Quantum TheoryQuantum Theory

Black Body RadiationBlack Body Radiation Temperature determines the wavelength of

emitted light. “Red hot”: mostly red light - 3,000 oC. “White hot”: all colors – 6,000 oC. It was assumed light could have any

energy. The math of the theory did not match the

distribution of wavelengths observed:

http://www.egglescliffe.org.uk/physics/astronomy/blackbody/bbody.html

Max Planck solved the Max Planck solved the black body radiation black body radiation dilemma dilemma

He created an equation that fit the observed distribution of radiation.

To do so, he had to assume that energy came in packets, called quanta.

Planck’s ConstantPlanck’s Constant

Frequency/energy = Planck’s constant

Planck’s constant (h) is one of the most important constants in nature.

(h) = 6.626 x 10-34 joule seconds

Photoelectric EffectPhotoelectric Effect Certain light beams can knock electrons

off of some metals. This was independent of the total energy

in the light beam. It WAS dependent on the wavelength of

the light. Short wavelengths have larger quanta

(packets of energy) to knock off electrons.

http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html

Light – particle or wave?Light – particle or wave?

Light followed the wave equation defined by James Clark Maxwell.

Light also seemed to exist as packets, like particles.

The particle/wave designation seems invalid for the subatomic world.

Particles are also WavesParticles are also Waves 1923: Louise de Broglie found that

matter had both particle and wavelike properties.

If E = hc/wavelength (from Planck) and E = mc2 (from Einstein), than wavelength = h/(mass x velocity).

Very small particles exhibit the same wave addition and cancellation characteristics as waves do.

Niels Bohr Planetary AtomNiels Bohr Planetary Atom

Electrons orbit the nucleus in specific circular orbits.

Problem: a charged particle in acceleration emits light.

Changing direction is a type of acceleration, yet orbiting electrons emitted no light.

Schrodinger’s SolutionSchrodinger’s Solution The orbit of an electron can only be a whole

number multiple of the electron’s wavelength.

The orbital is a standing wave of an electron.

There is no “changing direction” of the electron.

The electron simply exists in these locations, without actually moving from one point to another.

Schrodinger wave Schrodinger wave equations equations Any system can be treated as a wave

equation in quantum mechanics. The orbitals of chemistry are solutions

to Schrodinger wave equations. Electrons materialize from one location

to another without passing a plane of zero probability existence.

This is just quantum weirdness.

Paul Dirac’s improvements Paul Dirac’s improvements of Schrodinger’s wave of Schrodinger’s wave equations equations

He generalized the equations to relativistic theory.

He mathematically explained electron spin with angular momentum.

He postulated the existence of antimatter based on the negative square root of E=mc2.

Quantum Mechanics gives Quantum Mechanics gives probabilitiesprobabilities 1926, Max Born: the square of the

wave equation gave the probability of finding the particle in a given location.

Many felt that probability was not good enough.

If we really understood something, we should know what will happen and what is really going on “behind the scenes”.

Heisenberg Uncertainty Heisenberg Uncertainty Principle Principle We cannot know both the velocity and

location of an electron. The more we know about one, the less we know about the other.

High energy light gives a better location, but disrupts the velocity.

Low energy light disturbs the velocity less, but gives high uncertainty of location. Lower energy light gives worse resolution.

The uncertainty of position times the uncertainty of momentum is greater or equal to Planck’s constant divided by 4p.

Uncertainty vs. Uncertainty vs. DeterminismDeterminism Uncertainty was not just a result of

the crudeness of the instruments, it was a fundamental law of nature.

Determinism – the idea that you can state the future if you know everything about the present.

Einstein favored determinism, but uncertainty was found to rule.

Double slit experimentDouble slit experiment The same results are obtained with light,

electrons, or any other type of “wave”. http://www.upscale.utoronto.ca/GeneralIn

terest/Harrison/DoubleSlit/DoubleSlit.html

How does the particle going through the slit “know” that the other slit exists?

Since the electron, like all matter, has wave characteristics, its final location is defined by the probability given by the square of the wave equation for the given system it is in.

Bell’s TheromBell’s Therom John Bell used a thought experiment and

logic to prove that reality is non-local. Non-local means objects are affected by

distant objects and events that cannot reach them with a force, because they are outside of the light cone.

Outside the light cone, signals or forces from one object must travel faster than the speed of light to create the observed behavior.

Quantum Entanglement Quantum Entanglement

When two particles or events affect each other without any signal or force.

Determinism, and our common sense, says that this is totally impossible.

Quantum mechanics predicts when it will or will not happen, and what the probability of the outcome will be.

Collapsing Probability Collapsing Probability WavesWaves Quantum mechanics says that the

measurement of a particle, such as an electron, collapses the probability wave to a single event.

With entangled particles, the measurement of one collapses both of their probability waves simultaneously.

Any interaction, human or not, collapses probability waves.

Quantum Theory and the Quantum Theory and the UniverseUniverse Cause and effect gives way to probability. The things you do can instantaneously affect

things far away (non-local). Events can happen without a force or signal

to cause it to happen - the fabric of space allows, or even causes it to happen.

Objects do not always have specific properties until they are interacted with; the properties hang in some sort of limbo.

The Standard Model The Standard Model This is the current quantum theory. Many new subatomic particles have been

discovered. There are three families of particles. Each family contains two of the quarks,

an electron (or one of its cousins), and one of the neutrinos.

These are the building blocks of all matter.

Four Force ParticlesFour Force Particles Strong force – The gluon holds the

nucleus together. Weak force – The W and Z bosons cause

radioactivity. Electromagnetism – The photon causes

light. Gravity – The graviton is the cause. Experiments have established all force

particles except the graviton. Gravitons are expected to be discovered

soon.

Standard Model EquationStandard Model Equation It uses an input of 19 pieces of

information, which are properties of the force and mass particles.

It has been flawless at predicting experimental outcomes as probabilities.

Everything that happens in the universe, besides gravity, can be predicted by the Standard Model.

Newton’s equations fall out of Standard Model for normal conditions.

Particle Behavior Particle Behavior The uncertainty principle allows for

extreme particle behavior on the subatomic level.

There is a trade off between the energy a particle has and the time it takes to measure this energy, which allows the energy of a particle to fluctuate wildly over a very short duration of time, called the quantum jitters.

“Tunneling” is allowed.

More UnificationMore Unification

Steven Weinberg and his colleagues unified the weak and the electromagnetic forces.

They won a Nobel Prize for this work.

Weaknesses of Standard Weaknesses of Standard ModelModel

It explains how nature behaves, but not why it behaves in the way it does.

It does not include gravity; therefore, it cannot be a complete theory of the universe.

Its use is primarily for the subatomic level.