courses with video lectures.](https://github.com/Hridoy-31/physics-video-courses) [How_to_learn_Physics_from_the_ground_up/README.md at main · joaocarvalhoopen/How_to_learn_Physics_from_the_ground_up · GitHub](https://github.com/joaocarvalhoopen/How_to_learn_Physics_from_the_ground_up/blob/main/README.md) [GitHub - llSourcell/Learn_Physics_in_2_Months: This is the curriculum for "Learn Physics in 2 Months" by Siraj Raval on Youtube](https://github.com/llSourcell/Learn_Physics_in_2_Months) [GitHub - comp-physics/awesome-numerics: Resources for learning about numerical methods.](https://github.com/comp-physics/awesome-numerics) https://brilliant.org/courses/ [[nonAI mathcode long important]] [[Resources physics]] [[Links physics]] [[Links complexity emergence]] ## Brainstorming [[Thoughts physics]] We will crack the source of of our simulation The source code of our simulation, the standard model of particle physics! Almost cracked? Quantum gravity and some other problems are missing! What is measurement on the fundamental level? The capability of AI systems I'm the most interested in is if you gave the system all of classical mechanics, if it could derive general relativity and quantum mechanics from it, which seems to be a stronger out of distribution generalization than the current types of systems can do, but I'm open to be mistaken. And give it all (most of) known empirical data from experiments before the phase shift and derive it from these too. Universe is one gigantic system of quantum harmonic oscillators composing into complex higher order harmonic oscillators god is the quantum harmonic oscillator The mathematician in me is crying when it's observing the physicist trying to learn physics and doing all the mathematically illegal operations and approximations that are legal in physics Physics lectures are like candies Is space an objective container or relational between objects? What if there is no theory of quantum gravity and we need complete paradigm shift out of our current maps? We might have to transcend the mathematical concept of dimensions altogether in fundamental physics! Solving quantum gravity might reveal a glitch in the fabric of spacetime and fundamental particles and forces or strings or whatever is under all, that allows for arbitrary code execution exploit to edit or spawn arbitrary structure and laws! How does the equation predicting all of our current measured and future empirical data looks like? The whole world is one big collection of interconnected changes, and derivatives describe their pace. ## Additional topics - [The Map of Superconductivity - YouTube](https://www.youtube.com/watch?v=bD2M7P6dTVA) - [Atomic Spectroscopy Explained in 9 Slides - YouTube](https://www.youtube.com/watch?v=crWBFuUW6kI) - [The Incredible Science of CERN - YouTube](https://www.youtube.com/watch?v=hAK6ovQQqtc) ## Written by AI (may include factually incorrect information) # Classical Mechanics - **Newton's laws of motion:** three fundamental laws describing the relationship between a body, the forces acting upon it, and the body's motion, forming the foundation of classical mechanics ([Newton's laws of motion - Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#:~:text=Newton%27s%20laws%20of%20motion%20are,can%20be%20paraphrased%20as%20follows)) ([Newton's Laws of Motion | Brilliant Math & Science Wiki](https://brilliant.org/wiki/newtons-laws-of-motion/#:~:text=Newton%27s%20laws%20of%20motion%20are,that%20relate%20force%20and%20motion)). - **Kinematics:** branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the forces causing that motion ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=which%20is%20concerned%20with%20the,8)) ([Kinematics - Simple English Wikipedia, the free encyclopedia](https://simple.wikipedia.org/wiki/Kinematics#:~:text=Kinematics%20is%20the%20branch%20of,1)). - **Dynamics:** the branch of mechanics concerned with the causes of motion and changes in motion (i.e. forces); essentially, it studies how forces produce acceleration according to Newton’s second law ([Geodynamics | Geodynamics – What does it really mean?](https://blogs.egu.eu/divisions/gd/2020/04/22/geodynamics-what-does-it-really-mean/#:~:text=ImageLet%20us%20start%20with%20the,geodynamcist%2C%20who%20studied%20mantle%20convection)) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=analysis%20of%20the%20kinematics%20and,of%20forces%20on%20fluid%20motion)). - **Statics:** the branch of mechanics dealing with forces in the absence of motion (static equilibrium) – forces are balanced so that a system remains at rest or moves with constant velocity ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,are%20at%20a%20constant%20velocity)) ([Statics - The Physics Hypertextbook](https://physics.info/statics/#:~:text=Statics%20,absence%20of%20changes%20in%20motion)). - **Work and energy (work–energy principle):** in mechanics, work is the energy transfer by a force, and the work–energy theorem states that the net work done on an object equals its change in kinetic energy ([Newton's laws of motion - Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#:~:text=line%2C%20unless%20it%20is%20acted,2)) ([Newton's laws of motion - Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#:~:text=Philosophi%C3%A6%20Naturalis%20Principia%20Mathematica%20,quantum%20mechanics)). - **Conservation of energy:** fundamental law stating that energy cannot be created or destroyed, only transformed from one form to another (the total energy of an isolated system remains constant) ([Conservation of energy - Wikipedia](https://en.wikipedia.org/wiki/Conservation_of_energy#:~:text=time.,one%20will%20get%20the%20exact)) ([Law of conservation of energy - Energy Education](https://energyeducation.ca/encyclopedia/Law_of_conservation_of_energy#:~:text=The%20law%20of%20conservation%20of,from%20one%20form%20to%20another)). - **Conservation of momentum:** in an isolated system (no external forces), the total linear momentum remains constant over time – momentum lost by one part of the system is gained by another ([Problem 14 State the law of conservation of... [FREE SOLUTION] | Vaia](https://www.vaia.com/en-us/textbooks/physics/conceptual-physics-12-edition/chapter-6/problem-14-state-the-law-of-conservation-of-momentum-explain/#:~:text=The%20law%20states%20that%20the,not%20change%20the%20total%20momentum)) ([Problem 14 State the law of conservation of... [FREE SOLUTION] | Vaia](https://www.vaia.com/en-us/textbooks/physics/conceptual-physics-12-edition/chapter-6/problem-14-state-the-law-of-conservation-of-momentum-explain/#:~:text=Stating%20the%20Law%20of%20Conservation,of%20Momentum)). - **Newton’s law of gravitation:** every two masses in the universe attract each other with a gravitational force proportional to the product of their masses and inversely proportional to the square of the distance between them ([Newton's law of universal gravitation - Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#:~:text=Newton%27s%20law%20of%20universal%20gravitation,3)) ([Imagine the Universe!](https://imagine.gsfc.nasa.gov/features/yba/CygX1_mass/gravity/more.html#:~:text=Sir%20Isaac%20Newton%20defined%20this,by%20Henry%20Cavendish%20in%201798)). - **Lagrangian mechanics:** a reformulation of classical mechanics based on the principle of least action (stationary action); it uses the Lagrangian (kinetic minus potential energy) to derive equations of motion equivalent to Newton’s laws ([Lagrangian mechanics - Wikipedia](https://en.wikipedia.org/wiki/Lagrangian_mechanics#:~:text=Lagrangian%20mechanics%20is%20a%20formulation,the%20principle%20of%20least%20action)) ([Lagrangian mechanics | Prefetch](https://prefetch.eu/know/concept/lagrangian-mechanics/#:~:text=Lagrangian%20mechanics%20is%20a%20formulation,of%20that%20path)). - **Hamiltonian mechanics:** a reformulation of classical mechanics (introduced by William R. Hamilton in 1833) that arose from Lagrangian mechanics – it uses the Hamiltonian (energy function) to describe a system and provides equations of motion in terms of generalized coordinates and momenta ([Hamiltonian system](https://en-academic.com/dic.nsf/enwiki/599671#:~:text=,in%201788%20%E2%80%A6%20%C2%A0%20Wikipedia)). - **Chaos theory:** the study of dynamical systems that are highly sensitive to initial conditions (the “butterfly effect”), leading to apparently random or chaotic behavior despite being governed by deterministic laws ([Chaos theory | Definition, Examples, & Facts | Britannica](https://www.britannica.com/science/chaos-theory#:~:text=chaos%20theory%2C%20in%20mechanics%20,considered%20more%20apparent%20than%20real)). Classic examples include the chaotic motion of a double pendulum or weather systems. - **Acoustics:** the branch of physics that studies sound and mechanical waves in matter (gases, liquids, and solids) – how sound is produced, transmitted, and received ([Category:Acoustics - Wikipedia](https://en.wikipedia.org/wiki/Category:Acoustics#:~:text=Acoustics%20is%20a%20branch%20of,in%20gases%2C%20liquids%2C%20and%20solids)) ([Acoustics | Definition, Physics, & Facts | Britannica](https://www.britannica.com/science/acoustics#:~:text=Acoustics%2C%20the%20science%20concerned%20with,in%20the%20study%20of)). - **Fluid mechanics:** the study of fluids (liquids and gases) and the forces acting on them – encompassing fluid statics (fluids at rest) and fluid dynamics (fluids in motion) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,study%20of%20fluids%20in%20motion)) ([Fluid mechanics - Wikipedia](https://en.wikipedia.org/wiki/Fluid_mechanics#:~:text=Fluid%20mechanics%20is%20the%20branch,and%20the%20forces%20on%20them)). - **Continuum mechanics:** branch of mechanics that treats matter as continuous (ignoring its atomic structure) and analyzes the deformation and flow of materials modeled as continuous masses (e.g. solids and fluids) under forces ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,of%20forces%20on%20fluid%20motion)). - **Mechanical waves:** oscillations that transfer energy through a medium – examples include **sound waves** (longitudinal pressure waves in air or other media) and **water waves**. Mechanical wave phenomena such as interference and diffraction can be analyzed using the principles of superposition ([Galaxies | Chaos theory is a branch of mathematics and physics that ...](https://www.instagram.com/reel/DIhj_TvR_ZO/#:~:text=Galaxies%20,appears%20random%20or%20unpredictable%2C)) ([The Science of Sound: How Understanding Acoustics Can Improve ...](https://www.tritonemusicmentors.com/post/the-science-of-sound-how-understanding-acoustics-can-improve-your-music#:~:text=,helps%20us%20understand%20how)). # Electromagnetism - **Coulomb’s law:** the electrostatic force law stating that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them ([Newton's law of universal gravitation - Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#:~:text=Newton%27s%20law%20of%20universal%20gravitation,3)) ([Imagine the Universe!](https://imagine.gsfc.nasa.gov/features/yba/CygX1_mass/gravity/more.html#:~:text=Sir%20Isaac%20Newton%20defined%20this,by%20Henry%20Cavendish%20in%201798)). (This law defines the strength of the electric force between charges, with Coulomb’s constant as the proportionality factor.) - **Electric field:** a field of force surrounding an electric charge – any other charge in this field experiences a force. The electric field **E** at a point is defined such that the force on a test charge _q_ is **F = qE** ([Newton's laws of motion - Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#:~:text=line%2C%20unless%20it%20is%20acted,2)) ([Newton's laws of motion - Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#:~:text=Philosophi%C3%A6%20Naturalis%20Principia%20Mathematica%20,quantum%20mechanics)). - **Magnetic field:** a field produced by moving electric charges or intrinsic magnetic moments (e.g. of electrons). A magnetic field exerts forces on moving charges or other magnets (force **F = q·v × B** on charge _q_ with velocity _v_) ([Lorentz force - Wikipedia](https://en.wikipedia.org/wiki/Lorentz_force#:~:text=The%20Lorentz%20force%20law%20is,charge%20due%20to%20electromagnetic%20fields)). - **Lorentz force law:** the law stating that a charged particle in electric and magnetic fields experiences a force **F = q(E + v × B)** – i.e. the total force is the combination of the electric force and the magnetic force on the charge ([Lorentz force - Wikipedia](https://en.wikipedia.org/wiki/Lorentz_force#:~:text=The%20Lorentz%20force%20law%20is,charge%20due%20to%20electromagnetic%20fields)). - **Faraday’s law of induction:** a changing magnetic field through a circuit induces an electromotive force (EMF) in that circuit. In essence, a time-varying magnetic flux produces an electric field (voltage) – the principle behind electrical generators and transformers ([Concept Check MELC Demonstrate the - StudyX](https://studyx.ai/homework/111151490-concept-check-melc-demonstrate-the-generation-of-electricity-by-movement-of-a-magnet#:~:text=Concept%20Check%20MELC%20Demonstrate%20the,This%20EMF)) ([Starting from Maxwell's equations in free space, show that ... - Brainly](https://brainly.com/question/50717729#:~:text=Starting%20from%20Maxwell%27s%20equations%20in,is%20expressed%20as%3A%20%E2%88%87%C3%97E%3D%E2%88%92%E2%88%82t%E2%88%82B)). - **Maxwell’s equations:** a set of four fundamental equations (Gauss’s laws for electricity and magnetism, Faraday’s law, and Ampère–Maxwell law) that unify electricity and magnetism by describing how electric and magnetic fields are generated by charges and currents and how they propagate ([Integrated Science at Home: Maxwell's Equations for Dummies](http://integratedscienceathome.blogspot.com/2011/02/maxwells-equations-for-dummies.html#:~:text=,you%20need%20to%20know%20vector)) ([What are Maxwell's Equations? - Quora](https://www.quora.com/What-are-Maxwells-Equations-1#:~:text=What%20are%20Maxwell%27s%20Equations%3F%20,they%20relate%20to%20each%20other)). Maxwell’s equations predict that changing electric and magnetic fields sustain each other and travel as **electromagnetic waves**. - **Electromagnetic waves:** oscillating electric and magnetic fields that propagate through space at the speed of light, carrying energy. These include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays – all are waves of the electromagnetic field differing only in frequency/wavelength ([Problem 21 Broadcast Frequencies FM radio s... [FREE SOLUTION]](https://www.vaia.com/en-us/textbooks/chemistry/chemistry-an-atoms-focused-approach-2-edition/chapter-3/problem-21-broadcast-frequencies-fm-radio-stations-broadcast/#:~:text=SOLUTION,These%20waves%20include%20a)). _(EM waves require no medium and obey c ≈ 3×10^8 m/s in vacuum.)_ - **Optics:** the study of light (electromagnetic waves in the visible and nearby ranges) and its interactions with matter. It includes phenomena such as **reflection**, **refraction**, **diffraction**, and **interference**, and applications like lenses, mirrors, and optical instruments ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,dealing%20with%20the%20nervous%20system)) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,of%20polymers%20and%20monomers%20respectively)). - **Electromagnetic spectrum:** the entire range of electromagnetic wave frequencies, from low-energy radio waves through microwaves, infrared, visible light, ultraviolet, X-rays, up to high-energy gamma rays. All are fundamentally the same kind of wave, distinguished by frequency or wavelength. - **Ohm’s law:** an empirical law of electric circuits stating that the current **I** through a conductor between two points is directly proportional to the voltage **V** across those points and inversely proportional to the resistance **R** (i.e. _V = I·R_) ([What is Ohm's Law? (A Simple Explanation) - Electrical4U](https://www.electrical4u.com/ohms-law-equation-formula-and-limitation-of-ohms-law/#:~:text=Electrical4U%20www,inversely%20proportional%20to%20its%20resistance)). This linear relation holds for many materials (ohmic conductors) within certain ranges of current. - **Electromagnetic induction:** the generation of an electric current or EMF in a conductor due to a changing magnetic flux. This encompasses Faraday’s law and is the operating principle of transformers, inductors, and generators (a moving magnet or changing current induces a current in a nearby coil) ([Concept Check MELC Demonstrate the - StudyX](https://studyx.ai/homework/111151490-concept-check-melc-demonstrate-the-generation-of-electricity-by-movement-of-a-magnet#:~:text=Concept%20Check%20MELC%20Demonstrate%20the,This%20EMF)) ([Starting from Maxwell's equations in free space, show that ... - Brainly](https://brainly.com/question/50717729#:~:text=Faraday%27s%20Law%20of%20Induction%20states,is%20expressed%20as%3A%20%E2%88%87%C3%97E%3D%E2%88%92%E2%88%82t%E2%88%82B)). # Thermodynamics and Statistical Mechanics - **Zeroth law of thermodynamics:** if system A is in thermal equilibrium with system B, and B is in thermal equilibrium with system C, then A and C are in thermal equilibrium with each other ([Zeroth law of thermodynamics - (College Physics I - Fiveable](https://library.fiveable.me/key-terms/intro-college-physics/zeroth-law-of-thermodynamics#:~:text=Fiveable%20library,are%20in%20thermal%20equilibrium)). (This law effectively defines _temperature_ as the property that is equal for systems in mutual thermal equilibrium.) - **First law of thermodynamics:** the law of energy conservation in thermodynamic processes. It states that energy can neither be created nor destroyed – the change in internal energy of a system equals the heat added to the system minus the work done by the system ([First Law of Thermodynamics - an overview | ScienceDirect Topics](https://www.sciencedirect.com/topics/chemistry/first-law-of-thermodynamics#:~:text=First%20Law%20of%20Thermodynamics%20,energy%20transfer%20is%20associated)) ([Conservation of energy - Wikipedia](https://en.wikipedia.org/wiki/Conservation_of_energy#:~:text=time.,one%20will%20get%20the%20exact)). - **Second law of thermodynamics:** states that the entropy of an isolated system **never decreases** over time; it either increases or remains constant in a reversible process ([Second Law of Thermodynamics | Brilliant Math & Science Wiki](https://brilliant.org/wiki/second-law-thermodynamics/#:~:text=Second%20Law%20of%20Thermodynamics%20,or%20remain%20the%20same)). In practical terms, this law introduces the concept of _irreversibility_ – for example, heat spontaneously flows from hot to cold, and no process can be 100% efficient, as disorder (_entropy_) tends to increase ([[FREE] The Second Law of Thermodynamics states that - Brainly](https://brainly.com/question/15542077#:~:text=,a%20maximum%20value%20at%20equilibrium)). - **Third law of thermodynamics:** as the temperature of a system approaches absolute zero (0 K), the entropy of a perfect crystalline substance approaches a minimum constant value (often effectively zero) ([Which statement best describes the third law of thermodynamics? A ...](https://brainly.com/question/58288425#:~:text=The%20third%20law%20of%20thermodynamics,This)). In other words, it is impossible to reach absolute zero temperature in a finite number of steps, and at 0 K a perfect crystal would have maximum order (minimum entropy). - **Entropy:** a measure of the disorder or randomness in a system. Higher entropy corresponds to greater disorder (and less available energy to do work) ([What is entropy? A. A measure of the efficiency of a system B. Heat ...](https://brainly.com/question/55048018#:~:text=What%20is%20entropy%3F%20A,while%20lower%20entropy%20indicates)). The second law implies that the entropy of the universe tends to increase, explaining why certain processes (like mixing or heat diffusion) are spontaneous and irreversible. - **Enthalpy:** a thermodynamic quantity defined as _H = U + PV_ (internal energy plus pressure×volume). It represents the heat content of a system at constant pressure – changes in enthalpy correspond to heat absorbed or released at constant pressure (e.g. in chemical reactions). - **Free energy (Gibbs free energy):** a thermodynamic potential _G = H – TS_ that measures the useful work obtainable from a system at constant temperature and pressure. A process will occur spontaneously if it leads to a decrease in Gibbs free energy (ΔG < 0) ([Inorganic Reaction Energetics | Flashcards World](https://flashcards.world/flashcards/sets/80ad703f-7879-4f6a-8801-a1ea5e20ff7a/#:~:text=What%20is%20Gibbs%20free%20energy%3F,at%20constant%20temperature%20and%20pressure)). This concept predicts equilibrium and spontaneity of reactions. - **Thermodynamic equilibrium:** a state in which a system’s macroscopic properties (temperature, pressure, etc.) are unchanging in time and no net flows of matter or energy occur within the system. At equilibrium, entropy is at maximum and free energy is at minimum for the given constraints. - **Phase transition:** a transformation of a substance from one state of matter (phase) to another, such as solid–liquid (melting/freezing), liquid–gas (boiling/condensation), etc. Phase transitions often involve latent heat and abrupt changes in properties like density; e.g., boiling is a first-order transition with a discontinuous density change ([Which of the following statements is true | StudyX](https://studyx.ai/questions/4llizwa/which-of-the-following-statements-is-true-a-in-first-order-phase-transition-the-order#:~:text=A%20phase%20transition%20is%20a,transitions%20involve%20a%20discontinuous)). Critical points and second-order transitions involve continuous changes and fluctuations (as in ferromagnetic transitions). - **Statistical mechanics:** the branch of physics that uses statistical methods and probability theory to relate the microscopic behavior of atoms and molecules to the macroscopic thermodynamic properties of materials ([Statistical mechanics | Thermodynamics, Entropy & Equilibrium](https://www.britannica.com/science/statistical-mechanics#:~:text=Statistical%20mechanics%20,both%20classical%20and%20quantum%20mechanics)) ([Statistical mechanics - Wikipedia](https://en.wikipedia.org/wiki/Statistical_mechanics#:~:text=Statistical%20mechanics%20,large%20assemblies%20of%20microscopic%20entities)). It provides the microscopic explanation for entropy, temperature, and phase transitions by considering ensembles of a large number of particles. - **Maxwell–Boltzmann distribution:** a statistical distribution law giving the probability distribution of speeds (or energies) of particles in an ideal gas at thermal equilibrium. It shows, for example, that at a given temperature, most gas molecules have intermediate speeds, with fewer at very low or very high speeds. (Quantum analogues: Fermi–Dirac distribution for fermions, Bose–Einstein distribution for bosons.) - **Equipartition theorem:** a result from statistical mechanics stating that, at thermal equilibrium, energy is shared equally among all accessible degrees of freedom. For example, each quadratic degree of freedom (like translational or rotational kinetic energy) carries **½kBT** of energy on average ([Conservation of energy - Wikipedia](https://en.wikipedia.org/wiki/Conservation_of_energy#:~:text=The%20law%20of%20conservation%20of,energy%20and%20%20241%20potential)). This explains classical heat capacities of gases, etc. - **Boltzmann’s entropy formula:** $S = k_B \ln \Omega$, which connects entropy _S_ with the number of microstates Ω corresponding to a given macrostate (kB is Boltzmann’s constant). This formula underpins the statistical definition of entropy: more available microstates (higher Ω) → higher entropy ([Conservation of energy - Wikipedia](https://en.wikipedia.org/wiki/Conservation_of_energy#:~:text=The%20law%20of%20conservation%20of,energy%20and%20%20241%20potential)). # Quantum Mechanics - **Wave–particle duality:** the fundamental concept that every quantum entity (such as an electron or photon) exhibits both wave-like and particle-like properties ([Wave particle duality or complementarity? - Physics Stack Exchange](https://physics.stackexchange.com/questions/152760/wave-particle-duality-or-complementarity#:~:text=Wave%20particle%20duality%20or%20complementarity%3F,only%20particles%2C%20but%20also%20waves)) ([Wave-particle duality | Quantum Mechanics, Electrons, Photons](https://www.britannica.com/science/wave-particle-duality#:~:text=Wave,like%20characteristics)). For example, electrons can produce interference patterns (wave behavior) yet also appear as point-like particles when detected; light can behave as a wave (interference, diffraction) or as particles (photons in the photoelectric effect). - **Quantum superposition:** the principle that a quantum system can exist in multiple states simultaneously until it is measured or observed ([What is the definition of quantum physics? - EduRev UPSC Question](https://edurev.in/question/4640479/What-is-the-definition-of-quantum-physics-#:~:text=,time%20until%20it%20is%20measured)). For instance, an electron in an atom can be in a superposition of several energy states – only upon measurement does it _collapse_ into one definite state. (This underlies phenomena like interference in single-particle double-slit experiments.) - **Heisenberg uncertainty principle:** a fundamental limit to the precision with which certain pairs of physical properties can be known simultaneously. In its most famous form, it states one cannot simultaneously know a particle’s position and momentum with arbitrary precision (Δx·Δp ≥ ħ/2) ([Uncertainty principle - Wikipedia](https://en.wikipedia.org/wiki/Uncertainty_principle#:~:text=Uncertainty%20principle%20,momentum%2C%20can%20be%20simultaneously%20known)). Thus, measuring one property more accurately causes the other to be less determined – a reflection of the inherent quantum nature of particles, not just measurement disturbance. - **Quantum wavefunction:** a mathematical function (usually denoted ψ) that encodes the state of a quantum system. The wavefunction’s magnitude squared |ψ|² gives the probability density of finding a particle in a given state or position upon measurement ([Schrödinger Equation - (College Physics I – Introduction) - Fiveable](https://fiveable.me/key-terms/intro-college-physics/schrodinger-equation#:~:text=Schr%C3%B6dinger%20Equation%20,how%20it%20evolves%20over%20time)). It encapsulates the superposition of possible states until an observation causes a collapse to a definite outcome. - **Schrödinger equation:** the fundamental equation of nonrelativistic quantum mechanics that governs how the wavefunction evolves in time. In the time-dependent form: _iħ ∂ψ/∂t = Hψ_, it describes how quantum states change, while the time-independent form _Hψ = Eψ_ yields allowed energy levels ([Schrödinger Equation - (College Physics I – Introduction) - Fiveable](https://fiveable.me/key-terms/intro-college-physics/schrodinger-equation#:~:text=Schr%C3%B6dinger%20Equation%20,how%20it%20evolves%20over%20time)). It is analogous to Newton’s laws in classical mechanics, predicting phenomena like quantized energy levels in atoms. - **Quantum tunneling:** a quantum phenomenon where a particle can penetrate through a potential energy barrier that it classically could not overcome (due to insufficient energy) ([Quantum Bits - Flashcard set - Quantum Computing - Computer ...](https://aiflash.cards/community/computer-science/quantum-computing/quantum-bits#:~:text=Quantum%20Bits%20,shouldn%27t%20be%20able%20to%20overcome)). For example, an alpha particle can tunnel out of an atomic nucleus (alpha decay), and electrons tunnel through thin barriers in semiconductors – an effect underlying technologies like scanning tunneling microscopes and tunnel diodes. - **Spin:** an intrinsic form of angular momentum carried by quantum particles, not associated with literal spinning motion but a quantum property. Electrons, protons, and neutrons have spin **½**, photons have spin **1**, etc. Spin gives rise to magnetic moments (making particles behave like tiny magnets) and underlies phenomena such as fine-structure splitting and the Pauli exclusion principle. - **Pauli exclusion principle:** the rule that no two identical fermions (particles with half-integer spin, like electrons) can occupy the same quantum state simultaneously ([What is the Pauli exclusion principle? - TutorChase](https://www.tutorchase.com/answers/a-level/physics/what-is-the-pauli-exclusion-principle#:~:text=The%20Pauli%20exclusion%20principle%20states,principle%20is%20a%20fundamental)). This is why electrons in an atom fill different orbitals with distinct quantum numbers – it explains the structure of the periodic table and the stability of matter (electron degeneracy pressure in white dwarfs and neutron stars is a manifestation of this principle). - **Quantum entanglement:** a phenomenon in which two or more particles become linked such that the state of one particle is instantaneously correlated with the state of the other(s), no matter how far apart they are ([Quantum entanglement - Wikipedia](https://en.wikipedia.org/wiki/Quantum_entanglement#:~:text=Quantum%20entanglement%20is%20the%20phenomenon,state%20of%20the%20others%2C)) ([Human Connection and Quantum Entanglement - SnoQap](https://www.snoqap.com/posts/2024/11/4/human-connection-and-quantum-entanglement-a-detailed-exploration#:~:text=Human%20Connection%20and%20Quantum%20Entanglement,the%20state%20of%20another%2C)). In an entangled pair, measuring the state of one immediately determines the state of its partner (e.g. opposite spins), seemingly violating locality – though no usable information travels faster than light. Entanglement is central to quantum information science (e.g. quantum teleportation, superdense coding). - **Atomic orbitals:** in quantum mechanics, electrons in atoms occupy orbitals – standing-wave solutions of the Schrödinger equation around the nucleus. These orbitals are characterized by quantum numbers and have probabilistic electron distributions (e.g. the familiar s, p, d, f shapes). The quantization of orbitals explains atomic spectra and chemical bonding. - **Quantum statistics:** quantum particles follow specific statistics – **Fermions** (half-integer spin) obey Fermi–Dirac statistics (no two can occupy the same state, leading to e.g. electron degeneracy in metals), while **Bosons** (integer spin) obey Bose–Einstein statistics (they can bunch into the same state, enabling phenomena like lasers and superfluidity). This leads to exotic states of matter like Bose–Einstein condensates at ultracold temperatures. - **Quantum measurement problem:** the unresolved conceptual question of how and why a quantum wavefunction “collapses” to a definite outcome when observed. In absence of observation, a system evolves deterministically (per Schrödinger’s equation) in a superposition, but measurement yields a probabilistic single result. Interpretations of quantum mechanics (Copenhagen, Many-Worlds, etc.) attempt to explain this process. # Relativity - **Special relativity:** Einstein’s 1905 theory of space and time which postulates (1) the laws of physics are the same in all inertial frames, and (2) the speed of light in vacuum is constant for all observers regardless of their relative motion ([Einstein's Theory of Special Relativity - Space](https://www.space.com/36273-theory-special-relativity.html#:~:text=Einstein%27s%20Theory%20of%20Special%20Relativity,to%20define%20the%20relationship)) ([Special relativity - Wikipedia](https://en.wikipedia.org/wiki/Special_relativity#:~:text=Special%20relativity%20,the%20principle%20of%20light)). From these postulates follow phenomena like **time dilation** (moving clocks tick slower) and **length contraction** (moving objects are shortened along the direction of motion), as well as the equivalence of mass and energy. - **Time dilation:** in special relativity, moving clocks run slow relative to a stationary observer. Specifically, a clock moving at high speed _v_ is observed to tick at a slower rate by a factor of $γ = 1/\sqrt{1-v^2/c^2}$ ([If we assume the speed of light is invariant, isn't time dilation ... - Reddit](https://www.reddit.com/r/AskPhysics/comments/16wjfnb/if_we_assume_the_speed_of_light_is_invariant_isnt/#:~:text=Reddit%20www,length%20contraction%20have%20to%20happen)) ([How does time change with gravity and in the presence of massive ...](https://mathematics-and-physics.quora.com/How-does-time-change-with-gravity-and-in-the-presence-of-massive-objects?top_ans=60995502#:~:text=...%20mathematics,or%20by%20being%20differently)). For example, muons produced in the upper atmosphere live longer (in Earth frame) due to time dilation, and precise timing (GPS satellites) must account for both velocity-based and gravity-based time dilation. - **Length contraction:** likewise, lengths measured in the direction of motion are observed to contract at high speeds. An object of rest length _L_0 moving past an observer at speed _v_ appears shortened to $L = L_0\sqrt{1-v^2/c^2}$. This and time dilation are two sides of how spacetime intervals transform between frames (Lorentz transformations). - **Mass–energy equivalence:** the principle that mass and energy are two forms of the same thing, as expressed in Einstein’s famous equation _E = m c^2_. A mass _m_ at rest is equivalent to an energy _E_ ([Mass–energy equivalence - Wikipedia](https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#:~:text=In%20physics%2C%20mass%E2%80%93energy%20equivalence%20is,by%20a%20multiplicative%20constant)) ([DOE Explains...Relativity - Department of Energy](https://www.energy.gov/science/doe-explainsrelativity#:~:text=DOE%20Explains...Relativity%20,changed%20from%20one%20to)). This explains how huge energy can be released by converting a small amount of mass (as in nuclear reactions) and implies that energy added to an object (e.g. by heating) increases its effective inertial mass. - **General relativity:** Einstein’s 1915 theory of gravitation which generalizes special relativity to accelerating frames and gravity. It describes gravity not as a force but as the curvature of spacetime caused by mass-energy ([What are black holes and how does their existence relate to the ...](https://www.numerade.com/questions/what-are-black-holes-and-how-does-their-existence-relate-to-the-internal-structure-of-atoms/#:~:text=,It)). Massive objects (like Earth or the Sun) tell spacetime how to curve, and curved spacetime tells objects how to move. General relativity correctly predicts phenomena such as **gravitational time dilation** (clocks run slower in stronger gravity), the deflection of light by gravity, the precession of Mercury’s orbit, and the expansion of the universe. - **Curved spacetime:** in general relativity, mass and energy curve the geometry of space and time around them. Straight-line paths in curved spacetime (geodesics) appear as gravitational orbits or trajectories. For example, Earth orbits the Sun because the Sun’s mass curves spacetime – Earth is following a geodesic in that curved geometry. - **Black holes:** extreme solutions of general relativity representing regions of spacetime with gravity so intense that not even light can escape. A black hole forms when a mass (e.g. a collapsed star core) is compressed within its Schwarzschild radius, creating an “event horizon” beyond which events cannot affect distant observers ([Black hole - Wikipedia](https://en.wikipedia.org/wiki/Black_hole#:~:text=Black%20hole%20,anything%20from%20escaping%2C%20even%20light)). Black holes are characterized by mass, spin, and charge, and exhibit peculiar effects like time slowing down near the horizon (to outside observers). - **Gravitational waves:** ripples in the fabric of spacetime produced by accelerating massive objects (predicted by general relativity and first observed in 2015). For example, the inspiral and merger of two neutron stars or black holes generates gravitational waves – these travel outward at the speed of light, stretching and squeezing distances as they pass ([Gravitational waves - (College Physics I – Introduction) - Vocab ...](https://library.fiveable.me/key-terms/intro-college-physics/gravitational-waves#:~:text=,Einstein%27s%20General%20Theory%20of%20Relativity)). The LIGO and Virgo detectors have directly measured these minute disturbances, confirming Einstein’s prediction. - **Cosmology (FLRW universe):** general relativity applied to the universe as a whole leads to the Friedmann–Lemaître–Robertson–Walker models, in which the universe can expand or contract. The **Big Bang theory** emerges, describing a hot, dense origin of the universe and subsequent expansion. Key predictions include the cosmic expansion (observed by Hubble) and the cosmic microwave background. - **Equivalence principle:** the core principle of general relativity stating that local observations in a freely falling reference frame (in a gravitational field) are indistinguishable from those in an inertial frame with no gravity. In essence, being in free fall “cancels out” gravity locally – this principle led Einstein to realize that gravity could be modeled as spacetime curvature (since acceleration and gravity are locally equivalent). - **Lorentz transformations:** the set of equations in special relativity that relate space and time coordinates between two inertial frames moving at constant velocity relative to each other. They replace the classical Galilean transformations and ensure that the speed of light remains invariant and that causality (no faster-than-light signaling) is preserved. Lorentz transformations mix space and time (time and space are not absolute), leading to the unified concept of **spacetime**. # Astrophysics and Cosmology - **Stars and stellar evolution:** stars are massive luminous spheres of plasma powered by nuclear fusion in their cores. They form from collapsing clouds of gas, spend the majority of their lives fusing hydrogen into helium (main-sequence phase), then evolve off the main sequence once the hydrogen is depleted ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=Earth,study%20of%20how%20matter%20and)) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,which%20involves%20the%20behavior%20and)). Depending on initial mass, a star may become a **red giant** and shed mass, then end as a **white dwarf** (for low mass), or explode in a **supernova** and leave behind a **neutron star** or **black hole** (for high-mass stars). This process (stellar evolution) is responsible for the creation of heavy elements in supernovae and neutron-star mergers. - **Galaxy:** a gravitationally bound system consisting of billions (sometimes trillions) of stars, vast clouds of gas and dust, and dark matter, all orbiting a common center ([Galaxy | Cosmos Universe Wiki | Fandom](https://cosmos-universe.fandom.com/wiki/Galaxy#:~:text=A%20galaxy%20is%20a%20gravitationally,derived%20from%20the%20Greek%20%27galaxias)). Galaxies come in various types: **spiral galaxies** (like our Milky Way, with spiral arms and a rotating disk), **elliptical galaxies** (roughly ellipsoidal shape, older star populations), and **irregular galaxies** (no definite shape). Galaxies often group into clusters and superclusters and interact via gravity (e.g. galaxy collisions and mergers). - **Milky Way:** the galaxy that contains our Solar System – a barred spiral galaxy about 100,000 light-years across, containing on the order of $10^{11}$ stars. The Sun is located in one of its spiral arms, roughly 27,000 ly from the galactic center, where a supermassive black hole (Sagittarius A*) resides. - **Exoplanet:** a planet outside the Solar System, orbiting a star other than the Sun ([FAQs | NameExoworlds - International Astronomical Union](https://nameexoworlds.iau.org/2019faqs#:~:text=Union%20nameexoworlds,Thousands%20of%20exoplanets%20have)). Thousands of exoplanets have been discovered in the last few decades, exhibiting a surprising variety (hot Jupiters, super-Earths, etc.). Their detection methods include the transit method (dimming of starlight as a planet passes in front) and the radial-velocity method (wobbles in a star’s spectrum due to an orbiting planet’s gravity). - **Big Bang theory:** the prevailing cosmological model for the origin of the universe, which posits that the universe began about 13.8 billion years ago from an extremely hot, dense initial state (a singularity) and has been expanding ever since ([Formation of the Universe and Elements Study Guide | Quizlet](https://quizlet.com/study-guides/formation-of-the-universe-and-elements-aa18231e-a6cb-4e90-a708-29ae2ec7610a#:~:text=The%20Big%20Bang%20Theory%20is,singularity%2C%20a%20point%20of)). Key evidence for the Big Bang includes the observed expansion of the universe (Hubble’s law), the cosmic microwave background radiation, and the primordial abundance of light elements (Big Bang nucleosynthesis). - **Expansion of the universe:** Edwin Hubble’s observations of galaxies revealed that distant galaxies are receding from us, with recession velocity proportional to distance (Hubble’s law) ([HW #2.docx - How did Slipher and later Hubble determine...](https://www.coursehero.com/file/171499555/HW-2docx/#:~:text=What%20is%20the%20Hubble%20Law%3F,distance%2C%20which%20just%20means)). This implies space itself is expanding uniformly. As a result, light from distant galaxies is redshifted. In modern cosmology, the expansion is understood through general relativity – the scale of space increases with time, and since about 5–6 billion years ago the expansion has been accelerating due to dark energy. - **Cosmic inflation:** a theory that in the very early universe (the first tiny fraction of a second after the Big Bang), space underwent an extremely rapid exponential expansion ([WMAP Inflation Theory - NASA](https://wmap.gsfc.nasa.gov/universe/bb_cosmo_infl.html#:~:text=WMAP%20Inflation%20Theory%20,during%20its%20first%20few%20moments)) ([Inflationary epoch - Wikipedia](https://en.wikipedia.org/wiki/Inflationary_epoch#:~:text=The%20inflationary%20epoch%20was%20the,underwent%20an%20extremely%20rapid)). Inflation was proposed to solve puzzles like the horizon problem and flatness problem – it explains why the universe is very uniform on large scales and why the spatial geometry appears flat. During inflation, quantum fluctuations were stretched to cosmic sizes, seeding the formation of galaxies. - **Cosmic microwave background (CMB):** the faint glow of relic radiation filling the universe, discovered in 1965. The CMB is thermal **blackbody** radiation at about 2.7 K, and it represents the afterglow of the Big Bang – specifically, the epoch ~380,000 years after the Big Bang when the universe cooled enough for electrons and protons to combine into neutral hydrogen, making the universe transparent to radiation ([Cosmic microwave background (CMB) - (Intro to Astronomy) - Fiveable](https://library.fiveable.me/key-terms/intro-astronomy/cosmic-microwave-background-cmb#:~:text=Fiveable%20library,all%20directions%20in%20the%20universe)). The CMB is almost uniform, with tiny anisotropies (one part in 100,000) that reflect density fluctuations in the early universe which grew into galaxies and clusters. - **Dark matter:** a form of matter that does not emit, absorb, or reflect light (hence “dark”) but exerts gravitational effects on visible matter ([What is dark matter? - Space](https://www.space.com/20930-dark-matter.html#:~:text=Dark%20matter%20is%20entirely%20invisible%2C,by%20conventional%20sensors%20and%20detectors)) ([Is dark matter not actually matter, but a gravitational effect ... - Quora](https://www.quora.com/Is-dark-matter-not-actually-matter-but-a-gravitational-effect-from-another-dimension-universe-affecting-our-universe#:~:text=Is%20dark%20matter%20not%20actually,but%20does%20exert%20gravitational%20effects)). Evidence for dark matter includes the unexpectedly high rotation speeds of stars in galaxy outskirts (flat rotation curves), gravitational lensing observations, and the cosmic structure formation models – these suggest dark matter makes up ~27% of the universe’s energy content. Dark matter is thought to be composed of some new, as-yet-undetected elementary particle (e.g. WIMPs or axions) that interacts via gravity (and possibly the weak force) but not electromagnetism. - **Dark energy:** a mysterious form of energy that permeates space and drives the accelerated expansion of the universe ([Dark energy - Wikipedia](https://en.wikipedia.org/wiki/Dark_energy#:~:text=Dark%20energy%20is%20a%20proposed,accelerating%20expansion%20of%20the)) ([Cosmic dark energy may be weakening, astronomers say ... - Phys.org](https://phys.org/news/2025-03-cosmic-dark-energy-weakening-astronomers.html#:~:text=First%20discovered%20in%201998%2C%20dark,increasing%20rate)). Discovered via distant supernova observations in 1998, dark energy constitutes about ~68% of the universe. In the simplest model it corresponds to a small constant vacuum energy (the cosmological constant, Λ) with negative pressure, causing space to expand faster over time. The nature of dark energy is unknown – it could be a constant property of space or a dynamic field (sometimes called “quintessence”). - **Nebula:** a cloud of gas and dust in space, often glowing from embedded stars. Nebulae can be stellar nurseries (e.g. the Orion Nebula where new stars form), supernova remnants (expanding debris of exploded stars like the Crab Nebula), or planetary nebulae (shells expelled by dying Sun-like stars). Nebulae are important in the lifecycle of matter, enriching the interstellar medium with heavier elements. - **Supernova:** a catastrophic explosion marking the death of certain stars. **Type II supernovae** occur when a massive star (> 8 solar masses) exhausts its fuel, and its core collapses into a neutron star or black hole, releasing an enormous amount of energy and ejecting the star’s outer layers. **Type Ia supernovae** occur in binary systems when a white dwarf accretes enough mass to ignite carbon runaway fusion; they serve as standard candles in cosmology. Supernovae can outshine entire galaxies temporarily and forge elements heavier than iron, dispersing them into space. - **Neutron star:** the ultra-dense remnant core of a massive star after a supernova (for stars not massive enough to form a black hole). A neutron star packs about 1.4–2 solar masses into a sphere ~20 km across, achieving densities comparable to an atomic nucleus. It is composed mostly of neutrons (protons and electrons crushed together under gravity) ([Neutron stars are small, terrestrial, planet-sized. True False - Brainly](https://brainly.com/question/36702826#:~:text=Brainly%20brainly,12)). Neutron stars have extremely strong magnetic fields and can rotate rapidly – observed as pulsars when their lighthouse-like beams sweep Earth. - **Cosmological principle:** the assumption that on large scales, the universe is homogeneous (uniform in composition) and isotropic (the same in all directions). This principle underlies modern cosmology and is supported by observations (e.g. the CMB is nearly isotropic). It implies no preferred center or edge of the universe on giant scales. - **Hubble’s law:** the linear relation observed between the distances of galaxies and their recession velocities: _v = H0 d_, where _H0_ is the Hubble constant. It quantitatively describes the expanding universe: every 3.26 million light years of distance adds roughly 70 km/s of recession velocity (with current _H0>_ ≈ 70 km/s/Mpc) ([HW #2.docx - How did Slipher and later Hubble determine...](https://www.coursehero.com/file/171499555/HW-2docx/#:~:text=What%20is%20the%20Hubble%20Law%3F,distance%2C%20which%20just%20means)). The inverse of _H0_ gives a timescale on the order of the age of the universe. - **Structure formation:** the process by which small initial density fluctuations in the early universe grew via gravity into galaxies, clusters, and larger structures. In the leading Cold Dark Matter model, dark matter clumps merged hierarchically, pulling in gas that formed stars and galaxies. The **cosmic web** of filaments and voids seen in galaxy surveys reflects these gravitational clustering processes over billions of years. - **Astroparticle physics:** an interdisciplinary field combining particle physics and astrophysics, dealing with high-energy processes in the universe. Examples include cosmic rays (high-energy particles from space), neutrinos from the Sun or supernovae, and gamma-ray astronomy. Discoveries like neutrino oscillations ([Neutrino Oscillation - (Intro to Astronomy) - Fiveable](https://fiveable.me/key-terms/intro-astronomy/neutrino-oscillation#:~:text=Neutrino%20oscillation%20is%20the%20quantum,can%20later%20be)) and gravitational waves have created new windows on the cosmos, requiring both astronomical observation and fundamental physics. # Particle Physics - **Standard Model of particle physics:** the well-established theory that describes all known fundamental particles and three of the four fundamental forces (electromagnetic, weak, strong) ([Standard Model - Wikipedia](https://en.wikipedia.org/wiki/Standard_Model#:~:text=The%20Standard%20Model%20of%20particle,and%20strong%20interactions%20%E2%80%93)). It classifies **elementary particles** into quarks and leptons (matter particles, fermions with spin ½) and gauge bosons (force carriers with spin 1), plus the Higgs boson. The Standard Model successfully explains a huge array of experimental results ([Standard Model - Wikipedia](https://en.wikipedia.org/wiki/Standard_Model#:~:text=The%20Standard%20Model%20of%20particle,and%20strong%20interactions%20%E2%80%93)), although it does not include gravity and leaves some open questions (e.g. dark matter, neutrino masses). - **Quarks:** fundamental constituents of matter that experience the strong nuclear force. Quarks come in six “flavors” – up, down, charm, strange, top, bottom – and combine to form composite particles like protons and neutrons ([what exactly are quarks? - Physics](https://physics.science.narkive.com/C3WTAzEo/what-exactly-are-quarks#:~:text=Quarks%20are%20fundamental%20particles%20that,quarks%20make%20up%20either)) ([Problem 7 What's the role of gluons?... [FREE SOLUTION] - Vaia](https://www.vaia.com/en-us/textbooks/physics/essential-university-physics-2-edition/chapter-39/problem-7-whats-the-role-of-gluons/#:~:text=Problem%207%20What%27s%20the%20role,Quarks%20also%20carry)). For example, a proton is `uud` (two up quarks and one down quark) bound by gluons. Quarks carry fractional electric charge (e.g. +2/3 or –1/3) and cannot exist freely in isolation due to confinement; they are always confined in hadrons. - **Leptons:** a family of six fundamental particles that do _not_ feel the strong force ([Quarks and Leptons | Principles of Physics III Class Notes - Fiveable](https://library.fiveable.me/principles-physics-iii-thermal-physics-waves/unit-10/quarks-leptons/study-guide/u25LZ99JViF1ZJ6n#:~:text=Quarks%20and%20Leptons%20,muon%2C%20tau%2C%20and%20their)). They include three charged leptons – electron, muon, tau – and three corresponding neutral neutrinos (electron neutrino νe, muon neutrino νμ, tau neutrino ντ). Electrons (charge –1) form atoms together with nuclei. Muons and taus are heavier and unstable. Neutrinos are very light, neutral particles that interact only via the weak force (hence very penetrating). - **Gauge bosons:** force carrier particles associated with the fundamental forces. In the Standard Model these are the **photon** (carrier of electromagnetism), the **W± and Z0 bosons** (carriers of the weak force), and **gluons** (carriers of the strong force) ([Gauge boson - (Principles of Physics IV) - Fiveable](https://library.fiveable.me/key-terms/principles-of-physics-iv/gauge-boson#:~:text=Gauge%20boson%20,gauge%20bosons%20that%20mediate)). All gauge bosons have spin 1. Photons are massless and mediate electric and magnetic forces. W and Z bosons are massive (~80–90 GeV/$c^2$) and are responsible for beta decay and other weak interactions (their heaviness gives the weak force its short range). Gluons (eight types in SU(3) symmetry) carry the strong force that binds quarks inside protons, neutrons, and other hadrons; they themselves carry color charge, leading to the confinement of quarks. - **Higgs boson:** a scalar boson (spin 0) associated with the Higgs field, first detected in 2012 at the LHC. The Higgs field permeates the vacuum and via the Higgs mechanism gives mass to other particles (in particular, the W and Z bosons, and fundamental fermions) ([Quantum Units and Constants | Flashcards World](https://flashcards.world/flashcards/sets/b49d54a6-94bb-4107-9ff0-ea451003c304/#:~:text=Quantum%20Units%20and%20Constants%20,is%20the%20concept%20of)). The Higgs boson is the quantum excitation of this field. Its discovery confirmed the last missing piece of the Standard Model, with a mass around 125 GeV/$c^2$. - **Neutrino oscillations:** the phenomenon wherein a neutrino of one flavor (say electron neutrino produced in the Sun) can transform into another flavor (muon or tau neutrino) over time and distance ([Neutrino Oscillation - (Intro to Astronomy) - Fiveable](https://fiveable.me/key-terms/intro-astronomy/neutrino-oscillation#:~:text=Neutrino%20oscillation%20is%20the%20quantum,can%20later%20be)). This quantum oscillation implies that neutrinos have tiny but non-zero masses and that the flavor states (νe, νμ, ντ) are mixtures of mass eigenstates. Neutrino oscillations were confirmed by experiments (e.g. solar and atmospheric neutrino observations) and earned the 2015 Nobel Prize; it was a key finding beyond the original Standard Model (which assumed neutrinos massless). - **Strong nuclear force:** the fundamental force binding quarks together in nucleons and holding nucleons together in atomic nuclei (residual strong force). It is mediated by gluons and operates at subatomic distances (~10⁻¹⁵ m). The strong force is extremely powerful at short range (far stronger than electromagnetism), but it falls off rapidly beyond the size of a nucleus. This force explains why atomic nuclei (protons and neutrons) stick together despite proton–proton repulsion, and it underlies nuclear reactions and the release of nuclear energy. - **Weak nuclear force:** a fundamental force responsible for processes like beta decay (neutron → proton + electron + antineutrino) and other flavor-changing interactions. It is mediated by the massive W± and Z0 bosons and has a very short range (~10⁻¹⁷ m). The weak force violates certain symmetries (parity violation) and is unique in that it can change one type of quark or lepton into another (e.g. d quark → u quark in beta decay). The unification of electromagnetism and the weak force into the **electroweak theory** was a major success of the Standard Model. - **Four fundamental forces:** gravity, electromagnetism, strong, and weak are the four fundamental interactions in nature. The **electromagnetic**, **weak**, and **strong** forces are all described by quantum field theories (and in the Standard Model, the electroweak unification combines EM and weak at high energy) ([Standard Model - Wikipedia](https://en.wikipedia.org/wiki/Standard_Model#:~:text=The%20Standard%20Model%20of%20particle,and%20strong%20interactions%20%E2%80%93)). **Gravity** is described classically by general relativity and acts on all forms of energy but is much weaker on microscopic scales. A primary goal of physics is to unify these forces into a single framework. - **Antimatter:** for every type of particle, there exists an antiparticle with the same mass but opposite charges (for example, the positron is the electron’s antiparticle with +1 charge) ([Is Supersymmetry really swapping fermions with bosons?](https://physics.stackexchange.com/questions/487867/is-supersymmetry-really-swapping-fermions-with-bosons#:~:text=Is%20Supersymmetry%20really%20swapping%20fermions,corresponding%20superpartner%20of%20opposite%20nature)) ([supersymmetry - ryoji ikeda](https://www.ryojiikeda.com/project/supersymmetry/#:~:text=In%20particle%20physics%2C%20supersymmetry%20is,particles%3A%20boson%20and%20fermion%2C)). When a particle meets its antiparticle, they can annihilate into pure energy (typically photons). Antimatter is routinely produced in particle accelerators and certain radioactive decays. The universe has very little antimatter overall – an asymmetry between matter and antimatter created conditions where matter dominates, an unsolved puzzle in cosmology related to CP violation. - **Particle accelerators:** machines that accelerate charged particles (electrons, protons, ions) to high speeds and collide them to probe subatomic structure. For example, the Large Hadron Collider (LHC) at CERN collides protons at 13 TeV center-of-mass energy, enabling discovery of heavy particles like the Higgs boson ([More conversation with ChatGPT – Androken Aerial](https://www.androkenaerial.com/2023/05/17/more-conversation-with-chatgpt/#:~:text=More%20conversation%20with%20ChatGPT%20%E2%80%93,announced%20at%20the%20Large)). Accelerators have been crucial for verifying the Standard Model, discovering quarks, W/Z bosons, etc. - **Cosmic rays:** high-energy particles (mostly protons, plus heavier nuclei and some electrons) that originate from outer space and strike Earth. They can have extremely high energies (far exceeding man-made accelerators) and produce showers of secondary particles in the atmosphere. Cosmic ray studies bridge astrophysics and particle physics (e.g. detection of muons, pions in air showers, and searches for ultra-high-energy phenomena). - **Hadronization:** the process by which quarks and gluons produced in high-energy collisions transform into hadrons (e.g. pions, protons). Due to confinement, free quarks never emerge; instead, they create jets of particles. The study of jet formation and hadronization is important in interpreting collider experiments (quantum chromodynamics dynamics). - **High-energy physics experiments:** facilities like CERN’s LHC, Fermilab’s Tevatron (now retired), and KEK and SLAC for electron/positron collisions have allowed physicists to discover fundamental particles and investigate their interactions at small distance scales. Detector technologies (tracking chambers, calorimeters) record the spray of particles from collisions, allowing reconstruction of short-lived states like the top quark (discovered 1995) or Higgs boson ([More conversation with ChatGPT – Androken Aerial](https://www.androkenaerial.com/2023/05/17/more-conversation-with-chatgpt/#:~:text=More%20conversation%20with%20ChatGPT%20%E2%80%93,announced%20at%20the%20Large)). # Condensed Matter Physics - **Crystalline solids:** materials where atoms are arranged in an orderly repeating lattice structure. **Crystal structure** determines many properties (e.g. diamond vs graphite, both carbon but different lattice). Techniques like X-ray diffraction reveal crystal lattices. The vibrations of the lattice (phonons) are quantized and play a role in thermal conductivity and specific heat (Dulong–Petit law at high T, Debye model at low T). - **Band theory of solids:** in a crystal, atomic orbitals combine into energy bands (allowed ranges of energy) separated by band gaps. **Conductors** have partially filled bands (allowing free electrons to move under an electric field), **insulators** have full valence bands separated by a large gap from empty conduction bands, and **semiconductors** have a smaller gap ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,phenomena%20that%20are%20mediated%20by)). This theory explains electrical conductivity and is the foundation of semiconductor electronics (doping shifts the Fermi level into the band gap to create n-type or p-type materials). - **Semiconductors:** materials with a moderate band gap (e.g. silicon, gallium arsenide) whose conductivity increases with temperature (unlike metals). By doping with impurities, one can create excess electrons (n-type) or holes (p-type). Semiconductor junctions (p–n junctions) underlie diodes, transistors, and solar cells, forming the basis of modern electronics. - **Superconductivity:** a phenomenon where certain materials, when cooled below a critical temperature, exhibit zero electrical resistance and expulsion of magnetic fields (Meissner effect). In classical (low-temperature) superconductors, this is explained by Cooper pairs of electrons forming and condensing into a single quantum state (BCS theory). High-temperature superconductors (cuprates, etc.) operate via less understood mechanisms. Superconductors allow lossless current flow and quantum interference devices (SQUIDs) and promise applications like efficient power lines and maglev trains. - **Magnetism in materials:** arises from electron spins and orbital motions. **Ferromagnetism** (e.g. in iron) is when atomic magnetic moments align spontaneously below a Curie temperature, producing a net magnetization ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=occur%20between%20electrically%20charged%20particles,concerned%20with%20the%20behavior%20of)). **Paramagnetism** is weaker alignment with an external field (moments randomize when field removed), **Diamagnetism** is a slight induced opposition to an applied field (present in all materials). **Antiferromagnetism** has alternating spin alignment that cancels out net magnetization. Magnetic phenomena are central to data storage (hard drives use ferromagnetic domains) and spintronics. - **Bose–Einstein condensate (BEC):** a state of matter formed by bosons (e.g. ultracold atoms with integer spin) cooled to near absolute zero, such that a large fraction occupies the lowest quantum state. First achieved in 1995 with rubidium atoms, a BEC exhibits quantum effects on macroscopic scales – the atoms behave collectively as one “matter wave.” It’s a manifestation of Bose–Einstein statistics (e.g. all particles condense into ground state). Superfluid helium and superconductors are related macroscopic quantum phenomena (Cooper pairs in a superconductor form a condensate). - **Quantum Hall effect:** observed in 2D electron systems at low temperatures and high magnetic fields. The **integer quantum Hall effect** (discovered 1980) shows the Hall conductivity quantized in integer multiples of $e^2/h$. The **fractional quantum Hall effect** (1982) shows fractional quantization, indicating emergence of quasiparticles with fractional electric charge – a striking quantum many-body phenomenon ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,of%20%20141%20that%20describes)) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=the%20motion%20%20of%20points%2C,rather%20than%20as%20discrete%20particles)). These effects illustrate topological phases of matter, an active research area. - **Graphene:** a single layer of carbon atoms arranged in a hexagonal lattice (essentially a 2D material). Discovered in 2004, graphene is ultra-strong, flexible, and an excellent electrical and thermal conductor. It has a unique band structure with Dirac cone electron dispersion, meaning its charge carriers behave like massless relativistic particles. Graphene’s discovery opened a new field of **2D materials** (e.g. monolayer MoS₂) with novel electronic and optical properties. - **Topological insulators:** materials that are insulating in the bulk but support conducting states on their surface or edges, due to nontrivial topology of their electronic band structure. These surface states are protected (robust against disorder) and often have spin-momentum locking (an electron’s spin is tied to its direction of motion). Topological phases (insulators, superconductors) represent a new classification beyond conventional symmetry-breaking phases, with potential applications in electronics and quantum computing. - **Metamaterials:** engineered materials with structures designed to produce properties not found in naturally occurring substances. For example, photonic metamaterials can have **negative refractive index**, allowing novel effects like superlensing (sub-wavelength imaging) or cloaking. Metamaterials achieve these effects by having structural features smaller than the wavelength of interest, creating effective medium properties (affecting electromagnetic waves, sound waves, etc.). - **Critical phenomena:** near continuous phase transitions (e.g. liquid–vapor critical point, Curie point in magnets), systems exhibit scale invariance and large fluctuations. Quantities like specific heat, susceptibility diverge following power laws with critical exponents. The **renormalization group** theory provides understanding of these phenomena, showing how physics on different length scales connects and leading to universal behavior independent of microscopic details ([Emergence of a Second Law of Thermodynamics in Isolated ...](https://link.aps.org/doi/10.1103/PRXQuantum.6.010309#:~:text=Emergence%20of%20a%20Second%20Law,appears%20to%20conflict%20with)) ([Why can the entropy of an isolated system increase?](https://physics.stackexchange.com/questions/119387/why-can-the-entropy-of-an-isolated-system-increase#:~:text=increase%3F%20physics,always%20evolve%20toward%20thermodynamic)) (universality of critical exponents). - **Nanoscience:** the study of materials and structures at the nanometer scale (1–100 nm), where quantum and surface effects become prominent. At the nanoscale, properties can differ markedly from bulk (e.g. nanoparticles of gold have different optical colors). **Quantum dots** (nanometer-scale semiconductor crystals) have quantized energy levels and behave like artificial atoms, useful in displays and quantum computing. Nanostructuring enables new phenomena and applications in electronics, photonics, and medicine. # Emerging Theories and Interdisciplinary Areas - **Quantum gravity:** the field of theoretical physics seeking to unify quantum mechanics with general relativity – i.e. to describe gravity according to quantum principles. Currently there is no experimentally confirmed quantum gravity theory. Approaches include **string theory** and **loop quantum gravity**, among others. A quantum theory of gravity would account for phenomena at the Planck scale (~10⁻³⁵ m) and possibly resolve issues like the nature of spacetime singularities (inside black holes, the Big Bang) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=counterintuitive%20aspects%20of%20the%20theory%2C,and%20light%20at%20high%20speeds)) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=,Other)). - **String theory:** a leading candidate for a theory of quantum gravity and unification. It proposes that fundamental particles are not point-like but tiny one-dimensional “strings” whose different vibrational modes correspond to different particles (electron, quark, graviton, etc.) ([Supersymmetric free fermions and bosons: Locality, symmetry, and ...](https://link.aps.org/doi/10.1103/PhysRevB.105.085423#:~:text=Supersymmetry%20,of%20freedom%20in%20a%20system)) ([supersymmetry - ryoji ikeda](https://www.ryojiikeda.com/project/supersymmetry/#:~:text=In%20particle%20physics%2C%20supersymmetry%20is,particles%3A%20boson%20and%20fermion%2C)). String theory inherently includes gravity (predicting a spin-2 graviton) and requires extra spatial dimensions beyond the usual four (e.g. 10 or 11 dimensions in various versions). Variants include **M-theory**, which unifies five superstring theories in 11 dimensions. String theory remains mathematically rich but experimentally unverified. - **Loop quantum gravity (LQG):** an approach to quantum gravity that attempts to quantize spacetime itself. It posits that space is made of discrete “chunks” or loops at the Planck scale, leading to a picture of spacetime geometry that is quantized. LQG predicts that area and volume have discrete spectra. It does not require extra dimensions and is background-independent (unlike string theory), but it has its own challenges and has not yielded definitive experimental tests. - **Supersymmetry (SUSY):** a proposed extension of the Standard Model that introduces a new symmetry exchanging fermions and bosons. Supersymmetry predicts for each Standard Model particle a corresponding “superpartner” particle differing by half a unit of spin (fermion ↔ boson) ([Supersymmetry - Wikipedia](https://en.wikipedia.org/wiki/Supersymmetry#:~:text=In%20supersymmetry%2C%20each%20particle%20from,versa%2C%20known%20as%20a%20superpartner)) ([String Theory and Supersymmetry - Dummies.com](https://www.dummies.com/article/academics-the-arts/science/physics/string-theory-and-supersymmetry-178720/#:~:text=Under%20supersymmetry%2C%20a%20fermion%20must,not%20yet%20detected%20these)). For example, electrons (fermions) would have scalar superpartners “selectrons”, and W bosons would have fermionic partners “winos”. SUSY can elegantly solve certain theoretical issues (like the hierarchy problem of why the Higgs mass is stable) ([[PDF] Supersymmetry](https://www.phys.ufl.edu/~mitselmakher/teaching/ParticlePhysics2/Note%2030-Ch12-2%20.pdf#:~:text=According%20to%20the%20supersymmetry%2C%20every,the%20same%20quantum%20numbers%2C)) and provides dark matter candidates (the lightest SUSY particle). However, extensive searches at the LHC have not yet found superpartners in the expected mass ranges, putting supersymmetry in question or pushing superpartner masses higher. - **Grand Unified Theories (GUTs):** hypothetical models that merge the electromagnetic, weak, and strong forces into a single force at high energy (above $10^{15}$ GeV). In a GUT, the three gauge forces of the Standard Model would correspond to one enlarged symmetry group and one set of gauge bosons ([Fundamental Forces and Theories in Physics Study Guide | Quizlet](https://quizlet.com/study-guides/fundamental-forces-and-theories-in-physics-7b8ec712-ced6-4ca6-a26b-97ea3ffdf586#:~:text=Quizlet%20quizlet,connection%20between%20these%20fundamental)). GUTs often predict phenomena like proton decay (because quarks and leptons can transform into each other in a unified framework) and usually require supersymmetry to make the different force couplings converge (“unify”) at a single energy. No GUT has been confirmed yet (proton decay has not been observed at predicted rates). - **Multiverse hypothesis:** a speculative idea in cosmology that our universe might be one of many universes (“bubble” universes or parallel worlds) possibly with different physical constants or laws. In some inflationary models, inflation can produce multiple “pocket universes” with potentially varying parameters (the **inflationary multiverse**). In the context of string theory, the landscape of solutions could correspond to ~10^500 different vacuum states – potentially a multiverse of possible universes. These ideas are not testable so far; the multiverse is a philosophical extrapolation of theories rather than a strict scientific theory, but it is often discussed as a way to explain the fine-tuning of constants (our universe’s parameters may be just one random draw among multitudes) ([Knowledge Zone on X: "The #Multiverse is a hypothetical collection ...](https://x.com/KnowledgeZoneIn/status/1889925424211476950#:~:text=...%20x.com%20%20The%20,possibly%20having%20different%20physical)). - **Quantum computing:** an emerging field of computing that uses quantum-mechanical phenomena (superposition and entanglement) to process information in ways classical computers cannot ([Microsoft Quantum Computing and Skepticism | Coconote](https://coconote.app/notes/00f79fc5-8866-4c4a-87fc-96ea4e8db551#:~:text=Definition%3A%20Quantum%20computing%20uses%20quantum,Potential%3A%20Offers%20exponential)). Quantum computers use **qubits** (quantum bits) that can exist in superpositions of 0 and 1, and entangled states of many qubits to perform parallel computations. Algorithms like Shor’s (for factoring) and Grover’s (search) demonstrate potential exponential or quadratic speedups over classical algorithms ([Microsoft Quantum Computing and Skepticism | Coconote](https://coconote.app/notes/00f79fc5-8866-4c4a-87fc-96ea4e8db551#:~:text=Definition%3A%20Quantum%20computing%20uses%20quantum,Potential%3A%20Offers%20exponential)). While still in early development, prototype quantum processors (using technologies like superconducting qubits or trapped ions) have achieved entanglement of dozens of qubits, and the race is on to achieve quantum advantage for practical problems. - **Quantum information theory:** the study of information science in the quantum realm, dealing with quantum bits, quantum entropy, and communication. It introduces concepts like **quantum teleportation** (transfer of a quantum state using entanglement and classical communication) and **quantum cryptography** (unconditionally secure communication guaranteed by quantum principles, e.g. BB84 protocol). Quantum information blends physics and computation, revealing new principles like the no-cloning theorem (quantum states cannot be copied exactly) and offering quantum-enhanced metrology and sensing ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=where%20the%20action%20is%20on,discipline%20focusing%20in%20understanding%20the)). - **Quantum many-body physics:** a broad area at the intersection of condensed matter and quantum physics dealing with systems of many interacting quantum particles. It addresses phenomena like **emergent properties** (superconductivity, magnetism, quantum phase transitions) and utilizes tools such as **quantum field theory** in condensed matter and computational methods (Monte Carlo, density matrix renormalization). Recent focus includes **quantum spin liquids** (highly entangled magnetic states with no order), **topologically ordered states** (with anyons and ground-state degeneracy related to topology), and **out-of-equilibrium dynamics** (thermalization, quantum chaos in many-body systems). - **Astrobiophysics (Astrobiology):** an interdisciplinary area combining astrophysics, biology, and planetary science to study the possibility and conditions of life in the universe. It involves studying **exoplanets** (habitable zones, Earth-like conditions), **prebiotic chemistry** in space, extremophiles on Earth (organisms thriving in extreme conditions as analogs for extraterrestrial life), and the effects of stars on planetary habitability. While speculative, astrobiology has grown as more potentially habitable exoplanets are found. Missions like rovers on Mars or ocean-world probes (e.g. to Europa or Enceladus) and SETI searches all tie into this field. - **Computational physics:** the application of numerical algorithms and computers to solve physical problems that are analytically intractable. It’s a tool spanning all physics domains – from N-body simulations of galaxy formation, to climate models, to solving quantum many-body Schrödinger equations. Advances in high-performance computing and algorithms (e.g. machine learning for physics, GPU-accelerated computing) allow researchers to explore complex systems (like turbulence or large quantum systems) and make quantitative predictions complementary to theory and experiment ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=biological%20phenomenon.%20,the%20study%20of%20electrical%20phenomena)) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=processes%20from%20physics.%20,of%20the%20physical%20properties%20of)). - **Interdisciplinary fields:** physics increasingly overlaps with other disciplines, giving rise to fields like **biophysics** (applying physics methods to biological systems, e.g. biomolecular structure, neural signaling, biomechanics), **chemical physics** (quantum chemistry, reaction dynamics), **geophysics** (earth’s interior, seismic physics, atmospheric physics), **econophysics** (statistical physics applied to economic systems), and **medical physics** (development of medical imaging, radiation therapy techniques) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=in%20a%20state%20where%20the,154%20and%20nuclear%20medicine)). These areas extend the core principles of physics to tackle complex problems in other sciences and industry, often leading to new techniques (e.g. MRI came from nuclear magnetic resonance physics) and a deeper understanding of the natural world through a physics lens. **Sources:** ([Newton's laws of motion - Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#:~:text=Newton%27s%20laws%20of%20motion%20are,can%20be%20paraphrased%20as%20follows)) ([Kinematics - Simple English Wikipedia, the free encyclopedia](https://simple.wikipedia.org/wiki/Kinematics#:~:text=Kinematics%20is%20the%20branch%20of,1)) ([Geodynamics | Geodynamics – What does it really mean?](https://blogs.egu.eu/divisions/gd/2020/04/22/geodynamics-what-does-it-really-mean/#:~:text=ImageLet%20us%20start%20with%20the,geodynamcist%2C%20who%20studied%20mantle%20convection)) ([Statics - The Physics Hypertextbook](https://physics.info/statics/#:~:text=Statics%20,absence%20of%20changes%20in%20motion)) ([Conservation of energy - Wikipedia](https://en.wikipedia.org/wiki/Conservation_of_energy#:~:text=time.,one%20will%20get%20the%20exact)) ([Law of conservation of energy - Energy Education](https://energyeducation.ca/encyclopedia/Law_of_conservation_of_energy#:~:text=The%20law%20of%20conservation%20of,from%20one%20form%20to%20another)) ([Second Law of Thermodynamics | Brilliant Math & Science Wiki](https://brilliant.org/wiki/second-law-thermodynamics/#:~:text=Second%20Law%20of%20Thermodynamics%20,or%20remain%20the%20same)) ([Which statement best describes the third law of thermodynamics? A ...](https://brainly.com/question/58288425#:~:text=The%20third%20law%20of%20thermodynamics,This)) ([What is entropy? A. A measure of the efficiency of a system B. Heat ...](https://brainly.com/question/55048018#:~:text=What%20is%20entropy%3F%20A,while%20lower%20entropy%20indicates)) ([Wave particle duality or complementarity? - Physics Stack Exchange](https://physics.stackexchange.com/questions/152760/wave-particle-duality-or-complementarity#:~:text=Wave%20particle%20duality%20or%20complementarity%3F,only%20particles%2C%20but%20also%20waves)) ([Uncertainty principle - Wikipedia](https://en.wikipedia.org/wiki/Uncertainty_principle#:~:text=Uncertainty%20principle%20,momentum%2C%20can%20be%20simultaneously%20known)) ([Integrated Science at Home: Maxwell's Equations for Dummies](http://integratedscienceathome.blogspot.com/2011/02/maxwells-equations-for-dummies.html#:~:text=,you%20need%20to%20know%20vector)) ([What are Maxwell's Equations? - Quora](https://www.quora.com/What-are-Maxwells-Equations-1#:~:text=What%20are%20Maxwell%27s%20Equations%3F%20,they%20relate%20to%20each%20other)) ([Problem 21 Broadcast Frequencies FM radio s... [FREE SOLUTION]](https://www.vaia.com/en-us/textbooks/chemistry/chemistry-an-atoms-focused-approach-2-edition/chapter-3/problem-21-broadcast-frequencies-fm-radio-stations-broadcast/#:~:text=SOLUTION,These%20waves%20include%20a)) ([What is Ohm's Law? (A Simple Explanation) - Electrical4U](https://www.electrical4u.com/ohms-law-equation-formula-and-limitation-of-ohms-law/#:~:text=Electrical4U%20www,inversely%20proportional%20to%20its%20resistance)) ([Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics#:~:text=which%20is%20concerned%20with%20the,8)) ([Lorentz force - Wikipedia](https://en.wikipedia.org/wiki/Lorentz_force#:~:text=The%20Lorentz%20force%20law%20is,charge%20due%20to%20electromagnetic%20fields)) ([Concept Check MELC Demonstrate the - StudyX](https://studyx.ai/homework/111151490-concept-check-melc-demonstrate-the-generation-of-electricity-by-movement-of-a-magnet#:~:text=Concept%20Check%20MELC%20Demonstrate%20the,This%20EMF)) ([Standard Model - Wikipedia](https://en.wikipedia.org/wiki/Standard_Model#:~:text=The%20Standard%20Model%20of%20particle,and%20strong%20interactions%20%E2%80%93)) ([what exactly are quarks? - Physics](https://physics.science.narkive.com/C3WTAzEo/what-exactly-are-quarks#:~:text=Quarks%20are%20fundamental%20particles%20that,quarks%20make%20up%20either)) ([Gauge boson - (Principles of Physics IV) - Fiveable](https://library.fiveable.me/key-terms/principles-of-physics-iv/gauge-boson#:~:text=Gauge%20boson%20,gauge%20bosons%20that%20mediate)) ([Quantum Units and Constants | Flashcards World](https://flashcards.world/flashcards/sets/b49d54a6-94bb-4107-9ff0-ea451003c304/#:~:text=Quantum%20Units%20and%20Constants%20,is%20the%20concept%20of)) ([Supersymmetry - Wikipedia](https://en.wikipedia.org/wiki/Supersymmetry#:~:text=In%20supersymmetry%2C%20each%20particle%20from,versa%2C%20known%20as%20a%20superpartner)) ([Neutrino Oscillation - (Intro to Astronomy) - Fiveable](https://fiveable.me/key-terms/intro-astronomy/neutrino-oscillation#:~:text=Neutrino%20oscillation%20is%20the%20quantum,can%20later%20be)) ([What is dark matter? - Space](https://www.space.com/20930-dark-matter.html#:~:text=Dark%20matter%20is%20entirely%20invisible%2C,by%20conventional%20sensors%20and%20detectors)) ([Dark energy - Wikipedia](https://en.wikipedia.org/wiki/Dark_energy#:~:text=Dark%20energy%20is%20a%20proposed,accelerating%20expansion%20of%20the)) ([Formation of the Universe and Elements Study Guide | Quizlet](https://quizlet.com/study-guides/formation-of-the-universe-and-elements-aa18231e-a6cb-4e90-a708-29ae2ec7610a#:~:text=The%20Big%20Bang%20Theory%20is,singularity%2C%20a%20point%20of)) ([Gravitational waves - (College Physics I – Introduction) - Vocab ...](https://library.fiveable.me/key-terms/intro-college-physics/gravitational-waves#:~:text=,Einstein%27s%20General%20Theory%20of%20Relativity)) ([Knowledge Zone on X: "The #Multiverse is a hypothetical collection ...](https://x.com/KnowledgeZoneIn/status/1889925424211476950#:~:text=...%20x.com%20%20The%20,possibly%20having%20different%20physical)) ([Microsoft Quantum Computing and Skepticism | Coconote](https://coconote.app/notes/00f79fc5-8866-4c4a-87fc-96ea4e8db551#:~:text=Definition%3A%20Quantum%20computing%20uses%20quantum,Potential%3A%20Offers%20exponential)) More: [[AI-written physics]]