MadSci Network: Physics

Re: What is the connection between Quantum Theory & Super-Symmetry Theory

Date: Wed Aug 4 00:42:05 1999
Posted By: Martin Mayer, Faculty, Astrophysics, Private
Area of science: Physics
ID: 933278338.Ph

Hello Kirstin,

1. What is the relationship between Quatum Theory & Super-
Symmetry Theory?  Is it true that even the smallest sub-atomic 
particles have an invisible "pair"?  What does this mean in 
terms of energy/mass relationships?  ie. if we understand the 
Universe at the sub-atomic level, does this knowledge necessarily
explain the larger whole?

ANSWER PART 1) Since I am not sure what you know about Quantum physics: 
Let me first tell you a little about Quantum theory:

THE origin of quantum theory is connected with a well-known phenomenon, 
which did not belong to the central parts of atomic physics. Any piece of 
matter when it is heated starts to glow, gets red hot and white hot at 
higher temperatures. The colour does not depend much on the surface of the 
material, and for a black body it depends solely on the temperature. 
Therefore, the radiation emitted by such a black body at high temperatures 
is a suitable object for physical research; it is a simple phenomenon that 
should find a simple explanation in terms of the known laws for radiation 
and heat. The attempt made at the end of the nineteenth century by Lord 
Rayleigh and Jeans failed, however, and revealed serious difficulties. It 
would not be possible to describe these difficulties here in simple terms. 
It must be sufficient to state that the application of the known laws did 
not lead to sensible results. When Planck, in 1895, entered this line of 
research he tried to turn the problem from radiation to the radiating 
atom. This turning did not remove any of the difficulties inherent in the 
problem, but it simplified the interpretation of the empirical facts. It 
was just at this time, during the summer of 1900, that Curlbaum and Rubens 
in Berlin had made very accurate new measurements of the spectrum of heat 
radiation. When Planck heard of these results he tried to represent them 
by simple mathematical formulas which looked plausible from his research 
on the general connection between heat and radiation. One day Planck and 
Rubens met for tea in Planck's home and compared Rubens' latest results 
with a new formula suggested by Planck.(See Planck below) The comparison 
showed a complete agreement. This was the discovery of Planck's law of 
heat radiation. 

It was at the same time the beginning of intense theoretical work for 
Planck. What was the correct physical interpretation of the new formula? 
Since Planck could, from his earlier work, translate his formula easily 
into a statement about the radiating atom (the so-called oscillator), he 
must soon have found that his formula looked as if the oscillator could 
only contain discrete quanta of energy - a result that was so different 
from anything known in classical physics that he certainly must have 
refused to believe it in the beginning. But in a period of most intensive 
work during the summer of 1900 he finally convinced himself that there was 
no way of escaping from this conclusion. It was told by Planck's son that 
his father spoke to him about his new ideas on a long walk through the 
Grunewald, the wood in the suburbs of Berlin. On this walk he explained 
that he felt he had possibly made a discovery of the first rank, 
comparable perhaps only to the discoveries of Newton. So Planck must have 
realised at this time that his formula had touched the foundations of our 
description of nature, and that these foundations would one day start to 
move from their traditional present location toward a new and as yet 
unknown position of stability. Planck, who was conservative in his whole 
outlook, did not like this consequence at all, but he published his 
quantum hypothesis in December of 1900. 

The idea that energy could be emitted or absorbed only in discrete energy 
quanta was so new that it could not be fitted into the traditional 
framework of physics. An attempt by Planck to reconcile his new hypothesis 
with the older laws of radiation failed in the essential points. It took 
five years until the next step could be made in the new direction. 

This time it was the young Albert Einstein, a revolutionary genius among 
the physicists, who was not afraid to go further away from the old 
concepts. There were two problems in which he could make use of the new 
ideas. One was the so-called photoelectric effect, the emission of 
electrons from metals under the influence of light. The experiments, 
especially those of Lenard, had shown that the energy of the emitted 
electrons did not depend on the intensity of the light, but only on its 
colour or, more precisely, on its frequency. This could not be understood 
on the basis of the traditional theory of radiation. Einstein could 
explain the observations by interpreting Planck's hypothesis as saying 
that light consists of quanta of energy travelling through space. The 
energy of one light quantum should, in agreement with Planck's 
assumptions, be equal to the frequency of the light multiplied by Planck's 

The other problem was the specific heat of solid bodies. The traditional 
theory led to values for the specific heat which fitted the observations 
at higher temperatures but disagreed with them at low ones. Again Einstein 
was able to show that one could understand this behaviour by applying the 
quantum hypothesis to the elastic vibrations of the atoms in the solid 
body. These two results marked a very important advance, since they 
revealed the presence of Planck's quantum of action - as his constant is 
called among the physicists - in several phenomena, which had nothing 
immediately to do with heat radiation. They revealed at the same time the 
deeply revolutionary character of the new hypothesis, since the first of 
them led to a description of light completely different from the 
traditional wave picture. Light could either be interpreted as consisting 
of electromagnetic waves, according to Maxwell's theory, or as consisting 
of light quanta, energy packets travelling through space with high 
velocity. But could it be both? Einstein knew, of course, that the well-
known phenomena of diffraction and interference can be explained only on 
the basis of the wave picture. He was not able to dispute the complete 
contradiction between this wave picture and the idea of the light quanta; 
nor did he even attempt to remove the inconsistency of this 
interpretation. He simply took the contradiction as something which would 
probably be understood only much later. 

In the meantime the experiments of Becquerel, Curie and Rutherford had led 
to some clarification concerning the structure of the atom. In 1911 
Rutherford's observations on the interaction of a-rays penetrating through 
matter resulted in his famous atomic model. The atom is pictured as 
consisting of a nucleus, which is positively charged and contains nearly 
the total mass of the atom, and electrons, which circle around the nucleus 
like the planets circle around the sun. The chemical bond between atoms of 
different elements is explained as an interaction between the outer 
electrons of the neighbouring atoms; it has not directly to do with the 
atomic nucleus. The nucleus determines the chemical behaviour of the atom 
through its charge which in turn fixes the number of electrons in the 
neutral atom. Initially this model of the atom could not explain the most 
characteristic feature of the atom, its enormous stability. No planetary 
system following the laws of Newton's mechanics would ever go back to its 
original configuration after a collision with another such system. But an 
atom of the element carbon, for instance, will still remain a carbon atom 
after any collision or interaction in chemical binding. 

The explanation for this unusual stability was given by Bohr in 1913, 
through the application of Planck's quantum hypothesis. If the atom can 
change its energy only by discrete energy quanta, this must mean that the 
atom can exist only in discrete stationary states, the lowest of which is 
the normal state of the atom. Therefore, after any kind of interaction the 
atom will finally always fall back into its normal state. 

By this application of quantum theory to the atomic model, Bohr could not 
only explain the stability of the atom but also. in some simple cases, 
give a theoretical interpretation of the line spectra emitted by the atoms 
after the excitation through electric discharge or heat. His theory rested 
upon a combination of classical mechanics for the motion of the electrons 
with quantum conditions, which were imposed upon the classical motions for 
defining the discrete stationary states of the system. A consistent 
mathematical formulation for those conditions was later given by 
Sommerfeld. Bohr was well aware of the fact that the quantum conditions 
spoil in some way the consistency of Newtonian mechanics. In the simple 
case of the hydrogen atom one could calculate from Bohr's theory the 
frequencies of the light emitted by the atom, and the agreement with the 
observations was perfect. Yet these frequencies were different from the 
orbital frequencies and their harmonies of the electrons circling around 
the nucleus, and this fact showed at once that the theory was still full 
of contradictions. But it contained an essential part of the truth. It did 
explain qualitatively the chemical behaviour of the atoms and their line 
spectra; the existence of the discrete stationary states was verified by 
the experiments of Franck and Hertz, Stern and Gerlach. 

Bohr's theory had opened up a new line of research. The great amount of 
experimental material collected by spectroscopy through several decades 
was now available for information about the strange quantum laws governing 
the motions of the electrons in the atom. The many experiments of 
chemistry could be used for the same purpose. It was from this time on 
that the physicists learned to ask the right questions; and asking the 
right question is frequently more than halfway to the solution of the 

What were these questions? Practically all of them had to do with the 
strange apparent contradictions between the results of different 
experiments. How could it be that the same radiation that produces 
interference patterns, and therefore must consist of waves, also produces 
the photoelectric effect, and therefore must consist of moving particles? 
How could it be that the frequency of the orbital motion of the electron 
in the atom does not show up in the frequency of the emitted radiation? 
Does this mean that there is no orbital motion? But if the idea of orbital 
motion should be incorrect, what happens to the electrons inside the atom? 
One can see the electrons move through a cloud chamber, and sometimes they 
are knocked out of an atom- why should they not also move within the atom? 
It is true that they might be at rest in the normal state of the atom, the 
state of lowest energy. But there are many states of higher energy, where 
the electronic shell has an angular momentum. There the electrons cannot 
possibly be at rest. One could add a number of similar examples. Again and 
again one found that the attempt to describe atomic events in the 
traditional terms of physics led to contradictions. 

Gradually, during the early twenties, the physicists became accustomed to 
these difficulties, they acquired a certain vague knowledge about where 
trouble would occur, and they learned to avoid contradictions. They knew 
which description of an atomic event would be the correct one for the 
special experiment under discussion. This was not sufficient to form a 
consistent general picture of what happens in a quantum process, but it 
changed the minds of the physicists in such a way that they somehow got 
into the spirit of quantum theory. Therefore, even some time before one 
had a consistent formulation of quantum theory one knew more or less what 
would be the result of any experiment. 

One frequently discussed what one called ideal experiments. Such 
experiments were designed to answer a very critical question irrespective 
of whether or not they could actually be carried out. Of course it was 
important that it should be possible in principle to carry out the 
experiment, but the technique might be extremely complicated. These ideal 
experiments could be very useful in clarifying certain problems. If there 
was no agreement among the physicists about the result of such an ideal 
experiment, it was frequently possible to find a similar but simpler 
experiment that could be carried out, so that the experimental answer 
contributed essentially to the clarification of quantum theory. 

The strangest experience of those years was that the paradoxes of quantum 
theory did not disappear during this process of clarification; on the 
contrary, they became even more marked and more exciting. There was, for 
instance, the experiment of Compton on the scattering of X-rays. From 
earlier experiments on the interference of scattered light there could be 
no doubt that scattering takes place essentially in the following way: The 
incident light wave makes an electron in the beam vibrate in the frequency 
of the wave; the oscillating electron then emits a spherical wave with the 
same frequency and thereby produces the scattered light. However, Compton 
found in 1923 that the frequency of scattered X-rays was different from 
the frequency of the incident X-ray. This change of frequency could be 
formally understood by assuming that scattering is to be described as 
collision of a light quantum with an electron. The energy of the light 
quantum is changed during the collision; and since the frequency times 
Planck's constant should be the energy of the light quantum, the frequency 
also should be changed. But what happens in this interpretation of the 
light wave? The two experiments - one on the interference of scattered 
light and the other on the change of frequency of the scattered light - 
seemed to contradict each other without any possibility of compromise. 

By this time many physicists were convinced that these apparent 
contradictions belonged to the intrinsic structure of atomic physics. 
Therefore, in I924 de Broglie in France tried to extend the dualism 
between wave description and particle description to the elementary 
particles of matter, primarily to the electrons. He showed that a certain 
matter wave could 'correspond' to a moving electron, just as a light wave 
corresponds: to a moving light quantum. It was not clear at the time what 
the word 'correspond' meant in this connection. But de Broglie suggested 
that the quantum condition in Bohr's theory should be interpreted as a 
statement about the matter waves. A wave circling around a nucleus can for 
geometrical reasons only be a stationary wave; and the perimeter of the 
orbit must be an integer multiple of the wave length. In this way de 
Broglie's idea connected the quantum condition. which always had been a 
foreign element in the mechanics of the electrons, with the dualism 
between waves and particles. 

In Bohr's theory the discrepancy between the calculated orbital frequency 
of the electrons and the frequency of the emitted radiation had to be 
interpreted as a limitation to the concept of the electronic orbit. This 
concept had been somewhat doubtful from the beginning. For the higher 
orbits, however, the electrons should move at a large distance from the 
nucleus just as they do when one sees them moving through a cloud chamber. 
There one should speak about electronic orbits. It was therefore very 
satisfactory that for these higher orbits the frequencies of the emitted 
radiation approach the orbital frequency and its higher harmonics. Also 
Bohr had already suggested in his early papers that the intensities of the 
emitted spectral lines approach the intensities of the corresponding 
harmonics. This principle of correspondence had proved very useful for the 
approximative calculation of the intensities of spectral lines. In this 
way one had the impression that Bohr's theory gave a qualitative but not a 
quantitative description of what happens inside the atom; that some new 
feature of the behaviour of matter was qualitatively expressed by the 
quantum conditions, which in turn were connected with the dualism between 
waves and particles. 

The precise mathematical formulation of quantum theory finally emerged 
from two different developments. The one started from Bohr's principle of 
correspondence. One had to give up the concept of the electronic orbit, 
but still had to maintain it in the limit of high quantum numbers, i.e., 
for the large orbits. 

In this latter case the emitted radiation, by means of its frequencies and 
intensities, gives a picture of the electronic orbit; it represents what 
the mathematicians call a Fourier expansion of the orbit. The idea 
suggested itself that one should write down the mechanical laws not as 
equations for the positions and velocities of the electrons but as 
equations for the frequencies and amplitudes of their Fourier expansion. 
Starting from such equations and changing them very little one could hope 
to come to relations for those quantities which correspond to the 
frequencies and intensities of the emitted radiation, even for the small 
orbits and the ground state of the atom. This plan could actually be 
carried out; in the summer of 1925 it led to a mathematical formalism 
called matrix mechanics or, more generally, quantum mechanics. The 
equations of motion in Newtonian mechanics were replaced by similar 
equations between matrices; it was a strange experience to find that many 
of the old results of Newtonian mechanics, like conservation of energy, 
etc., could be derived also in the new scheme. Later the investigations of 
Born, Jordan and Dirac showed that the matrices representing position and 
momentum of the electron did not commute. This latter fact demonstrated 
clearly the essential difference between quantum mechanics and classical 

The other development followed de Broglie's idea of matter waves. 
Schrödinger tried to set up a wave equation for de Broglie's stationary 
waves around the nucleus. Early in 1926 he succeeded in deriving the 
energy values of the stationary states of the hydrogen atom as 
'Eigenvalues' of his wave equation and could give a more general 
prescription for transforming a given set of classical equations of motion 
into a corresponding wave equation in a space of many dimensions. Later he 
was able to prove that his formalism of wave mechanics was mathematically 
equivalent to the earlier formalism of quantum mechanics. 

Thus one finally had a consistent mathematical formalism, which could be 
defined in two equivalent ways starting either from relations between 
matrices or from wave equations. This formalism gave the correct energy 
values for the hydrogen atom: it took less than one year to show that it 
was also successful for the helium atom and the more complicated problems 
of the heavier atoms. But in what sense did the new formalism describe the 
atom? The paradoxes of the dualism between wave picture and particle 
picture were not solved; they were hidden somehow in the mathematical 

A first and very interesting step toward a real understanding Of quantum 
theory was taken by Bohr, Kramers and Slater in 192,+. These authors tried 
to solve the apparent contradiction between the wave picture and the 
particle picture by the concept of the probability wave. The 
electromagnetic waves were interpreted not as 'real' waves but as 
probability waves, the intensity of which determines in every point the 
probability for the absorption (or induced emission) of a light quantum by 
an atom at this point. This idea led to the conclusion that the laws of 
conservation of energy and momentum need not be true for the single event, 
that they are only statistical laws and are true only in the statistical 
average. This conclusion was not correct, however, and the connections 
between the wave aspect and the particle aspect of radiation were still 
more complicated. 

But the paper of Bohr, Kramers and Slater revealed one essential feature 
of the correct interpretation of quantum theory. This concept of the 
probability wave was something entirely new in theoretical physics since 
Newton. Probability in mathematics or in statistical mechanics means a 
statement about our degree of knowledge of the actual situation. In 
throwing dice we do not know the fine details of the motion of our hands 
which determine the fall of the dice and therefore we say that the 
probability for throwing a special number is just one in six. The 
probability wave of Bohr, Kramers, Slater, however, meant more than that; 
it meant a tendency for something. It was a quantitative version of the 
old concept of 'potentia' in Aristotelian philosophy. It introduced 
something standing in the middle between the idea of an event and the 
actual event, a~~ strange kind of physical reality just in the middle 
between possibility and reality. r Later when the mathematical framework 
of quantum theory was fixed, Born took up this idea of the probability 
wave and gave a clear definition of the mathematical quantity in the 
formalism. which was to be interpreted as the probability wave. It X as 
not a three-dimensional wave like elastic or radio waves, but a wave in 
the many-dimensional configuration space, and therefore a rather abstract 
mathematical quantity, 

Even at this time, in the summer of I926, it was not clear in every case 
how the mathematical formalism should be used to describe a given 
experimental situation. One knew how to describe the stationary states of 
an atom, but one did not know how to describe a much simpler event - as 
for instance an electron moving through a cloud chamber. 

When Schrödinger in that summer had shown that his formalism of wave 
mechanics was mathematically equivalent to quantum mechanics he tried for 
some time to abandon the idea of quanta and 'quantum jumps' altogether and 
to replace the electrons in the atoms simply by his three-dimensional 
matter waves. He was inspired to this attempt by his result, that the 
energy levels of the hydrogen atom in his theory seemed to be simply the 
eigenfrequencies of the stationary matter waves. Therefore, he thought it 
was a mistake to call them energies: they were just frequencies. But in 
the discussions which took place in the autumn of I926 in Copenhagen 
between Bohr and Schrödinger and the Copenhagen group of physicists it 
soon became apparent that such an interpretation would not even be 
sufficient to explain Planck's formula of heat radiation. 

During the months following these discussions an intensive study of all 
questions concerning the interpretation of quantum theory in Copenhagen 
finally led to a complete and, as many physicists believe, satisfactory 
clarification of the situation. But it was not a solution which one could 
easily accept. I remember discussions with Bohr which went through many 
hours till very late at night and ended almost in despair; and when at the 
end of the discussion I went alone for a walk in the neighbouring park I 
repeated to myself again and again the question: Can nature possibly be as 
absurd as it seemed to us in these atomic experiments? 

The final solution was approached in two different ways. The one was a 
turning around of the question. Instead of asking: How can one in the 
known mathematical scheme express a given experimental situation? the 
other question was put: Is it true, perhaps, that only such experimental 
situations can arise in nature as can be expressed in the mathematical 
formalism? The assumption that this was actually true led to limitations 
in the use of those concepts that had been the basis of classical physics 
since Newton. One could speak of the position and of the velocity of an 
electron as in Newtonian mechanics and one could observe and measure these 
quantities. But one could not fix both quantities simultaneously with an 
arbitrarily high accuracy. Actually the product of these two inaccuracies 
turned out to be not less than Planck's constant divided by the mass of 
the particle. Similar relations could be formulated for other experimental 
situations. They are usually called relations of uncertainty or principle 
of indeterminacy. One had learned that the old concepts fit nature only 

lie other way of approach was Bohr's concept of complementarity. 
Schrödinger had described the atom as a system not of a nucleus and 
electrons but of a nucleus and matter waves. This picture of the matter 
waves certainly also contained an element of truth. Bohr considered the 
two pictures - particle picture and wave picture - as two complementary 
descriptions of the same reality. Any of these descriptions can be only 
partially true, there must be limitations to the use of the particle 
concept as well as of wave concept, else one could not avoid 
contradictions. If one takes into account those limitations which can be 
expressed by the uncertainty relations, the contradictions disappear. 

In this way since the spring of I927 one has had a consistent 
interpretation of quantum theory, which is frequently called the 
'Copenhagen interpretation'. This interpretation received its crucial test 
in the autumn of 1927 at the Solvay conference in Brussels. Those 
experiments which had always led to the worst paradoxes were again and 
again discussed in all details, especially by Einstein. New ideal 
experiments were invented to trace any possible inconsistency of the 
theory, but the theory was shown to be consistent and seemed to fit the 
experiments as far as one could see. 

The details of this Copenhagen interpretation will be the subject of the 
next chapter. It should be emphasised at this point that it has taken more 
than a quarter of a century to get from the first idea of the existence of 
energy quanta to a real understanding of the quantum theoretical laws. 
This indicates the great change that had to take place in the fundamental 
concepts concerning reality before one could understand the new situation.


Quantum Theory, also quantum mechanics, in physics, a theory based on 
using the concept of the quantum unit to describe the dynamic properties 
of subatomic particles and the interactions of matter and radiation. The 
foundation was laid by the German physicist Max Planck, who postulated in 
1900  that energy can be emitted or absorbed by matter only in small, 
discrete units called quanta. Also fundamental to the development of 
quantum mechanics was the uncertainty principle, formulated by the German 
physicist Werner Heisenberg in 1927, which states that the position and 
momentum of a subatomic particle cannot be specified simultaneously.
II.EARLY HISTORY In the 18th and 19th centuries, Newtonian, or classical, 
mechanics appeared to provide a wholly accurate description of the motions 
of bodies-for example, planetary motion. In the late 19th and early 20th 
centuries, however, experimental findings raised doubts about the 
completeness of Newtonian theory. Among the newer observations were the 
lines that appear in the spectra of light emitted by heated gases, or 
gases in which electric discharges take place. From the model of the atom 
developed in the early 20th century by the English physicist Ernest 
Rutherford, in which negatively charged electrons circle a positive 
nucleus in orbits prescribed by Newton's laws of motion, scientists had 
also expected that the electrons would emit light over a broad frequency 
range, rather than in the narrow frequency ranges that form the lines in a 
Another puzzle for physicists was the coexistence of two theories of 
light: the corpuscular theory, which explains light as a stream of 
particles, and the wave theory, which views light as electromagnetic 
waves. A third problem was the absence of a molecular basis for 
thermodynamics. In his book Elementary Principles in Statistical Mechanics 
(1902), the American mathematical physicist J. Willard Gibbs conceded the 
impossibility of framing a theory of molecular action that reconciled 
thermodynamics, radiation, and electrical phenomena as they were then 
physicists did not yet clearly recognize that these and other difficulties 
in physics were in any way related. The first development that led to the 
solution of these difficulties was Planck's introduction of the concept of 
the quantum, as a result of physicists' studies of blackbody radiation 
during the closing years of the 19th century. (The term blackbody refers 
to an ideal body or surface that absorbs all radiant energy without any 
reflection.) A body at a moderately high temperature-a "red heat"-gives 
off most of its radiation in the low frequency (red and infrared) regions; 
a body at a higher temperature-"white heat"-gives off comparatively more 
radiation in higher frequencies (yellow, green, or blue). During the 1890s 
physicists conducted detailed quantitative studies of these phenomena and 
expressed their results in a series of curves or graphs. The classical, or 
prequantum, theory predicted an altogether different set of curves from 
those actually observed. What Planck did was to devise a mathematical 
formula that described the curves exactly; he then deduced a physical 
hypothesis that could explain the formula. His hypothesis was that energy 
is radiated only in quanta of energy hu, where u is the frequency and h is 
the quantum action, now known as Planck's constant.
IVEINSTEIN'S CONTRIBUTION The next important developments in quantum 
mechanics were the work of German-born American physicist and Nobel 
laureate Albert Einstein. He used Planck's concept of the quantum to 
explain certain properties of the photoelectric effect-an experimentally 
observed phenomenon in which electrons are emitted from metal surfaces 
when radiation falls on these surfaces.
According to classical theory, the energy, as measured by the voltage of 
the emitted electrons, should be proportional to the intensity of the 
radiation. The energy of the electrons, however, was found to be 
independent of the intensity of radiation-which determined only the number 
of electrons emitted-and to depend solely on the frequency of the 
radiation. The higher the frequency of the incident radiation, the greater 
is the electron energy; below a certain critical frequency no electrons 
are emitted. These facts were explained by Einstein by assuming that a 
single quantum of radiant energy ejects a single electron from the metal. 
The energy of the quantum is proportional to the frequency, and so the 
energy of the electron depends on the frequency.
VTHE BOHR ATOM In 1911 Rutherford established the existence of the atomic 
nucleus. He assumed, on the basis of experimental evidence obtained from 
the scattering of alpha particles by the nuclei of gold atoms, that every 
atom consists of a dense, positively charged nucleus, surrounded by 
negatively charged electrons revolving around the nucleus as planets 
revolve around the sun. The classical electromagnetic theory developed by 
the British physicist James Clerk Maxwell unequivocally predicted that an 
electron revolving around a nucleus will continuously radiate 
electromagnetic energy until it has lost all its energy, and eventually 
will fall into the nucleus. Thus, according to classical theory, an atom, 
as described by Rutherford, is unstable. This difficulty led the Danish 
physicist Niels Bohr, in 1913, to postulate that in an atom the classical 
theory does not hold, and that electrons move in fixed orbits. Every 
change in orbit by the electron corresponds to the absorption or emission 
of a quantum of radiation.
The application of Bohr's theory to atoms with more than one electron 
proved difficult. The mathematical equations for the next simplest atom, 
the helium atom, were solved during the 1910s and 1920s, but the results 
were not entirely in accordance with experiment. For more complex atoms, 
only approximate solutions of the equations are possible, and these are 
only partly concordant with observations.
VIWAVE MECHANICS The French physicist Louis Victor de Broglie suggested in 
1924 that because electromagnetic waves show particle characteristics, 
particles should, in some cases, also exhibit wave properties. This 
prediction was verified experimentally within a few years by the American 
physicists Clinton Joseph Davisson and Lester Halbert Germer and the 
British physicist George Paget Thomson. They showed that a beam of 
electrons scattered by a crystal produces a diffraction pattern 
characteristic of a wave (see Diffraction). The wave concept of a particle 
led the Austrian physicist Erwin Schrödinger to develop a so-called wave 
equation to describe the wave properties of a particle and, more 
specifically, the wave behavior of the electron in the hydrogen atom.
Although this differential equation was continuous and gave solutions for 
all points in space, the permissible solutions of the equation were 
restricted by certain conditions expressed by mathematical equations 
called eigenfunctions (German eigen,"own"). The Schrödinger wave equation 
thus had only certain discrete solutions; these solutions were 
mathematical expressions in which quantum numbers appeared as parameters. 
(Quantum numbers are integers developed in particle physics to give the 
magnitudes of certain characteristic quantities of particles or systems.) 
The Schrödinger equation was solved for the hydrogen atom and gave 
conclusions in substantial agreement with earlier quantum theory. 
Moreover, it was solvable for the helium atom, which earlier theory had 
failed to explain adequately, and here also it was in agreement with 
experimental evidence. The solutions of the Schrödinger equation also 
indicated that no two electrons could have the same four quantum numbers-
that is, be in the same energy state. This rule, which had already been 
established empirically by Austro-American physicist and Nobel laureate 
Wolfgang Pauli in 1925, is called the exclusion principle.
VIIMATRIX MECHANICS Simultaneously with the development of wave mechanics, 
Heisenberg evolved a different mathematical analysis known as matrix 
mechanics. According to Heisenberg's theory, which was developed in 
collaboration with the German physicists Max Born and Ernst Pascual 
Jordan, the formula was not a differential equation but a matrix: an array 
consisting of an infinite number of rows, each row consisting of an 
infinite number of quantities. Matrix mechanics introduced infinite 
matrices to represent the position and momentum of an electron inside an 
atom. Also, different matrices exist, one for each observable physical 
property associated with the motion of an electron, such as energy, 
position, momentum, and angular momentum. These matrices, like 
Schrödinger's differential equations, could be solved; in other words, 
they could be manipulated to produce predictions as to the frequencies of 
the lines in the hydrogen spectrum and other observable quantities. Like 
wave mechanics, matrix mechanics was in agreement with the earlier quantum 
theory for processes in which the earlier quantum theory agreed with 
experiment; it was also useful in explaining phenomena that earlier 
quantum theory could not explain.
VIIITHE MEANING OF QUANTUM MECHANICS Schrödinger subsequently succeeded in 
showing that wave mechanics and matrix mechanics are different 
mathematical versions of the same theory, now called quantum mechanics. 
Even for the simple hydrogen atom, which consists of two particles, both 
mathematical interpretations are extremely complex. The next simplest 
atom, helium, has three particles, and even in the relatively simple 
mathematics of classical dynamics, the three-body problem (that of 
describing the mutual interactions of three separate bodies) is not 
entirely soluble. The energy levels can be calculated accurately, however, 
even if not exactly. In applying quantum-mechanics mathematics to 
relatively complex situations, a physicist can use one of a number of 
mathematical formulations. The choice depends on the convenience of the 
formulation for obtaining suitable approximate solutions.
Although quantum mechanics describes the atom purely in terms of 
mathematical interpretations of observed phenomena, a rough verbal 
description can be given of what the atom is now thought to be like. 
Surrounding the nucleus is a series of stationary waves; these waves have 
crests at certain points, each complete standing wave representing an 
orbit. The absolute square of the amplitude of the wave at any point is a 
measure of the probability that an electron will be found at that point at 
any given time. Thus, an electron can no longer be said to be at any 
precise point at any given time.
IXTHE UNCERTAINTY PRINCIPLE The impossibility of pinpointing an electron 
at any precise time was analyzed by Heisenberg, who in 1927 formulated the 
uncertainty principle. This principle states the impossibility of 
simultaneously specifying the precise position and momentum of any 
particle. In other words, the more accurately a particle's momentum is 
measured and known, the less accuracy there can be in the measurement and 
knowledge of its position. This principle is also fundamental to the 
understanding of quantum mechanics as it is generally accepted today: The 
wave and particle character of electromagnetic radiation can be understood 
as two complementary properties of radiation.
Another way of expressing the uncertainty principle is that the wavelength 
of a quantum mechanical principle is inversely proportional to its 
momentum. As atoms are cooled they slow down and their corresponding 
wavelength grows larger. At a low enough temperature this wavelength is 
predicted to exceed the spacing between particles, causing atoms to 
overlap, becoming indistinguishable, and melding into a single quantum 
state. In 1995 a team of Colorado scientists, led by National Institutes 
of Standards and Technology physicist Eric Cornell and University of 
Colorado physicist Carl Weiman, cooled rubidium atoms to a temperature so 
low that the particles entered this merged state, known as a Bose-Einstein 
condensate. The condensate essentially behaves like one atom even though 
it is made up of thousands.
XRESULTS OF QUANTUM THEORY Quantum mechanics solved all of the great 
difficulties that troubled physicists in the early years of the 20th 
century. It gradually enhanced the understanding of the structure of 
matter, and it provided a theoretical basis for the understanding of 
atomic structure (see Atom and Atomic Theory) and the phenomenon of 
spectral lines: Each spectral line corresponds to the energy of a photon 
transmitted or absorbed when an electron makes a transition from one 
energy level to another. The understanding of chemical bonding was 
fundamentally transformed by quantum mechanics and came to be based on 
Schrödinger's wave equations. New fields in physics emerged-condensed 
matter physics, superconductivity, nuclear physics, and elementary 
particle physics (see Physics)-that all found a consistent basis in 
quantum mechanics.
XIFURTHER DEVELOPMENTS In the years since 1925, no fundamental 
deficiencies have been found in quantum mechanics, although the question 
of whether the theory should be accepted as complete has come under 
discussion. In the 1930s the application of quantum mechanics and special 
relativity to the theory of the electron (see Quantum Electrodynamics) 
allowed the British physicist Paul Dirac to formulate an equation that 
referred to the existence of the spin of the electron. It further led to 
the prediction of the existence of the positron, which was experimentally 
verified by the American physicist Carl David Anderson.
The application of quantum mechanics to the subject of electromagnetic 
radiation led to explanations of many phenomena, such as bremsstrahlung 
(German, "braking radiation," the radiation emitted by electrons slowed 
down in matter) and pair production (the formation of a positron and an 
electron when electromagnetic energy interacts with matter). It also led 
to a grave problem, however, called the divergence difficulty: Certain 
parameters, such as the so-called bare mass and bare charge of electrons, 
appear to be infinite in Dirac's equations. (The terms bare mass and bare 
charge refer to hypothetical electrons that do not interact with any 
matter or radiation; in reality, electrons interact with their own 
electric field.) This difficulty was partly resolved in 1947-49 in a 
program called renormalization, developed by the Japanese physicist 
Shin'ichirô Tomonaga, the American physicists Julian S. Schwinger and 
Richard Feynman, and the British physicist Freeman Dyson. In this program, 
the bare mass and charge of the electron are chosen to be infinite in such 
a way that other infinite physical quantities are canceled out in the 
equations. Renormalization greatly increased the accuracy with which the 
structure of atoms could be calculated from first principles.
XIIFUTURE PROSPECTS Quantum mechanics underlies current attempts to 
account for the strong nuclear force (see Quantum Chromodynamics) and to 
develop a unified theory for all the fundamental interactions of matter 
(see Physics: Modern Physics: Unified Field Theories). Nevertheless, 
doubts exist about the completeness of quantum theory. The divergence 
difficulty, for example, is only partly resolved. Just as Newtonian 
mechanics was eventually amended by quantum mechanics and relativity, many 
scientists-and Einstein was among them-are convinced that quantum theory 
will also undergo profound changes in the future. Great theoretical 
difficulties exist, for example, between quantum mechanics and chaos 
theory, which began to develop rapidly in the 1980s. Ongoing efforts are 
being made by theorists such as the British physicist Stephen Hawking, to 
develop a system that encompasses both relativity and quantum mechanics.

Now to the SUPERSYMMETRY and to answer what connects it to the Quantum 

Supersymmetry (SUSY) is a generalization of the space time symmetrics of 
quantum field theory tthat performs fermions into bosons and vice versa.It 
also provides a frame work for the unification of particle physics and 
gravity,which is governed by the Planck Scale (please see my scans for 
equations)(definded to be the enegery scale where the gravitational 
interactions of elementary particles become compareable to their gauge 
interactions) If supersymmetry were an exact symmetry of nature,then 
particles and their superpartners(which differ in spin by half a unit) 
would be degenerate in mass. Thus supersummetry cannot be an exact 
symmetry of nature and must be broken . In theories of "low energy" 
supersymmetry the effective scale of supersymmetry breaking is tied to the 
electroweak scale which is characterized by the Standard Model Higgs 
vaccum expectaions value v=246GeV. It is thus possible that supersymmetry 
will ultimatley explain the origin of the large hirachy of energy scales 
from W and Z masses to the Planck Scale.
At present there is no unambiguous eperimental results that require  the 
existence of low-energy supersymmetry. However if experimentation  at 
future colliders uncovers evidence for supersymmetry,this would have a 
profoiund effect on the study of Te-scale physicsand the development of a 
more fundamentaltheory of mass and symmetry breaking phenomena in particle 

Now back to your other questions: If we would completly understand the 
uuniverse on it's supernatural level...would we understand the Universe? I 
honestly don't know but it woudl surley deepen our understanding a great 
For every answer there is at least two new questions. 
For example we need a whole new set of physics to describe what goes on in 
a Singularity ...

. How does the Mandelbrot set help in understanding our 

It is a start to tackle the "CHASO THEORY" and I recommend that you check 

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