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Perpetual Motion Machine

In Uncategorized on April 3, 2011 by Swami Uddipayan

Perpetual motion describes hypothetical machines that operate or produce useful work indefinitely and, more generally, hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not.

There is undisputed scientific consensus that perpetual motion would violate either the first law of thermodynamics, the second law of thermodynamics, or both. Machines which comply with both laws of thermodynamics but access energy from obscure sources are sometimes referred to as perpetual motion machines, although they do not meet the standard criteria for the name.

Despite the fact that successful perpetual motion devices are physically impossible in terms of our current understanding of the laws of physics, the pursuit of perpetual motion remains popular.

Basic principles

The zeroth law of thermodynamics is a generalization principle of thermal equilibrium among bodies, or thermodynamic systems, in contact.

The zeroth law states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

The first law of thermodynamics is an expression of the principle of conservation of energy.

The law expresses that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed. It is usually formulated by stating that the change in the internal energy of a system is equal to the amount of heat supplied to the system, minus the amount of work performed by the system on its surroundings.

The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and explains the phenomenon of irreversibility in nature. The second law declares the impossibility of machines that generate usable energy from the abundant internal energy of nature by processes called perpetual motion of the second kind.

A change in the entropy (S) of a system is the infinitesimal transfer of heat (Q) to a closed system driving a reversible process, divided by the equilibrium temperature (T) of the system.

The entropy of an isolated system that is in equilibrium is constant and has reached its maximum value.

There is an undisputed scientific consensus that perpetual motion violates either the first law of thermodynamics, the second law of thermodynamics, or both. The first law of thermodynamics is essentially a statement of conservation of energy. The second law can be phrased in several different ways, the most intuitive of which is that heat flows spontaneously from hotter to colder places; the most well-known statement is that entropy tends to increase, or at the least stay the same; another statement is that no heat engine (an engine which produces work while moving heat between two separate places) can be more efficient than a Carnot heat engine.

Machines which comply with both laws of thermodynamics by accessing energy from unconventional sources are sometimes referred to as perpetual motion machines, although they do not meet the standard criteria for the name. By way of example, clocks and other low-power machines, such as Cox’s timepiece, have been designed to run on the differences in barometric pressure or temperature between night and day. These machines have a source of energy, albeit one which is not readily apparent so that they only seem to violate the laws of thermodynamics.

Classification

One classification of perpetual motion machines refers to the particular law of thermodynamics the machines purport to violate:
A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.
A perpetual motion machine of the second kind is a machine which spontaneously converts thermal energy into mechanical work. When the thermal energy is equivalent to the work done, this does not violate the law of conservation of energy. However it does violate the more subtle second law of thermodynamics (see also entropy). The signature of a perpetual motion machine of the second kind is that there is only one heat reservoir involved, which is being spontaneously cooled without involving a transfer of heat to a cooler reservoir. This conversion of heat into useful work, without any side effect, is impossible, according to the second law of thermodynamics.

A more obscure category is a perpetual motion machine of the third kind, usually (but not always) defined as one that completely eliminates friction and other dissipative forces, to maintain motion forever (due to its mass inertia). Third in this case refers solely to the position in the above classification scheme, not the third law of thermodynamics. Although it is impossible to make such a machine, as dissipation can never be 100% eliminated in a mechanical system, it is nevertheless possible to get very close to this ideal (see examples in the Low Friction section). Such a machine would not serve as a source of energy but would have utility as a perpetual energy storage device.

Use of the term “impossible” and perpetual motion

While the laws of physics are incomplete and stating that physical things are absolutely impossible is un-scientific, “impossible” is used in common parlance to describe those things which absolutely cannot occur within the context of our current formulation of physical laws.

The conservation laws are particularly robust from a mathematical perspective. Noether’s theorem, which was proven mathematically in 1915, states that any conservation law can be derived from a corresponding continuous symmetry of the action of a physical system. This means that if the laws of physics (not simply the current understanding of them, but the actual laws, which may still be undiscovered) and the various physical constants remain invariant over time — if the laws of the universe are fixed — then the conservation laws must hold. On the other hand, if the conservation laws are invalid, then much of modern physics would be incorrect as well.

Scientific investigations as to whether the laws of physics are invariant over time use telescopes to examine the universe in the distant past to discover, to the limits of our measurements, whether ancient stars were identical to stars today. Combining different measurements such as spectroscopy, direct measurement of the speed of light in the past and similar measurements demonstrates that physics has remained substantially the same, if not identical, for all of observable history spanning billions of years.

The principles of thermodynamics are so well established, both theoretically and experimentally, that proposals for perpetual motion machines are universally met with disbelief on the part of physicists. Any proposed perpetual motion design offers a potentially instructive challenge to physicists: one is almost completely certain that it can’t work, so one must explain how it fails to work. The difficulty (and the value) of such an exercise depends on the subtlety of the proposal; the best ones tend to arise from physicists’ own thought experiments and often shed light upon certain aspects of physics.

The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. — Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)

Thought experiments

Serious work in theoretical physics often involves thought experiments that expand our understanding of physical laws. Some thought experiments involve apparent perpetual motion machines, questioning why they either work or do not work in compliance with the laws of physics.
Maxwell’s demon: A thought experiment which led to physicists considering the interaction between entropy and information.
Feynman’s “Brownian ratchet”: A “perpetual motion” machine which extracts work from thermal fluctuations and appears to run forever but really only runs as long as the environment is warmer than the ratchet.

Techniques

“One day man will connect his apparatus to the very wheelwork of the universe […] and the very forces that motivate the planets in their orbits and cause them to rotate will rotate his own machinery.
” —Nikola Tesla

Some common ideas recur repeatedly in perpetual motion machine designs. Many ideas that continue to appear today were stated as early as 1670 by John Wilkins, Bishop of Chester and an official of the Royal Society. He outlined three potential sources of power for a perpetual motion machine, “Chemical Extractions”, “Magnetical Virtues” and “the Natural Affection of Gravity”.

The seemingly mysterious ability of magnets to influence motion at a distance without any apparent energy source has long appealed to inventors. One of the earliest examples of a system using magnets was proposed by Wilkins and has been widely copied since: it consists of a ramp with a magnet at the top, which pulled a metal ball up the ramp. Near the magnet was a small hole that was supposed to allow the ball to drop under the ramp and return to the bottom, where a flap allowed it to return to the top again. The device simply could not work: any magnet strong enough to pull the ball up the ramp would necessarily be too powerful to allow it to drop through the hole. Faced with this problem, more modern versions typically use a series of ramps and magnets, positioned so the ball is to be handed off from one magnet to another as it moves. The problem remains the same.

Perpetuum Mobile of Villard de Honnecourt (about 1230).
Gravity also acts at a distance, without an apparent energy source. But to get energy out of a gravitational field (for instance, by dropping a heavy object, producing kinetic energy as it falls) you have to put energy in (for instance, by lifting the object up), and some energy is always dissipated in the process. A typical application of gravity in a perpetual motion machine is Bhaskara’s wheel in the 12th century, whose key idea is itself a recurring theme, often called the overbalanced wheel: Moving weights are attached to a wheel in such a way that they fall to a position further from the wheel’s center for one half of the wheel’s rotation, and closer to the center for the other half. Since weights further from the center apply a greater torque, the result is (or would be, if such a device worked) that the wheel rotates forever. The moving weights may be hammers on pivoted arms, or rolling balls, or mercury in tubes; the principle is the same.

Yet another theoretical machine involves a frictionless environment for motion. This involves the use of diamagnetic or electromagnet levitation to float an object. This is done in a vacuum to eliminate air friction and friction from an axle. The levitated object is then free to rotate around its center of gravity without interference. However, this machine has no practical purpose because the rotated object cannot do any work as work requires the levitated object to cause motion in other objects, bringing friction into the problem.

To extract work from heat, thus producing a perpetual motion machine of the second kind, the most common approach (dating back at least to Maxwell’s demon) is unidirectionality. Only molecules moving fast enough and in the right direction are allowed through the demon’s trap door. In a Brownian ratchet, forces tending to turn the ratchet one way are able to do so while forces in the other direction aren’t. A diode in a heat bath allows through currents in one direction and not the other. These schemes typically fail in two ways: either maintaining the unidirectionality costs energy (Maxwell’s demon needs light to look at all those particles and see what they’re doing)[dubious – discuss], or the unidirectionality is an illusion and occasional big violations make up for the frequent small non-violations (the Brownian ratchet will be subject to internal Brownian forces and therefore will sometimes turn the wrong way).

History of perpetual motion machines

Orffyreus Wheel. The device was designed by Johann Bessler.
The 8th century Bavarian “magic wheel” was a disc mounted on an axle powered by lodestones, claimed to be able to rotate forever.

Indian mathematician-astronomer, Bhāskara II, described a wheel, dating to 1150 that would run forever.

Villard de Honnecourt in 1235 described, in a 33 page manuscript, a perpetual motion machine of the first kind. His idea was based on the changing torque of a series of weights attached with hinges to the rim of a wheel. While ascending they would hang close to the wheel and have little torque, but they would topple after reaching the top and drag the wheel down on descent due to their greater torque during the swing. His device spawned a variety of imitators who continued to refine the basic design.

Following the example of Villard, Peter of Maricourt designed a magnetic globe which when mounted without friction parallel to the celestial axis would rotate once a day and serve as an automatic armillary sphere.

In 1607 Cornelius Drebbel in “Wonder-vondt van de eeuwighe bewegingh” dedicated a Perpetuum motion machine to James I of England. It was described by Heinrich Hiesserle von Chodaw in 1621. Also in the 17th century, Robert Boyle’s proposed self-flowing flask purports to fill itself through siphon action and Blaise Pascal introduced a primitive form of roulette and the roulette wheel in his search for a perpetual motion machine.

In the 18th century, Johann Bessler (also known as Orffyreus) created a series of claimed perpetual motion machines. In 1775 the Royal Academy of Sciences in Paris issued the statement that the Academy “will no longer accept or deal with proposals concerning perpetual motion”.

In the 19th century, the invention of perpetual motion machines became an obsession for many scientists. Many machines were designed based on electricity. John Gamgee developed the Zeromotor, a perpetual motion machine of the second kind. Devising these machines is a favourite pastime of many eccentrics, who often devised elaborate machines in the style of Rube Goldberg or Heath Robinson. Such designs appeared to work on paper, though various flaws or obfuscated external energy sources are eventually understood to have been incorporated into the machine (unintentionally or intentionally).

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Articles

ATOMIC ORBITAL MODEL

In Uncategorized on April 3, 2011 by Swami Uddipayan

ATOMIC ORBITAL MODEL

The atomic orbital model is the currently accepted model of the placement of electrons in an atom. It is sometimes called the wave mechanics model. In the atomic orbital model, the atom consists of a nucleus surrounded by orbiting electrons. These electrons exist in atomic orbitals, which are a set of quantum states of the negatively charged electrons trapped in the electrical field generated by the positively charged nucleus. The atomic orbital model can only be described by quantum mechanics, in which the electrons are most accurately described as standing waves surrounding the nucleus.

Despite the obvious analogy to planets revolving around the Sun, electrons cannot be described as solid particles. In addition, atomic orbitals do not closely resemble a planet’s elliptical path in ordinary atoms. A more accurate analogy might be that of a large and often oddly-shaped “atmosphere” (the electron), distributed around a relatively tiny planet (the atomic nucleus). One difference is that some of an atom’s electrons have zero angular momentum, so they cannot in any sense be thought of as moving “around” the nucleus, as a planet does. Other electrons do have varying amounts of angular momentum.

An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom’s nucleus. These functions may serve as three-dimensional graphs of an electron’s likely location. The term may thus refer directly to the physical region defined by the function where the electron is likely to be. Specifically, atomic orbitals are the possible quantum states of an individual electron in the collection of electrons around a single atom, as described by the orbital function.

Atomic orbitals exactly describe the shape of this “atmosphere” only when a single electron is present in an atom. When more electrons are added to a single atom, the additional electrons tend to more evenly fill in a volume of space around the nucleus so that the resulting collection (sometimes termed the atom’s “electron cloud” tends toward a generally spherical zone of probability describing where the atom’s electrons will be found.

The idea that electrons might revolve around a compact nucleus with definite angular momentum was convincingly argued in 1913 by Niels Bohr, and the Japanese physicist Hantaro Nagaoka published an orbit-based hypothesis for electronic behavior as early as 1904. However, it was not until 1926 that the solution of the Schrödinger equation for electron-waves in atoms provided the functions for the modern orbitals.

Because of the difference from classical mechanical orbits, the term “orbit” for electrons in atoms, has been replaced with the term orbital—a term first coined by chemist Robert Mulliken in 1932. Atomic orbitals are typically described as “hydrogen-like” (meaning one-electron) wave functions over space, categorized by n, l, and m quantum numbers, which correspond to the electrons’ energy, angular momentum, and an angular momentum direction, respectively. Each orbital is defined by a different set of quantum numbers and contains a maximum of two electrons. The simple names s orbital, p orbital, d orbital and f orbital refer to orbitals with angular momentum quantum number l = 0, 1, 2 and 3 respectively. These names indicate the orbital shape and are used to describe the electron configurations as shown on the right. They are derived from the characteristics of their spectroscopic lines: sharp, principal, diffuse, and fundamental, the rest being named in alphabetical order (omitting j).

In the mathematics of atomic physics, it is also often convenient to reduce the electron functions of complex systems into combinations of the simpler atomic orbitals. Although each electron in a multi-electron atom is not confined to one of the “one-or-two-electron atomic orbitals” in the idealized picture above, still the electron wave-function may be broken down into combinations which still bear the imprint of atomic orbitals; as though, in some sense, the electron cloud of a many-electron atom is still partly “composed” of atomic orbitals, each containing only one or two electrons. The physicality of this view is still best-illustrated in the repetitive nature of the chemical and physical behavior of elements which results in the natural ordering known from the 19th century as the periodic table of the elements. Niels Bohr was the first to propose (1923) that the periodicity in the properties of the elements might be explained by the periodic filling of the electron energy levels, resulting in the electronic structure of the atom. In this view, pairs of electrons are arranged in simple repeating patterns of increasing odd numbers (1,3,5,7..), suggesting something like what we now recognize as atomic orbitals within the total electron configuration of complex atoms. In this ordering, the repeating periodicity of the blocks of 2, 6, 10, and 14 elements in the periodic table, corresponds with the total number of electrons which occupy a complete set of s, p, d and f atomic orbitals, respectively.

Introduction

With the development of quantum mechanics, it was found that the orbiting electrons around a nucleus could not be fully described as particles, but needed to be explained by the wave-particle duality. In this sense, the electrons have the following properties:

Wave-like properties

The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves. The lowest possible energy an electron can take is therefore analogous to the fundamental frequency of a wave on a string. Higher energy states are then similar to harmonics of the fundamental frequency.

The electrons are never in a single point location, although the probability of interacting with the electron at a single point can be found from the wavefunction of the electron.

Particle-like properties

There is always an integer number of electrons orbiting the nucleus.

Electrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon.

The electrons retain particle like-properties such as: each wave state has the same electrical charge as the electron particle. Each wave state has a single discrete spin (spin up or spin down).

Orbital names

Orbitals are given names in the form:

where X is the energy level corresponding to the principal quantum number n, type is a lower-case letter denoting the shape or subshell of the orbital and it corresponds to the angular quantum number l, and y is the number of electrons in that orbital.

For example, the orbital 1s2 (pronounced “one ess two”) has two electrons and is the lowest energy level (n = 1) and has an angular quantum number of l = 0. In X-ray notation, the principal quantum number is given a letter associated with it. For n = 1, 2, 3, 4, 5, …, the letters associated with those numbers are K, L, M, N, O, … respectively.

Formal quantum mechanical definition

In quantum mechanics, the state of an atom, i.e. the eigenstates of the atomic Hamiltonian, is expanded (see configuration interaction expansion and basis set) into linear combinations of anti-symmetrized products (Slater determinants) of one-electron functions. The spatial components of these one-electron functions are called atomic orbitals. (When one considers also their spin component, one speaks of atomic spin orbitals.)

In atomic physics, the atomic spectral lines correspond to transitions (quantum leaps) between quantum states of an atom. These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated to particular electron configurations, i.e. by occupations schemes of atomic orbitals (e.g. 1s2 2s2 2p6 for the ground state of neon — term symbol: 1S0).

This notation means that the corresponding Slater determinants have a clear higher weight in the configuration interaction expansion. The atomic orbital concept is therefore a key concept for visualizing the excitation process associated to a given transition. For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital. Nevertheless one has to keep in mind that electrons are fermions ruled by the Pauli exclusion principle and cannot be distinguished from the other electrons in the atom. Moreover, it sometimes happens that the configuration interaction expansion converges very slowly and that one cannot speak about simple one-determinantal wave function at all. This is the case when electron correlation is large.

Fundamentally, an atomic orbital is a one-electron wavefunction, even though most electrons do not exist in one-electron atoms, and so the one-electron view is an approximation. When thinking about orbitals, we are often given an orbital vision which (even if it is not spelled out) is heavily influenced by this Hartree–Fock approximation, which is one way to reduce the complexities of molecular orbital theory.

Connection to uncertainty relation

Immediately after Heisenberg formulated his uncertainty relation, it was noted by Bohr that the existence of any sort of wave packet implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet itself. In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space. In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy. In quantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packet requires a larger and larger range of momenta, and thus larger kinetic energy. Thus, the binding energy to contain or trap a particle in a smaller region of space, increases without bound, as the region of space grows smaller. Particles cannot be restricted to a geometric point in space, since this would require an infinite particle momentum.

In chemistry, Schrödinger, Pauling, Mulliken and others noted that the consequence of Heisenberg’s relation was that the electron, as a wave packet, could not be considered to have an exact location in its orbital. Max Born suggested that the electron’s position needed to be described by a probability distribution which was connected with finding the electron at some point in the wave-function which described its associated wave packet. The new quantum mechanics did not give exact results, but only the probabilities for the occurrence of a variety of possible such results. Heisenberg held that the path of a moving particle has no meaning if we cannot observe it, as we cannot with electrons in an atom.

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number n for each orbital became known as an n-sphere in a three dimensional atom and was pictured as the mean energy of the probability cloud of the electron’s wave packet which surrounded the atom.

Although Heisenberg used infinite sets of positions for the electron in his matrices, this does not mean that the electron could be anywhere in the universe. Rather there are several laws that show the electron must be in one localized probability distribution. An electron is described by its energy in Bohr’s atom which was carried over to matrix mechanics. Therefore, an electron in a certain n-sphere had to be within a certain range from the nucleus depending upon its energy. This restricts its location.

Hydrogen-like atoms

The simplest atomic orbitals are those that occur in an atom with a single electron, such as the hydrogen atom. In this case the atomic orbitals are the eigenstates of the hydrogen Hamiltonian. They can be obtained analytically. An atom of any other element ionized down to a single electron is very similar to hydrogen, and the orbitals take the same form.

For atoms with two or more electrons, the governing equations can only be solved with the use of methods of iterative approximation. Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen, and in the simplest models, they are taken to have the same form. For more rigorous and precise analysis, the numerical approximations must be used.

A given (hydrogen-like) atomic orbital is identified by unique values of three quantum numbers: n, l, and ml. The rules restricting the values of the quantum numbers, and their energies (see below), explain the electron configuration of the atoms and the periodic table.

The stationary states (quantum states) of the hydrogen-like atoms are its atomic orbital. However, in general, an electron’s behavior is not fully described by a single orbital. Electron states are best represented by time-depending “mixtures” (linear combinations) of multiple orbitals. See Linear combination of atomic orbitals molecular orbital method.

The quantum number n first appeared in the Bohr model where it determines the radius of each circular electron orbit. In modern quantum mechanics however, n determines the mean distance of the electron from the nucleus; all electrons with the same value of n lie at the same average distance. For this reason, orbitals with the same value of n are said to comprise a “shell”. Orbitals with the same value of n and also the same value of l are even more closely related, and are said to comprise a “subshell”.

Quantum numbers

Because of the quantum mechanical nature of the electrons around a nucleus, they cannot be described by a location and momentum. Instead, they are described by a set of quantum numbers that encompasses both the particle-like nature and the wave-like nature of the electrons. An atomic orbital is uniquely identified by the values of the three quantum numbers, and each set of the three quantum numbers corresponds to exactly one orbital, but the quantum numbers only occur in certain combinations of values. The quantum numbers, together with the rules governing their possible values, are as follows:

The principal quantum number, n, describes the energy of the electron and is always a positive integer. In fact, it can be any positive integer, but for reasons discussed below, large numbers are seldom encountered. Each atom has, in general, many orbitals associated with each value of n; these orbitals together are sometimes called electron shells.

The azimuthal quantum number describes the orbital angular momentum of each electron and is a non-negative integer. Within a shell where n is some integer n0, ranges across all (integer) values satisfying the relation? For instance, the n = 1 shell has only orbitals with, and the n = 2 shell has only orbitals with, and. The set of orbitals associated with a particular value of are sometimes collectively called a subshell.

The magnetic quantum number, describes the magnetic moment of an electron in an arbitrary direction, and is also always an integer. Within a subshell where is some integer, ranges thus:

Subshells are usually identified by their n- and -values. n is represented by its numerical value, but is represented by a letter as follows: 0 is represented by ‘s’, 1 by ‘p’, 2 by ‘d’, 3 by ‘f’, and 4 by ‘g’. For instance, one may speak of the subshell with n = 2 and as a ‘2s subshell’.

Each electron also has a spin quantum number, s, which describes the spin of each electron (spin up or spin down). The number s can be +1⁄2 or -1⁄2.

The Pauli exclusion principle states that no two electrons can occupy the same quantum state: every electron in an atom must have a unique combination of quantum numbers.

The shapes of orbitals

Cross-section of computed hydrogen atom orbital (ψ2) for the 6s (n=6, l=0, m=0) orbital. Note that s orbitals, though spherically symmetrical, have radially placed wave-nodes for n > 1. However, only s orbitals invariably have a center anti-node; the other types never do.
Any discussion of the shapes of electron orbitals is necessarily imprecise, because a given electron, regardless of which orbital it occupies, can at any moment be found at any distance from the nucleus and in any direction due to the uncertainty principle.

However, the electron is much more likely to be found in certain regions of the atom than in others. Given this, a boundary surface can be drawn so that the electron has a high probability to be found somewhere within the surface, and all regions outside the surface have low values. The precise placement of the surface is arbitrary, but any reasonably compact determination must follow a pattern specified by the behavior of |ψ|2, the square of the absolute value (also called magnitude or modulus) of the complex-valued wavefunction. This boundary surface is sometimes what is meant when the “shape” of an orbital is referred to. Sometimes the ψ function will be graphed to show its phases, rather than the |ψ|2 which shows probability density but has no phases (which have been lost is the process of taking the absolute value, since ψ is a complex number). |ψ|2 orbital graphs tend to have less spherical, thinner lobes than ψ graphs, but have the same number of lobes in the same places, and otherwise are recognizable.

Generally speaking, the number n determines the size and energy of the orbital for a given nucleus: as n increases, the size of the orbital increases. However, in comparing different elements, the higher nuclear charge, Z, of heavier elements causes their orbitals to contract by comparison to lighter ones, so that the overall size of the whole atom remains very roughly constant, even as the number of electrons in heavier elements (higher Z) increases.

Also in general terms, determines an orbital’s shape, and its orientation. However, since some orbitals are described by equations in complex numbers, the shape sometimes depends on also.

The single s-orbitals () are shaped like spheres. For n = 1 the sphere is “solid” (it is most dense at the center and fades exponentially outwardly), but for n = 2 or more, each single s-orbital is composed of spherically symmetric surfaces which are nested shells (i.e., the “wave-structure” is radial, following a sinusoidal radial component as well). See illustration of a cross-section of these nested shells, at right. The s-orbitals for all n numbers are the only orbitals with an anti-node (a region of high wave function density) at the center of the nucleus. All other orbitals (p, d, f, etc.) have angular momentum, and thus avoid the nucleus (having a wave node at the nucleus).

The three p-orbitals for n = 2 have the form of two ellipsoids with a point of tangency at the nucleus (the two-lobed shape is sometimes referred to as a “dumbbell”). The three p-orbitals in each shell are oriented at right angles to each other, as determined by their respective linear combination of values of .

The five d orbitals in ψ2 form, with a combination diagram showing how they fit together to fill space around an atomic nucleus.
Four of the five d-orbitals for n = 3 look similar, each with four pear-shaped lobes, each lobe tangent to two others, and the centers of all four lying in one plane, between a pair of axes. Three of these planes are the xy-, xz-, and yz-planes, and the fourth has the centres on the x and y axes. The fifth and final d-orbital consists of three regions of high probability density: a torus with two pear-shaped regions placed symmetrically on its z axis.

There are seven f-orbitals, each with shapes more complex than those of the d-orbitals.

For each s, p, d, f and g set of orbitals, the set of orbitals which composes it forms a spherically symmetrical set of shapes. For non-s orbitals, which have lobes, the lobes point in directions so as to fill space as symmetrically as possible for number of lobes which exist for a set of orientations. For example, the three p orbitals have six lobes which are oriented to each of the six primary directions of 3-D space; for the 5 d orbitals, there are a total of 18 lobes, in which again six point in primary directions, and the 12 additional lobes fill the 12 gaps which exist between each pairs of these 6 primary axes.

Additionally, as is the case with the s orbitals, individual p, d, f and g orbitals with n values higher than the lowest possible value, exhibit an additional radial node structure which is reminiscent of harmonic waves of the same type, as compared with the lowest (or fundamental) mode of the wave. As with s orbitals, this phenomenon provides p, d, f, and g orbitals at the next higher possible value of n (for example, 3p orbitals vs. the fundamental 2p), an additional node in each lobe. Still higher values of n further increase the number of radial nodes, for each type of orbital.

The shapes of atomic orbitals in one-electron atom are related to 3-dimensional spherical harmonics. These shapes are not unique, and any linear combination is valid, like a transformation to cubic harmonics, in fact it is possible to generate sets where all the d’s are the same shape, just like the px, py, and pz are the same shape.

Understanding why atomic orbitals take these shapes

The shapes of atomic orbitals can be understood qualitatively by considering the analogous case of standing waves on a circular drum. The many modes of the vibrating disk form the shape of atomic orbitals. It follows that the shapes of atomic orbitals are a direct consequence of the wave nature of the electrons.

A number of modes are shown below together with their quantum numbers. The analogous wave functions of the hydrogen atom are also indicated.

Mode u01 (1s orbital)

Mode u02 (2s orbital)

Mode u03 (3s orbital)

Mode u11 (2p orbital)

Mode u12 (3p orbital)

Mode u13 (4p orbital)

Mode u21 (3d orbital)

Mode u22 (4d orbital)

Mode u23 (5d orbital)

Orbital energy

Electron shell

In atoms with a single electron (hydrogen-like atoms), the energy of an orbital (and, consequently, of any electrons in the orbital) is determined exclusively by n. The n = 1 orbital has the lowest possible energy in the atom. Each successively higher value of n has a higher level of energy, but the difference decreases as n increases. For high n, the level of energy becomes so high that the electron can easily escape from the atom. In single electron atoms, all levels with different within a given n are (to a good approximation) degenerate, and have the same energy. [This approximation is broken to a slight extent by the effect of the magnetic field of the nucleus, and by quantum electrodynamics effects. The latter induce tiny binding energy differences especially for s electrons that go nearer the nucleus, since these feel a very slightly different nuclear charge, even in one-electron atoms.

In atoms with multiple electrons, the energy of an electron depends not only on the intrinsic properties of its orbital, but also on its interactions with the other electrons. These interactions depend on the detail of its spatial probability distribution, and so the energy levels of orbitals depend not only on n but also on . Higher values of are associated with higher values of energy; for instance, the 2p state is higher than the 2s state. When = 2, the increase in energy of the orbital becomes so large as to push the energy of orbital above the energy of the s-orbital in the next higher shell; when = 3 the energy is pushed into the shell two steps higher. The filling of the 3d orbitals does not occur until the 4s orbitals have been filled.

The increase in energy for subshells of increasing angular momentum in larger atoms is due to electron-electron interaction effects, and it is specifically related to the ability of low angular momentum electrons to penetrate more effectively toward the nucleus, where they are subject to less screening from the charge of intervening electrons. Thus, in atoms of higher atomic number, the of electrons becomes more and more of a determining factor in their energy, and the principal quantum numbers n of electrons becomes less and less important in their energy placement.

Electron configuration and electron shell

Several rules govern the placement of electrons in orbitals (electron configuration). The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the Pauli exclusion principle). These quantum numbers include the three that define orbitals, as well as s, or spin quantum number. Thus, two electrons may occupy a single orbital, so long as they have different values of s. However, only two electrons, because of their spin, can be associated with each orbital.

Additionally, an electron always tends to fall to the lowest possible energy state. It is possible for it to occupy any orbital so long as it does not violate the Pauli exclusion principle, but if lower-energy orbitals are available, this condition is unstable. The electron will eventually lose energy (by releasing a photon) and drop into the lower orbital. Thus, electrons fill orbitals in the order specified by the energy sequence given above.

This behavior is responsible for the structure of the periodic table. The table may be divided into several rows (called ‘periods’), numbered starting with 1 at the top. The presently known elements occupy seven periods. If a certain period has number i, it consists of elements whose outermost electrons fall in the ith shell.

The periodic table may also be divided into several numbered rectangular ‘blocks’. The elements belonging to a given block have this common feature: their highest-energy electrons all belong to the same -state (but the n associated with that -state depends upon the period). For instance, the leftmost two columns constitute the ‘s-block’. The outermost electrons of Li and Be respectively belong to the 2s subshell, and those of Na and Mg to the 3s subshell.

The following is the order for filling the “subshell” orbitals, which also gives the order of the “blocks” in the periodic table:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p
The “periodic” nature of this filling of orbitals is more obvious if the order is given with increasing principle quantum numbers starting new rows, and repeating each subshell is given as many times as required for each pair of electrons it may contain:

1s
2s 2p, 2p, 2p
3s 3p, 3p, 3p
4s 3d, 3d, 3d, 3d, 3d, 4p, 4p, 4p
5s 4d, 4d, 4d, 4d, 4d, 5p, 5p, 5p
6s (4f) 5d, 5d, 5d, 5d, 5d, 6p, 6p, 6p
7s (5f) 6d, 6d, 6d, 6d, 6d, 7p, 7p, 7p

The number of electrons in a neutral atom increases with the atomic number. The electrons in the outermost shell, or valence electrons, tend to be responsible for an element’s chemical behavior. Elements that contain the same number of valence electrons can be grouped together and display similar chemical properties.

Main article: Relativistic quantum chemistry

For elements with high atomic number Z, the effects of relativity become more pronounced, and especially so for s electrons, which move at relativistic velocities as they penetrate the screening electrons near the core of high Z atoms. This relativistic increase in momentum for high speed electrons causes a corresponding decrease in wavelength and contraction of 6s orbitals relative to 5d orbitals (by comparison to corresponding s and d electrons in lighter elements in the same column of the periodic table); this results in 6s valence electrons becoming lowered in energy.

Examples of significant physical outcomes of this effect include the lowered melting temperature of mercury (which results from 6s electrons not being available for metal bonding) and the golden color of gold and caesium (which results from narrowing of 6s to 5d transition energy to the point that visible light begins to be absorbed).

In the Bohr Model, an n = 1 electron has a velocity given by v = Zαc, where Z is the atomic number, α is the fine-structure constant, and c is the speed of light. In non-relativistic quantum mechanics, therefore, any atom with an atomic number greater than 137 would require its 1s electrons to be traveling faster than the speed of light. Even in the Dirac equation, which accounts for relativistic effects, the wavefunction of the electron for atoms with Z > 137 is oscillatory and unbounded. The significance of element 137, also known as untriseptium, was first pointed out by the physicist Richard Feynman. Element 137 is sometimes informally called feynmanium (symbol Fy). However, Feynman’s approximation fails to predict the exact critical value of Z due to the non-point-charge nature of the nucleus and very small orbital radius of inner electrons, resulting in a potential seen by inner electrons which is effectively less than Z. The critical Z value which makes the atom unstable with regard to high-field breakdown of the vacuum and production of electron-positron pairs, does not occur until Z is about 173. These conditions are not seen except transiently in collisions of very heavy nuclei such as lead or uranium in accelerators, where such electron-positron production from these effects has been claimed to be observed. See Extension of the periodic table beyond the seventh period.

Transitions between orbitals

Under quantum mechanics, each quantum state has a well-defined energy. When applied to atomic orbitals, this means that each state has a specific energy, and that if an electron is to move between states, the energy difference is also very fixed.

Consider two states of the Hydrogen atom:

State 1) n=1, l=0, ml=0 and s=+1⁄2

State 2) n=2, l=0, ml=0 and s=+1⁄2

By quantum theory, state 1 has a fixed energy of E1, and state 2 has a fixed energy of E2. Now, what would happen if an electron in state 1 were to move to state 2? For this to happen, the electron would need to gain an energy of exactly E2 – E1. If the electron receives energy that is less than or greater than this value, it cannot jump from state 1 to state 2. Now, suppose we irradiate the atom with a broad-spectrum of light. Photons that reach the atom that have an energy of exactly E2 – E1 will be absorbed by the electron in state 1, and that electron will jump to state 2. However, photons that are greater or lower in energy cannot be absorbed by the electron, because the electron can only jump to one of the orbitals, it cannot jump to a state between orbitals. The result is that only photons of a specific frequency will be absorbed by the atom. This creates a line in the spectrum, known as an absorption line, which corresponds to the energy difference between states 1 and 2.

The atomic orbital model thus predicts line spectra, which are observed experimentally. This is one of the main validations of the atomic orbital model.

The atomic orbital model is nevertheless an approximation to the full quantum theory, which only recognizes many electron states. The predictions of line spectra are qualitatively useful but are not quantitatively accurate for atoms and ions other than those containing only one electron.

Historical context

Main article: Atomic theory

The Rutherford Bohr model of the hydrogen atom.
After the discovery of the photoelectric effect, the connection between the structure of electrons in atoms and the emission and absorption spectra of atoms became an increasingly useful tool in the understanding of electrons in atoms. The most prominent feature of emission and absorption spectra was that these spectra contained discrete lines. The significance of the Bohr model was that it related the lines in emission and absorption spectra to the energy differences between the orbits that electrons could take around an atom. This was achieved by giving the electrons some kind of wave-like properties. In particular, electrons were assumed to have a wavelength (a property that had previously been discovered, but not entirely understood). The Bohr model was therefore not only a significant step towards the understanding of electrons in atoms, but also a significant step towards the development of the wave/particle duality of quantum mechanics.

The premise of the model was that electrons had a wavelength, which was a function of its momentum, and therefore an orbiting electron would need to orbit at a multiple of the wavelength. The Bohr model was thus a classical model with an additional constraint provided by the ‘wavelength’ argument. In our current understanding of physics, this ‘wavelength’ argument is known to be an element of quantum mechanics, and for that reason the Bohr model is called a semi-classical model.

The Bohr model was able to explain the emission and absorption spectra of Hydrogen. The energies of electrons in the n=1, 2, 3, etc. states in the Bohr model match those of current physics. However, this did not explain similarities between different atoms, as expressed by the periodic table, such as why Helium (2 electrons), Neon (10 electrons), and Argon (18 electrons) exhibits similar chemical behaviour. Modern physics explains this by noting that the n=1 state can hold 2 electrons, the n=2 state can hold 8 electrons, and the n=3 state can hold 8 electrons. In the end, this was solved by the discovery of modern quantum mechanics and the Pauli Exclusion Principle.

Articles

What is Karma?

In Uncategorized on April 3, 2011 by Swami Uddipayan

What is Karma?

Karma is the concept of “action” or “deed”, understood as that which causes the entire cycle of cause and effect (i.e., the cycle called samsara) originating in ancient India and treated in Hindu, Jain, Buddhist and Sikh philosophies.

‘Karma’ is an Indian religious concept in contradistinction to ‘faith’ espoused by Abrahamic religions (Judaism, Christianity, and Islam), which view all human dramas as the will of God as opposed to present—and past—life actions. In theistic schools of Hinduism, humans have free will to choose their own actions, which require only the will of God to implement karma’s consequences. Buddhism and Jainism do not accord any role to a supreme God or Gods, but the principal belief is the same. In Indian beliefs, the karmic effects of all deeds are viewed as actively shaping past, present, and future experiences. The results or ‘fruits’ of actions are called karma-phala.

Origins

A concept of karma (along with samsara and moksha) may originate in the shramana tradition of which Buddhism and Jainism are continuations. This tradition influenced the Brahmanic religion in the early Vedantic (Upanishadic) movement of the 1st millennium BC. This worldview was adopted from this religious culture by Brahmin orthodoxy, and Brahmins wrote the earliest recorded scriptures containing these ideas in the early Upanishads. Until recently, the scholarly consensus was that reincarnation is absent from the earliest strata of Brahminical literature. However, a new translation of two stanzas of the Rig Veda indicate that the Brahmins may have had the idea, common among small-scale societies around the world, that an individual cycles back and forth between the earth and a heavenly realm of ancestors. In this worldview, moral behavior has no influence on rebirth. The idea that the moral quality of one’s actions influences one’s rebirth is absent from India until the period of the shramana religions, and the Brahmins appear to have adopted this idea from other religious groups.

Views

Some traditions (i.e., the Vedanta), believe that a supreme being plays some kind of role, for example, as the dispenser of the ‘fruits’ of karma or as exercising the option to change one’s karma in rare instances. In general, followers of the Buddhism and many followers of Hinduism traditions consider the natural laws of causation sufficient to explain the effects of karma. Another view holds that a Sadguru, acting on a god’s behalf, can mitigate or work out some of the karma of the disciple. And according to the Jainism perspective, neither a god nor a guru have any role in a person’s karma—the individual is considered to be the sole doer and enjoyer of his karmas and their ‘fruits’. Laws of karma are codified in some books.

Karma in Hinduism

Karma in Hinduism is also considered to be a spiritually originated law. Many Hindus see God’s direct involvement in this process; others consider the natural laws of causation sufficient to explain the effects of karma. However, followers of Vedanta, the leading extant school of Hinduism today, consider Ishvara, a personal supreme God, as playing a role in the delivery of karma. Theistic schools of Hinduism such as Vedanta thus disagree with the Buddhist and Jain views and other Hindu views that karma is merely a law of cause and effect but rather is also dependent on the will of a personal supreme God. Examples of a personal supreme God include Shiva in Shaivism or Vishnu in Vaishnavism. A good summary of this theistic view of karma is expressed by the following: “God does not make one suffer for no reason nor does He make one happy for no reason. God is very fair and gives you exactly what you deserve.”

Karma is not punishment or retribution but simply an extended expression or consequence of natural acts. Karma means “deed” or “act” and more broadly names the universal principle of cause and effect, action and reaction, that governs all life. The effects experienced are also able to be mitigated by actions and are not necessarily fated. That is to say, a particular action now is not binding to some particular, pre-determined future experience or reaction; it is not a simple, one-to-one correspondence of reward or punishment.

Karma is not fate, for humans act with free will creating their own destiny. According to the Vedas, if one sows goodness, one will reap goodness; if one sows evil, one will reap evil. Karma refers to the totality of our actions and their concomitant reactions in this and previous lives, all of which determines our future. The conquest of karma lies in intelligent action and dispassionate response.

One of the first and most dramatic illustrations of Karma can be found in the Bhagavad Gita. In this poem, Arjuna the protagonist is preparing for battle when he realizes that the enemy consists of members of his own family and decides not to fight. His charioteer, Krishna (an avatar of god), explains to Arjuna the concept of dharma (duty) among other things and makes him see that it is his duty to fight. The whole of the Bhagavad Gita within the Mahabharata is a dialogue between these two on aspects of life including morality and a host of other philosophical themes. The original Hindu concept of karma was later enhanced by several other movements within the religion, most notably Vedanta, and Tantra.

In this way, so long as the stock of sanchita karma lasts, a part of it continues to be taken out as prarabdha karma for being experienced in one lifetime, leading to the cycle of birth and death. A Jiva cannot attain moksha until the accumulated sanchita karmas are completely exhausted.

Sikhism

Within Sikhism, all living beings are described as being under the influence of Maya’s three qualities. Always present together in varying mix and degrees, these three qualities of Maya bind the Soul to the body and to the earth plane. Above these three qualities is the eternal time. Due to the influence of three modes of Maya’s nature, jivas (individual beings) perform activities under the control and purview of the eternal time. These activities are called Karma. The underlying principle is that karma is the law that brings back the results of actions to the person performing them.

This life is likened to a field (Khet) in which our Karma is the seed. We harvest exactly what we sow. No less, no more. This infallible law of Karma holds everyone responsible for what the person is or is going to be. Based on the total sum of past Karma, some feel close to the Pure Being in this life, and others feel separated. This is the Gurbani’s (Sri Guru Granth Sahib, SGGS) law of Karma. Like other Indian as well as oriental schools of thought, the Gurbani also accepts the doctrines of Karma and reincarnation as the facts of nature.

Karma in Buddhism

In Buddhism, karma (Pāli kamma) is strictly distinguished from vipāka, meaning “fruit” or “result”. Karma is categorized within the group or groups of cause (Pāli hetu) in the chain of cause and effect, where it comprises the elements of “volitional activities” (Pali sankhara) and “action” (Pali bhava). Any action is understood as creating “seeds” in the mind that will sprout into the appropriate result (Pāli vipaka) when met with the right conditions. Most types of karmas, with good or bad results, will keep one within the wheel of samsara, while others will liberate one to nirvana.

Buddhism links karma directly to the motives behind an action. Motivation usually makes the difference between “good” and “bad” actions; but included in the motivation is also the aspect of ignorance such that a well-intended action from an ignorant mind can subsequently be interpreted as a “bad” action in the sense that it creates unpleasant results for the “actor”.

Other causal categories

In Buddhism, karma is not the only cause of everything that happens. The commentarial tradition classified causal mechanisms governing the universe as taught in the early texts in five categories, known as Niyama Dhammas:
Kamma Niyama—Consequences of one’s actions
Utu Niyama—Seasonal changes and climate
Biija Niyama—Laws of heredity
Citta Niyama—Will of mind
Dhamma Niyama—Nature’s tendency to produce a perfect type

Karma in Jainism

Karma in Jainism conveys a totally different meaning as commonly understood in the Hindu philosophy and western civilization. In Jainism, karma is referred to as karmic dirt, as it consists of very subtle and microscopic particles i.e. pudgala that pervade the entire universe. Karmas are attracted to the karmic field of a soul on account of vibrations created by activities of mind, speech, and body as well as on account of various mental dispositions. Hence the karmas are the subtle matter surrounding the consciousness of a soul. When these two components, i.e., consciousness and karma, interact, we experience the life we know at present.

Herman Kuhn quoting from Tattvarthasutra describes karmas as – a mechanism that makes us thoroughly experience the themes of our life until we gained optimal knowledge from them and until our emotional attachment to these themes falls off.

According to Padmanabh Jain “this emphasis on reaping the fruits only of one’s own karma was not restricted to the Jainas; both Hindus and Buddhist writers have produced doctrinal materials stressing the same point. Each of the latter traditions, however, developed practices in basic contradiction to such belief. In addition to shrardha (the ritual Hindu offerings by the son of deceased), we find among Hindus widespread adherence to the notion of divine intervention in one’s fate, while Buddhists eventually came to propound such theories like boon-granting bodhisattvas, transfer of merit and like. Only Jainas have been absolutely unwilling to allow such ideas to penetrate their community, despite the fact that there must have been tremendous amount of social pressure on them to do so.”

The key points where the theory of Karma in Jainism differs from the other religions such as theistic traditions of Hinduism can be stated as follows:
1. Karma in Jainism operates as a self-sustaining mechanism as natural universal law, without any need of an external entity to manage them. (absence of the exogenous “Divine Entity” in Jainism)
2. Jainism advocates that a soul’s karma changes even with the thoughts, and not just the actions. Thus, to even think evil of someone would endure a “karm-bandh” or an increment in bad karma. For this reason, Jainism gives a very strong emphasis to “samyak dhyan” (rationality in thoughts) and “samyak darshan” (rationality in perception) and not just “samyak charitra” (rationality in conduct).
3. Under Jain theology, a soul is released of worldly affairs as soon as it is able to emancipate from the “karm-bandh”. A famous illustration is that of Mata Marudevi, the mother of Shri Rishabh Dev, the first Tirthankar of present time cycle, who reached such emancipation by elevating sequentially her thought processes, while she was visiting her Tirthankar son. This illustration explains how “Nirvana” and “Moksha”, in Jainism, are different from other religions. In the presence of a Tirthankar, another soul achieved Keval Gyan and subsequently Nirvana, without any need of intervention by the Tirthankar.
4. The karmic theory in Jainism operates endogenously. Tirthankars are not attributed “godhood” under Jainism. Thus, even the tirthankars themselves have to go through the stages of emancipation, for attaining that state. While Buddhism does give a similar and to some extent a matching account for Shri Gautama Buddha, Hinduism maintains a totally different theory where “divine grace” is needed for emancipation.
5. Jainism treats all souls equally, inasmuch as it advocates that all souls have the same potential of attaining “nirvana”. Only those who make effort really attain it, but nonetheless, each soul is capable on its own to do so by gradually reducing its karma.

Western interpretation

An academic and religious definition was mentioned above. The concept of karma is part of the world view of many millions of people throughout the world. Many in western cultures or with a Christian upbringing have incorporated a notion of karma. The Christian concept of reaping what you sow from Galatians 6:7 can be considered equivalent to Karma.

According to karma, performing positive actions results in a good condition in one’s experience, whereas a negative action results in a bad effect. The effects may be seen immediately or delayed. Delay can be until later in the present life or in the next. Thus, meritorious acts may mean rebirth into a higher station, such as a superior human or a godlike being, while evil acts result in rebirth as a human living in less desirable circumstances, or as a lower animal. Some observers [who?] have compared the action of karma to Western notions of sin and judgment by God or Gods, while others understand karma as an inherent principle of the universe without the intervention of any supernatural Being. In Hinduism, God does play a role and is seen as a dispenser of karma; see Karma in Hinduism for more details. The non-interventionist view is that of Buddhism and Jainism.

Most teachings say that for common mortals, being involved with karma is an unavoidable part of daily living. However, in light of the Hindu philosophical school of Vedanta, as well as Gautama Buddha’s teachings, one is advised to either avoid, control or become mindful of the effects of desires and aversions as a way to moderate or change one’s karma (or, more accurately, one’s karmic results or destiny).

Spiritist doctrine

In Spiritism, karma is known as “the law of cause and effect”, and plays a central role in determining how one’s life should be lived. Spirits are encouraged to choose how (and when) to suffer retribution for the wrong they did in previous lives. Disabilities, physical or mental impairment or even an unlucky life are due to the choices a spirit makes before reincarnating (that is, before being born to a new life).

What sets Spiritism apart from the more traditional religious views is that it understands karma as a condition inherent to the spirit, whether incarnated or not: the consequences of the crimes committed by the spirit last beyond the physical life and cause him (moral) pain in the afterlife. The choice of a life of hardships is, therefore, a way to rid oneself of the pain caused by moral guilt and to perfect qualities that are necessary for the spirit to progress to a higher form.

Because Spiritism always accepted the plurality of inhabited worlds, its concept of karma became considerably complex. There are worlds that are “primitive” (in the sense that they are home to spirits newly born and still very low on intellect and morals) and a succession of more and more advanced worlds to where spirits move as they are elevated. A spirit may choose to be born on a world inferior to his own as a penance or as a mission.

New Age and Theosophy

The idea of karma was popularized in the Western world through the work of the Theosophical Society. In this conception, karma is affiliated with the Neopagan law of return or Threefold Law, the idea that the beneficial or harmful effects one has on the world will return to oneself. Colloquially this may be summed up as ‘what goes around comes around.’

In the west, karma is often confused with concepts such as the soul, psychic energy, synchronicity (a concept originally from psychoanalyst Carl Jung, which says that things that happen at the same time are related), and ideas from quantum or theoretical physics (which most physicists would not grant as having any bearing on morality or codes of conduct, much less on supernatural notions). This mishmash of word associations is well illustrated by the once-common bumper sticker “My karma ran over your dogma.”

Karma and emotions

Since the 20th century emergence of emotional intelligence as a novel paradigm for viewing human experience, karma has become a sectarian term which umbrellas the entire collection (both conscious and subconscious) of human emotionality. This modern view of karma, devoid of any spiritual exigencies, obviates the need for an acceptance of reincarnation in Judeo-Christian societies and attempts to portray karma as a universal psychological phenomenon which behaves predictably, like other physical forces such as gravity.

Sakyong Mipham eloquently summed this up when he said; Like gravity, karma is so basic we often don’t even notice it.

This view of karma, as a universal and personally impacting emotional constant, correlates with Buddhist and Jungian understanding that volition (or libido, created from personal and cultural biases) is the primary instigator of karma. Any conscious thought, word and/or action, arising from a cognitively unresolved emotion (cognitive dissonance), results in karma.

Jung once opined on unresolved emotions and the synchronicity of karma; ‘When an inner situation is not made conscious, it appears outside as fate.

Popular methods for negating cognitive dissonance include meditation, metacognition, counseling, psychoanalysis, etc., whose aim is to enhance emotional self-awareness and thus avoid negative karma. This results in better emotional hygiene and reduced karmic impacts. Permanent neuronal changes within the amygdala and left prefrontal cortex of the human brain attributed to long-term meditation and metacognition techniques have been proven scientifically. This process of emotional maturation aspires to a goal of Individuation or self-actualisation. Such peak experiences are hypothetically devoid of any karma (nirvana).

As Rabindranath Tagore most eloquently explained about the heat of human emotions; Nirvana is not the blowing out of the candle. It is the extinguishing of the flame because day is come
action” or “deed”, understood as that which causes the entire cycle of cause and effect (i.e., the cycle called samsara) originating in ancient India and treated in Hindu, Jain, Buddhist and Sikh philosophies.

‘Karma’ is an Indian religious concept in contradistinction to ‘faith’ espoused by Abrahamic religions (Judaism, Christianity, and Islam), which view all human dramas as the will of God as opposed to present—and past—life actions. In theistic schools of Hinduism, humans have free will to choose their own actions, which require only the will of God to implement karma’s consequences. Buddhism and Jainism do not accord any role to a supreme God or Gods, but the principal belief is the same. In Indian beliefs, the karmic effects of all deeds are viewed as actively shaping past, present, and future experiences. The results or ‘fruits’ of actions are called karma-phala.

Origins

A concept of karma (along with samsara and moksha) may originate in the shramana tradition of which Buddhism and Jainism are continuations. This tradition influenced the Brahmanic religion in the early Vedantic (Upanishadic) movement of the 1st millennium BC. This worldview was adopted from this religious culture by Brahmin orthodoxy, and Brahmins wrote the earliest recorded scriptures containing these ideas in the early Upanishads. Until recently, the scholarly consensus was that reincarnation is absent from the earliest strata of Brahminical literature. However, a new translation of two stanzas of the Rig Veda indicate that the Brahmins may have had the idea, common among small-scale societies around the world, that an individual cycles back and forth between the earth and a heavenly realm of ancestors. In this worldview, moral behavior has no influence on rebirth. The idea that the moral quality of one’s actions influences one’s rebirth is absent from India until the period of the shramana religions, and the Brahmins appear to have adopted this idea from other religious groups.

Views

Some traditions (i.e., the Vedanta), believe that a supreme being plays some kind of role, for example, as the dispenser of the ‘fruits’ of karma or as exercising the option to change one’s karma in rare instances. In general, followers of the Buddhism and many followers of Hinduism traditions consider the natural laws of causation sufficient to explain the effects of karma. Another view holds that a Sadguru, acting on a god’s behalf, can mitigate or work out some of the karma of the disciple. And according to the Jainism perspective, neither a god nor a guru have any role in a person’s karma—the individual is considered to be the sole doer and enjoyer of his karmas and their ‘fruits’. Laws of karma are codified in some books.

Karma in Hinduism

Karma in Hinduism is also considered to be a spiritually originated law. Many Hindus see God’s direct involvement in this process; others consider the natural laws of causation sufficient to explain the effects of karma. However, followers of Vedanta, the leading extant school of Hinduism today, consider Ishvara, a personal supreme God, as playing a role in the delivery of karma. Theistic schools of Hinduism such as Vedanta thus disagree with the Buddhist and Jain views and other Hindu views that karma is merely a law of cause and effect but rather is also dependent on the will of a personal supreme God. Examples of a personal supreme God include Shiva in Shaivism or Vishnu in Vaishnavism. A good summary of this theistic view of karma is expressed by the following: “God does not make one suffer for no reason nor does He make one happy for no reason. God is very fair and gives you exactly what you deserve.”

Karma is not punishment or retribution but simply an extended expression or consequence of natural acts. Karma means “deed” or “act” and more broadly names the universal principle of cause and effect, action and reaction, that governs all life. The effects experienced are also able to be mitigated by actions and are not necessarily fated. That is to say, a particular action now is not binding to some particular, pre-determined future experience or reaction; it is not a simple, one-to-one correspondence of reward or punishment.

Karma is not fate, for humans act with free will creating their own destiny. According to the Vedas, if one sows goodness, one will reap goodness; if one sows evil, one will reap evil. Karma refers to the totality of our actions and their concomitant reactions in this and previous lives, all of which determines our future. The conquest of karma lies in intelligent action and dispassionate response.

One of the first and most dramatic illustrations of Karma can be found in the Bhagavad Gita. In this poem, Arjuna the protagonist is preparing for battle when he realizes that the enemy consists of members of his own family and decides not to fight. His charioteer, Krishna (an avatar of god), explains to Arjuna the concept of dharma (duty) among other things and makes him see that it is his duty to fight. The whole of the Bhagavad Gita within the Mahabharata is a dialogue between these two on aspects of life including morality and a host of other philosophical themes. The original Hindu concept of karma was later enhanced by several other movements within the religion, most notably Vedanta, and Tantra.

In this way, so long as the stock of sanchita karma lasts, a part of it continues to be taken out as prarabdha karma for being experienced in one lifetime, leading to the cycle of birth and death. A Jiva cannot attain moksha until the accumulated sanchita karmas are completely exhausted.

Sikhism

Within Sikhism, all living beings are described as being under the influence of Maya’s three qualities. Always present together in varying mix and degrees, these three qualities of Maya bind the Soul to the body and to the earth plane. Above these three qualities is the eternal time. Due to the influence of three modes of Maya’s nature, jivas (individual beings) perform activities under the control and purview of the eternal time. These activities are called Karma. The underlying principle is that karma is the law that brings back the results of actions to the person performing them.

This life is likened to a field (Khet) in which our Karma is the seed. We harvest exactly what we sow. No less, no more. This infallible law of Karma holds everyone responsible for what the person is or is going to be. Based on the total sum of past Karma, some feel close to the Pure Being in this life, and others feel separated. This is the Gurbani’s (Sri Guru Granth Sahib, SGGS) law of Karma. Like other Indian as well as oriental schools of thought, the Gurbani also accepts the doctrines of Karma and reincarnation as the facts of nature.

Karma in Buddhism

In Buddhism, karma (Pāli kamma) is strictly distinguished from vipāka, meaning “fruit” or “result”. Karma is categorized within the group or groups of cause (Pāli hetu) in the chain of cause and effect, where it comprises the elements of “volitional activities” (Pali sankhara) and “action” (Pali bhava). Any action is understood as creating “seeds” in the mind that will sprout into the appropriate result (Pāli vipaka) when met with the right conditions. Most types of karmas, with good or bad results, will keep one within the wheel of samsara, while others will liberate one to nirvana.

Buddhism links karma directly to the motives behind an action. Motivation usually makes the difference between “good” and “bad” actions; but included in the motivation is also the aspect of ignorance such that a well-intended action from an ignorant mind can subsequently be interpreted as a “bad” action in the sense that it creates unpleasant results for the “actor”.

Other causal categories

In Buddhism, karma is not the only cause of everything that happens. The commentarial tradition classified causal mechanisms governing the universe as taught in the early texts in five categories, known as Niyama Dhammas:
Kamma Niyama—Consequences of one’s actions
Utu Niyama—Seasonal changes and climate
Biija Niyama—Laws of heredity
Citta Niyama—Will of mind
Dhamma Niyama—Nature’s tendency to produce a perfect type

Karma in Jainism

Karma in Jainism conveys a totally different meaning as commonly understood in the Hindu philosophy and western civilization. In Jainism, karma is referred to as karmic dirt, as it consists of very subtle and microscopic particles i.e. pudgala that pervade the entire universe. Karmas are attracted to the karmic field of a soul on account of vibrations created by activities of mind, speech, and body as well as on account of various mental dispositions. Hence the karmas are the subtle matter surrounding the consciousness of a soul. When these two components, i.e., consciousness and karma, interact, we experience the life we know at present.

Herman Kuhn quoting from Tattvarthasutra describes karmas as – a mechanism that makes us thoroughly experience the themes of our life until we gained optimal knowledge from them and until our emotional attachment to these themes falls off.

According to Padmanabh Jain “this emphasis on reaping the fruits only of one’s own karma was not restricted to the Jainas; both Hindus and Buddhist writers have produced doctrinal materials stressing the same point. Each of the latter traditions, however, developed practices in basic contradiction to such belief. In addition to shrardha (the ritual Hindu offerings by the son of deceased), we find among Hindus widespread adherence to the notion of divine intervention in one’s fate, while Buddhists eventually came to propound such theories like boon-granting bodhisattvas, transfer of merit and like. Only Jainas have been absolutely unwilling to allow such ideas to penetrate their community, despite the fact that there must have been tremendous amount of social pressure on them to do so.”

The key points where the theory of Karma in Jainism differs from the other religions such as theistic traditions of Hinduism can be stated as follows:
1. Karma in Jainism operates as a self-sustaining mechanism as natural universal law, without any need of an external entity to manage them. (absence of the exogenous “Divine Entity” in Jainism)
2. Jainism advocates that a soul’s karma changes even with the thoughts, and not just the actions. Thus, to even think evil of someone would endure a “karm-bandh” or an increment in bad karma. For this reason, Jainism gives a very strong emphasis to “samyak dhyan” (rationality in thoughts) and “samyak darshan” (rationality in perception) and not just “samyak charitra” (rationality in conduct).
3. Under Jain theology, a soul is released of worldly affairs as soon as it is able to emancipate from the “karm-bandh”. A famous illustration is that of Mata Marudevi, the mother of Shri Rishabh Dev, the first Tirthankar of present time cycle, who reached such emancipation by elevating sequentially her thought processes, while she was visiting her Tirthankar son. This illustration explains how “Nirvana” and “Moksha”, in Jainism, are different from other religions. In the presence of a Tirthankar, another soul achieved Keval Gyan and subsequently Nirvana, without any need of intervention by the Tirthankar.
4. The karmic theory in Jainism operates endogenously. Tirthankars are not attributed “godhood” under Jainism. Thus, even the tirthankars themselves have to go through the stages of emancipation, for attaining that state. While Buddhism does give a similar and to some extent a matching account for Shri Gautama Buddha, Hinduism maintains a totally different theory where “divine grace” is needed for emancipation.
5. Jainism treats all souls equally, inasmuch as it advocates that all souls have the same potential of attaining “nirvana”. Only those who make effort really attain it, but nonetheless, each soul is capable on its own to do so by gradually reducing its karma.

Western interpretation

An academic and religious definition was mentioned above. The concept of karma is part of the world view of many millions of people throughout the world. Many in western cultures or with a Christian upbringing have incorporated a notion of karma. The Christian concept of reaping what you sow from Galatians 6:7 can be considered equivalent to Karma.

According to karma, performing positive actions results in a good condition in one’s experience, whereas a negative action results in a bad effect. The effects may be seen immediately or delayed. Delay can be until later in the present life or in the next. Thus, meritorious acts may mean rebirth into a higher station, such as a superior human or a godlike being, while evil acts result in rebirth as a human living in less desirable circumstances, or as a lower animal. Some observers [who?] have compared the action of karma to Western notions of sin and judgment by God or Gods, while others understand karma as an inherent principle of the universe without the intervention of any supernatural Being. In Hinduism, God does play a role and is seen as a dispenser of karma; see Karma in Hinduism for more details. The non-interventionist view is that of Buddhism and Jainism.

Most teachings say that for common mortals, being involved with karma is an unavoidable part of daily living. However, in light of the Hindu philosophical school of Vedanta, as well as Gautama Buddha’s teachings, one is advised to either avoid, control or become mindful of the effects of desires and aversions as a way to moderate or change one’s karma (or, more accurately, one’s karmic results or destiny).

Spiritist doctrine

In Spiritism, karma is known as “the law of cause and effect”, and plays a central role in determining how one’s life should be lived. Spirits are encouraged to choose how (and when) to suffer retribution for the wrong they did in previous lives. Disabilities, physical or mental impairment or even an unlucky life are due to the choices a spirit makes before reincarnating (that is, before being born to a new life).

What sets Spiritism apart from the more traditional religious views is that it understands karma as a condition inherent to the spirit, whether incarnated or not: the consequences of the crimes committed by the spirit last beyond the physical life and cause him (moral) pain in the afterlife. The choice of a life of hardships is, therefore, a way to rid oneself of the pain caused by moral guilt and to perfect qualities that are necessary for the spirit to progress to a higher form.

Because Spiritism always accepted the plurality of inhabited worlds, its concept of karma became considerably complex. There are worlds that are “primitive” (in the sense that they are home to spirits newly born and still very low on intellect and morals) and a succession of more and more advanced worlds to where spirits move as they are elevated. A spirit may choose to be born on a world inferior to his own as a penance or as a mission.

New Age and Theosophy

The idea of karma was popularized in the Western world through the work of the Theosophical Society. In this conception, karma is affiliated with the Neopagan law of return or Threefold Law, the idea that the beneficial or harmful effects one has on the world will return to oneself. Colloquially this may be summed up as ‘what goes around comes around.’

In the west, karma is often confused with concepts such as the soul, psychic energy, synchronicity (a concept originally from psychoanalyst Carl Jung, which says that things that happen at the same time are related), and ideas from quantum or theoretical physics (which most physicists would not grant as having any bearing on morality or codes of conduct, much less on supernatural notions). This mishmash of word associations is well illustrated by the once-common bumper sticker “My karma ran over your dogma.”

Karma and emotions

Since the 20th century emergence of emotional intelligence as a novel paradigm for viewing human experience, karma has become a sectarian term which umbrellas the entire collection (both conscious and subconscious) of human emotionality. This modern view of karma, devoid of any spiritual exigencies, obviates the need for an acceptance of reincarnation in Judeo-Christian societies and attempts to portray karma as a universal psychological phenomenon which behaves predictably, like other physical forces such as gravity.

Sakyong Mipham eloquently summed this up when he said; Like gravity, karma is so basic we often don’t even notice it.

This view of karma, as a universal and personally impacting emotional constant, correlates with Buddhist and Jungian understanding that volition (or libido, created from personal and cultural biases) is the primary instigator of karma. Any conscious thought, word and/or action, arising from a cognitively unresolved emotion (cognitive dissonance), results in karma.

Jung once opined on unresolved emotions and the synchronicity of karma; ‘When an inner situation is not made conscious, it appears outside as fate.

Popular methods for negating cognitive dissonance include meditation, metacognition, counseling, psychoanalysis, etc., whose aim is to enhance emotional self-awareness and thus avoid negative karma. This results in better emotional hygiene and reduced karmic impacts. Permanent neuronal changes within the amygdala and left prefrontal cortex of the human brain attributed to long-term meditation and metacognition techniques have been proven scientifically. This process of emotional maturation aspires to a goal of Individuation or self-actualisation. Such peak experiences are hypothetically devoid of any karma (nirvana).

As Rabindranath Tagore most eloquently explained about the heat of human emotions; Nirvana is not the blowing out of the candle. It is the extinguishing of the flame because day is come

Articles

The Science of Living

In Uncategorized on February 10, 2011 by Swami Uddipayan

My Pain = Total Pain in the world / No. of living beings + the pain caused by me + the hatred spread by me – My sacrifices – The hurt suffered by me.

My Happiness = Absence of Pain + the happiness spread by me – the hatred spread by me + My sacrifices + The reaction avoided for a hurt caused.

Pain makes a Man think & Thinking makes him wise, Wisdom makes pain endurable.

One can reduce his pain and increase his happiness by

Support Life – Every life supported will ensure that there is an additional being alive to share your share of pain and increase your share of happiness. As life reduces due to global warming the remaining life on planet has to take a greater share of suffering. Just see the surrounding world and observe how much pain is there compared to a few years ago. Water a plant, feed a fish, get a pet, help children to grow. Surround yourselves with life always. Sit at the top of pyramid of life. More life supported by you higher up you are.

Spread Happiness not pain – There is already enough pain in the world one should not add to it by causing some more. Most pain is caused at home to ones own near & dear ones. We should be soft in speech with our children, neighbors, subordinates, colleagues etc. Remember any pain or happiness caused will increase our share.

By sacrificing – A sacrifice can be by giving up some pleasure, giving up a habit, giving up a desire, giving up an asset small or big tangible or intangible etc. Every sacrifice lowers your assets but increases your living energy just as a balloon sheds weight so it can rise higher. When life itself is threatened why do we cling to material processions?

Hurt suffered – Imagine you are a molecule the hurt causer has hurt you. To finance for the hurt caused he has to transfer a couple of electrons. By reacting you may end up transferring back more electrons than you have received, So do not react as the other molecule is already poorer by 2 electrons. How much poor can he get, very soon he will be begging for energy to live.

Hatred Spread – Hatred causes pain to spread and happiness to reduce.

Each one of us is a wave in the ocean of life. Each wave exists as long as other waves exist. Each wave rises as high as other waves rise. Our position is determined by the company of waves in which we live and how much we help our surrounding waves to rise up. We rise or fall in a group.

Remember each one of us is an embodiment of an energy which has a field like that of a magnet. We react to waves of energy (People) around us the way a magnet would do with other magnets. The kind of reaction is a function of our own energy levels and that of the people with whom we are reacting and the background energy level due to the time and place this reaction is happening. Many a person has no control on his emotions like a child crying for a chocolate as soon as it sees one. We are unable to observe the energy flows and blindly react to a situation. If you are feeling like cursing a person it is because of different energy levels existing. The fastest way to equalize is through a swearword. Just hold back and observe the object of the curse and give them some work to do ask for a favor, maybe bring you a cup of coffee, pick up a book, ask to use their cell phone, borrow something etc. You will observe that the person will voluntarily comply because he is trying to equalize by serving you. This is a productive way of equalizing instead of causing a hurt. You can also equalize through Love which is like a long term loan payable at the discretion of the receiver whenever he is able to with no strings attached. Try to be a neutral observer of your emotions and slowly see the play of forces and how unproductive is our choice of response. If only every person engages in a productive exchange we will not see so much of pain in this world.

Your’s With Love,

Swami Uddipayan