Summary of Class 2 - January 10, 2002

Introduction: Some modern physicists on mathematics and understanding

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain they do not refer to reality."

Einstein, Sidelights on Relativity, pg 28.

"Never make a calculation until you know the answer."

Wheeler, Spacetime Physics, pg 60.

"Our mathematical procedures seem to obscure our intuitive and imaginative understanding."

Bohm, Foundations of Physics 5, 93 (1975).

"I feel that we do not have definite physical concepts at all if we just apply working mathematical rules; that's not what the physicist should be satisfied with."

Dirac,Physicist's Conception of Nature, pg 11.

Today's Class

We briefly talked about mathematics, science, and this class.

We spent the rest of class talking about the Double Slit Experiment for electrons and its implications. We went beyond the materials in the Supplementary Notes on this topic. One distinction which I introduced, not for the last time:

• In classical physics there is a notion of an observer safely behind a pane of glass observing the physical world that exists on the other side of the glass. Although we know that any observation disturbs the system, classically we assume that in principle the disturbance can be reduced to a negligible level.
• In modern physics the whole idea of an observer has collapsed, being replaced by the participator, who in some sense creates the reality by interacting with it. The Heisenberg Uncertainty Principle places a fundamental limit on how much we can reduce the disturbance of a system when making measurements on it.

I ended the class with yet another quotation:

What you see is what you get!
-- Tina Turner