Monday, May 15, 2006

A Brief History of Quantum Mechanics

40+ Key Events in the Development of Quantum Mechanics

James Clerk Maxwell argues that the positions and velocities of molecules are initially at random. Later he will introduce the Maxwell distribution curve plotting the number of molecules vs their respective velocities for given temperatures.

Ludwig Boltzmann introduces the field of Statistical Mechanics. Introduces theorem of the equipartition of energy.

Blackbody Radiation arises. Experimental work carried out by Wilhelm Wien.

Lord Rayleigh and James Jeans introduce the concept of the ultra-violet catastrophe.

Max Planck saves the day (and opens up a can of worms) by introducing concept of discrete units of energy quanta where each quanta has an energy = hf. h = Planck’s constant and f = frequency of the quanta (or photon in the case of light).

Phillip Lennard works on problem of photo-electric effect.

Albert Einstein explains how photons of light above a threshold frequency can liberate electrons and provide them with kinetic energy. He will win a Nobel Prize for his work.

Joseph von Fraunhofer discovers dark lines in solar spectrum (later Fraunhofer lines). These will become the basis for Astrophysical spectroscopy.

Gustav Kirchoff discovers Helium on the sun using Fraunhofer solar spectrum.

J.J. Thompsopn discovers the electron.

Ernest Rutherford discovers positive nucleus of atom. Experiments carried out by Geiger and Marsden.

Arthur Compton works out the momentum of a photon. Shows the effect of photon scattering and wavelength shift.

Niels Bohr explains Bright Line Light Spectra. Introduces concept of probability waves. Explains working of Hydrogen atom. Bohr uses relies heavily on analysis of hydrogen spectrum by Swiss math teacher Johann Balmer.

Most scientists will grow to accept probability description. A noteable exception is Albert Einstein.

Pieter Zeeman demonstrates the Zeeman Effect ie. The extraneous spectral lines which appear when excited atoms are placed in a magnetic field.

Bohr introduces the n, k and m quantum numbers. N = orbit size, k = orbit shape and m = orbit direction.

Wolfgang Pauli speaks about the Pauli Exclusion Principle. Adds fourth quantum # for spin. No two electrons can have the same set of four quantum numbers.

Bohr uses quantum Mechanics to explain the nature of Mendeleev’s Periodic Table. Concept of Closed and Open Electron shells introduced.

Wave Particle/Duality appears to be winning out in the battle to describe the nature of light.

Louis De Broglie introduces the concept of Matter Waves.

G. P. Thomson proves that Matter Waves do exist.

Werner Heisenberg introduces Matrix Mechanics. Introduces Uncertainty Principle. Probable death of the Philosophy of Determinism.

Max Born and Erwin Schrodinger further develop Matrix Mechanic.

Schrodinger introduces his famous equation – contains wave function, position and energy of photon.

Fourier analysis builds on Scrodinger’s work – looks at the number of nodes in a vibrating system.

Schrodinger argues that particles may not even exist. Wants to describe all particles as superposition of waves.

Henrik Lorentz argues otherwise. Wave function that Schrodinger felt did not spread out. Appears to spread out.

Schrodinger introduces famous cat problem.

Born introduces concept of quantum mechanical probability. Speaks about Probability Amplitude of an Electron.

Consciousness and the Collapsing Wave Function problems are addressed by Eugene Wigner.

Paul Dirac brings together a new solution that looks at the problems of Bohr, Einstein and Planck’s Quantum Theories.

Dirac Introduces Transformation Theory.

Birth of Quantum Electrodynamics. Richard Feynman’s field

Dirac uses equation to solve problem of Electron Spin.

Dirac predicts existence of Anti-matter.

Bohr speaks about complementarity.

Formalization of Copenhagen Interpretation.

Einstein speaks of his box of light.

EPR Challenge to Bohr.

The Non-Locality Issue rises to the fore.

Bell’s non-inequality principle argues that nature is non-local.

Period of New Advances: Action at a Distance, String Theory, Quantum Loop Gravity.
The Future: We will await and see.

Quiz # 4 Birds


1.What common name is used to describe the internal structure of bird bones?
2.What Class do birds belong to?
3.Which bird is the fastest swimmer?
4.This type of falcon can reach a speed of 250km/hr in one of its swooping dives. Name the bird?
5.A certain type of anatomical markings on a swan provide a similar uniqueness to fingerprinting. What are they?
6.What is the largest bird?0
7.What bird has the widest wingspan?
8.This four letter extinct bird is associated with the Indian Ocean island of Mauriitius. Name the bird?
9.What is the smallest bird?
10.Another name for the breast plate or sternum of a bird is the…
11.The last living member of this species of bird was seen in Iceland in 1844. Name the bird?
12.What bird has the largest beak?

Answers to Birds

1,Honeycombed. Adds strength to the bird bones while reducing weight. An engineer’s dream.
2.Class: Aves
3.The Penguin. It can swim at 10m/second which is roughly the speed that a top class male human runner achieves in a sprint.
4. The Peregrine Falcon.
5.Bill markings. Male swans have more feathers on them than any other bird.
6.The African Ostrich.
7.Most experts argue that it is the Andean condor which has a wingspan of 3m. However a male wandering albatross was found in 1965 to have a wingspan of 3.63 m (that is over twice the height of an average person).
9.The bee hummingbird from Cuba. It weighs in at 1.6g.
10.Keel. Helps with flight.
11.The Auk.
12.The Pelican of course.

Sunday, May 07, 2006

A Quantum Mechanical Consideration

An object follows a Path P through Space (and time). It then collides with another particle resulting in momentum and energy transfer.
Modern Physics only concerns itself with this actual collision as it demonstrates the shifting of energies.(and therefore states). From its philosophical point of view the history of this path is inconsequential. What only matters is the conditions before and after the collision. I am somewhat bothered by this. Why is the history ‘meaningless’? Is it really so or do we choose to omit it in order to simplify the problem? I would argue the latter and go one step further by reasoning that it is the history that may contribute to the ‘uncertainty’ that so defines interactions at the quantum level. I do not believe that ‘history’ is lost. Physics abhors the loss of ‘information’ (look at the laws of conservation of mass, energy and momentum).Somehow it must be conserved (maybe not in its original form but in some other form). I propose that historical information is transformed maybe into quantum foam but more likely into one of the higher dimensions that string theory supports. What happens to it in these dimensions is anyone’s guess. But here is an idea. What if this information was churned (by some black box process) into an entity that returns to form the ‘Dark Energy’ needed the Inflationary Expansion of our own universe. I have no proof for any of this but is it more outrageous than the current ideas on the boiler right now (branes, strings, quantum loops etc)?

Philosophy Test

Here is a copy of the philosophy test I gave my Grade 12 students. We had just completed the Ethics and Political Philosophy Units.

1.What is the difference between Kant and Aristotle’s concept of Ethics? (2)

2.How does Utilitarianism differ from Hedonism and Egoism? (3)

3.Give two weaknesses of Ethical Relativism? (2)

4.Why has Marxism failed as a force in the West? (4)

5.How do Hobbes, Locke and Rawls differ with respect to the social contract? (3)

6.What is meant by the concept of totalitarianism? (1)

7.With which ideas that you have studied do you associate the following thinkers:

JJ Rousseau
Ayn Rand
Jeremy Bentham
Edmund Burke
Baron Montesquieu (5)

8.Is the concept of a Just War workable in a Utilitarian framework? Argue using Examples? (5)

9.With axes of economic and personal freedom. Plot the following individuals

Stephen Harper
Joseph Stalin
Jack Layton (3)

10. What is the a. Bourgeoise
b. Hegelian Dialectic
c. Diktat of the Proletariat (3)