• 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

Wave-Particle Dualism:

• The wave-like nature of light explains most of its properties:
  1. reflection/refraction
  2. diffraction/interference
  3. 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 wave-particle dualism and continues the strange characteristics to the new science of quantum physics
• wave-particle 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 Two-Slit Experiment:

• the two slit experiment is key to understand the microscopic world

• 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 wave-like 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

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, built-in 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

Many-Worlds 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 (nano-AI'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 sub-atomic 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 2ⁿ 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.