Myswizard

Theoretical physics employs mathematical models and abstractions, as opposed to experimental processes, in an attempt to understand Nature. Central to it is mathematical physics 1, though other conceptual techniques are also used. The goal is to rationalize, explain and predict physical phenomena. The advancement of science depends in general on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigor while giving little weight to experiments and observations. For example, while developing special relativity, Einstein was concerned with the Lorentz transformation which left Maxwell’s equations invariant, but was apparently uninterested in the Michelson-Morley experiment on Earth’s drift through a luminiferous ether. On the other hand, Einstein was awarded the Nobel Prize for explaining the photoelectric effect, previously an experimental result lacking a theoretical formulation.

Overview
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.

An Einstein manifold, used in general relativity to describe the curvature of spacetime

Hence, more is involved than the application, or even invention, of mathematics — to wit: concept formation. Archimedes realized that one could determine the volume of an irregularly-shaped object by immersing it in a liquid, and that a ship floats by displacing its weight of water. Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces, and how to calculate the length of a rectangle’s diagonal. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that (action and) energy are not continuously variable. Sometimes it is the vision of mathematicians which provides the clue; e.g., the notion, due to Riemann and others, that space itself might be curved.

Theoretical advances often consist in setting aside old paradigms

Heat is a fluid called caloric.
Burning consists of evolving phlogiston.
Astronomical bodies revolve around the Earth.
often replacing them with new ones

Physical objects are made up of molecules and atoms.
Diseases can be caused by unseen microbes.
Energy is exchanged in discrete packets called quanta.
Physical theories become accepted if they are able to make correct predictions and avoid incorrect ones. The theory should have, at least as a secondary objective, a certain economy and elegance (compare to mathematical beauty), a notion sometimes called “Occam’s razor” after the 13th-century English philosopher William of Occam (or Ockham), in which the simpler of two theories that describe the same matter just as adequately is preferred. (But conceptual simplicity may mean mathematical complexity.) They are also more likely to be accepted if they connect a wide range of phenomena. Testing the consequences of a theory is part of the scientific method.

Physical theories can be grouped into three categories: mainstream theories, proposed theories and fringe theories.

History
For more details on this topic, see History of physics.
Theoretical physics began, at least 2,300 years ago under the pre-Socratic Greek philosophers, and continued by Plato; and Aristotle, whose views held sway for a millennium. In medieval times, during the rise of the universities, the only acknowledged intellectual disciplines were theology, mathematics, medicine, and law. As the concepts of matter, energy, space, time and causality slowly began to acquire the form we know today, other sciences spun off from the rubric of natural philosophy. During the Renaissance, the modern concept of experimental science, the counterpoint to theory, began with Francis Bacon. The modern era of theory began perhaps with the Copernican paradigm shift in astronomy, soon followed by the actual planetary orbits due to Kepler, based on the meticulous observations of Tycho.

The great push toward the modern concept of explanation started with Galileo, one of the few physicists who was both a consummate theoretician and a great experimentalist. The analytic geometry and mechanics of Descartes was incorporated into the calculus and mechanics of Isaac Newton, another theoretician/experimentalist of the highest order. Joseph-Louis Lagrange, Leonhard Euler and William Rowan Hamilton would extend the theory of classical mechanics considerably. Each of these individuals picked up the interactive intertwining of mathematics and physics begun two millennia earlier by Pythagoras.

Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of the idea of energy by the inclusion of heat, then electricity and magnetism and light, and finally mass. The laws of thermodynamics, and especially the introduction of the singular concept of entropy, filled in a great missing link in the attempt to explain why things happen.

The pillars of modern physics, and perhaps the most revolutionary theories in the history of physics, have been relativity theory and quantum mechanics. Newtonian mechanics was subsumed under special relativity and Newton’s gravity was given a kinematic explanation by general relativity. Quantum mechanics led to an understanding of blackbody radiation and of anomalies in the specific heats of solids — and finally to an understanding of the internal structures of atoms and molecules.

All of these achievements depended on the theoretical physics as a moving force both to suggest experiments and to consolidate results — often by ingenious application of existing mathematics, or, as in the case of Descartes and Newton (with Leibniz), by inventing new mathematics. Fourier’s studies of heat conduction lead to a new branch of mathematics: infinite, orthogonal series.

Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand the Universe, from the cosmological to the elementary particle scale. Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models.

Prominent theoretical physicists
Famous theoretical physicists include Isaac Newton, Albert Einstein, Stephen Hawking, Niels Henrik Bohr, Werner Heisenberg, Max Born, Hendrik A. Lorentz, Max Planck, Erwin Schrödinger, Paul Dirac, Richard Feynman, Lev Landau, Abdus Salam, Enrico Fermi, Louis Victor Broglie and Wolfgang Pauli.

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. There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation and possible composition are subjects of debate.

Examples
Physical cosmology
Classical mechanics
Condensed matter physics
Dynamics
Dark matter
Electromagnetism
Field theory
Fluid dynamics
General relativity
Particle physics
Quantum mechanics
Quantum field theory
Quantum electrochemistry
Solid state physics or Condensed Matter Physics and the electronic structure of materials
Special relativity
Standard Model
Statistical mechanics
String Theory
Thermodynamics
Particle Cosmology

Proposed theories
The proposed theories of physics are usually 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. However, some proposed theories include theories that have been around for decades and have eluded methods of discovery and testing. 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
Dark energy or Einstein’s Cosmological Constant
Einstein-Rosen Bridge
Emergence
Grand unification theory*
Loop quantum gravity*
M-theory
String theory
Supersymmetry
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 a 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
Dynamic theory of gravity
Grand unification theory*
Loop quantum gravity*
Luminiferous aether
Steady state theory
Theory of everything*
Metatheory
* These theories are both proposed and fringe theories.

Notes
Note 1: Sometimes mathematical physics and theoretical physics are used synonymously to refer to the latter.
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “Theoretical physics”.

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String theory is a part of (Advanced) Theoretical Physics. There are components of the theory having to do with multiple dimensions. My reason for exploring these theories is because of the interconnectedness of All That Exists and It’s perfection and complexities. If you visit The Superstring site under “links” you will have fun exploring these theories. I love this science because it all leads back to the big unanswerable question. Scientists label these “problems.” __Myswizard

String Theory

Interaction in the subatomic world: world lines of point like particles in the Standard Model or a world sheet swept up by closed strings in 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 point like particles in a physical theory. Studies of string theories have revealed that they require not just strings, but also higher-dimensional objects.

The basic idea is that the fundamental constituents of reality are strings of energy of the Planck length (about 10-35 m) which vibrate at resonant specific frequencies[1]. Another key claim of the theory is that no measurable differences can be detected between strings that wrap around dimensions smaller than themselves and those that move along larger dimensions (i.e., physical processes in a dimension of size R match those in a dimension of size 1/R). Singularities are avoided because the observed consequences of “big crunches” never reach zero size. In fact, should the universe begin a “big crunch” sort of process, string theory dictates that the universe could never be smaller than the size of a string, at which point it would actually begin expanding.

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 will be able to describe a universe with the precise collection of forces and matter that is observed, nor how much freedom to choose those details that 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. Hence critics of string theory occasionally remark that the theory “… is not even wrong,” quoting a quip attributed to Wolfgang Pauli.

Work on string theory has led to advances in mathematics, mainly in algebraic geometry. String theory has also led to other theories, super symmetric gauge theories, which will be tested at the new Large Hadron Collider experiment.

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 presented a physical explanation for 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, and independently Tamiaki Yoneya, studied the messenger-like patterns of string vibration and found that their properties exactly matched those of the gravitational force’s hypothetical messenger particle — the 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.

Edward Witten In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of a new 11-dimensional theory called M-theory. These discoveries sparked the second superstring revolution. When Witten named it M-theory, he did not specify what the “M” stood for, presumably because he did not feel he had the right to name a theory which he had not been able to fully describe. Guessing what the “M” stands for has become a kind of game among theoretical physicists. The “M” sometimes is said to stand for Mystery, or Magic, or Mother. More serious suggestions include Matrix or Membrane. Sheldon Glashow has noted that the “M” might be an upside down “W”, standing for Witten. Others have suggested that the “M” in M-theory should stand for Missing, Monstrous or even Murky. According to Witten himself, as quoted in the PBS documentary based on Brian Greene’s The Elegant Universe, the “M” in M-theory stands for “magic, mystery, or matrix according to taste.”

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 created by adding supersymmetry. Nowadays, ’string theory’ usually refers to the supersymmetric variant while the earlier is given its full name, ‘bosonic string theory’.

String Theories
Type Spacetime dimensions
Bosonic 26 Only bosons, no fermions means only forces, no matter, with both open and closed strings; major flaw: a particle with imaginary mass, called the tachyon, representing an instability in the theory.
I 10 Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO(32)
IIA 10 Supersymmetry between forces and matter, with closed strings and open strings bound to D-branes, no tachyon, massless fermions spin both ways (nonchiral)
IIB 10 Supersymmetry between forces and matter, with closed strings and open strings bound to D-branes, no tachyon, massless fermions only spin one way (chiral)
HO 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is SO(32)
HE 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E8×E8

Note that in the type IIA and type IIB string theories closed strings are allowed to move everywhere throughout the ten-dimensional space-time (called the bulk), while open strings have their ends attached to D-branes, which are membranes of lower dimensionality (their dimension is odd - 1,3,5,7 or 9 - in type IIA and even - 0,2,4,6 or 8 - in type IIB, including the time direction).

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.

Worldsheet
Imagine a point-like particle. If we draw a graph which depicts the progress of the particle as time passes by, the particle will draw a line in space-time. This line is called the particle’s worldline. Now imagine a similar graph depicting the progress of a string as time passes by; the string (a one-dimensional object - a small line - by itself) will draw a surface (a two-dimensional manifold), known as the worldsheet. The different string modes (representing different particles, such as photon or graviton) are surface waves on this manifold.

A closed string looks like a small loop, so its worldsheet will look like a pipe, or - more generally - as a Riemannian manifold (a two-dimensional oriented surface) with no boundaries (i.e. no edge). An open string looks like a short line, so its worldsheet will look like a strip, or - more generally - as a Riemannian manifold with a boundary.

Strings can split and connect. This is reflected by the form of their worldsheet (more accurately, by its topology). For example, if a closed string splits, its worldsheet will look like a single pipe splitting (or connected) to two pipes (see drawing at the top of this page). If a closed string splits and its two parts later reconnects, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like torus connected to two pipes (one representing the ingoing string, and the other - the outgoing one). An open string doing the same thing will have its worldsheet looking like a ring connected to two strips.

Note that the process of a string splitting (or strings connecting) is a global process of the worldsheet, not a local one: locally, the worldsheet looks the same everywhere, and it is not possible to determine unambiguously at which point on the worldsheet the splitting occurs. Therefore these processes are an integral part of the theory, and are described by the same dynamics that controls the string modes.

In some string theories (namely closed strings in Type I and string in some version of the bosonic string), strings can split and reconnect in an opposite orientation (as in a Möbius strip or a Klein bottle). These theories are called unoriented. Formally, the worldsheet in these theories is an unoriented surface).

Dualities
Before the 1990s, string theorists believed there were five distinct superstring theories: type I, types IIA and IIB, and the two heterotic string theories (SO(32) and E8×E8). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the theory whose low energy limit, with ten dimensions space-time compactified down to four, matched the physics observed in our world today. But now it is known that this naive picture was wrong, and that the five superstring theories are connected to one another as if they are each a special case of some more fundamental theory, of which there is only one. These theories are related by transformations that are called dualities. If two theories are related by a duality transformation, it means that the first theory can be transformed in some way so that it ends up looking just like the second theory. The two theories are then said to be dual to one another under that kind of transformation. Put differently, the two theories are two different mathematical descriptions of the same phenomena.

These dualities link quantities that were also thought to be separate. Large and small distance scales, strong and weak coupling strengths – these quantities have always marked very distinct limits of behavior of a physical system, in both classical field theory and quantum particle physics. But strings can obscure the difference between large and small, strong and weak, and this is how these five very different theories end up being related.

Suppose we’re in ten spacetime dimensions, which means we have nine space and one time. Take one of those nine space dimensions and make it a circle of radius R, so that traveling in that direction for a distance L = 2πR takes you around the circle and brings you back to where you started. A particle traveling around this circle will have a quantized momentum around the circle, because its momentum is linked to its wavelength (see Wave-particle duality), and 2πR must be a multiple of that. In fact, the particle momentum around the circle - and the contribution to its energy - is of the form n/R (in standard units, for an integer n), so that at large R there will be many more states compared to small R (for a given maximum energy). A string, in addition to traveling around the circle, may also wrap around it. The number of times the string winds around the circle is called the winding number, and that is also quantized (as it must be an integer). Winding around the circle requires energy, because the string must be streched against its tension, so it contributes an amount of energy of the form , where Lst is the string length and w is the winding number (an integer). Now (for a given maximum energy) there will be many different states (with different momenta) at large R, but there will also be many different states (with different windings) at small R. In fact, a theory with large R and a theory with small R are equivalent, where the role of momentum in the first is played by the winding in the second, and vice versa. Mathematically, taking R to and switching n and w will yield the same equations. So exchanging momentum and winding modes of the string exchanges a large distance scale with a small distance scale.

This type of duality is called T-duality. T-duality relates type IIA superstring theory to type IIB superstring theory. That means if we take type IIA and Type IIB theory and compactify them both on a circle, then switching the momentum and winding modes, and switching the distance scale, changes one theory into the other. The same is also true for the two heterotic theories. T-duality also relates type I superstring theory to both type IIA and type IIB superstring theories with certain boundary conditions (termed orientifold).

Formally, the location of the string on the circle is described by two fields living on it, one which is left-moving and another which is right-moving. The movement of the string center (and hence its momentum) is related to the sum of the fields, while the string stretch (and hence its winding number) is related to their difference. T-duality can be formally described by taking the left-moving field to minus itself, so that the sum and the difference are interchanged, leading to switching of momentum and winding.

On the other hand, every force has a coupling constant, which is a measure of its strength, and determines the chances of one particle to emit or receive another particle. For electromagnetism, the coupling constant is proportional to the square of the electric charge. When physicists study the quantum behavior of electromagnetism, they can’t solve the whole theory exactly, because every particle may emit and receive many other particles, which may also do the same, endlessly. So events of emission and reception are considered as perturbations and are dealt with by a series of approximations, first assuming there is only one such event, then correcting the result for allowing two such events, etc (this method is called Perturbation theory. This is a reasonable approximation only if the coupling constant is small, which is the case for electromagnetism. But if the coupling constant gets large, that method of calculation breaks down, and the little pieces become worthless as an approximation to the real physics.

This also can happen in string theory. String theories have a coupling constant. But unlike in particle theories, the string coupling constant is not just a number, but depends on one of the oscillation modes of the string, called the dilaton. Exchanging the dilaton field with minus itself exchanges a very large coupling constant with a very small one. This symmetry is called S-duality. If two string theories are related by S-duality, then one theory with a strong coupling constant is the same as the other theory with weak coupling constant. The theory with strong coupling cannot be understood by means of perturbation theory, but the theory with weak coupling can. So if the two theories are related by S-duality, then we just need to understand the weak theory, and that is equivalent to understanding the strong theory.

Superstring theories related by S-duality are: type I superstring theory with heterotic SO(32) superstring theory, and type IIB theory with itself.

Extra dimensions

Calabi-Yau manifold (an artist’s impression)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 for a different number of dimensions, the theory has a gauge anomaly. This can be understood by noting that in a consistent theory which includes a photon (technically, a particle carrying a force related to an unbroken gauge symmetry), it must be massless. The mass of the photon which is predicted by string theory depends on the energy of the string mode which represents the photon. This energy includes a contribution from Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions since for a larger number of dimensions, there are more possible fluctuations in the string position. Therefore, the photon will be massless - and the theory consistent - only for a particular number of dimensions.

Note that the calculation of the number of dimensions can be circumvented by adding a degree of freedom which compensates for the “missing” quantum fluctuations. However, this degree of freedom behaves similar to spacetime dimensions only in some aspects, and the produced theory is not Lorentz invariant, and has other charateristics which don’t appear in nature. This is known as the linear dilaton or non-critical string.

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 (see technical details in the preprint “Quantum Geometry of Bosonic Strings - Revisited”). However, these results appear to contradict the observed four dimensional space-time.

Calabi-Yau manifold (3D projection)Two different ways have been proposed to solve this apparent contradiction. 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. Indeed, think of a ball small enough to enter the hose but not too small. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be one-dimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This “extra dimension” is only visible within a relatively close range to the hose, or if one “throws in” small enough objects. Similarly, the extra compact dimensions are only visible at extremely small distances, or by experimenting with particles with extremely small wave lengths (of the order of the compact dimension’s radius), which in quantum mechanics means very high energies (see wave-particle duality).

Another possibility is that we are stuck in a 3+1 dimensional (i.e. three spatial dimensions plus the time dimension) subspace of the full universe. This subspace is supposed to be a D-brane, hence this is known as a braneworld theory.

In either case, gravity acting in the hidden dimensions affects 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. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.

Unsolved problems in physics: Is string theory, superstring theory, or M-theory, or some other variant on this theme, a step on the road to a “theory of everything,” or just a blind alley?

Aspects of quantum field theory
Many first principles in quantum field theory are explained, or get further insight, in string theory:

Emission and absorption: one of the most basic building blocks of quantum field theory, is the notion that particles (such as electrons) can emit and absorb other particles (such as photons). Thus, an electron may just “split” into an electron plus a photon, with a certain probability (which is, roughly, the coupling constant). This is described in string theory as one string spliting into two. As is explained above (under worldsheet), this process is an integral part of the theory. The mode on the original string also “splits” between its two parts, resulting in two strings which possibly have different modes, representing two different particles.
Coupling constant: in quantum field theory this is, roughly, the probability for one particle to emit or absorb another particle, the latter typically being a gauge boson (a particle carrying a force). In string theory, the coupling constant is no longer a constant, but is rather determined by the abundance of strings in a particular mode, the dilaton. Strings in this mode couple to the worldsheet curvature of other strings, so their abundance through space-time determines the measure by which an average string worldsheet will be curved. This determines its probabilty to split or connect to other strings: the more a worldsheet is curved, it has a higher chance of splitting and reconnecting.

Spin: each particle in quantum field theory has a particuar spin s, which is an internal angular momentum. Classically, the particle rotates in a fixed frequency, but this cannot be understood if particles are point-like. In string theory spin is understood by the rotation of the string; For example, a photon with well-defined spin components (i.e. in circular polarization) looks like a tiny straight line revolving around its center.

gauge symmetry: in quantum field theory, the mathematical description of physical fields include non-physical states. In order to omit these states from the description of every physical process, a mechanism called gauge symmetry is used. This is true for string theory as well, but in string theory it is often more intuitive to understand why the non-physical states should be disposed of. The simplest example is the photon: a photon is a vector particle (it has an inner “arrow” which points to some direction - its polarization). Mathematically, it can point towards any direction in space-time. Suppose the photon is moving in the z direction; then it may either point towards the x, y or z spatial directions, or towards the t (time) direction (or any diagonal direction). Physically, however, the photon may not point towards the z or t directions (longitudinal polarization), but only in the x-y plane (transverse polarization). A gauge symmetry is used to dispose of the non-physical states. In string theory, a photon is described by a tiny oscillating line, with the axis of the line being the direction of the polarization (i.e. the inner direction of the photon is the axis of the string which the photon is made of). If we look at the worldsheet, the photon will look like a long strip which streches along the time direction with an angle towards the z-direction (because it is moving along the z-direction as time goes by); its short dimension is therefore in the x-y plane. The short dimension of this strip is precisely the direction of the photon (its polarization) in a certain moment in time. Thus the photon cannot point towards the z or t directions, and its polarization must be transverse.
Note: formally, gauge symmetries in string theory are (at least in most cases) a result of the existence of a global symmetry together with the profound gauge symmetry of string theory, which is the symmetry of the worldsheet under a local change of coordinates and scales.

renormalization: in particle physics the behaviour of particles in the smallest scales is largely known. In order to avoid this difficulty, the particles are treated as point-like objects, and a mathematical tool known as renormalization is used to describe the unknown aspects by only few parameters, which can be adjusted so that calculations give adequate results. In string theory, this is unnecessary since the behaviour of the strings is presumed to be known to every scale.
fermions: in the bosonic string, a string can be described as an elastic one-dimensional object (i.e. a line) “living” in spacetime. In superstring theory, every point of the string is not only located at some point in spacetime, but it may also have a small arrow “drawn” on it, pointing at some direction in spacetime. These arrows are described by a field “living” on the string. This is a fermionic field, because at each point of the string there is only one arrow - thus one cannot bring two arrows to the same point. This fermionic field (which is a field on the worldsheet) is ultimately responsible for the appearance of fermions in spacetime: roughly, two strings with arrows drawn on them cannot coexist at the same point in spacetime, because then one would effectively have one string with two sets of arrows at the same point, which is not allowed, as explained above.
(a technical note: this argument uses the zero picture representation, in which states of the Neveu-Schwarz sector have an even number of excited fermionic oscillators and states of the Ramond sector an odd number thereof. The spacetime statistics of states in scattering amplitudes is a consequence of their worldsheet statistics, which in the zero picture is a consequence of the number of excited fermionic oscillators)

The AdS-CFT duality
There is a conjecture that string theory on a product of a five-dimensional Anti de Sitter space and a five-dimensional sphere is dual to N=4 supersymmetric Yang-Mills theory in four dimensions.

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 is properly a mathematical theory but is not yet a physical theory. It possesses many features of mathematical interest and 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[2] 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.

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.

Another problem is the theory describes not just one but some 10500 universes, all of which can have different physical laws and constants.[3]

Testing the theory
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, such as primordial black holes.

String theory and cosmic strings
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”.

Popular culture
The book The Elegant Universe by Brian Greene, Professor of Physics at Columbia University, was adapted into a three-hour documentary for Nova and also shown on British television. It was also shown by Discovery Channel on Indian television.

String theory is also a series of books based in the Star Trek: Voyager universe.

In the TV series Angel, the character of Winifred Burkle (aka Fred) puts forward a theory about String Theory & Alternate Dimensions to the Physics Institute following her own experience of being trapped in one such delicate alternate dimension for five years. The episode which this is referenced to is “Supersymmetry”.

A theory named string theory was used in the science fiction television series Quantum Leap. In the series it relates to a theory of time travel. It views a person’s life as a string that moves from one end to the other. However, if it were possible to roll up this string into a ball it would be possible to leap from one section to another. This was the explanation given to the time travelling occurring in the series.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “String Theory”.

Samkhya, also Sankhya, (Sanskrit: सांख्य - Enumeration) is one of the schools of Indian philosophy. It is one of the six astika (that which recognizes vedic authority) systems of Hindu philosophy. It is regarded as the oldest of the orthodox philosophical systems in Hinduism, predating Buddhism of circa 500 BCE. Its philosophy regards the universe as consisting of two eternal realities: Purusha and Prakrti; it is therefore a strongly dualist and enumerationist philosophy. The Purusha is the center of consciousness, whereas the Prakriti is the source of all material existence.

The Sankhya school has deeply influenced the Hindu Yoga school of philosophy. They are sometimes referred togeather as Samkhya - yoga school. Sage Kapila is traditionally considered to be the founder of the Sankhya school, although no historical verification is possible. The definitive text of classical Sankhya is the extant Sankhya Karika, written by Ishvara Krishna, circa 200 CE.

Epistemology of Sankhya
According to the Sankhya school, knowledge is possible through three pramanas or proofs -

Pratyaksha - direct sense perception
Anumana - logical inference
Sabda - Verbal testimony

Metaphysics of Samkhya
Metaphysically, Samkhya maintains a radical duality between spirit/consciousness (Purusha) and matter (Prakrti). All physical events are considered to be manifestations of the evolution of Prakrti, or primal Nature (from which all physical bodies are derived). Each sentient being is a Purusha, and is limitless and unrestricted by its physical body. Samsaara or bondage arises when the Purusha does not have the discriminate knowledge and so is misled as to its own identity, confusing itself with the physical body - which is actually an evolute of Prakriti. The spirit is liberated when the discriminate knowledge of the difference between conscious Purusha and unconscious Prakriti is realized.

The most notable feature of Sankhya is its unique theory of Cosmic evolution (not connected with Darwin’s evolution). Sankhya theorizes that Prakriti is the source of the world of becoming. It is pure potentiality that evolves itself successively into twenty four tattvas or principles. The evolution itself is possible because Prakriti is always in a state of tension among its constituent strands -

Satva - a template of balance or equilibrium;
Rajas - a template of expansion or activity;
Tamas - a template of inertia or resistance to action.

All macrocosmic and microcosmic creation uses these templates. The twenty four principles that evolves are -

Prakriti - The most subtle potentiality that is behind whatever that is created in the physical universe.
Mahat - first product of evolution from Prakriti, pure potentiality. Mahat is also considered to be the principle responsible for the rise of buddhi or intelligence in living beings.
Ahamkara or ego-sense - second product of evolution. It is responsible for the self-sense in living beings.
Manas or instinctive mind - evolves from the satva aspect of ahamkara.
Panch jnana indriya or five sense organs - also evolves from the satva aspect of Ahamkara.
Panch karma indriya or five organs of action - The organs of action are hands, legs, vocal apparatus, urino-genital organ and anus. They too evolve from the satva aspect of Ahamkara
Panch tanmatras or five subtle elements - evolves from the Tamas aspect of Ahamkara. The subtle elements are the root energies of sound, touch, sight, taste and sound.
Panch mahabhuta or five great substances - ether, air, fire, water and earth. This is the revealed aspect of the physical universe.

The evolution of primal Nature is also considered to be purposeful - Prakrti evolves for the spirit in bondage. The spirit who is always free is only a witness to the evolution, even though due to the absence of discriminate knowledge, he misidentifies himself with it.

The evolution obeys causality relationships, with primal Nature itself being the material cause of all physical creation. The cause and effect theory of Sankhya is called Satkaarya-vaada (theory of existent causes), and holds that nothing can really be created from or destroyed into nothingness - all evolution is simply the transformation of primal Nature from one form to another.

The evolution of matter occurs when the relative strengths of the attributes changes. The evolution ceases when the spirit realises that it is distinct from primal Nature and thus cannot evolve. This destroys the purpose of evolution, thus stopping Prakrti from evolving for Purusha.

This was a dualistic philosophy. But there are differences between the Samkhya and Western forms of dualism. In the West, the fundamental distinction is between mind and body. In Samkhya, however, it is between the self (purusha) and matter, and the latter incorporates what Westerners would normally refer to as “mind”. This means that the Self as the Samkhya understands it is more transcendent than “mind”.

Samkhyan cosmology describes how life emerges in the universe; the relationship between Purusha and Prakriti is crucial to Patanjali’s yoga system. The evolution of forms at the basis of Samkhya is quite unique. The strands of Sankhyan thought can be traced back to the Vedic speculation of creation. It is also frequently mentioned in the Mahabharata and Yogavasishta.

Sankhya also has a strong cognitive theory built into it; curiously, while consciousness/spirit is considered to be radically different from any physical entities, the mind (manas), ego (ahamkara) and intellect (buddhi) are all considered to be manifestations of Prakrti (physical entity).

There is no philosophical place for a creator God in the Sankhya philosophy; indeed, the concept of God was incorporated into the Sankhya viewpoint only after it became associated with the theistic Yoga system of philosophy.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “Samkhya”.

Thermodynamic equations
Laws of thermodynamics
Zeroth law
First law
Second law
Third law
Conjugate variables
Pressure / Volume
Temperature / Entropy
Chem. potential / Particle no.
Thermodynamic potentials
Internal energy
Helmholtz free energy
Enthalpy
Gibbs free energy
Material properties
specific heat
compressibility
thermal expansion
Maxwell relations
Bridgman’s equations
Exact differential

The laws of thermodynamics in principle describe the specifics for the transport of heat and work in thermodynamic processes. Since their conception, however, these laws have become some of the most important in all of physics and many other branches of science. They are often associated with concepts far beyond what is directly stated in the wording.

Zeroth law
If systems A and B are in thermodynamic equilibrium, and systems B and C are in thermodynamic equilibrium, then systems A and C are also in thermodynamic equilibrium.

When two systems are put in contact with each other, there will be a net exchange of energy and/or matter between them unless they are in thermodynamic equilibrium. While this is a fundamental concept of thermodynamics, the need to state it explicitly as a law was not perceived until the first third of the 20th century, long after the first three laws were already widely in use, hence the zero numbering.

Thermodynamic equilibrium includes thermal equilibrium (associated to heat exchange and parameterized by temperature), mechanical equilibrium (associated to work exchange and parameterized generalized forces such as pressure), and chemical equilibrium (associated to matter exchange and parameterized by chemical potential).

First law
The increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings.

This is the statement of the conservation of energy for a thermodynamic system. It refers to the two main ways that a system transfers energy between itself and its surroundings - by the process of heating (or cooling) and the process of mechanical work. The rate of gain or loss in the internal, or stored, energy of a system is determined by the rates of these two processes. In fact, these are only the two most well known processes. Other processes (e.g. adding more particles) may contribute to the gain or loss of internal energy, and for these cases, extra terms must be included in the expression of the first law.

A second aspect of the first law is to clarify the nature of the internal energy. It is a stored quantity. The amount does not depend on which processes put it there. More generally, the amount is independent of the history of the system. If a thermodynamic system goes through changes, becoming warmer, cooler, larger, smaller, whatever, but returns to its original state, then it will have the same amount of internal energy as it did to begin with. Mathematically speaking, the internal energy is a state function and infinitesimal changes in the internal energy are exact differentials.

Second law
It is impossible to obtain a process that, operating in cycle, produces no other effect than the subtraction of a positive amount of heat from a reservoir and the production of an equal amount of work. (the so-called Kelvin-Planck Statement)

The entropy of a thermally isolated macroscopic system never decreases (see Maxwell’s demon), however a microscopic system may exhibit fluctuations of entropy opposite to that dictated by the second law (see Fluctuation Theorem). In fact the mathematical proof of the Fluctuation Theorem from time-reversible dynamics and the Axiom of Causality, constitutes a proof of the Second Law. In a logical sense the Second Law thus ceases to be a “Law” of Physics and instead becomes a theorem which is valid for large systems or long times.

Third law
As temperature approaches absolute zero, the entropy of a system approaches a constant.

Except for the first law, the laws of thermodynamics are statistical and simply describe the tendencies of macroscopic systems. For microscopic systems with few particles, the variations in the parameters become larger than the parameters themselves, and the assumptions of thermodynamics become meaningless. The first law of thermodynamics, however, i.e. the law of conservation, has become the most sound of all laws in science. Its validity has never been disproved.

Extended interpretations
The laws of thermodynamics are sometimes interpreted to have a wider significance and implication than simply encoding the experimental results upon which the science of thermodynamics is based. See, for example:

Principles of energetics
Heat Death

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “Laws of thermodynamics”.
See also: First Law of Thermodynamics and Thermodynamics

Conservation of energy
Conservation of energy is possibly the most important, and certainly the most practically useful of several conservation laws in physics.

The law states that the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. In other words, energy can be converted from one form to another, but it cannot be created or destroyed.

In thermodynamics, the first law of thermodynamics is a statement of the conservation of energy for thermodynamic systems.

The law of conservation of energy excludes the possibility of perpetuum mobile of the first kind.

Historical development
To understand the significance of the conservation of energy in the context of the development of thermodynamics, see Thermodynamics timeline Edit

Although ancient philosophers as far back as Thales of Miletus had inklings of the first law, it was the German Gottfried Wilhelm Leibniz during 1676-1689 who first attempted a mathematical formulation. Leibniz noticed that in many mechanical systems (of several masses, mi each with velocity vi) the quantity:

was conserved. He called this quantity the vis viva or living force of the system. The principle represents an accurate statement of the approximate conservation of kinetic energy in many situations. However, many physicists were influenced by the prestige of Sir Isaac Newton in England and of René Descartes in France, both of whom had set great store by the conservation of momentum as a guiding principle.

It was largely engineers such as John Smeaton, Peter Ewart, Karl Hotzmann, Gustave-Adolphe Hirn and Marc Séguin who objected that conservation of momentum alone was not adequate for practical calculation and who made use of Leibniz’s principle. The principle was also championed by some chemists such as William Hyde Wollaston.

Members of the academic establishment such as John Playfair were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the second law of thermodynamics but in the 18th and 19th centuries, the fate of the lost energy was still unknown. Gradually it came to be suspected that the heat inevitably generated by motion was another form of vis viva. In 1783, Antoine Lavoisier and Pierre-Simon Laplace reviewed the two competing theories of vis viva and caloric[1]. Count Rumford’s 1798 observations of heat generation during the boring of cannons added more weight to the view that mechanical motion could be converted into heat. Vis viva now started to be known as energy, after the term was first used in that sense by Thomas Young in 1807.

In a paper Uber die Natur der Warme, published in the Zeitschrift für Physik in 1837, Karl Friedrich Mohr gave one of the earliest general statements of the doctrine of the conservation of energy in the words: “besides the 54 known chemical elements there is in the physical world one agent only, and this is called Kraft [energy]. It may appear, according to circumstances, as motion, chemical affinity, cohesion, electricity, light and magnetism; and from any one of these forms it can be transformed into any of the others.”

A key stage in the development of the modern conservation principle was the demonstration of the mechanical equivalent of heat. The caloric theory maintained that heat could neither be created nor destroyed but conservation of energy entails the contrary principle that heat and mechanical work are interchangeable.

The mechanical equivalence principle was first stated in its modern form by the German surgeon Julius Robert von Mayer.[2] Mayer reached his conclusion on a voyage to the Dutch East Indies, where he found that his patients’ blood was a deeper red because they were consuming less oxygen, and therefore less energy, to maintain their body temperature in the hotter climate. He had discovered that heat and mechanical work were both forms of energy, and later, after improving his knowledge of physics, he calculated a quantitative relationship between them.

Joule’s apparatus for measuring the mechanical equivalent of heatMeanwhile, in 1843 James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. In the most famous, now called the “Joule apparatus”, a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the gravitational potential energy lost by the weight in descending was equal to the thermal energy (heat) gained by the water by friction with the paddle.

Over the period 1840-1843, similar work was carried out by engineer Ludwig A. Colding though it was little-known outside his native Denmark.

Both Joule’s and Mayer’s work suffered from resistance and neglect but it was Joule’s that, perhaps unjustly, eventually drew the wider recognition.

For the dispute between Joule and Mayer over priority, see Mechanical equivalent of heat: Priority
Drawing on the earlier work of Joule, Sadi Carnot and Émile Clapeyron, in 1847, Hermann von Helmholtz postulated a relationship between mechanics, heat, light, electricity and magnetism by treating them all as manifestations of a single force (energy in modern terms). He published his theories in his book Über die Erhaltung der Kraft (On the Conservation of Force, 1847). The general modern acceptance of the principle stems from this publication.

In 1877, Peter Guthrie Tait claimed that the principle originated with Sir Isaac Newton, based on a creative reading of propositions 40 and 41 of the Philosophiae Naturalis Principia Mathematica. This is now generally regarded as nothing more than an example of Whig history.

Modern physics
With the discovery of special relativity by Albert Einstein, it was found that energy is one component of an energy-momentum 4-vector. Each of the four components (one of energy and three of momentum) of this vector is separately conserved. The relativistic energy of a massive particle contains a term related to its rest mass in addition to its kinetic energy of motion. In the limit of zero kinetic energy (or equivalently in the rest frame of the massive particle), its total energy is related to its rest mass via the famous equation E = mc2. Thus, the rule of conservation of energy was shown to be a special case of a more general rule, the conservation of mass and energy, which is now usually just referred to as conservation of energy.

The conservation of energy can be shown through Noether’s theorem to be the direct consequence of nature possessing the continuous symmetry of time-translation invariance.

Within the realm of quantum mechanics, the product of the uncertainty in the measurement of energy and the uncertainty in the time interval over which the former is measured is bounded below by Planck’s constant divided by two Pi. uncertainty principle.

The first law of thermodynamics
Laws of thermodynamics
Zeroth law of thermodynamics
First law of thermodynamics
Second law of thermodynamics
Third law of thermodynamics

The first law of thermodynamics
The essence of the First Law of Thermodynamics declares: energy cannot be destroyed. The first law of thermodynamics basically states that an isolated thermodynamic system can store or hold energy and that this internal energy is conserved. Heat is a process by which energy is added to a system from a high-temperature heat source, or lost to a low-temperature heat sink. In addition, energy may be lost by the system when it does mechanical work on its surroundings, or conversely, it may gain energy as a result of work done on it by its surroundings. The first law states that this energy is conserved: The change in the internal energy is equal to the amount added by heating minus the amount lost by doing work on the environment.

Notes
Lavoisier, A.L. & Laplace, P.S. (1780) “Memoir on Heat”, Académie Royal des Sciences pp4-355 von Mayer, J.R. (1842) “Remarks on the forces of inorganic nature” in Annalen der Chemie und Pharmacie, 43, 233

References

Modern accounts
Kroemer, Herbert; Kittle, Charles (1980). Thermal Physics (2nd ed.), W. H. Freeman Company. ISBN 0716710889.
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed., William C. Brown Publishers.
Oxtoby & Nachtrieb (1996). Principles of Modern Chemistry, 3rd ed., Saunders College Publishing.
Papineau, D. (2002). Thinking about Consciousness, Oxford University Press: Oxford.
Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.), Brooks/Cole. ISBN 0534408427.
Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.), W. H. Freeman. ISBN 0716708094.

History of ideas
Cardwell, D.S.L. (1971). From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age, Heinemann: London. ISBN 0435541501.
Guillen, M. (1999). Five Equations That Changed the World. ISBN 0349110646.
Hiebert, E.N. (1981). Historical Roots of the Principle of Conservation of Energy, Ayer Co Pub. ISBN 0405138806.
Kuhn, T.S. (1957) “Energy conservation as an example of simultaneous discovery”, in M. Clagett (ed.) Critical Problems in the History of Science pp.321–56
Smith, C. (1998). The Science of Energy: Cultural History of Energy Physics in Victorian Britain, Heinemann: London. ISBN 0485114313.

Classic accounts
Mach, E. (1872). History and Root of the Principles of the Conservation of Energy, Open Court Pub. Co., IL.
Poincaré, H. (1905). Science and Hypothesis, Walter Scott Publishing Co. Ltd; Dover reprint, 1952. ISBN 0486602214., Chapter 8, “Energy and Thermo-dynamics”

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “Conservation of Energy”.

Osho: The Path of Yoga - Part 1

We live in a deep illusion — the illusion of hope, of future, of tomorrow. As man is, man cannot exist without self-deception.

Nietzsche says somewhere that man cannot live with the true: he needs dreams, he needs illusions, he needs lies to exist. And Nietzsche is true. As man is he cannot exist with the truth. This has to be understood very deeply, because without understanding it there can be no entry into the inquiry which is called Yoga.

The mind has to be understood deeply — the mind which needs lies, the mind which needs illusions, the mind which cannot exist with the real, the mind which needs dreams. You are not only dreaming in the night; even while awake you are continuously dreaming. You may be looking at me, you may be listening to me, but a dream current goes on within you. The mind is continuously creating dreams, images, fantasies.

Now scientists say that a man can live without sleep but he cannot live without dreams. In the old days it was understood that sleep was a necessity, but now modern research says sleep is not really a necessity; sleep is needed only so that you can dream. Dreaming is the necessity. If you are allowed to sleep but not allowed to dream, you will not feel fresh, alive, in the morning. You will feel tired, as if you have not been able to sleep at all.

In the night there are periods — periods for deep sleep and periods for dreaming. There is a rhythm, just like day and night. There is a rhythm: in the beginning you fall into deep sleep for near about forty, forty-five minutes, then the dream phase comes in; then you dream; then again dreamless sleep, then again dreaming. This goes on the whole night. If your sleep is disturbed while you are deeply asleep without dreaming, in the morning you will not feel that you have missed anything. But while you are dreaming if your dream is disturbed then in the morning you will feel completely tired, exhausted.

Now this can be known from the outside. If someone is sleeping you can judge whether he is dreaming or asleep. If he is dreaming his eyes will be continuously moving, as if he is seeing something with closed eyes. When he is fast asleep the eyes will not move; they will remain steady. So if your sleep is disturbed while your eyes are moving, in the morning you will feel tired. While your eyes are not moving sleep can be disturbed; in the morning you will not feel anything is missing.

Many researchers have proved that the human mind feeds on dreams; dreaming is a necessity, and dreaming is total auto-deception. And this is so not only in the night: while awake also the same pattern follows. Even in the day you can notice — sometimes there will be dreams floating in the mind, sometimes there will be no dreams.

When there are dreams you will be doing something but you will be absent. Inside you are occupied. For example, you are here. If your mind is passing through a dream-state you will listen to me without listening at all, because your mind will be occupied within. If you are not in a dreaming state, only then can you listen to me.

Day and night, mind goes on moving from no-dream to dream, then from dream to no-dream again. This is an inner rhythm.

Not only do we continuously dream, in life also we project hopes into the future.

The present is almost always a hell: you can prolong this hell only because of the hope that you have projected into the future. You can live today because of the tomorrow. You are hoping something is going to happen tomorrow — some doors of paradise will open tomorrow. They never open today, and when tomorrow will come it will not come as tomorrow, it will come as today, but by that time your mind has moved again. You go on moving ahead of you: this is what dreaming means. You are not one with the real, that which is nearby, that which is here and now, you are somewhere else — moving ahead, jumping ahead.

And that tomorrow, that future, you have named it in so many ways. People call it heaven, some people call it moksha, but it is always in the future. Somebody is thinking in terms of wealth, but that wealth is going to be in the future. And somebody is thinking in terms of paradise, and that paradise is going to be after you are dead — far away in the future. You waste your present for that which is not: this is what dreaming means. You cannot be here and now. To be just in the moment seems to be arduous.

You can be in the past, because again that is dreaming — memories, remembrance of things which are no more — or you can be in the future, which is projection, which again is creating something out of the past. The future is nothing but the past projected again — more colorful, more beautiful, more pleasant, but it is the past refined.

You cannot think anything other than the past: the future is nothing but the past projected again — and both are not. The present is, but you are never in the present. This is what dreaming means. And Nietzsche is right when he says that man cannot live with the truth. He needs lies, he lives through lies. Nietzsche says that we go on saying that we want the truth, but no one wants it. Our so-called truths are nothing but lies, beautiful lies. No one is ready to see the naked reality.

This mind cannot enter on the path of Yoga because Yoga means a methodology to reveal the truth. Yoga is a method to come to a non-dreaming mind. Yoga is the science to be in the here and now. Yoga means now you are ready not to move into the future. Yoga means now you are ready not to hope, not to jump ahead of your being.

Yoga means to encounter the reality as it is.

So one can enter Yoga, or the path of Yoga, only when he is totally frustrated with his own mind as it is. If you are still hoping that you can gain something through your mind, Yoga is not for you. A total frustration is needed — the revelation that this mind which projects is futile, the mind that hopes is nonsense, it leads nowhere. It simply closes your eyes, it intoxicates you, it never allows reality to be revealed to you. It protects you against reality.

Your mind is a drug. It is against that which is. So unless you are totally frustrated with your mind, with your way of being, with the way you have existed up to now…if you can drop it unconditionally, then you can enter on the path.

So many become interested but very few enter, because your interest may be just because of your mind. You may be hoping that now, through Yoga, you may gain something, but the achieving motive is there — that you may become perfect through Yoga, you may reach to the blissful state of perfect being, you may become one with the Brahman, you may achieve the satchitananda…. This may be the cause of why you are interested in Yoga. If this is the cause then there can be no meeting between you and the path which is Yoga. Then you are totally against it, moving in a totally opposite dimension.

Yoga means: “Now no hope, now no future, now no desires. But I am ready to know what is. I am not interested in what can be, what should be, what ought to be. I am not interested! I am interested only in that which is” — because only the real can free you, only the reality can become liberation.

Total despair is needed. That despair is called dukkha by Buddha. If you are really in misery don’t hope, because your hope will only prolong the misery. Your hope is a drug. It can help you to continue, but where are you moving? It will help you to reach only death and nowhere else. All your hopes can lead you only to death — they are leading.

Become totally hopeless — no future, no hope. Difficult…it needs courage to face the real. But such a moment comes to everyone, sometime or other. A moment comes to every human being when he feels total hopelessness. Absolute meaninglessness happens to him. When he becomes aware that whatsoever he is doing is useless, wheresoever he is going he is going to nowhere, all life is meaningless — suddenly hopes drop. Future drops, and for the first time you are in tune with the present, for the first time you are face to face with reality.

Unless this moment comes to you…you can go on doing asanas, postures; that is not Yoga. Yoga is an inward turning. It is a total about-turn. When you are not moving into the future, not moving towards the past, then you start moving within yourself — because your being is here and now, it is not in the future. You are present here and now, you can enter this reality. But then mind has to be here.

This moment is indicated by the first sutra of Patanjali. Before we talk about the first sutra, a few other things have to be understood.

Yoga is not a religion, remember that. Yoga is not Hindu, it is not Mohammedan. Yoga is a pure science just like mathematics, physics or chemistry. Physics is not Christian, physics is not Buddhist. If Christians have discovered the laws of physics, then too physics is not Christian. It is just accidental that Christians have come to discover the laws of physics. But physics remains just a science. Yoga is a science — it is just an accident that Hindus discovered it. It is not Hindu. It is a pure mathematics of the inner being. So a Mohammedan can be a yogi, a Christian can be a yogi, a Jaina, a Buddhist can be a yogi.

Yoga is pure science.

And Patanjali is the greatest name as far as the world of Yoga is concerned. This man is rare — there is no other name comparable to Patanjali. For the first time in the history of humanity this man brought religion to the status of a science. He made religion a science: pure laws, no belief is needed.

So-called religions need beliefs. There is no other difference between one religion and another; the difference is only of beliefs. A Mohammedan has certain beliefs, a Hindu certain others, a Christian certain others. The difference is of beliefs. Yoga has nothing as far as belief is concerned; Yoga doesn’t say to believe in anything. Yoga says “Experience.” Just as science says “Experiment,” Yoga says “Experience.” Experiment and experience are both the same; their directions are different. Experiment means there is something you can do outside; experience means there is something you can do inside. Experience is an inner experiment.

Science says, “Don’t believe, doubt as much as you can,” but also, “Don’t disbelieve” — because disbelief is again a sort of belief. You can believe in God, you can believe in the concept of no-God. You can say, “God is” with a fanatic attitude; you can say quite the reverse, that “God is not,” with the same fanaticism. Atheists, theists, are all believers, and belief is not the realm for science. Science means to experience something, that which is; no belief is needed.

So the second thing to remember is that Yoga is existential, experiential, experimental. No belief is required, no faith is needed — only courage to experience — and that’s what is lacking. You can believe easily because in belief you are not going to be transformed. Belief is something added to you, something superficial. Your being is not changed, you are not passing through some mutation. You may be a Hindu — you can become a Christian the next day. You simply change, you change the Gita for a Bible. You can change it for a Koran, but the man who was holding the Gita and is now holding the Bible remains the same. He has changed his beliefs.

Beliefs are like clothes. Nothing substantial is transformed, you remain the same. Dissect a Hindu, dissect a Mohammedan — inside they are the same. The Hindu goes to a temple, the Mohammedan hates the temple. The Mohammedan goes to the mosque and the Hindu hates the mosque but inside they are the same human beings.

Belief is easy because you are not really required to do anything, just a superficial dressing, a decoration, something which you can put aside any moment you like. Yoga is not belief; that’s why it is difficult, arduous — and sometimes it seems impossible. It is an existential approach. You will come to the truth not through belief but through your own experience, through your own realization. That means you will have to be totally changed — your viewpoints, your way of life, your mind; your psyche as it is has to be shattered completely. Something new has to be created. Only with that new will you come in contact with the reality.

So Yoga is both a death and a new life. As you are you will have to die, and unless you die the new cannot be born. The new is hidden in you. You are just a seed for it and the seed must fall down, be absorbed by the earth. The seed must die, only then will the new arise out of you. Your death will become your new life. Yoga is both a death and a new birth. Unless you are ready to die you cannot be reborn. So it is not a question of changing beliefs.

Yoga is not a philosophy.

I say it is not a religion and I say it is not a philosophy. It is not something you can think about. It is something you will have to be; thinking won’t do. Thinking goes on in your head. It is not really deep into the roots of your being, it is not your totality. It is just a part, a functional part. It can be trained and you can argue logically, you can think rationally, but your heart will remain the same. Your heart is your deepest center, your head is just a branch. You can be without the head but you cannot be without the heart. Your head is not basic.

Yoga is concerned with your total being, with your roots. It is not philosophical. So with Patanjali we will not be thinking, speculating. With Patanjali we will be trying to know the ultimate laws of being, the laws for its transformation, the laws of how to die and how to be reborn again, the laws for a new order of being. That is why I call it a science.

Patanjali is rare. He is an enlightened person like Buddha, like Krishna, like Christ, like Mahavira, Mohammed, Zarathustra, but he is different in one way. Buddha, Krishna, Mahavira, Zarathustra, Mohammed — none of them has a scientific attitude. They are great founders of religions. They have changed the whole pattern of the human mind and its structure, but their approach is not scientific.

Patanjali is like an Einstein in the world of buddhas. He is a phenomenon. He could easily have been a Nobel Prize winner like an Einstein or Bohr or Max Planck or Heisenberg. He has the same attitude, the same approach as a rigorous, scientific mind. He is not a poet; Krishna is a poet. He is not a moralist; Mahavira is a moralist. He is basically a scientist who is thinking in terms of laws. And he has come to deduce absolute laws of the human being, the ultimate working structure of the human mind and of reality.

And if you follow Patanjali you will come to know that he is as exact as any mathematical formula. Simply do what he says and the result will happen. The result is bound to happen — it is just like two plus two become four; it is just like you heat water up to one hundred degrees and it evaporates. No belief is needed, you simply do it and know. It is something to be done and known. That’s why I say there is no comparison: never again has a man existed on this Earth like Patanjali.

You can find poetry in Buddha’s utterances; it is bound to be there. Many times while Buddha is expressing himself he becomes poetic. The realm of ecstasy, the realm of ultimate knowing is so beautiful, the temptation is so strong to become poetic…the beauty is such, the benediction is such, the bliss is such that one starts talking in poetic language.

But Patanjali resists that. It is very difficult, no one else has been able to resist. Jesus, Krishna, Buddha, they all became poetic. When the splendor, the beauty explode within you, you will start dancing, you will start singing. In that state you are just like a lover who has fallen in love with the whole universe.

Patanjali resists that. He will not use poetry; he will not even use a single poetic symbol. He will not do anything with poetry. He will not talk in terms of beauty: he will talk in terms of mathematics, he will be exact. And he will give you maxims — those maxims are just indications of what is to be done. He will not explode into ecstasy, he will not say things that cannot be said, he will not try the impossible. He will just put down the foundation and if you follow the foundation you will reach the peak which is beyond. He is a rigorous mathematician, remember this.

The first sutra: Now the discipline of Yoga.

Athayoganushasanam: Now the discipline of Yoga.

Each single word has to be understood, because Patanjali will not use a single superfluous word.

Now the discipline of Yoga…. First try to understand the word “now.” This “now” is an indication to the state of mind I was just talking to you about.

If you are disillusioned, if you are hopeless, if you have completely become aware of the futility of all desires; if you see your life as meaningless; whatsoever you have been doing up to now has simply fallen dead…. Nothing remains in the future, you are in absolute despair — what Kierkegaard calls anguish — you are in anguish, suffering…. Not knowing what to do, not knowing where to go, not knowing to whom to turn, just on the verge of madness or suicide or death, your whole pattern of life has suddenly become futile…. If this moment has come, Patanjali says, “Now the discipline of Yoga” — only now can you understand the science of Yoga, the discipline of Yoga.

If that moment has not come you can go on studying Yoga: you can become a great scholar but you will not be a yogi. You can write theses on it, you can give discourses on it, but you will not be a yogi. The moment has not come for you. Intellectually you can become interested, through your mind you can be related to Yoga, but Yoga is nothing if it is not a discipline. Yoga is not a shastra; it is not a scripture. It is a discipline, it is something you have to do. It is not curiosity, it is not philosophical speculation. It is deeper than that — it is a question of life and death.

If the moment has come when you feel that all directions have become confused, all roads have disappeared, the future is dark and every desire has become bitter and through every desire you have known only disappointment, all movement into hopes and dreams has ceased: Now the discipline of Yoga.

This “now” may not have come. Then I may go on talking about Yoga but you will not listen. You can listen only if the moment is present in you. Are you really dissatisfied? Everybody will say yes, but that dissatisfaction is not real. You are dissatisfied with this, you may be dissatisfied with that, but you are not totally dissatisfied. You are still hoping. You are dissatisfied because of your past hopes but you are still hoping for the future. Your dissatisfaction is not total: you are still hankering for some satisfaction somewhere, for some gratification somewhere.

Sometimes you feel hopeless but that hopelessness is not true. You feel hopeless because certain hopes have not been achieved, certain hopes have fallen away — but hoping is still there, hoping has not fallen away. You will still hope. You are dissatisfied with this hope, that hope, but you are not dissatisfied with hope as such. If you are disappointed with hope as such the moment has come, and then you can enter Yoga. And then this entry will not be an entering into a mental, speculative phenomenon. This entry will be an entry into a discipline.

What is discipline?

Discipline means what creates an order within you. As you are you are a chaos. As you are you are totally disorderly. Gurdjieff used to say — and Gurdjieff is in many ways like Patanjali, he was again trying to make the core of religion a science…. Gurdjieff said that you are not one, you are a crowd; not even when you say “I,” is there any I. There are many I’s in you, many egos. In the morning one I, in the afternoon another I, in the evening a third I, but you never become aware of this mess — because who will become aware of it? There is not a center that can become aware.

The discipline of Yoga means Yoga wants to create a crystallized center in you. As you are you are a crowd and a crowd has many phenomena. One is that you cannot believe a crowd. Gurdjieff used to say that man cannot promise. Who will promise? You are not there. If you promise who will fulfill the promise? Next morning the one who promised is no more.

People come to me and they say, “Now I will take the vow. I promise to do this,” and I tell them, “Think twice before you promise something. Are you confident that the next moment the one who promised it will be there?” You decide from tomorrow to get up early in the morning at four o’clock, and at four o’clock somebody in you says, “Don’t bother. It is so cold outside. And why are you in such a hurry? We can do it tomorrow” — and you fall asleep again. When you get up you repent and you think, “This is not good. I should have done it.” You decide again, “Tomorrow I will do it”; and the same is going to happen tomorrow because at four in the morning the one who promised is no more there, somebody else is in the chair. You are a Rotary Club: the chairman goes on changing and every member becomes a Rotary chairman. There is rotation: every moment someone else is the master.

Gurdjieff used to say, “This is the chief characteristic of man — that he cannot promise.” You cannot fulfill a promise. You go on giving promises, and you know well that you cannot fulfill them because you are not one; you are a disorder, a chaos. Hence Patanjali says, “Now the discipline of Yoga.” If your life has become an absolute misery, if you have realized that whatsoever you do creates hell, then the moment has come. This moment can change your dimension, your direction of being.

Up until now you have lived as a chaos, a crowd. Yoga means now you will have to be a harmony, you will have to become one. A crystallization is needed, a centering is needed. And unless you attain a center all that you do is useless; it is wasting life and time. A center is the first necessity, and