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For Descartes, matter has only the property of extension, so its only activity aside from locomotion is to exclude other bodies[17]: this is the mechanical philosophy. Descartes makes an absolute distinction between mind, which he defines as unextended, thinking substance, and matter, which he defines as unthinking, extended substance.[18] They are independent things. In contrast, Aristotle defines matter and the formal/forming principle as complementary principles which together compose one independent thing (substance). In short, Aristotle defines matter (roughly speaking) as what things are actually made of (with a potential independent existence), but Descartes elevates matter to an actual independent thing in itself.

The continuity and difference between Descartes' and Aristotle's conceptions is noteworthy. In both conceptions, matter is passive or inert. In the respective conceptions matter has different relationships to intelligence. For Aristotle, matter and intelligence (form) exist together in an interdependent relationship, whereas for Descartes, matter and intelligence (mind) are definitionally opposed, independent substances.[19]

Descartes' justification for restricting the inherent qualities of matter to extension is its permanence, but his real criterion is not permanence (which equally applied to color and resistance), but his desire to use geometry to explain all material properties.[20] Like Descartes, Hobbes, Boyle, and Locke argued that the inherent properties of bodies were limited to extension, and that so-called secondary qualities, like color, were only products of human perception.[21]

Isaac Newton (1643–1727) inherited Descartes' mechanical conception of matter. In the third of his "Rules of Reasoning in Philosophy," Newton lists the universal qualities of matter as "extension, hardness, impenetrability, mobility, and inertia."[22] Similarly in Optics he conjectures that God created matter as "solid, massy, hard, impenetrable, movable particles", which were "even so very hard as never to wear or break in pieces."[23] The "primary" properties of matter were amenable to mathematical description, unlike "secondary" qualities such as color or taste. Like Descartes, Newton rejected the essential nature of secondary qualities.[24]

Newton developed Descartes' notion of matter by restoring to matter intrinsic properties in addition to extension (at least on a limited basis), such as mass. Newton's use of gravitational force, which worked "at a distance," effectively repudiated Descartes' mechanics, in which interactions happened exclusively by contact.[25]

Though Newton's gravity would seem to be a power of bodies, Newton himself did not admit it to be an essential property of matter. Carrying the logic forward more consistently, Joseph Priestley argued that corporeal properties transcend contact mechanics: chemical properties require the capacity for attraction.[25] He argued matter has other inherent powers besides the so-called primary qualities of Descartes, et al.[26]

Later developments

There is an entire literature concerning the "structure of matter", ranging from the "electrical structure" in the early 20th century,[33] to the more recent "quark structure of matter", introduced today with the remark: Understanding the quark structure of matter has been one of the most important advances in contemporary physics.[34][further explanation needed] In this connection, physicists speak of matter fields, and speak of particles as "quantum excitations of a mode of the matter field".[8][9] And here is a quote from de Sabbata and Gasperini: "With the word "matter" we denote, in this context, the sources of the interactions, that is spinor fields (like quarks and leptons), which are believed to be the fundamental components of matter, or scalar fields, like the Higgs particles, which are used to introduced mass in a gauge theory (and which, however, could be composed of more fundamental fermion fields)."[35][further explanation needed]

The modern conception of matter has been refined many times in history, in light of the improvement in knowledge of just what the basic building blocks are, and in how they interact.

In the late 19th century with the discovery of the electron, and in the early 20th century, with the discovery of the atomic nucleus, and the birth of particle physics, matter was seen as made up of electrons, protons and neutrons interacting to form atoms. Today, we know that even protons and neutrons are not indivisible, they can be divided into quarks, while electrons are part of a particle family called leptons. Both quarks and leptons are elementary particles, and are currently seen as being the fundamental constituents of matter.[36]

These quarks and leptons interact through four fundamental forces: gravity, electromagnetism, weak interactions, and strong interactions. The Standard Model of particle physics is currently the best explanation for all of physics, but despite decades of efforts, gravity cannot yet be accounted for at the quantum-level; it is only described by classical physics (see quantum gravity and graviton).[37] Interactions between quarks and leptons are the result of an exchange of force-carrying particles (such as photons) between quarks and leptons.[38] The force-carrying particles are not themselves building blocks. As one consequence, mass and energy (which cannot be created or destroyed) cannot always be related to matter (which can be created out of non-matter particles such as photons, or even out of pure energy, such as kinetic energy). Force carriers are usually not considered matter: the carriers of the electric force (photons) possess energy (see Planck relation) and the carriers of the weak force (W and Z bosons) are massive, but neither are considered matter either.[39] However, while these particles are not considered matter, they do contribute to the total mass of atoms, subatomic particles, and all systems which contain them.[40][41]
Summary

The term "matter" is used throughout physics in a bewildering variety of contexts: for example, one refers to "condensed matter physics",[42] "elementary matter",[43] "partonic" matter, "dark" matter, "anti"-matter, "strange" matter, and "nuclear" matter. In discussions of matter and antimatter, normal matter has been referred to by Alfvén as koinomatter.[44] It is fair to say that in physics, there is no broad consensus as to a general definition of matter, and the term "matter" usually is used in conjunction with a specifying modifier.

Common definition
The DNA molecule is an example of matter under the "atoms and molecules" definition.

The common definition of matter is anything that has both mass and volume (occupies space).[45][46] For example, a car would be said to be made of matter, as it occupies space, and has mass.

The observation that matter occupies space goes back to antiquity. However, an explanation for why matter occupies space is recent, and is argued to be a result of the Pauli exclusion principle.[47][48] Two particular examples where the exclusion principle clearly relates matter to the occupation of space are white dwarf stars and neutron stars, discussed further below.
Relativity

In the context of relativity, mass is not an additive quantity.[1] Thus, in relativity usually a more general view is taken that it is not mass, but the energy–momentum tensor that quantifies the amount of matter. Matter therefore is anything that contributes to the energy–momentum of a system, that is, anything that is not purely gravity.[49][50] This view is commonly held in fields that deal with general relativity such as cosmology.
Atoms and molecules definition

A definition of "matter" that is based upon its physical and chemical structure is: matter is made up of atoms and molecules.[51] As an example, deoxyribonucleic acid molecules (DNA) are matter under this definition because they are made of atoms. This definition can be extended to include charged atoms and molecules, so as to include plasmas (gases of ions) and electrolytes (ionic solutions), which are not obviously included in the atoms and molecules definition. Alternatively, one can adopt the protons, neutrons and electrons definition.
Protons, neutrons and electrons definition

A definition of "matter" more fine-scale than the atoms and molecules definition is: matter is made up of what atoms and molecules are made of, meaning anything made of positively charged protons, neutral neutrons, and negatively charged electrons.[52] This definition goes beyond atoms and molecules, however, to include substances made from these building blocks that are not simply atoms or molecules, for example white dwarf matter — typically, carbon and oxygen nuclei in a sea of degenerate electrons. At a microscopic level, the constituent "particles" of matter such as protons, neutrons and electrons obey the laws of quantum mechanics and exhibit wave–particle duality. At an even deeper level, protons and neutrons are made up of quarks and the force fields (gluons) that bind them together (see Quarks and leptons definition below).