A hypothesis based on the exchange and the inter-conversion of the “real” and the equivalent “virtual” particles of the quantum vacuum can resolve the contradiction of waveparticle duality, the “spookiness” and the other conflicting properties of the quantum particles. It can be shown using simple mathematics that the extent of the wave or the particle nature of a quantum particle depends on th...

Abstract The literature on proof by contradiction (PBC) is nearly unanimous in claiming that this technique “more difficult” for students than direct proof, and offers multiple hypotheses as to why might be the case. To examine claim evaluate some of hypotheses, we analyzed student work construction problems from homework examinations a university “Introduction Proof” course taught one authors....

Xinyong Fu & Zitao Fu Shanghai Jiao Tong University [email protected]