Topic 18

The Double-Slit Experiment, Causality, and Schroedinger's Cat - The 'Unreality' of Quantum Mechanics

 

The Copenhagen Interpretation

Bohr argued in 1927 that quantum mechanics had certain intrinsic characteristics. This view became known as the Copenhagen Interpretation and is still the prevalent view of quantum mechanics.

Key characteristics of quantum mechanics as viewed by Bohr are :

Heisenberg Uncertainty Principle

Pauli Exclusion Principle

wave/particle duality - Complementarity

actions are goverened by probability theory

These characteristics lead to the belief that an observer interacts with a system under study to such an extent that the system cannot be thought of as having an independent existance. This goes contrary to one of classical physics key postulates (unproven assumptions) that the universe exists independent of an observer.

Another way to say the same thing is that no experiment can measure both position and momentum at the same time. Also, no experiment can see both particle-like and wave-like characteristics at the same time.

A related question is what happens when an electron in energy state A changes to energy state B? Does the electron 'jump' from one orbit to another? The Coenhagen Interpretation would argue that what happens between A and B is meaningless. (We will see the same type of discussion in the macroscopic world with Chaos Theory. There are changes of state that are truly discontinuous. There is no meaningful purpose in asking how one gets from one state to the other.)

 

The Double-Slit Experiment

Richard Feynmann argues that the Double-Slit experiment is the hardest and most fundamental problem in quantum mechanics. If one can understand it, everything else is easy. The pupose of the experiment is to test the wave/particle duality of matter. The starting point is probably to visualize a particle moving along - the 'particle-like' charadcteristics help us visualize the motion of the particle, the 'wave-like' characteristics more properly define a probability function of the particle's real location. The problem is that if we 'peek' or look for the location or momentum of the particle (one, not both), we have 'collapsed' the wave-function charcteristics of the particle and see only the particle-like characteristics.

The experiment is as follows:

Let a beam of electrons pass through two narrow slits in a sheet of paper. Another sheet of paper is placed behind the first one and the locations of where electrons 'hit' is measured.

If we don't look at electron paths until they hit the back paper, the electrons will arrive in a complex pattern defined by the interference pattern of the particle wave-functions. If we close one hole, the electrons arrive in a simpler 'bell-shaped' or Gaussian distribution centered on the hole that is open.

If one 'peeks' at the electrons while they are in transit, they lose their wave-like characteristics, become 'billiard-ball' particles and arrive at the back paper without interference. Thus the argument that only by observing the system does each electron become real and behave like billiard-balls in the amcroscopic universe.

The various possible location of an electron defined by its wave function can be thought of as a seriesof 'ghost' electrons, one of which becomes real when it hits the paper. Alternatively, the 'ghost' electrons may reflect alternative realities, one of which becomes our reality when it hits the paper.

 

The EPR Experiments

A series of thought experiments were devised between 1927-1970 to test the ideas of the Copenhagen Interpretation. The first thought experiments were devised by Einstein and refuted by Bohr.

All of the experiments tried to repudiate the Coenhagen Interpretation by finding some method for measuring two aspects of a particle at once - momentum and position or both wave and particle characteristics.

In the 1970's Bell and colleagues were able to use new technology to devise real EPR experiments which verified all elements of the Copenhagen Interpretation.

One fallout from this is the idea of causality.In order for the Copenhagen Interpretation to work and explain the EPR experiments, especially the real experiments of Bell and colleagues, one must admit to some 'communication' between particles that occurs at speeds faster than the speed of light. This argues for a local loss of causality. (Remember the murder at the Train Depot in Mr. Thompkins.) The reason we never are aware of aloss of causality is because it only occurs locally at the atomic scale and we could never devise an experiment to test its limits.

 

Schroedinger's Cat

Another test of the Copenhagen Interpretation is a thought experiment which has been called Schroedinger's Cat.

The experiment is as follows:

Place a cat in a closed box with a glass bottle filled with cyanide gas and some apparatus which breaks the glass if ine radioactive atom happens to decay.

The question is whether the cat is alive or dead at any instant. The only way to know is to look into the box.

The argument is whether, unless we look in the box, the cat even exists or that it may behave like a wave-function defining its possible outcomes. Alternatively, one might imagine two cats in parallel universes, the 'real' universe is the outcome we see when we open the box.

 

Mr. Thompkins Meets Quantum Mechanics

There are several stories in Mr. Thompkins which elucidate the concepts of quantum mechanics. Each one is based on the premise that Planck's constant becomes close to unity, thus bringing the world of quantum mechanics into view of the macroscopic world.

Quantum Billiards:

- billiard balls, when hit, 'spread out'.

- when one ball hits another, there are a large number of faint balls rushing around in different directions (wave-function of ball interactions)

- when ball is placed at one spot, it develops fuzzy group of balls around it which move rapidly (can't know exactly both position and momentum)

- when a ball is placed in the billiard triangle, it eventully 'leaks' out (due to uncertainty principle)

Quantum Jungles:

- when an elephant of the quantum jungle is purchased, MT finds that its skin is fuzzy (big elephant, big mass, only a little uncertainty in position)

-large pack of tigers attacks MT and Sir Richard on elephant (really only one tiger)

- when Sir Richard tries to shoot tigers, professor tells him to shoot many places (increase probability of hitting real tiger)

- one gazelle leaves a forest, appears as a line of gazelles due to interference of its motion through trees (diffraction pattern)

Gay Tribe of Electrons:

- MT finds himself in an atom. sees pairs of electrons spinning about nucleus. MT is alone at outer edgres. MT is a valence (unpaired) electron in outer orbit of a sodium (Na) atom

- MT joins seven other outer electrons in a neighboring chlorine (Cl) atom, the Na atom tags along (creating a molecule of NaCl, table salt)

- in talking with other Cl atomd, Mt is told that being in an ionic bond (as between Na anc Cl) is great. Being in a homopolar bond is bad because electron spends all time jumping back and forth between atoms.

- an electron is hit out of its inner orbit and another electron in an outerorbit jumps down to replace it, during jump it gives off light.

 

Steller Evolution/Black Holes

Aspects of quantum mechanics can be seen even at macroscopic scales in Black Holes.

Normal stars form from a gas nebula by gravitational attraction. As the gas heats up and pressure from gravitational contraction reaches a special point, hydrogen atoms combine to form helium atoms (fusion) giving off lots of energy in the process. This is where stars get their energy.

During the lifetime of a star, heat and pressure balance gravitational forces creating a star of stable size. When H fuel is gone the normal star contracts to form a White Dwarf. It can't normally collapse more because the Pauli Exclusion principle won't let electrons go into nucleus.

If stars have a mass about 1-2x our star Sol, the collapse can push electrons into nucleus forming a much small and denser Neutron star.

If star mass is above Chandrasekhar's limit (~1.5-2x Sol), the star may collapse to infinite density and become a singularity called a Black Hole.

Stephen Hawking and colleagues have studied theoretically what should happen around black holes. They argue that pairs of ghost particles are constantly forming and annhilating one another throughout the universe. At the edges of black holes, some of the ghost particles become sucked into the black holes,causing there to appear 'new' mass moving away from the black holes.

 

Arrows of Time

The universe sees time in different ways:

thermodynamic time - increasing entropy

psychological time - memories with no assurance of the future

cosmological time - expansion of the universe

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