## Tuesday, September 13, 2011 ... /////

### Ten new things that science has learned about matter

This blog entry is somewhat analogous to the text about Ten new things modern physics has learned about time.

1. Matter is made of atoms. This is the proposition that Richard Feynman would have chosen as the single most important insight of the scientific research. The atomic theory, confirming guesses of some ancient Greek philosophers, explains why different materials have different properties; how matter stores heat in the microscopic motion of the atoms and other constituents (all thermal phenomena may be interpreted as statistical properties of large ensembles of atoms); why tiny particles exhibit the Brownian motion; how chemical reactions proceed at the microscopic level; how living creatures store and reproduce their genetic information, and many other things. Atoms are not indivisible; they're composed of small nuclei and electrons that orbit them. Nuclei are made of protons and neutrons and protons and neutrons are made of quarks.

2. Properties of materials depend on chemical composition as well as details of the bonds between atoms. Alchemists believed that only the relative concentration of different elements (materials composed of a single type of an atom only) matters and they were able to figure out that the mixing ratios for every compound were rational numbers in some units. However, the diamond and the graphite (both of which are pure carbon) are the simplest example that the character of the bonds between the atoms heavily influences the material properties as well. Gases are made of free, well-separated individual atoms; liquids are made of individual atoms whose density is however so large that they are in constant contact; solids are either amorphous materials, similar to "very slow liquids" (glass), or crystals (diamond, ice) where the atoms are arranged to regular lattices. Gases in which the free particles are electrically charged (including electrons and ions, i.e. atoms with removed/added electrons) are also possible at high temperatures and they're called plasma.
3. Matter is impenetrable because of a combination of Pauli's exclusion principle, Heisenberg's uncertainty principle, and Coulomb's electrostatic force. Matter is made out of atoms, bound states of electrons and nuclei that electrically attract each other. However, the electrons can't be orbiting at arbitrarily short distances near the nuclei because it would violate the uncertainty principle (one would have a well-defined momentum as well as position, which the principle forbids, unless the average squared momentum would be too large to make the configuration energetically disfavored). A compromise between the kinetic and potential energy, fighting with each other according tothe uncertainty principle, determines the size of the atoms. Atoms can't be squeezed much more densely than their natural size indicates because Pauli's exclusion principle guarantees that you can't squeeze more than one electron into the same state (e.g. into the same volume for an atom, into the energy ground state in this volume). The white dwarfs maximize the density of "electron-degenerate matter": the Chandrasekhar limit determines the highest possible mass of stars arranged in this way. The neutron stars obey similar principles but it's the neutrons, not electrons, that maximize their density in this case.
4. Elementary particles that make up matter are either bosons or fermions. Fermions have spin (internal angular momentum) being a half-integral multiple of $\hbar$, the reduced Planck constant; for bosons, it is an integer multiple. The spin-statistics theorem due to Pauli guarantees that the half-integral spin requires the particles to obey Pauli's exclusion principle which makes the matter composed of fermions "impenetrable" – what we would normally call "matter". The fermions' wave function flips the sign under permutations of two identical particles. On the other hand, the bosons don't change the sign which is why they don't obey Pauli's exclusion principle. Consequently, bosons like to overlap with their siblings and they are often interpreted as "particles of forces" (e.g. the photon is a particle of the electromagnetic force) which love to overlap with their siblings much like the electric and magnetic field lines. That's why lasers produce coherent light (lots of photons which are examples of bosons) and why one can have Bose-Einstein condensates (out of atoms which behave as bosons).
5. Elementary particles behave as quanta of waves and waves are made out of particles. Niels Bohr's complementarity principle guarantees that basic building blocks of matter behave both as particles and waves in different contexts. The more they behave as waves, the less they behave as particles, and vice versa. Such a unified picture reconciles the particle-like properties of matter and the wave-like properties (such as interference in double-slit experiments). Electrons (fermions) may be viewed as quanta of a Dirac field; photons are quanta (basic packages of energy) of the electromagnetic field. Alternatively, the electromagnetic field can't carry a continuously varying energy. The energy of an electromagnetic wave of frequency $\omega$ (above the vacuum energy) is equal to $E=N\hbar\omega$ where $N$ has to be an integer and may be interpreted as the number of photons.
6. Sound is made of waves in the air or the environment but there's no luminiferous eather. The sounds and music result from vibrations of the air: "A" is 440 Hz (periods per second). Sound may propagate in the form of vibrations through other materials, too. On the other hand, the electromagnetic waves and radiation don't require any atoms to be present: the electromagnetic field is a property of the vacuum itself. Even in the vacuum, there is an electric vector and a magnetic vector at each point of space and at each moment of time. Consequently, there is no aether wind (observations that would allow us to "feel" that we are moving relatively to the aether); as special relativity assumes/shows, the speed of light is always 299,792,458 m/s, regardless of the speed of the source or the speed of the observer.
7. Inertial mass is equal to gravitational mass. This so-called equivalence principle guarantees that all objects accelerate by the same rate in gravitational fields (e.g. on Earth's surface, assuming it is in the vacuum, i.e. in the absence of friction forces), as we can observe. On the theoretical front, this property of the gravitational force is the basic insight behind Einstein's general theory of relativity that explains gravity as a consequence of the curvature of spacetime.
8. The total mass is conserved but the total mass is the same thing as the total energy. Whether you define the overall mass of an object as the inertial mass (force you need to exert to achieve a unit acceleration) or the gravitational mass (the strength of the gravitational field around the object, as measured by the acceleration of other objects at a fixed distance), the overall mass is conserved. However, you must also include mass of "pure energy" to the equation, according to Einstein's $E=mc^2$ obtained from the special theory of relativity, otherwise the conservation law would be violated: nuclear fission or fusion may convert about 0.1% or 1% of the mass into pure energy, respectively. This new unified energy-mass conservation law exists because the laws of physics are time-translationally invariant (Emmy Noether's law) and it becomes vacuous or invalid in the context of cosmology (where the effective laws of physics or background is quickly evolving with time).
9. The number of elementary particles isn't conserved. Indeed, one may create lots of new particles, typically coming in particle-antiparticle pairs, by particle collisions. Particle-antiparticle pairs may annihilate, too. The possibility to create matter out of pure energy is the most characteristic prediction of quantum field theory. Quantum field theory also implies that there exists antimatter: for each particle, there exists an antiparticle with the same (positive) mass and the opposite signs of all charges (whose magnitudes are identical). The antimatter has to behave analogously to the matter, especially if it is in the mirror and observed backwards in time (in the latter case, the identical behavior of matter and antimatter is guaranteed by the CPT theorem).
10. There exist heavier particle species which are relevant for shorter distance scales. Most of the matter around us is composed of electrons, protons, and neutrons, or – using the more elementary description – electrons, up-quarks, and down-quarks (which are attracted by forces mediated by photons and gluons). However, there exist many other particle species similar to electrons – the so-called leptons – and many other quarks. Many of those particles are unstable, and therefore unimportant in the composition of stable materials. But even if heavier particles are stable, they are less important than the light ones because it is hard to create them and because their potential existence only affects the phenomena at ever shorter distances. Elementary particles heavier than the Planck mass or so – $10^{-8}$ kilograms or so – also exist and there are many of them. However, they may be interpreted as black hole microstates and their description in terms of Einstein's general theory of relativity becomes more natural than their description in terms of quantum field theory. String/M-theory provides us with many detailed interpolations between the regular light particle species and the black holes – e.g. Kaluza-Klein modes i.e. particles moving in extra dimensions; excited string states and branes, and others.