1 1 – Radioactivity 13 N decays into 13 C + electron (e - ) + antineutrino v Tendency of an atom to decay: the “half-life” For a large sample of atoms, in one half-life one half of the sample will decay. The half-life of 13 N is almost exactly 10 minutes

2 1.A – Simulating Radioactive Decay A.Heads: You have “decayed” and will not be available for the next half-life B.Tails: You did not “decay” C.You decayed in a previous trial.

3 1.B - Is Anything Random? “Consider an intelligence which, at any instant, could have a knowledge of all forces controlling nature together with the momentary conditions of all the entities of which nature consists. If this intelligence were powerful enough to submit all this data to analysis it would be able to embrace in a single formula the movements of the largest bodies in the universe and those of the lightest atoms; for it nothing would be uncertain; the future and the past would be equally present to its eyes.” – Laplace, 1819

4 2 – Were the 2 Atoms Identical? They were apparently identical The Quantum Mechanical description (the “wave function”) was identical for the two atoms If they were not really identical, the difference was hidden from us “Hidden Variable”: some difference between the two atoms that influenced the decay

5 Quantum Mechanics Says whether or not a particular atom decays in one half-life is truly random Einstein never accepted Quantum Mechanics: “God does not play dice with the universe.” Bohr: “Quit telling God what to do!” Krishna: “I am the game of dice. I am the self centered in the heart of all beings.” (Bhagavad Gita)

6 4 – Schrödinger’s Cat “At the end of [one half-life] the total wave function for the system will have a form in which the living cat and dead cat are mixed in equal portions.” – DeWitt, The Many-Worlds Interpretation of Quantum Mechanics

7 4 According to Special Relativity, no signal or influence can travel faster than the speed of light This is sometimes called “locality”

8 Bell (1964) Recall: Hidden Variable - some hidden difference between two apparently identical atoms that influences when each will decay Locality – there can be no influences that instantaneously connect two simultaneous events occurring at different places Bell’s Theorem: There are no local hidden variables Experimentally proved “The most profound result of science.” -- Stapp

9 Consequences of Bell’s Theorem Quantum Computers Quantum Cryptography more Recently an international team, including Prof. Daniel James of this Department, did the first successful quantum computation: factoring 15 Daniel jokingly says the result of the calculation was 4 ± 1