Planck's constant:
 Planck makes `quantum' assumption to resolve atomic structure
 a quantum is a discrete, and smallest, unit of energy
 all forms of energy are transfered in quantums, not continuous
 electron transition from orbit to orbit must be in discrete quantum jumps
 experiments show that there is no `inbetween' for quantum transitions = new kind of reality
 despite strangeness, experiments confirm quantum predictions and resolves UV catastrophe
WaveParticle Dualism:
 The wavelike nature of light explains most of its properties:
 reflection/refraction
 diffraction/interference
 Doppler effect
 however, a particle description is suggested by the photoelectric effect, the release of electrons by a beam
of energetic blue/UV light
 wavelike descriptions of light fail to explain the lack of the photoelectric effect for red light
 particle and wave properties to light is called waveparticle dualism and continues the strange
characteristics to the new science of quantum physics
 waveparticle dualism is extended to matter particles, i.e. electrons act as waves
Bohr Atom:
 classical physics fails to describe the properties of atoms, Planck's constant served to bridge the gap
between the classical world and the new physics
 Bohr proposed a quantized shell model for the atom using the same basic structure as Rutherford, but
restricting the behavior of electrons to quantized orbits
 Bohr's calculation produce an accurate map of the hydrogen atom energy levels
 changes in electron orbits requires the release or gain of energy in the form of photons
 Bohr's atom perfectly explains the spectra in stars as gaps due to the absorption of photons of particular
wavelengths that match the electron orbits of the various elements
 larger formulations explain all the properties outlined by Kirchoff's laws
de Broglie Matter Waves:
 early quantum physics did not ask the question of `why' quantum effects are found in the microscopic world

One way of thinking of a matter wave (or a photon) is to think of a wave packet.
Normal waves look with this:

having no beginning and no end. A composition of several waves of different
wavelength can produce a wave packet that looks like this:
 the wave packet interpretation requires the particle to have no set position
 momentum of a particle is proportional to the wavelength of the particle

Lastly, the wave nature of the electron makes for an elegant explanation to
quantized orbits around the atom. Consider what a wave looks like around an orbit,
as shown below
 only certain wavelengths will fit into orbit, so quantiziation is due to wavelike nature of particles
 wavelike nature also means that a particles existence is spread out, a probability field
 the idea of atoms being solid billiard ball type objects fails with quantum physics
 quantum effects fade on larger scales since macroscopic objects have high momentum values and therefore small
wavelengths
Young TwoSlit Experiment:
 the two slit experiment is key to understand the microscopic world
click here to interference movie
click here to see a wave experiment
 waves can interfere, for light this will make a series of light and dark bands
 matter particles, such as electrons, also produce interference patterns due to their wavelike nature
 so with a high flux of either photons or electrons, the characteristic interference pattern is visible
 if we lower the intensity of light, or the flux of electrons (the electric current), we should be able to see
each photon strike the screen
 each photon makes a dot on the screen, but where is the interference pattern?
 the interference pattern is still there, it simply takes some time for enough photons, or electrons, to
strike the screen to build up a recognizable pattern
 interference, or a wave phenomenon, is still occurring even if we only let the photons, or electrons, through
one at a time
 so what are the individual particles interfering with? apparently, themselves
 in order for a particle to interfere with itself, it must pass through both slits
 this forces us to give up the common sense notion of location
click here to see a particle experiment
Quantum Wave Function:
 a wave packet interpretation for particles means there is an intrinsic fuzziness assign to them
 the wave function is the mathematical tool to describe quantum entities
 wave function express likelihood *until* a measurement is made
Superposition:
 quantum physics is a science of possibilities rather than exactness of Newtonian physics
 quantum objects and quantities becomes actual when observed
 key proof of quantum superpositions is the phenomenon of quantum tunneling
 the position of the electron, the wave function, is truly spread out, not uncertain
 observation causes the wave function to collapse to an actual
 quantum existence is tied to the environment, opposite to the independence of macroscopic objects
Uncertainty Principle:
 the uncertainty principle states that the position and velocity
cannot both be measured,exactly, at the same time (actually pairs of position, energy and
time)
 uncertainty principle derives from the measurement problem, the intimate connection between the wave and
particle nature of quantum objects
 the change in a velocity of a particle becomes more ill defined as the wave function is confined to a smaller
region
 the wave nature to particles means a particle is a wave packet, the composite of many waves
 many waves = many momentums, observation makes one momentum out of many
 exact knowledge of complementarity pairs (position, energy, time) is impossible
 complementary also means that different experiments yield different results (e.g. the two slit experiment)
 therefore, a single reality can not be applied at the quantum level
 the mathematical form of the uncertainty principle relates complementary to Planck's constant
 knowledge is not unlimited, builtin indeterminacy exists, but only in the microscopic world, all collapses
to determinism in the macroscopic world
Quantum Mechanics:
 quantum mechanics is to the microscopic world what classic mechanics and calculus is to the macroscopic world
 it is the operational process of calculating quantum physics phenomenon
 its primary task is to bring order and prediction to the uncertainty of the quantum world, its main tool is
Schrodinger's equation
 the key difference between quantum and classical mechanics is the role of probability and chance
 quantum objects are described by probability fields, however, this does not mean they are indeterminit, only
uncertain
Schrodinger's Cat and Quantum Reality:
 an example of the weirdness of the quantum world is given by the famous Schrodinger cat paradox
 the paradox is phrased such that a quantum event determines if a cat is killed or not
 from a quantum perspective, the whole system state is tied to the wave function of the quantum event, i.e.
the cat is both dead and alive at the same time
 the paradox in some sense is not a paradox, but instead points out the tension between the microscopic and
macroscopic worlds and the importance of the observer in a quantum scenario
 quantum objects exist in superposition, many states, as shown by interference
 the observer collapses the wave function
Macroscopic/Microscopic World Interface:
 events in the microscopic world can happen *without* cause = indeterminacy
 phenomenon such as tunneling shows that quantum physics leaks into the macroscopic world
 decoherence prevents a macroscopic Schrodinger cat paradox
 new technology allows the manipulation of objects at the quantum level
 future research will investigate areas such as quantum teleportation and quantum computing
Hidden Variables Hypothesis:
 macroscopic physics states that all variables are there, just hard to measure
 Copenhagen Interpretation states that variables are not there, randomness is fundamental
 indeterminacy was unpopular (not platonic)
 Bell hypothesis is that quantum variables exist, but are hidden, special forces required
 hidden variables are not testable, poor science
ManyWorlds Hypothesis :
 collapse of the wave function still presents a problem for deterministic physics
 solution is to not collapse the wave function, rather split reality
 many worlds hypothesis is allows for the existence of all quantum states, observation splits the worlds
containing the states
 macroscopic systems exhibit irreversible behavior (entropy) that prevents the reconnection o fpast worlds and
present the observed world as real to individuals
 many worlds does not allow communicatation between the worlds, but their existence can be tested in two slit
experiments (the other worlds are doing the interfering) and with reversable mind experiements (nanoAI's)
Holism:
 holism is a philosophy that the whole is primary and often greater than the sum of the parts
 a holist is concerned with relationships not the pieces
 quantum physics is difficult to reconsile with reductionism, requires a holistic view of Nature
 the particle or wave aspect of a quantum entity requires a dialogue with the environment
 numerous experiments have shown that quantum interactions produce results that are not predictable by
analysis of components
 the rules of the quantum world follow logic, but a logic of both/and rather than the logic of either/or of
the macroscopic world
Theory of Everything :
 the Standard model is our current theory of the matter/energy worldview, and has had great success with
particle physics
 missing is a full formulation of gravity and particle physics, quantum gravity
 limitations to the Standard Model suggests a more encompassing theory awaits formulation
Supergravity:
 a theory that brings gravity, relativity and quantum physics together is called a Theory of Everything (TOE)
 one recent attempt is called supergravity, which explains the microscopic world as extra dimensions
 using pure geometry is a popular feature to TOE's since they become fundamental in their mathematics as well
as physics
String Theory:
 another example of a TOE is string theory, the explanation of quantum entities as tiny loops or membranes
 the various subatomic particles are explained as different vibration modes of the tiny strings
 the rules for string interactions looks alot like spacetime and relativity
Brane World Scenario:
 A combination of string theory and supergravity leads to an eleven dimensional description of the Universe
called the brane world scenario
 Each brane universe is composed of 4D spacetime and 6D quantum space.
 Strong, weak and electromagnetic forces are carried by open strings, each attached to their branes
 Gravity is carried by closed strings, free to travel between branes
Quantum Computers:
 The speed of a computer is inversely proportional to the size of its components, i.e.
smaller parts = faster computers, more computing power
 when the size of the compenents enters the subatomic world, it is ruled by quantun rules
 From a physical point of view a bit is a physical system which can be prepared in one of the two different
states representing two logical values  no or yes, false or true, or simply 0 or 1.
 Quantum bits, called qubits, are implemented using quantum mechanical two state systems; these are not
confined to their two basic states but can also exist in superpositions: effectively this means that the qubit is
both in state 0 and state 1.
 Any classical register composed of three bits can store in a given moment of time only one out of eight
different numbers. A quantum register composed of three qubits can store in a given moment of time all eight
numbers in a quantum superposition.
 Once the register is prepared in a superposition of different numbers one can perform operations on all of
them.
 Thus quantum computers can perform many different calculations in parallel: a system with n qubits can
perform 2^{n} calculations at once! This has impact on the execution time and memory required in the process of
computation and determines the efficiency of algorithms.
 In principle we know how to build a quantum computer; we start with simple quantum logic gates and connect
them up into quantum networks.
 A quantum logic gate, like a classical gate, is a very simple computing device that
performs one elementary quantum operation, usually on two qubits, in a given time. Of course, quantum logic gates
differ from their classical counterparts in that they can create and perform operations on quantum
superpositions.