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String Theory

String theory

String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that are the basis of the Standard Model of particle physics. For this reason, string theories are able to avoid problems associated with the presence of pointlike particles in a physical theory. Study of string theories has revealed that they require not just strings but other objects, variously including points, membranes, and higher-dimensional objects. Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. It is a possible solution of the quantum gravity problem, and in addition to gravity it can naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry. It is not yet known whether string theory is able to describe a universe with the precise collection of forces and matter that is observed, nor how much freedom to choose those details the theory will allow. String theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various special corners of the theory are accessible to planned observations and experiments. Work on string theory has led to advances in mathematics, mainly in algebraic geometry. String theory has also led to insight into supersymmetric gauge theories, which will be tested at the new Large Hadron Collider experiment.

History

String theory was originally invented to explain peculiarities of hadron (subatomic particle which experiences the strong nuclear force) behavior. In particle-accelerator experiments, physicists observed that the spin of a hadron is never larger than a certain multiple of the square of its energy. No simple model of the hadron, such as picturing it as a set of smaller particles held together by spring-like forces, was able to explain these relationships. In 1968, theoretical physicist Gabriele Veneziano was trying to understand the strong nuclear force when he made a startling discovery. Veneziano found that a 200-year-old formula created by Swiss mathematician Leonhard Euler (the Euler beta function) perfectly matched modern data on the strong force. Veneziano applied the Euler beta function to the strong force, but no one could explain why it worked. In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind unveiled the physics beneath Euler’s strictly theoretical formula. By representing nuclear forces as vibrating, one-dimensional strings, these physicists showed how Euler’s function accurately described those forces. But even after physicists understood the physical explanation for Veneziano’s insight, the string description of the strong force made many predictions that directly contradicted experimental findings. The scientific community soon lost interest in string theory, and the standard model, with its particles and fields, remained unthreatened. Then, in 1974, John Schwarz and Joel Scherk studied the messenger-like patterns of string vibration and found that their properties exactly matched those of the gravitational force’s hypothetical messenger particle — graviton. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. This led to the development of bosonic string theory, which is still the version first taught to many students. (The original need for a viable theory of hadrons has been fulfilled by quantum chromodynamics, the theory of quarks and their interactions. It is now hoped that string theory or some descendant of it will provide a fundamental understanding of the quarks themselves.) Bosonic string theory is formulated in terms of the Polyakov action, a mathematical quantity which can be used to predict how strings move through space and time. By applying the ideas of quantum mechanics to the Polyakov action — a procedure known as quantization — one can deduce that each string can vibrate in many different ways, and that each vibrational state appears to be a different particle. The mass the particle has, and the fashion with which it can interact, are determined by the way the string vibrates — in essence, by the "note" which the string sounds. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory. These early models included both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop. The two types of string behave in slightly different ways, yielding two spectra. Not all modern string theories use both types; some incorporate only the closed variety. However, the bosonic theory has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon which obey particular rules of behavior. While bosons are a critical ingredient of the Universe, they are not its only constituents. Investigating how a string theory may include fermions in its spectrum led to supersymmetry, a mathematical relation between bosons and fermions which is now an independent area of study. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described. Roughly between 1984 and 1986, physicists realized that string theory could describe all elementary particles and interactions between them, and hundreds of them started to work on string theory as the most promising idea to unify theories of physics. This first superstring revolution was started by a discovery of anomaly cancellation in type I string theory by Michael Green and John Schwarz in 1984. The anomaly is cancelled due to the Green-Schwarz mechanism. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985. In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of an unknown 11-dimensional theory called M-theory. These discoveries sparked the second superstring revolution. When Witten named M-theory, he didn't specify what the "M" stood for, presumably because he didn't feel he had the right to name a theory which he hadn't been able to fully describe. Guessing what the "M" stands for has become a kind of game among theoretical physicists. "M" sometimes is said to stand for Mystery, or Magic, or Mother. More serious suggestions include Matrix or Membrane. Cynics have noted that the M might be an upside down "W", standing for Witten. Others have suggested that for now, the "M" in M-theory should stand for Missing or even Murky. Many recent developments in the field relate to D-branes, objects which physicists discovered must also be included in any theory which includes open strings of the super string theory.

Basic properties

The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories discovered by adding supersymmetry. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name, 'bosonic string theory'. While understanding the details of string and superstring theories requires considerable mathematical sophistication, some qualitative properties of quantum strings can be understood in a fairly intuitive fashion. For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the theory. The tension of a quantum string is closely related to its size. Consider a closed loop of string, left to move through space without external forces. Its tension will tend to contract it into a smaller and smaller loop. Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. The characteristic size of the string loop will be a balance between the tension force, acting to make it small, and the uncertainty effect, which keeps it "stretched". Consequently, the minimum size of a string must be related to the string tension.

Extra dimensions

One intriguing feature of string theory is that it predicts the number of dimensions which the universe should possess. Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand". The first person to add a fifth dimension to Einstein's four was the German mathematician Theodor Kaluza in 1919. The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926. Instead, string theory allows one to compute the number of spacetime dimensions from first principles. Technically, this happens because Lorentz invariance can only be satisfied in a certain number of dimensions. This is roughly like saying that if an observer measures the distance between two points, then rotates by some angle and measures again, the observed distance only stays the same if the universe has a particular number of dimensions. The only problem is that when the calculation is done, the universe's dimensionality is not four as one may expect (three axes of space and one of time), but twenty-six. More precisely, bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions. In bosonic string theories, the 26 dimensions come from the Polyakov equation

Z=\int D^F \left [\rho \left (\xi \right ) \right ] \exp \left (  \int_\xi \left [   \right ] + \int_\xi \mu_R^2 \rho^2 \right )

(see technical details in the preprint [http://doc.cern.ch/archive/electronic//scan/9910/SCAN-9910077.tif "Quantum Geometry of Bosonic Strings - Revisited"]). However, these models appear to contradict observed phenomena. Physicists usually solve this problem in one of two different ways. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience. The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. In 7 dimensions, they are termed G₂ manifolds. Essentially these extra dimensions are compactified by causing them to loop back upon themselves. A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. If, however, one approaches the hose, one discovers that it contains a second dimension, its circumference. This "extra dimension" is only visible within a relatively close range to the hose, just as the extra dimensions of the Calabi-Yau space are only visible at extremely small distances, and thus are not easily detected. (Of course, everyday garden hoses exist in three spatial dimensions, but for the purpose of the analogy, its thickness is neglected and only motion on the surface of the hose is considered. A point on the hose's surface can be specified by two numbers, a distance along the hose and a distance along the circumference, just as points on the Earth's surface can be uniquely specified by latitude and longitude. In either case, the object has two spatial dimensions. Like the Earth, garden hoses have an interior, a region that requires an extra dimension; however, unlike the Earth, a Calabi-Yau space has no interior.) Another possibility is that we are stuck in a 3+1 dimensional subspace of the full universe, where the "3+1" reminds us that time is a different kind of dimension than space. Because it involves mathematical objects called D-branes, this is known as a braneworld theory. In either case, gravity acting in the hidden dimensions produces other non-gravitational forces such as electromagnetism. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility.

Problems

String theory remains to be verified. No version of string theory has yet made a prediction which differs from those made by other theories—at least, not in a way that could be checked by a currently feasible experiment. In this sense, string theory is still in a "larval stage": it possesses many features of mathematical interest, and it may yet become supremely important in our understanding of the Universe, but it requires further developments before it is accepted or falsified. Since string theory may not be tested in the foreseeable future, some scientists have asked if it even deserves to be called a scientific theory: it is not yet falsifiable in the sense of Popper. It is by no means the only theory currently being developed which suffers from this difficulty; any new development can pass through a stage of uncertainty before it becomes conclusively accepted or rejected. As Richard Feynman noted in The Character of Physical Law, the key test of a scientific theory is whether its consequences agree with the measurements taken in experiments. It does not matter who invented the theory, "what his name is", or even how aesthetically appealing the theory may be—"if it disagrees with experiment, it's wrong." (Of course, there are subsidiary issues: something may have gone wrong with the experiment, or perhaps the person computing the consequences of the theory made a mistake. All these possibilities must be checked, which may take a considerable time.) These developments may be in the theory itself, such as new methods of performing calculations and deriving predictions, or they may be advances in experimental science, which make formerly ungraspable quantities measurable. Since the influence of quantum effects upon gravity only become significant at distances many orders of magnitude smaller than human beings have the technology to observe (or at roughly the Planck length, about 10^-35 meters), string theory, or any other candidate theory of quantum gravity, will be very difficult to test experimentally. Eventually, scientists may be able to test string theory by observing cosmological phenomena which may be sensitive to string physics. In the early 2000s, string theorists revived interest in an older concept, the cosmic string. Originally discussed in the 1980s, cosmic strings are a different type of object than the entities of superstring theories. For several years, cosmic strings were a popular model for explaining various cosmological phenomena, such as the way galaxies formed in the early Universe. However, further experiments — and in particular the detailed measurements of the cosmic microwave background — failed to support the cosmic-string model's predictions, and the cosmic string fell out of vogue. If such objects did exist, they must be few and far between. Several years later, it was pointed out that the expanding Universe could have stretched a "fundamental" string (the sort which superstring theory considers) until it was of intergalactic size. Such a stretched string would exhibit many of the properties of the old "cosmic" string variety, making the older calculations useful again. Furthermore, modern superstring theories offer other objects which could feasibly resemble cosmic strings, such as highly elongated one-dimensional D-branes (known as "D-strings"). As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Older proposals for detecting cosmic strings could now be used to investigate superstring theory. For example, astronomers have also detected a few cases of what might be string-induced gravitational lensing. Superstrings, D-strings or other stringy objects stretched to intergalactic scales would radiate gravitational waves, which could presumably be detected using experiments like LIGO. They might also cause slight irregularities in the cosmic microwave background, too subtle to have been detected yet but possibly within the realm of future observability. While intriguing, these cosmological proposals fall short in one respect: testing a theory requires that the test be capable, at least in principle, of falsifying the theory. For example, if observing the Sun during a solar eclipse had not shown that the Sun's gravity deflected light, Einstein's general relativity theory would have been proven wrong. Not finding cosmic strings would not demonstrate that string theory is fundamentally wrong — merely that the particular idea of highly stretched strings acting "cosmic" is in error. While many measurements could in principle be made that would suggest that string theory is on the right track, scientists have not at present devised a stringent "test". On a more mathematical level, another problem is that, like quantum field theory, much of string theory is still only formulated perturbatively (i.e., as a series of approximations rather than as an exact solution). Although nonperturbative techniques have progressed considerably — including conjectured complete definitions in space-times satisfying certain asymptotics — a full nonperturbative definition of the theory is still lacking.

References and further reading

Footnote

# Prominent critics include Philip Anderson ("string theory is the first science in hundreds of years to be pursued in pre-Baconian fashion, without any adequate experimental guidance", New York Times, 4 January 2005), Sheldon Glashow ("there ain't no experiment that could be done nor is there any observation that could be made that would say, `You guys are wrong.' The theory is safe, permanently safe", [http://www.pbs.org/wgbh/nova/elegant/view-glashow.html NOVA interview]), Lawrence Krauss ("String theory [is] yet to have any real successes in explaining or predicting anything measurable", New York Times, 8 November 2005) and Peter Woit (see his [http://math.columbia.edu/~woit/blog/ blog], [http://www.americanscientist.org/template/AssetDetail/assetid/18638 article] and forthcoming [http://www.amazon.com/exec/obidos/tg/detail/-/0224076051/qid=1132091894/sr=8-1/ref=sr_8_xs_ap_i1_xgl14/104-3157701-1966314?v=glance&s=books&n=507846 book]).

Textbooks

- Green, Michael, John Schwarz and Edward Witten, Superstring theory, Cambridge University Press (1987). The original textbook.
- Vol. 1: Introduction, ISBN 0-521-35752-7.
- Vol. 2: Loop amplitudes, anomalies and phenomenology, ISBN 0-521-35753-5.
- Johnson, Clifford, D-branes, Cambridge University Press (2003). ISBN 0-521-80912-6.
- Polchinski, Joseph, String Theory, Cambridge University Press (1998). A modern textbook.
- Vol. 1: An introduction to the bosonic string, ISBN 0-521-63303-6.
- Vol. 2: Superstring theory and beyond, ISBN 0-521-63304-4.
- Zwiebach, Barton. A First Course in String Theory. Cambridge University Press (2004). ISBN 0-521-83143-1. Errata are available [http://xserver.lns.mit.edu/~zwiebach/firstcourse.html online].

External links

- [http://superstringtheory.com/ Superstringtheory.com] - The "Official String Theory Web Site", created by Patricia Schwarz.
- [http://www.pbs.org/wgbh/nova/elegant/ The Elegant Universe] - A Three-Hour Miniseries with Brian Greene by NOVA (original PBS Broadcast Dates: October 28, 8-10 PM and November 4, 8-9 PM, 2003). Various images, texts, videos and animations explaining string theory.
- [http://tena4.vub.ac.be/beyondstringtheory/ Beyond String Theory] - An ongoing project by [http://www.lpt.ens.fr/~troost/ Jan Troost], a string physicist working for the French [http://www.cnrs.fr/ CNRS].
- [http://www.sukidog.com/jpierre/strings/ Superstrings! String Theory Home Page] - Online tutorial.
- [http://www.damtp.cam.ac.uk/user/mbg15/superstrings/superstrings.html Superstrings] - Michael Green on string theory in a Scientific American article, September 1986.
- [http://www.msnbc.com/news/201650.asp The Symphony of Everything] - A short interactive introduction to string theory.
- [http://schwinger.harvard.edu/~sps/ SCI.physics.STRINGS] - The home page of a newsgroup dedicated to string theory.
- [http://xxx.arxiv.org/abs/hep-th/0311044 Resource Letter] - A guide to the string theory literature.
- [http://thenthdimension.com/ The Nth Dimension] - A comprehensive compilation of materials concerning string theory. Created by an international team of students.
- [http://arxiv.org/abs/astro-ph/0410073 "Cosmic strings reborn?"] - A talk given by Tom Kibble in September 2004.
- [http://online.itp.ucsb.edu/online/plecture/witten/ Ed Witten's KITP Public Lecture] - Slides and audio from an Ed Witten lecture where he introduces string theory and discusses its challenges.
- [http://motls.blogspot.com/ The Reference Frame] - A blog supporting string theory
- [http://www.math.columbia.edu/~woit/blog/ Not Even Wrong] - A blog critical of string theory
- [http://www.americanscientist.org/template/AssetDetail/assetid/18638 Is string theory even wrong?] - A criticism of string theory. Category:String theory Category:Protoscience Category:Cosmology ko:끈 이론 simple:String theory

Physical theory

Theoretical physics is physics that employs mathematical models and abstractions rather than experimental processes. Theoretical physics attempts to understand the natural world by making a model of reality, used for rationalizing, explaining, and predicting physical phenomena in what are called "physical theories." There are three types of theories in physics: mainstream theories, proposed theories and fringe theories. Some physical theories are backed by observation, whereas others are not. A physical theory is a model of physical events and cannot be proven from basic axioms. A physical theory is different from a mathematical theorem; physical theories model reality and are a statement of what has been observed, and provide predictions of new observations. Physical theories can become accepted if they are able to make correct predictions and avoid incorrect ones. All else being equal, physical theories which are simpler tend to be accepted over theories which are complex. Physical theories are also more likely to be accepted if they connect a wide range of phenomena. The process of testing a physical theory is part of the scientific method. Famous theoretical physicists include Sir Isaac Newton, Albert Einstein, Stephen Hawking, Niels Hendrik Bohr, Werner Heisenberg, Max Born, Hendrik A. Lorentz, Max Planck, Erwin Schrödinger, Paul Dirac, J. Robert Oppenheimer, Richard Feynman, Lev Landau, Abdus Salam, Enrico Fermi, Louis Victor Broglie, Wolfgang Pauli and Peter Higgs. Theoretical physics is just one important part of physics; the other parts are experimental physics and mathematical physics. The difference between theoretical physics and mathematical physics is that mathematical physics finds the mathematical rigor required in mathematics to be more important than the contact with experiments and observations.

Mainstream theories

Mainstream theories (sometimes referred to as central theories) are the body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation.

Examples

- Classical mechanics
- Condensed matter physics
- Dynamics
- Electromagnetism
- Field theory
- Fluid dynamics
- General relativity
- Particle physics
- Quantum mechanics
- Quantum field theory
- Quantum electrochemistry
- Solid state physics and the electronic structure of materials
- Special relativity
- Standard Model
- Statistical mechanics
- Thermodynamics

Proposed theories

The proposed theories of physics are relatively new theories which deal with the study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory. Proposed theories can include fringe theories in the process of becoming established (and, sometimes, gaining wider acceptance). Proposed theories usually have not been tested.

Examples

- Emergence
- Grand unification theory
-
- Loop quantum gravity
-
- M-theory
- Plasma Universe
- String theory
- Theory of everything
-

Fringe theories

Fringe theories include any new area of scientific endeavor in the process of becoming established and some proposed theories. It can include speculative sciences. This includes physics fields and physical theories presented in accordance with known evidence, and a body of associated predictions have been made according to that theory. Some fringe theories go on to become an widely accepted part of physics. Other fringe theories end up being disproven. Some fringe theories are a form of protoscience and others are a form of pseudoscience. The falsification of the original theory sometimes leads to reformulation of the theory.

Examples

- Cold fusion
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- Dynamic theory of gravity
- Grand unification theory
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- Loop quantum gravity
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- Luminiferous aether
- Steady state theory
- Theory of everything
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- These theories are both proposed and fringe theories.

Notes

# Sometimes mathematical physics and theoretical physics are used synonymously to refer to the latter. ko:이론물리학 ja:理論物理学

Standard Model

The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. Developed between 1970 and 1973, it is a quantum field theory, and consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model is not a complete theory of fundamental interactions, primarily because it does not describe gravity.

The Standard Model

The Standard Model contains both fermionic and bosonic fundamental particles. Fermions are particles which possess half-integer spin and obey the Pauli exclusion principle, which states that no fermions can share the same quantum state. Bosons possess integer spin and do not obey the Pauli exclusion principle. Informally speaking, fermions are particles of matter and bosons are particles that transmit forces. For a detailed description of the differences between fermions and bosons, see the article on identical particles. In the Standard Model, the theory of the electroweak interaction (which describes the weak and electromagnetic interactions) is combined with the theory of quantum chromodynamics. All of these theories are gauge theories, meaning that they model the forces between fermions by coupling them to bosons which mediate (or "carry") the forces. The Lagrangian of each set of mediating bosons is invariant under a transformation called a gauge transformation, so these mediating bosons are referred to as gauge bosons. The bosons in the Standard Model are:
- Photons, which mediate the electromagnetic interaction.
- W and Z bosons, which mediate the weak nuclear force.
- Eight species of gluons, which mediate the strong nuclear force.
- The Higgs bosons, which induce spontaneous symmetry breaking of the electroweak gauge group and are responsible for the existence of inertial mass. It turns out that the gauge transformations of the gauge bosons can be exactly described using a unitary group called a "gauge group". The gauge group of the strong interaction is SU(3), and the gauge group of the electroweak interaction is SU(2)×U(1). Therefore, the Standard Model is often referred to as SU(3)×SU(2)×U(1). The Higgs boson is the only boson in the theory which is not a gauge boson. The Higgs has never been observed in experiments, and finding it is a major goal of experimental particle physics today. Gravitons, the bosons believed to mediate the gravitational interaction, are not accounted for in the Standard Model. There are twelve different types, or "flavours", of fermions in the Standard Model. The proton, neutron are made up of two of these: the up quark and down quark, bound together by the strong nuclear force. Together with the electron (bound to the nucleus in atoms by the electromagnetic force), those fermions constitute the vast majority of everyday matter. All of the fundamental fermions in the Standard Model are given in the table.

Table

Left handed fermions in the Standard Model
Generation 1
Fermion (Left-handed)	Symbol	Electric charge	Weak charge -	Weak isospin	Hypercharge	Color charge -	Mass -
Electron	$e$	−1	$\bold$	−1/2	−1/2	$\bold$	0.511 MeV
Electron neutrino	$\nu_e$	0	$\bold$	+1/2	−1/2	$\bold$	< 50 eV
Positron	$e^c$	+1	$\bold$	0	+1	$\bold$	0.511 MeV
Electron antineutrino	$\nu_e^c$	0	$\bold$	0	0	$\bold$	< 50 eV
Up quark	$u$	+2/3	$\bold$	+1/2	+1/6	$\bold$	~5 MeV -
Down quark	$d$	−1/3	$\bold$	−1/2	+1/6	$\bold$	~10 MeV -
Anti-up antiquark	$u^c$	−2/3	$\bold$	0	−2/3	$\bold$	~5 MeV -
Anti-down antiquark	$d^c$	+1/3	$\bold$	0	+1/3	$\bold$	~10 MeV -

Generation 2
Fermion (Left-handed)	Symbol	Electric charge	Weak charge -	Weak isospin	Hypercharge	Color charge -	Mass -
Muon	$\mu$	−1	$\bold$	−1/2	−1/2	$\bold$	105.6 MeV
Muon neutrino	$\nu_\mu$	0	$\bold$	+1/2	−1/2	$\bold$	< 0.5 MeV
Anti-Muon	$\mu^c$	+1	$\bold$	0	+1	$\bold$	105.6 MeV
Muon antineutrino	$\nu_\mu^c$	0	$\bold$	0	0	$\bold$	< 0.5 MeV
Charm quark	$c$	+2/3	$\bold$	+1/2	+1/6	$\bold$	~1.5 GeV
Strange quark	$s$	−1/3	$\bold$	−1/2	+1/6	$\bold$	~100 MeV
Anti-charm antiquark	$c^c$	−2/3	$\bold$	0	−2/3	$\bold$	~1.5 GeV
Anti-strange antiquark	$s^c$	+1/3	$\bold$	0	+1/3	$\bold$	~100 MeV

Generation 3
Fermion (Left-handed)	Symbol	Electric charge	Weak charge -	Weak isospin	Hypercharge	Color charge -	Mass -
Tau lepton	$\tau$	−1	$\bold$	−1/2	−1/2	$\bold$	1.784 GeV
Tau neutrino	$\nu_\tau$	0	$\bold$	+1/2	−1/2	$\bold$	< 70 MeV
Anti-Tau	$\tau^c$	+1	$\bold$	0	+1	$\bold$	1.784 GeV
Tau antineutrino	$\nu_\tau^c$	0	$\bold$	0	0	$\bold$	< 70 MeV
Top quark	$t$	+2/3	$\bold$	+1/2	+1/6	$\bold$	173 GeV
Bottom quark	$b$	−1/3	$\bold$	−1/2	+1/6	$\bold$	~4.7 GeV
Anti-top antiquark	$t^c$	−2/3	$\bold$	0	−2/3	$\bold$	173 GeV
Anti-bottom antiquark	$b^c$	+1/3	$\bold$	0	+1/3	$\bold$	~4.7 GeV
- - These are not ordinary abelian charges which can be added together but labels of group representations of lie groups. - - Mass is really a coupling between a left-handed fermion and a right-handed fermion. For example, the mass of an electron is really a coupling between a left-handed electron and a right-handed electron, which is the antiparticle of a left-handed positron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left-handed electron neutrino and a right-handed electron neutrino have the same mass as this table seems to suggest. - - What is actually measured experimentally are the masses of baryons and hadrons and various cross-sections. Since quarks can't be isolated because of QCD confinement, the quantity here is supposed to be the mass of the quark at the renormalization scale of the QCD phase transition. In order to compute this quantity, physicists have to compute the hadron spectrum using lattice gauge theory and try out various masses for the quarks until the model comes up with a close fit with experimental data. Since the masses of the first-generation quarks are significantly below the QCD scale, the uncertainties are pretty large. In fact, current lattice QCD models seem to suggest a significantly lower mass of these quarks from that of this table.

lattice QCD The fermions can be arranged in three generations, the first one consisting of the electron, the up and down quarks, and the electron neutrino. All ordinary matter is made from first-generation particles; the higher-generation particles decay quickly into the first-generation ones and can only be generated for a short time in high-energy experiments. The reason for arranging them in generations is that the four fermions in each generation behave almost exactly like their counterparts in the other generations; the only difference is in their masses. For example, the electron and the muon both have half-integer spin, unit electric charge and do not participate in the strong interaction, but the muon is about 200 times more massive than the electron. The electron and the electron neutrino, and their counterparts in the other generations, are called "leptons". Unlike the quarks, they do not possess a quality called "color", and their interactions are only weak and electromagnetic, and fall off with distance. On the other hand, the strong or "color" force between quarks gets stronger with distance, so that quarks are always found in colorless combinations called hadrons, a phenomenon known as quark confinement. These colorless combinations are either fermionic baryons composed of three quarks (the proton and neutron being the most familiar example) or bosonic mesons composed of a quark-antiquark pair (such as pions). The mass of such aggregates exceeds that of the components due to their binding energy.

Tests and predictions

The Standard Model predicted the existence of W and Z bosons, the gluon, the top quark and the charm quark before these particles had been observed. Their predicted properties were experimentally confirmed with good precision. The Large Electron-Positron collider at CERN tested various predictions about the decay of Z bosons, and found them confirmed. To get an idea of the success of the Standard Model a comparison between the measured and the predicted values of some quantities are shown in the following table:

Challenges to the Standard Model

Although the Standard Model has had great success in explaining experimental results, it cannot be a complete theory of fundamental physics. This is because it has two important defects: #The model contains 19 free parameters, such as particle masses, which must be determined experimentally (plus another 10 for neutrino masses). These parameters cannot be independently calculated. #The model does not describe the gravitational interaction. Since the completion of the Standard Model, many efforts have been made to address these problems. One attempt to address the first defect is known as grand unification. The so-called grand unified theories (GUTs) hypothesized that the SU(3), SU(2), and U(1) groups are actually subgroups of a single large symmetry group. At high energies (far beyond the reach of current experiments), the symmetry of the unifying group is preserved; at low energies, it reduces to SU(3)×SU(2)×U(1) by a process known as spontaneous symmetry breaking. The first theory of this kind was proposed in 1974 by Georgi and Glashow, using SU(5) as the unifying group. A distinguishing characteristic of these GUTs is that, unlike the Standard Model, they predict the existence of proton decay. In 1999, the Super-Kamiokande neutrino observatory reported that it had not detected proton decay, establishing a lower limit on the proton half-life of 6.7× 10³² years. This and other experiments have falsified numerous GUTs, including SU(5). Another effort to address the first defect has been to develop preon models which attempt to set forth a substructure of more fundamental particles than those set forth in the Standard Model. In addition, there are cosmological reasons why the Standard Model is believed to be incomplete. In the Standard Model, matter and antimatter are related by the CPT symmetry, which suggests that there should be equal amounts of matter and antimatter after the Big Bang. While the preponderance of matter in the universe can be explained by saying that the universe just started out this way, this explanation strikes most physicists as inelegant. Furthermore, the Standard Model provides no mechanism to generate the cosmic inflation that is believed to have occurred at the beginning of the universe. The Higgs boson, which is predicted by the Standard Model, has not been observed as of 2005 (though some phenomena were observed in the last days of the LEP collider that could be related to the Higgs). One of the reasons for building the LHC is that the increase in energy is expected to make the Higgs observable. The first experimental deviation from the Standard Model (as proposed in the 1970's) came in 1998, when Super-Kamiokande published results indicating neutrino oscillation. Under the Standard Model, a massless neutrino cannot oscillate, so this observation implied the existence of non-zero neutrino masses. It was therefore necessary to revise the Standard Model to allow neutrinos to have mass; this may be simply achieved by adding 10 more free parameters beyond the initial 19. A further extension of the Standard Model can be found in the theory of supersymmetry, which proposes a massive supersymmetric "partner" for every particle in the conventional Standard Model. Supersymmetric particles have been suggested as a candidate for explaining dark matter. Although supersymmetric particles have not been observed experimentally to date, the theory is one of the most popular avenues of research in theoretical particle physics.

References

Textbooks

Journal Articles

- Y. Hayato et al., Search for Proton Decay through p → νK⁺ in a Large Water Cherenkov Detector. Phys. Rev. Lett. 83, 1529 (1999).
- S.F. Novaes, Standard Model: An Introduction, [http://arxiv.org/abs/hep-ph/0001283 hep-ph:0001283]

External links

- [http://www.newscientist.com/news/news.jsp?id=ns9999404 New Scientist story: Standard Model may be found incomplete]
- [http://arXiv.org/abs/astro-ph/0401347 The Universe Is A Strange Place, a lecture by Frank Wilczek]
- [http://www-cdf.fnal.gov/top_status/top.html Observation of the Top Quark at Fermilab]
- [http://35.9.69.219/home/modules/pdf_modules/m305.pdf MISN-0-305 The Standard Model of Fundamental Particles and Their Interactions] (PDF file) by Mesgun Sebhatu for [http://www.physnet.org Project PHYSNET].
- [http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html PostScript version of the Standard Model Lagrangian]
- [http://particleadventure.org/particleadventure/ The particle adventure.] Category:Particle physics
- ko:표준 모형 ja:標準模型

Theory of everything

A theory of everything (TOE) is a theory of theoretical physics and mathematics that fully explains and links together all known physical phenomena. Initially, the term was used with an ironic connotation to refer to various overgeneralized theories. For example, a great-grandfather of Ijon Tichy — a character from a cycle of Stanisław Lem's science fiction stories of 1960s — was known to work on "General Theory of Everything" (Polish: "Ogólna Teoria Wszystkiego"). Over time, the term stuck in popularizations of quantum physics to describe a theory that would unify the theories of the four fundamental interactions of nature. There have been numerous theories of everything proposed by theoretical physicists over the last century, but as yet none has been able to stand up to experimental scrutiny or there is tremendous difficulty in getting the theories to produce even experimentally testable results. The primary problem in producing a TOE is that quantum mechanics and general relativity have radically different descriptions of the universe, and the obvious ways of combining the two lead quickly to the renormalization problem in which the theory does not give finite results for experimentally testable quantities.

Mainstream physics

Albert Einstein was the first serious scientist who spent most of his life trying to find a TOE; he believed that the only task was to unify general relativity and electromagnetism. Current mainstream physics concepts require that a TOE unify the four fundamental interactions of nature: gravity, the strong nuclear force, the weak nuclear force, and the electromagnetic force; it should also explain the spectrum of elementary particles. There has been progress toward a TOE in unifying electromagnetism and the weak nuclear force in an electroweak unified field theory and in unifying all of the forces except for gravity (which in the present theory of general relativity is not a force) in the grand unified theory. One missing piece in a theory of everything involves combining quantum mechanics and general relativity into a theory of quantum gravity. The only serious candidate for a theory of everything at the moment is superstring theory / M-theory; current research on loop quantum gravity may eventually play a fundamental role in a TOE, but that is not its primary aim. These theories attempt to deal with the renormalization problem by setting up some lower bound on the length scales possible. Also, early 21st century theories of everything tend to suppose that the universe actually has more dimensions than the easily observed three of space and one of time. The motivation behind this approach began with the Kaluza-Klein theory in which it was noted that adding one dimension to general relativity would produce the electromagnetic Maxwell's equations. This has led to efforts to work with theories with large number of dimensions in the hopes that this would produce equations which are similar to known laws of physics. The notion of extra dimensions also helps to resolve the hierarchy problem which is the question of why gravity is so much weaker than any other force. The common answer involves gravity leaking into the extra dimensions in ways that the other forces do not. In the late 1990s, it was noted that one problem with several of the candidates for theories of everything was that they did not constrain the characteristics of the predicted universe. For example, many theories of quantum gravity can create universes with arbitrary numbers of dimensions or with arbitrary cosmological constants. One bit of speculation is that there may indeed be a huge number of universes, but that only a small number of them are habitable, and hence the fundamental constants of the universe are ultimately the result of the anthropic principle rather than a consequence of the theory of everything. Max Tegmark has taken this principle to its logical conclusion with his "Ultimate Ensemble", whose only postulate is that "all structures that exist mathematically exist also physically". In this theory, certain mathematical structures are complex enough to contain self aware substructures, who subjectively perceive themselves as existing in a physically real world. There is also a philosophical debate within the physics community as to whether or not a "theory of everything" should be seen as the fundamental law of the universe. One view is the hard reductionist view that the TOE is the fundamental law of the universe and that all other theories of the universe are a consequence of the TOE. Another view is that there are laws which Steven Weinberg calls free floating laws which govern the behavior of complex systems, and while these laws are related to the theory of everything, they cannot be seen as less fundamental than the TOE. Some argue that this explanation would violate Occam's Razor if a completely valid TOE were formulated. Other possibilities which may frustrate the explanatory capacity of a TOE may include sensitivity to the boundary conditions of the universe, or the existence of mathematical chaos in its solutions, making its predictions precise, but useless. There have been several attempts to advance the general theory of relativity as a theory of everything, including as mentioned above, by Einstein himself. With Rosen he attempted to model particles as tiny wormholes, hence the term Einstein-Rosen Bridge. Wormholes have also been proposed at various times (for instance, by Shimony and by Durand [http://stacks.iop.org/ob/4/S351]) to explain Bell violations not as superluminal influences but influences that take a shortcut through a wormhole. Such theories face a number of hurdles: the creation of wormholes changes the topology of spacetime by creating a new "handle" which implies violations of causality (see Hadley [http://arxiv.org/abs/quant-ph/9706018]), and the general theory of relativity predicts its own breakdown at a Gravitational singularity by theorems of Hawking and Penrose. A recent effort to surmount this hurdle notes that the equivalence principle can be applied along curves rather than at a single point (Iliev [http://arxiv.org/abs/gr-qc/9709053]), which would imply that time dilation of

(1-v^2)^

is indistinguishable locally (along the curve) from a relative velocity

v

and the unbounded time dilation observed as an event horizon emerges at the center of a collapsing star implies that the center is in reality as well as appearance receding at a velocity approaching the speed of light, producing a bubble-like local inflation of the star's interior (Monroe [http://arxiv.org/abs/astro-ph/0506506]). This approach skirts the trapped surface assumption of the theorems of Hawking and Penrose.

Where the Standard Model comes up short

The Standard Model of physics is among the most successful theories in history, but it fails to explain everything. It doesn't explain the origins of the universe before the big bang. There are 18 arbitrary constants and several dozen elementary particles in the Standard Model. Why are there so many? The Standard Model also fails to explain over 90% of the apparent mass-energy of the universe. The existence of dark matter and dark energy, although never observed directly, is all but guaranteed if current theory is correct. Why is so much of the universe invisible? What is the state of matter within a black hole? Is spacetime curved, or is it flat? How many dimensions of space and time are there? What is the origin of matter and energy? What is the reason for them at all? Is there a most fundamental particle? What happens beyond Planck scales? Why is momentum quantized? Is the speed of light the fastest speed in the universe? These are among the many questions left unanswered by the most modern theories in physics. A successful TOE would explain each of these questions and provide solutions to every situation which could exist in the universe.

Amateur Efforts

Attempts to create theories of everything are common among people outside the professional physics community. Some are created by amateurs, and their theories are often criticised on the basis of inability to make quantifiable and/or falsifiable predictions. For example, a theory of everything would provide some insight into the relative strength of forces, and predictions of particle lifetimes and cross sections. It would need to be shown to explain all known universal phenomena. Unlike professional physicists, who are generally aware that their proposed theory is incomplete, untested, and likely to be wrong and who are aware of the huge difficulties and challenges involved in creating a TOE, amateurs who create TOE's tend to be unaware of what work has already been done, the mechanisms for testing scientific theories and the fact that most proposed theories are wrong.

Burkhard Heim and quantised general relativity

Burkhard Heim's theory of quantised general relativity purports to be a TOE but this theory, begun in the 1950s and still under development, had until recently sunk into obscurity. A sign that it is undergoing a renewal of interest is that a paper by Droescher and Haeuser on aerospace applications of Heim Theory was published by the AIAA in 2005 and was awarded the prize for best paper of the year by the Nuclear and Future Flight Propulsion Technical Committee. Supporters claim that Heim's six dimensional theory can predict the masses of some fundamental particles with considerable accuracy, which no established theory has yet been able to do.

Eino Kaila

The prolific Finnish philosopher Eino Kaila attempted to construct a theory of everything based on the philosophical implications of quantum mechanics in the 1950s. His attempt did not get much attention outside Finland, and he only managed to write the first part of what he planned on making an extensive study on the subject. "Terminalkausalität als die Grundlage eines unitarischen Naturbegriffs" ("terminal causality as the foundation of a unitarian notion of nature"), published in 1956, formulated a new type of causality and was meant to be followed by similar works on psychology and biology.

Time Cube

Gene Ray's Time Cube concept is an example of an amateur TOE that is quite well-known, although some argue this to be due to a claimed entertainment value rather than its scientific merit. Mr. Ray claims to explain all known universal phenomena through the postulate that "Time is cubic, not linear". See list of alternative, speculative and disputed theories. Like many similar theories, it is regarded by some as pseudoscience.

Expansion Theory

Expansion Theory purports to offer a theory of everything in which all physical phenomena are explained by universal accelerating expansion. Author Mark McCutcheon described the theory in the book The Final Theory: Rethinking our Scientific Legacy, in 2002, although the theory itself is much older. The theory argues that current scientific theory is inconsistent and incomplete in that it predicts yet doesn't explain Action at a distance, violates its own conservation laws, and fails to live up to experimental data or concur with the laws of common sense. Under expansion theory, Classical Mechanics, General Relativity, Special Relativity, Quantum Mechanics are discarded and replaced with an atomic expansion that, according to the author, accounts for phenomena like magnetism, light, gravity, and atomic forces. [http://www.thefinaltheory.com] Expansion Theory holds little to no acceptance within the scientific community. Many of the predictions of the theory don't hold empirically, and the theory doesn't explain any anomalous data. Like other purported theories of everything, many regard the theory to be a form of pseudoscience.

TOE and religion

Many theistic people hold the apophatic belief that the TOE will never be found. Other theists believe that a Theory of Everything would ultimately prove the power of their ultimate being's intellect to design such an elegant universe, or even generate an unanticipated new conception of God. Furthermore, others think that the TOE may be unable to prove or disprove the existence of a God, gods or other supernatural ultimate being, although the theory may establish the falsehood of certain claims in religious scriptures.

References

- The Theory of Everything: The Origin and Fate of the Universe is an unauthorized 2002 book taken from lectures recorded by Stephen Hawking (ISBN 1893224791)
- A Theory of Everything: An Integral Vision for Business, Politics, Science and Spirituality, 2000 (ISBN 1570628556) is a book by philosopher Ken Wilber which considers "everything" to include the metaphysical as well as the physical.

External links

- [http://www.theoryofeverything.co.uk Difficulties in attaining a Theory of Everything] - an analysis of the interplay of the origin of gravity and of gravitational and inertial mass.
- [http://www.pbs.org/wgbh/nova/elegant/program.html The Elegant Universe-Nova online]- a 3 hour PBS show about the search for the Theory of everything and string theory.
- [http://www.pabird.supanet.com/gravityprobeb.html Gravity Probe B, the Large Hadron Collider and The Theory of Everything] What future experiments may tell us about the Theory Of Everything. Category:Theoretical physics Category:Theories of gravitation

Electromagnetism

Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess a property known as electric charge, and is in turn affected by the presence and motion of such particles. The term electrodynamics is sometimes used to refer to the combination of electromagnetism with mechanics, and deals with the effects of the electromagnetic field on the dynamic behavior of electrically-charged particles.

Electric and magnetic fields

It is often convenient to understand the electromagnetic field in terms of two separate fields: the electric field and the magnetic field. A non-zero electric field is produced by the presence of electrically charged particles, and gives rise to the electric force; this is the force that causes static electricity and drives the flow of electric charge (electric current) in electrical conductors. The magnetic field, on the other hand, can be produced by the motion of electric charges, or electric current, and gives rise to the magnetic force associated with magnets. The term "electromagnetism" comes from the fact that the electric and magnetic fields generally cannot be described independently of one another. A changing magnetic field produces an electric field (this is the phenomenon of electromagnetic induction, which underlies the operation of electrical generators, induction motors, and transformers). Similarly, a changing electric field generates a magnetic field. Because of this inter-dependence between the electric and magnetic fields, it makes sense to consider them as a single, theoretically coherent entity — the electromagnetic field. This unification, which was completed by James Clerk Maxwell, is one of the triumphs of 19th century physics. It had far-reaching consequences, one of which was the elucidation of the nature of light: as it turns out, what we think of as "light" is actually a propagating oscillatory disturbance in the electromagnetic field, i.e., an electromagnetic wave. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies. The theoretical implications of electromagnetism led to the development of special relativity by Albert Einstein in 1905.

The electromagnetic force

The force that the electromagnetic field exerts on electrically charged particles, called the electromagnetic force, is one of the four fundamental forces. The other fundamental forces are the strong nuclear force (which holds atomic nuclei together), the weak nuclear force (which causes certain forms of radioactive decay), and the gravitational force. All other forces are ultimately derived from these fundamental forces. As it turns out, the electromagnetic force is the one responsible for practically all the phenomena one encounters in daily life, with the exception of gravity. Roughly speaking, all the forces involved in interactions between atoms can be traced to the electromagnetic force acting on the electrically charged protons and electrons inside the atoms. This includes the forces we experience in "pushing" or "pulling" ordinary material objects, which come from the intermolecular forces between the individual molecules in our bodies and those in the objects. It also includes all forms of chemical phenomena, which arise from interactions between electron orbitals.

Origins of electromagnetic theory

The scientist William Gilbert proposed, in his De Magnete (1600), that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had the ability to disturb a compass needle, but the link between lightning and electricity was not confirmed until Franklin's proposed experiments (performed initially by others) in 1752. One of the first to discover and publish a link between man-made electric current and magnetism was Romagnosi, who in 1802 noticed that connecting a wire across a Voltaic pile deflected a nearby compass needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment. Ørsted's work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation. An accurate theory of electromagnetism, known as classical electromagnetism, was developed by various physicists over the course of the 19th century, culminating in the work of James Clerk Maxwell, who unified the preceding developments into a single theory and discovered the electromagnetic nature of light. In classical electromagnetism, the electromagnetic field obeys a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law. One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity. According to Maxwell's equations, the speed of light is a universal constant, dependent only on the electrical permittivity and magnetic permeability of the vacuum. This violates Galilean invariance, a long-standing cornerstone of classical mechanics. One way to reconcile the two theories is to assume the existence of a luminiferous aether through which the light propagates. However, subsequent experiments efforts failed to detect the presence of the aether. In 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaces classical kinematics with a new theory of kinematics that is compatible with classical electromagnetism. In addition, Relativity theory shows that in moving frames of reference a magnetic field becomes an electrostatic field and vice versa; thus firmly showing that they are two sides of the same coin, and thus the term Electromagnetism.

Failures of classical electromagnetism

In another paper published in that same year, Einstein undermined the very foundations of classical electromagnetism. His theory of the photoelectric effect (for which he won the Nobel prize for physics) posited that light could exist in discrete particle-like quantities, which later came to be known as photons. Einstein's theory of the photoelectric effect extended the insights that appeared in the solution of the ultraviolet catastrophe presented by Max Planck in 1900. In his work, Planck showed that hot objects emit electromagnetic radiation in discrete packets, which leads to a finite total energy emitted as black body radiation. Both of these results were in direct contradiction with the classical view of light as a continuous wave. Planck's and Einstein's theories were progenitors of quantum mechanics, which, when formulated in 1925, necessitated the invention of a quantum theory of electromagnetism. This theory, completed in the 1940s, is known as quantum electrodynamics (or "QED"), and is one of the most accurate theories known to physics.

SI electricity units

References

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External links

- [http://www.rmcybernetics.com/science/physics/electromagnetism_intro_electric_force.htm Introduction to Electromagnetism] From the basics to advanced level science
- [http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-and-MagnetismSpring2002/VideoLectures/index.htm MIT Video Lectures - Electricity and Magnetism] from Spring 2002. Taught by Professor Walter Lewin.
- [http://www.lightandmatter.com/area1book4.html Electricity and Magnetism] - an online textbook (uses algebra, with optional calculus-based sections)
- [http://www.plasma.uu.se/CED/Book/ Electromagnetic Field Theory] - an online textbook (uses calculus)
- [http://farside.ph.utexas.edu/teaching/em/em.html Classical Electromagnetism: An intermediate level course] - an online intermediate level texbook downloadable as PDF file ko:전자기학 ja:電磁気学

Fermion

Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. As a result, they are subject to the Pauli exclusion principle and obey Fermi-Dirac statistics. The spin-statistics theorem states that fermions have half-integer spin. One possible way of visualizing spin is that particles with a 1/2 spin, i.e. fermions, have to be rotated by two full rotations to return them to their initial state. All elementary particles are either fermions or bosons. Composite particles composed of fermions may be either bosons (such as mesons) or fermions (such as baryons) depending on their total spin. The elementary particles which make up matter are fermions, belonging to either the quarks (which form protons and neutrons) or the leptons (such as electrons). The Pauli exclusion of fermions is responsible for the stability of the electron shells of atoms, making complex chemistry possible. It also allows the stability of degenerate matter under extreme pressures. Examples of fermions:
- electrons
- quarks
- protons
- neutrons
- neutrinos

Matter

Matter is commonly referred to as the substance of which physical objects are composed. In physics, it is everything that is constituted of elementary fermions. Philosophically, matter constitutes the formless substratum of all things, which exists only potentially and from which reality is produced. In the sense of content, matter is also used in contrast to form.

Matter in physics

Matter occupies space and has mass. It is composed predominantly of atoms, which consist of protons, neutrons, and electrons. All gauge bosons (of which the photon is one), which mediate the four fundamental forces, are not considered matter, even though they certainly have energy and some also mass. Matter thus consists of quarks and leptons. There are six types of quarks (strange, charm, top, bottom, up, and down) which combine to form hadrons, primarily baryons and mesons, through the strong interaction and are actually thought to always be confined. Among the baryons are the proton and the neutron, which further combine to form the nuclei of all elements of the periodic table. Usually these nuclei are surrounded by a cloud of electrons. A nucleus with as many electrons as protons, which is thus electrically neutral, is called an atom, otherwise it is an ion. Chemistry is the science that studies how nuclei and electrons combine to form compounds. In bulk, matter can exist in several different phases, according to particle density and energy density or alternatively pressure and temperature. These phases include gases, plasmas, liquids, fluids, superfluids, solids, and Bose-Einstein condensate. As circumstances change, matter may change from one phase into another. These phenomena are called phase transitions, and their energetics are studied in the field of thermodynamics. In small quantities, matter can exhibit properties that are entirely different from those of bulk material. Homogeneous matter has a definite composition and properties and any amount of the matter has the same composition and properties. Homogenous matter may or may not be a mixture. Iron and brass would examples of each. Heterogeneous matter does not have a definite composition, for example, granite. Matter constitutes the observable Universe. It can be converted to energy (see annihilation), and vice versa - can be created out of energy (see matter creation) and undergo other formations and alterations.

Falsifiability

:This page discusses how a theory or assertion is "falsifiable" ("disprovable" opp: "verifiable"), rather than the non-philosophical use of "falsification", meaning "counterfeiting." The idea comes from the work of the philosophers Sir Karl Popper and Ernest Gellner. Falsifiability is an important concept in the philosophy of science that amounts to the apparently paradoxical idea that a proposition or theory cannot be scientific if it does not admit the possibility of being shown false. Falsifiable does not mean false. For a proposition to be falsifiable, it must be at least in principle possible to make an observation that would show the proposition to be false, even if that observation had not been made. For example, the proposition "All crows are black" would be falsified by observing one white crow. Falsificationists claim that any theory that is not falsifiable is unscientific. Psychoanalytic theory, for example, is held up by the proponents of Karl Popper as an example of an ideology rather than a science. A patient regarded by his psychoanalyst as "in denial" about his sexual orientation may be viewed as confirming he is homosexual simply by denying that he is; and if he has sex with women, he may be accused of trying to buttress his denials. In other words, there is no way the patient could convincingly demonstrate his heterosexuality to the analyst. This is an example of what Popper called a "closed circle". The proposition that the patient is homosexual is not falsifiable.

Naïve falsification

Falsifiability was first developed by Karl Popper in the 1930s. Popper noticed that two types of statements are of particular value to scientists. The first are statements of observations, such as 'this is a white swan'. Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They can be parsed in the form: There is an x which is a swan and x is white. The second type of statement of interest to scientists categorizes all instances of something, for example "All swans are white". Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan then x is white. Scientific laws are commonly supposed to be of the second type. Perhaps the most difficult question in the methodology of science is: how does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements? Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from ‘this is a white swan', “that is a white swan”, and so on, to a universal statement such as 'all swans are white'. This method is clearly logically invalid, since it is always possible that there may be a non-white swan that has somehow avoided observation. Yet some philosophers of science claim that science is based on such an inductive method. Popper held that science could not be grounded on such an invalid inference. He proposed falsification as a solution to the problem of induction. Popper noticed that although a singular existential statement such as 'there is a white swan' cannot be used to affirm a universal statement, it can be used to show that one is false: the singular existential observation of a black swan serves to show that the universal statement 'all swans are white' is false - in logic this is called modus tollens. 'There is a black swan' implies 'there is a non-white swan' which in turn implies 'there is something which is a swan and which is not white', hence 'all swans are white' is false, because that is the same as 'there is nothing which is a swan and which is not white'. Although the logic of naïve falsification is valid, it is rather limited. Popper drew attention to these limitations in The Logic of Scientific Discovery, in response to anticipated criticism from Duhem and Carnap. W. V. Quine is also well-known for his observation in his influential essay, "Two Dogmas of Empiricism" (which is reprinted in From a Logical Point of View), that nearly any statement can be made to fit with the data, so long as one makes the requisite "compensatory adjustments". In order to logically falsify a universal, one must find a true falsifying singular statement. But Popper pointed out that it is always possible to change the universal statement or the existential statement so that falsification does not occur. On hearing that a black swan has been observed in Australia, one might introduce the ad hoc hypothesis, 'all swans are white except those found in Australia'; or one might adopt another, more cynical view about some observers, 'Australian ornithologists are incompetent'. As Popper put it, a decision is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it. At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it.

Falsificationism

In place of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements. Falsified theories are to be replaced by theories which can account for the phenomena which falsified the prior theory, that is, with greater explanatory power. Thus, Aristotelian mechanics explained observations of objects in everyday situations, but was falsified by Galileo’s experiments, and was itself replaced by Newtonian mechanics which accounted for the phenomena noted by Galileo (and others). Newtonian mechanics' reach included the observed motion of the planets and the mechanics of gases. Or at least most of them; the size of the precession of the orbit of Mercury wasn't predicted by Newtonian mechanics, but was by Einstein's general relativity. The Youngian wave theory of light (i.e., waves carried by the luminiferous ether) replaced Newton's (and many of the Classical Greeks') particles of light but in its turn was falsified by the Michelson-Morley experiment, whose results were eventually understood as incompatible with an ether and was superseded by Maxwell's electrodynamics and Einstein's special relativity, which did account for the new phenomena. At each stage, experimental observation made a theory untenable (i.e., falsified it) and a new theory was found which had greater 'explanatory power' (i.e., could account for the previously unexplained phenomena), and as a result provided greater opportunity for its own falsification. Naïve falsificationism is an unsuccessful attempt to prescribe a rationally unavoidable method for science. Falsificationism proper, on the other hand, is a prescription of a way in which scientists ought to behave as a matter of choice.

Popper's swan argument

special relativity and North America]] One notices a white swan, from this one can conclude: :At least one swan is white. From this, one may wish to infer that: :All swans are white. However, to prove this, one must find all the swans in the world and verify that they are white. This is nigh impossible, and extensions such as, All swans have always been white would require a time machine as would all swans will always be white. Therefore, this cannot be proven. time machine]] As it turns out, not all swans are white. By finding a black swan, one has falsified the statement all swans are white; it is not true. We have to refine our paradigm to a more specific statement, thus :All swans except Cygnus atratus are white; C. atratus is black.

Formal logical arguments

The falsification of theories occurs through modus tollens, via some observation. Suppose some theory T implies an observation O: :

T \rightarrow O

The required observation, however, is not made, therefore :

\sim O

So by Modus Tollens, :

\sim T

The criterion of demarcation

Popper proposed falsification as a way of determining if a theory is scientific or not. If a theory is falsifiable, then it is scientific; if it is not falsifiable, then it is not science. Popper uses this criterion of demarcation to draw a sharp line between scientific and unscientific theories. Some have taken this principle to an extreme to cast doubt on the scientific validity of many disciplines (such as macroevolution and Cosmology). Falsifiability was one of the criteria used by Judge William Overton to determine that 'creation science' was not scientific and should not be taught in Arkansas public schools. In the philosophy of science, verificationism (also known as the verifiability theory of meaning) held that a statement must be in principle empirically verifiable in order to be both meaningful and scientific. This was an essential feature of the logical empiricism of the so-called Vienna Circle that featured such philosophers as Moritz Schlick, Rudolf Carnap, Otto Neurath, and Hans Reichenbach. After Popper, verifiability came to be replaced by falsifiability as the criterion of demarcation. In other words, in order to be scientific, a statement had to be, in principle, falsifiable. Popper noticed that the philosophers of the Vienna Circle had mixed two different problems, and had accordingly given a single solution to both of them, namely verificationism. In opposition to this view, Popper emphasized that a theory might well be meaningful without being scientific, and that, accordingly, a criterion of meaningfulness may not necessarily coincide with a criterion of demarcation. His own falsificationism, thus, is not only an alternative to verificationism, it is also an acknowledgment of the conceptual distinction that previous theories had ignored. Falsifiability is a property of statements and theories, and is itself neutral. As a demarcation criterion, it seeks to take this property and make it a base for affirming the superiority of falsifiable theories over non-falsifiable ones as a part of science, in effect setting up a political position that might be called falsificationism. Much that would be considered meaningful and useful, however, is not falsifiable. Certainly non-falsifiable statements have a role in scientific theories themselves. The Popperian criterion provides a definition of science that excludes much that is of value; it does not provide a way to distinguish meaningful statements from meaningless ones. It is nevertheless very useful to know if a statement or theory is falsifiable, if for no other reason than that it provides us with an understanding of the ways in which one might assess the theory. One might at the least be saved from attempting to falsify a non-falsifiable theory, or come to see an unfalsifiable theory as unsupportable.

Criticism

Thomas Kuhn’s influential book The Structure of Scientific Revolutions argued that scientists work within a conceptual paradigm that determines the way in which they view the world. Scientists will go to great length to defend their paradigm against falsification, by the addition of ad hoc hypotheses to existing theories. Changing one's 'paradigm' is not easy, and only through some pain and angst does science (at the level of the individual scientist) change paradigms. Some falsificationists saw Kuhn’s work as a vindication, since it showed that science progressed by rejecting inadequate theories. More commonly, it has been seen as showing that sociological factors, rather than adherence to a strict, logically obligatory method, play the determining role in deciding which scientific theory is accepted. This was seen as a profound threat to those who seek to show that science has a special authority in virtue of the methods that it employs. Imre Lakatos attempted to explain Kuhn’s work in falsificationist terms by arguing that science progresses by the falsification of research programs rather than the more specific universal statements of naïve falsification. In Lakatos' approach, a scientist works within a research program that corresponds roughly with Kuhn's 'paradigm'. Whereas Popper rejected the use of ad hoc hypothesis as unscientific, Lakatos accepted their place in the development of new theories. Paul Feyerabend examined the history of science with a more critical eye, and ultimately rejected any prescriptive methodology at all. He went beyond Lakatos’ argument for ad hoc hypothesis, to say that science would not have progressed without making use of any and all available methods to support new theories. He rejected any reliance on a scientific method, along with any special authority for science that might derive from such a method. Rather, he claimed, ironically, that if one is keen to have a universally valid methodological rule, anything goes would be the only candidate. For Feyerabend, any special status that science might have derives from the social and physical value of the results of science rather than its method. Following from Feyerabend, the whole "Popper project" to define science around one particular methodology—which accepts nothing except itself—is a perverse example of what he supposedly decried: a closed circle argument. The Popperian criterion itself is not falsifiable. Moreover, it makes Popper effectively a philosophical nominalist, which has nothing to do with empirical sciences at all. Although Popper's claim of the singular characteristic of falsifiability does provide a way to replace invalid inductive thinking (empiricism) with deductive, falsifiable reasoning, it appeared to Feyerabend that doing so is neither necessary for, nor conducive to, scientific progress.

From scientists

Many actual physicists, including Nobel Prize winner Steven Weinberg and Alan Sokal (Fashionable Nonsense), have criticized falsifiability on the grounds that it does not accurately describe the way science really works. Take astrology, an example most would agree is not science. Astrology constantly makes falsifiable predictions -- a new set is printed every day in the newspapers -- yet few would argue this makes it scientific. One might respond that astrological claims are rather vague and can be excused or reinterpreted. But the same is true of actual science: a physical theory predicts that performing a certain operation will result in a number in a certain range. Nine times out of ten it does; the tenth the physicists blame on a problem with the machine -- perhaps someone slammed the door too hard or something else happened that shook the machine. Falsifiability does not help us decide between these two cases. In reality, of course, theories are used because of their successes, not because of their failures. As Sokal writes, "When a theory successfully withstands an attempt at falsification, a scientist will, quite naturally, consider the theory to be partially confirmed and will accord it a greater likelihood or a higher subjective probability. ... But Popper will have none of this: throughout his life he was a stubborn opponent of any idea of 'confirmation' of a theory, or even of its 'probability'. ... [but] the history of science teaches us that scientific theories come to be accepted abo

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