Physics is one of the oldestacademic disciplines.[5] Over much of the past two millennia, physics,chemistry,biology, and certain branches of mathematics were a part ofnatural philosophy, but during theScientific Revolution in the 17th century, these natural sciences branched into separate research endeavors. Physics intersects with manyinterdisciplinary areas of research, such asbiophysics andquantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences[2] and suggest new avenues of research in these and other academic disciplines such as mathematics and philosophy.
The wordphysics comes from theLatinphysica ('study of nature'), which itself is a borrowing of theGreekφυσική (phusikḗ 'natural science'), a term derived fromφύσις (phúsis 'origin, nature, property').[6][7][8]
Astronomy is one of the oldestnatural sciences. Early civilizations dating before 3000 BCE, such as theSumerians,ancient Egyptians, and theIndus Valley Civilization, had a predictive knowledge and a basic awareness of the motions of the Sun, Moon, and stars. The stars and planets, believed to represent gods, were often worshipped. While the explanations for the observed positions of the stars were often unscientific and lacking in evidence, these early observations laid the foundation for later astronomy, as the stars were found to traversegreat circles across the sky,[5] which could not explain the positions of theplanets.
Natural philosophy has its origins inGreece during theArchaic period (650 BCE – 480 BCE), whenpre-Socratic philosophers likeThales rejectednon-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause.[12] They proposed ideas verified by reason and observation, and many of their hypotheses proved successful in experiment;[13] for example,atomism was found to be correct approximately 2000 years after it was proposed byLeucippus and his pupilDemocritus.[14]
During theclassical period in Greece (6th, 5th and 4th centuries BCE) and inHellenistic times,natural philosophy developed along many lines of inquiry.Aristotle (Greek:Ἀριστοτέλης,Aristotélēs) (384–322 BCE), a student ofPlato,wrote on many subjects, including a substantial treatise on "Physics" – in the 4th century BC.Aristotelian physics was influential for about two millennia. His approach mixed some limited observation with logical deductive arguments, but did not rely on experimental verification of deduced statements. Aristotle's foundational work in Physics, though very imperfect, formed a framework against which later thinkers further developed the field. His approach is entirely superseded today.
He explained ideas such asmotion (andgravity) with the theory offour elements.Aristotle believed that each of the four classical elements (air, fire, water, earth) had its own natural place.[15] Because of their differing densities, each element will revert to its own specific place in the atmosphere.[16] So, because of their weights, fire would be at the top, air underneath fire, then water, then lastly earth. He also stated that when a small amount of one element enters the natural place of another, the less abundant element will automatically go towards its own natural place. For example, if there is a fire on the ground, the flames go up into the air in an attempt to go back into its natural place where it belongs. His laws of motion included: that heavier objects will fall faster, the speed being proportional to the weight and the speed of the object that is falling depends inversely on the density object it is falling through (e.g. density of air).[17] He also stated that, when it comes to violent motion (motion of an object when a force is applied to it by a second object) that the speed that object moves, will only be as fast or strong as the measure of force applied to it.[17] The problem of motion and its causes was studied carefully, leading to the philosophical notion of a "prime mover" as the ultimate source of all motion in the world (Book 8 of his treatisePhysics).
TheWestern Roman Empire fell to invaders and internal decay in the fifth century, resulting in a decline in intellectual pursuits in western Europe. By contrast, the Eastern Roman Empire (usually known as theByzantine Empire) resisted the attacks from invaders and continued to advance various fields of learning, including physics.[19] In the sixth century,John Philoponus challenged the dominant Aristotelian approach to science although much of his work was focused on Christian theology.[20]
The most notable innovations under Islamic scholarship were in the field ofoptics and vision,[21] which came from the works of many scientists likeIbn Sahl,Al-Kindi,Ibn al-Haytham,Al-Farisi andAvicenna. In his Book of Optics (also known as Kitāb al-Manāẓir) Ibn al-Haytham presented the idea of light rays as an alternative to the ancient Greek idea about visual rays. Like Ptolemy, Ibn al-Haytham applied controlled experiments, verifying the laws of refraction and reflection with the new concept of light rays, but still lacking the concept of image formation.[22][23][24]
The discovery of laws inthermodynamics,chemistry, andelectromagnetics resulted from research efforts during theIndustrial Revolution as energy needs increased.[30] By the end of the 19th century, theories of thermodynamics,mechanics, and electromagnetics matched a wide variety of observations. Taken together these theories became the basis for what would later be calledclassical physics.[31]: 2
A few experimental results remained inexplicable. Classical electromagnetism presumed a medium, anluminiferous aether to support the propagation of waves, but this medium could not be detected. The intensity of light from hot glowingblackbody objects did not match the predictions of thermodynamics and electromagnetism. The character ofelectron emission of illuminated metals differed from predictions. These failures, seemingly insignificant in the big picture would upset the physics world in first two decades of the 20th century.[31]
Modern physics began in the early 20th century with the work ofMax Planck in quantum theory andAlbert Einstein's theory of relativity. Both of these theories came about due to inaccuracies in classical mechanics in certain situations.Classical mechanics predicted that thespeed of light depends on the motion of the observer, which could not be resolved with the constant speed predicted byMaxwell's equations of electromagnetism. This discrepancy was corrected by Einstein's theory ofspecial relativity, which replaced classical mechanics for fast-moving bodies and allowed for a constant speed of light.[35]Black-body radiation provided another problem for classical physics, which was corrected when Planck proposed that the excitation of material oscillators is possible only in discrete steps proportional to their frequency. This, along with thephotoelectric effect and a complete theory predicting discreteenergy levels ofelectron orbitals, led to the theory of quantum mechanics improving on classical physics at very small scales.[36]
Physics deals with a wide variety of systems, although certain theories are used by all physicists. Each of these theories was experimentally tested numerous times and found to be an adequate approximation of nature.These central theories are important tools for research into more specialized topics, and any physicist, regardless of their specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics andstatistical mechanics,electromagnetism, and special relativity.
Classical mechanics works for larger and slower objects; modern theories are needed otherwise.
In the first decades of the 20th century physics was revolutionized by the discoveries of quantum mechanics and relativity. The changes were so fundamental that these new concepts became the foundation of "modern physics", with other topics becoming "classical physics". The majority of applications of physics are essentially classical.[40]: xxxi The laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light.[40]: xxxii Outside of this domain, observations do not match predictions provided by classical mechanics.[31]: 6
Classical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, thermodynamics, and electromagnetism.[31]: 2 Classical mechanics is concerned with bodies acted on byforces and bodies inmotion and may be divided intostatics (study of the forces on a body or bodies not subject to an acceleration),kinematics (study of motion without regard to its causes), anddynamics (study of motion and the forces that affect it); mechanics may also be divided intosolid mechanics andfluid mechanics (known together ascontinuum mechanics), the latter include such branches ashydrostatics,hydrodynamics andpneumatics. Acoustics is the study of how sound is produced, controlled, transmitted and received.[41] Important modern branches of acoustics includeultrasonics, the study of sound waves of very high frequency beyond the range of human hearing;bioacoustics, the physics of animal calls and hearing,[42] andelectroacoustics, the manipulation of audible sound waves using electronics.[43]
Optics, the study of light, is concerned not only withvisible light but also withinfrared andultraviolet radiation, which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light. Heat is a form of energy, the internal energy possessed by the particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy. Electricity andmagnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; anelectric current gives rise to amagnetic field, and a changing magnetic field induces an electric current.Electrostatics deals withelectric charges at rest,electrodynamics with moving charges, andmagnetostatics with magnetic poles at rest.
The discovery of relativity and of quantum mechanics in the first decades of the 20th century transformed the conceptual basis of physics without reducing the practical value of most of the physical theories developed up to that time. Consequently the topics of physics have come to be divided into "classical physics" and "modern physics", with the latter category including effects related to quantum mechanics and relativity.[31]: 2Classical physics is generally concerned with matter and energy on the normal scale of observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on a very large or very small scale. For example,atomic andnuclear physics study matter on the smallest scale at whichchemical elements can be identified. Thephysics of elementary particles is on an even smaller scale since it is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary to produce many types of particles inparticle accelerators. On this scale, ordinary, commonsensical notions of space, time, matter, and energy are no longer valid.[44]
The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics. Classical mechanics approximates nature as continuous, while quantum theory is concerned with the discrete nature of many phenomena at the atomic and subatomic level and with the complementary aspects of particles and waves in the description of such phenomena. The theory of relativity is concerned with the description of phenomena that take place in aframe of reference that is in motion with respect to an observer; the special theory of relativity is concerned with motion in the absence of gravitational fields and thegeneral theory of relativity with motion and its connection withgravitation. Both quantum theory and the theory of relativity find applications in many areas of modern physics.[45]
Physicists use the scientific method to test the validity of aphysical theory. By using a methodical approach to compare the implications of a theory with the conclusions drawn from its related experiments and observations, physicists are better able to test the validity of a theory in a logical, unbiased, and repeatable way. To that end, experiments are performed and observations are made in order to determine the validity or invalidity of a theory.[46]
A scientific law is a concise verbal or mathematical statement of a relation that expresses a fundamental principle of some theory, such as Newton's law of universal gravitation.[47]
Theorists seek to developmathematical models that both agree with existing experiments and successfully predict future experimental results, whileexperimentalists devise and perform experiments to test theoretical predictions and explore new phenomena. Althoughtheory and experiment are developed separately, they strongly affect and depend upon each other. Progress in physics frequently comes about when experimental results defy explanation by existing theories, prompting intense focus on applicable modeling, and when new theories generate experimentally testablepredictions, which inspire the development of new experiments (and often related equipment).[48]
Physicists who work at the interplay of theory and experiment are calledphenomenologists, who study complex phenomena observed in experiment and work to relate them to afundamental theory.[49]
Theoretical physics has historically taken inspiration from philosophy; electromagnetism was unified this way.[a] Beyond the known universe, the field of theoretical physics also deals with hypothetical issues,[b] such asparallel universes, amultiverse, andhigher dimensions. Theorists invoke these ideas in hopes of solving particular problems with existing theories; they then explore the consequences of these ideas and work toward making testable predictions.
Experimental physics expands, and is expanded by, engineering and technology. Experimental physicists who are involved inbasic research design and perform experiments with equipment such as particle accelerators andlasers, whereas those involved inapplied research often work in industry, developing technologies such asmagnetic resonance imaging (MRI) andtransistors.Feynman has noted that experimentalists may seek areas that have not been explored well by theorists.[50]
Scope and aims
Physics involves modeling the natural world with theory, usually quantitative. Here, the path of a particle is modeled with the mathematics ofcalculus to explain its behavior: the purview of the branch of physics known asmechanics.
Physics covers a wide range ofphenomena, fromelementary particles (such asquarks,neutrinos, andelectrons) to the largestsuperclusters of galaxies. Included in these phenomena are the most basic objects composing all other things. Therefore, physics is sometimes called the "fundamental science".[51] Physics aims to describe the various phenomena that occur in nature in terms of simpler phenomena. Thus, physics aims to both connect the things observable to humans to root causes, and then connect these causes together.
For example, theancient Chinese observed that certain rocks (lodestone andmagnetite) were attracted to one another by an invisible force. This effect was later called magnetism, which was first rigorously studied in the 17th century. But even before the Chinese discovered magnetism, theancient Greeks knew of other objects such asamber, that when rubbed with fur would cause a similar invisible attraction between the two.[52] This was also first studied rigorously in the 17th century and came to be called electricity. Thus, physics had come to understand two observations of nature in terms of some root cause (electricity and magnetism). However, further work in the 19th century revealed that these two forces were just two different aspects of one force—electromagnetism. This process of "unifying" forces continues today, and electromagnetism and theweak nuclear force are now considered to be two aspects of theelectroweak interaction. Physics hopes to find an ultimate reason (theory of everything) for why nature is as it is (see sectionCurrent research below for more information).[53]
In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications thatneutrinos have non-zeromass. These experimental results appear to have solved the long-standingsolar neutrino problem, and the physics of massive neutrinos remains an area of active theoretical and experimental research. The Large Hadron Collider has already found the Higgs boson, but future research aims to prove or disprove thesupersymmetry, which extends the Standard Model of particle physics. Research on the nature of the major mysteries of dark matter anddark energy is also currently ongoing.[57]
Although much progress has been made in high-energy,quantum, and astronomical physics, many everyday phenomena involvingcomplexity,[58] chaos,[59] orturbulence[60] are still poorly understood. Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include the formation of sandpiles, nodes in trickling water, the shape of water droplets, mechanisms ofsurface tensioncatastrophes, and self-sorting in shaken heterogeneous collections.[c][61]
These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabledcomplex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the study of turbulence in aerodynamics and the observation ofpattern formation in biological systems. In the 1932Annual Review of Fluid Mechanics,Horace Lamb said:[62]
I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic.
Since the 20th century, the individual fields of physics have become increasingly specialized, and today most physicists work in a single field for their entire careers. "Universalists" such as Einstein (1879–1955) andLev Landau (1908–1968), who worked in multiple fields of physics, are now very rare.[d]
Particle physics is the study of the elementary constituents ofmatter and energy and theinteractions between them.[64] In addition, particle physicists design and develop the high-energy accelerators,[65] detectors,[66] andcomputer programs[67] necessary for this research. The field is also called "high-energy physics" because many elementary particles do not occur naturally but are created only during high-energycollisions of other particles.[68]
Currently, the interactions of elementary particles andfields are described by theStandard Model.[69] The model accounts for the 12 known particles of matter (quarks andleptons) that interact via thestrong, weak, and electromagneticfundamental forces.[69] Dynamics are described in terms of matter particles exchanginggauge bosons (gluons,W and Z bosons, andphotons, respectively).[70] The Standard Model also predicts a particle known as the Higgs boson.[69] In July 2012 CERN, the European laboratory for particle physics, announced the detection of a particle consistent with the Higgs boson,[71] an integral part of theHiggs mechanism.
Atomic,molecular, and optical physics (AMO) is the study of matter—matter and light—matter interactions on the scale of single atoms and molecules. The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of their relevant energy scales. All three areas include both classical, semi-classical andquantum treatments; they can treat their subject from a microscopic view (in contrast to a macroscopic view).
Atomic physics studies theelectron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions,[72][73][74] low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by thenucleus (seehyperfine splitting), but intra-nuclear phenomena such asfission andfusion are considered part of nuclear physics.
Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light.Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects but on the fundamental properties ofoptical fields and their interactions with matter in the microscopic realm.
Velocity-distribution data of a gas ofrubidium atoms, confirming the discovery of a new phase of matter, theBose–Einstein condensate
Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter.[75][76] In particular, it is concerned with the "condensed"phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong.[55]
Condensed matter physics is the largest field of contemporary physics. Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields.[82] The termcondensed matter physics was apparently coined byPhilip Anderson when he renamed his research group—previouslysolid-state theory—in 1967.[83] In 1978, the Division of Solid State Physics of theAmerican Physical Society was renamed as the Division of Condensed Matter Physics.[82] Condensed matter physics has a large overlap with chemistry,materials science,nanotechnology and engineering.[55]
The deepest visible-light image of theuniverse, theHubble Ultra-Deep Field. The vast majority of objects seen above are distant galaxies.
Astrophysics and astronomy are the application of the theories and methods of physics to the study ofstellar structure,stellar evolution, the origin of the Solar System, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.[84]
The discovery byKarl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science ofradio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the Earth's atmosphere make space-based observations necessary forinfrared,ultraviolet,gamma-ray, andX-ray astronomy.
Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century,Hubble's discovery that the universe is expanding, as shown by theHubble diagram, prompted rival explanations known as thesteady state universe and theBig Bang.
An Atwood's machine is a machine consisting of a pulley and two masses that is commonly used in physics classrooms to demonstrate Newton's laws of motionPhysics education or physics teaching refers to theeducation methods currently used toteach physics. The occupation is called physics educator or physics teacher.Physics education research refers to an area of pedagogical research that seeks to improve those methods. Historically, physics has been taught at the high school and college level primarily by the lecture method together with laboratory exercises aimed at verifying concepts taught in the lectures. These concepts are better understood when lectures are accompanied with demonstration, hand-on experiments, and questions that require students to ponder what will happen in an experiment and why. Students who participate inactive learning for example with hands-on experiments learn through self-discovery. By trial and error they learn to change their preconceptions about phenomena in physics and discover the underlying concepts. Physics education is part of the broader area ofscience education.
Aphysicist is ascientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.[85][86] Physicists generally are interested in the root or ultimate causes ofphenomena, and usually frame their understanding in mathematical terms. They work across a wide range ofresearch fields, spanning all length scales: fromsub-atomic andparticle physics, throughbiological physics, tocosmological length scales encompassing theuniverse as a whole. The field generally includes two types of physicists:experimental physicists who specialize in the observation of natural phenomena and the development and analysis of experiments, andtheoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena.[85]
Thisparabola-shapedlava flow illustrates an application of mathematics in physics — in this case, Galileo'slaw of falling bodies.Mathematics and ontology are used in physics. Physics is used in chemistry andcosmology.
Mathematics provides a compact and exact language used to describe the order in nature. This was noted and advocated byPythagoras,[99]Plato,[100] Galileo,[101] and Newton. Some theorists, likeHilary Putnam andPenelope Maddy, hold that logical truths, and therefore mathematical reasoning, depend on theempirical world. This is usually combined with the claim that the laws of logic express universal regularities found in the structural features of the world, which may explain the peculiar relation between these fields.
Physics uses mathematics[102] to organize and formulate experimental results. From those results,precise orestimated solutions are obtained, or quantitative results, from which new predictions can be made and experimentally confirmed or negated. The results from physics experiments are numerical data, with theirunits of measure and estimates of the errors in the measurements. Technologies based on mathematics, likecomputation have madecomputational physics an active area of research.
The distinction between mathematics and physics is clear-cut, but not always obvious, especially in mathematical physics.
Ontology is a prerequisite for physics, but not for mathematics. It means physics is ultimately concerned with descriptions of the real world, while mathematics is concerned with abstract patterns, even beyond the real world. Thus physics statements are synthetic, while mathematical statements are analytic. Mathematics contains hypotheses, while physics contains theories. Mathematics statements have to be only logically true, while predictions of physics statements must match observed and experimental data.
The distinction is clear-cut, but not always obvious. For example,mathematical physics is the application of mathematics in physics. Its methods are mathematical, but its subject is physical.[103] The problems in this field start with a "mathematical model of a physical situation" (system) and a "mathematical description of a physical law" that will be applied to that system. Every mathematical statement used for solving has a hard-to-find physical meaning. The final mathematical solution has an easier-to-find meaning, because it is what the solver is looking for.[clarification needed]
Physics is a branch offundamental science (also called basic science). Physics is also called "the fundamental science" because all branches of natural science including chemistry, astronomy, geology, and biology are constrained by laws of physics.[51] Similarly, chemistry is often calledthe central science because of its role in linking the physical sciences. For example, chemistry studies properties, structures, andreactions of matter (chemistry's focus on the molecular and atomic scaledistinguishes it from physics). Structures are formed because particles exert electrical forces on each other, properties include physical characteristics of given substances, and reactions are bound by laws of physics, likeconservation of energy,mass, andcharge. Fundamental physics seeks to better explain and understand phenomena in all spheres, without a specific practical application as a goal, other than the deeper insight into the phenomema themselves.
Applied physics is a general term for physics research and development that is intended for a particular use. An applied physics curriculum usually contains a few classes in an applied discipline, like geology or electrical engineering. It usually differs from engineering in that an applied physicist may not be designing something in particular, but rather is using physics or conducting physics research with the aim of developing new technologies or solving a problem.
The approach is similar to that ofapplied mathematics. Applied physicists use physics in scientific research. For instance, people working onaccelerator physics might seek to build betterparticle detectors for research in theoretical physics.
Physics is used heavily in engineering. For example, statics, a subfield ofmechanics, is used in the building of bridges and other static structures. The understanding and use of acoustics results in sound control and better concert halls; similarly, the use of optics creates better optical devices. An understanding of physics makes for more realisticflight simulators, video games, and movies, and is often critical inforensic investigations.
With thestandard consensus that thelaws of physics are universal and do not change with time, physics can be used to study things that would ordinarily be mired inuncertainty. For example, in the study of the origin of the Earth, a physicist can reasonably model Earth's mass, temperature, and rate of rotation, as a function of time allowing the extrapolation forward or backward in time and so predict future or prior events. It also allows for simulations in engineering that speed up the development of a new technology.
^Concepts which are denotedhypothetical can change with time. For example, theatom of nineteenth-century physics was denigrated by some, includingErnst Mach's critique ofLudwig Boltzmann's formulation ofstatistical mechanics. By the end of World War II, the atom was no longer deemed hypothetical.
^See the work ofIlya Prigogine, on 'systems far from equilibrium', and others.
^Yet, universalism is encouraged in the culture of physics. For example, theWorld Wide Web, which was innovated atCERN byTim Berners-Lee, was created in service to the computer infrastructure of CERN, and was/is intended for use by physicists worldwide. The same might be said forarXiv.org
References
^Maxwell 1878, p. 9 "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events."
^abcYoung & Freedman 2014, p. 1 "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."
^Young & Freedman 2014, p. 2 "Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena."
^Holzner 2006, p. 7 "Physics is the study of your world and the world and universe around you."
^Wildberg, Christian (2021). Zalta, Edward N. (ed.)."John Philoponus". Metaphysics Research Lab, Stanford University.Archived from the original on 22 April 2018. Retrieved6 February 2025.
^Dallal, Ahmad (2010).Islam, Science, and the Challenge of History. New Haven: Yale University Press. p. 38.Within two centuries, the field of optics was radically transformed
^Womersley, J. (February 2005)."Beyond the Standard Model"(PDF).Symmetry. Vol. 2, no. 1. pp. 22–25.Archived(PDF) from the original on 24 September 2015.
^abThorne, Kip S.; Blandford, R.D. (2017).Modern Classical Physics Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. United States: Princeton University Press.
^Feynman 1965, p. 157 "In fact experimenters have a certain individual character. They ... very often do their experiments in a region in which people know the theorist has not made any guesses."
^Mastin 2010 "Although usually remembered today as a philosopher, Plato was also one of ancient Greece's most important patrons of mathematics. Inspired by Pythagoras, he founded his Academy in Athens in 387 BC, where he stressed mathematics as a way of understanding more about reality. In particular, he was convinced that geometry was the key to unlocking the secrets of the universe. The sign above the Academy entrance read: 'Let no-one ignorant of geometry enter here.'"
^Toraldo Di Francia 1976, p. 10 'Philosophy is written in that great book which ever lies before our eyes. I mean the universe, but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.' – Galileo (1623),The Assayer"
^"Journal of Mathematical Physics".Archived from the original on 18 August 2014. Retrieved31 March 2014.[Journal of Mathematical Physics] purpose is the publication of papers in mathematical physics—that is, the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories.
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![Johannes Kepler (1571–1630) explained planetary motions, formulating the first "natural laws" in the modern sense[29]](/mt/?noimg=&dark=on&url=http%3a%2f%2fen.wikipedia.org%2fwiki%2fFile%3aJKepler.jpg)
