Carl David Anderson, 85, a professor who won the Nobel Prize for Physics in 1936 and had to borrow $500 to go to Stockholm, Sweden, to collect his prize, died Friday in San Marino, Calif. During World War II, Mr. Anderson was asked to direct the development of the atomic bomb. He declined and worked on a solid-propellant rocket project. Mr. Anderson discovered the positron, the first particle of antimatter shown to exist. He designed and built during the early 1930s an apparatus consisting of a giant electromagnet wrapped around a cloud chamber. A camera was focused on the window of the chamber to record visible vapor trails of electrons or other charged particles passing through. Mr. Anderson realized he had found something new when his cloud chamber photographs showed what appeared to be a positively charged electron. The particle was eventually named the positron, and its existence was the first confirmation of the concept of antimatter.