By Hans Günter Dosch

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**Example text**

In our case we expect 500 events, and the square root of 500 is about 22, and so we expect with a probability of 66% to observe between 478 and 522 decays. But with a probability of 34% there can be more or fewer decays. If an experimentalist tests the theory with 1,000 copies and finds in one second 450 decays, such a result by no means disproves the theory. It is only slightly more than two standard deviations away from the mean value, which occurs with a probability of a few percent. In particle physics one speaks of an interesting effect if the deviation from an expected result is more than three standard deviations, and of a discovery if the deviation is more than five standard deviations.

In quantum mechanics, one assigns certain operatorsto observable properties such as position, momentum, and energy. This differs from classical physics, in which functions are assigned to these observables, the values of which are the specific results of measurement. Operators are identified by their actions, not by their values. The energy of a state is determined by the way in which the energy operator acts on the state. If certain mathematically possible results of a measurement, such as the negative energy values mentioned above, are disposed of, this action modifies the operator.

Heisenberg’s answer was that the trace in the cloud chamber is not a trajectory in the mathematical sense, and the size of the droplets indicates some uncertainty about the position of the ionizing particle. 4 Quantum Physics Becomes Decisive Quantum physics was developed in order to describe atomic phenomena. For a time, it was unclear whether it would also be applicable to subatomic phenomena, for example, to processes in the atomic nucleus. It was widely believed that, for nuclear physics, new laws had to be found, which might be as different from those of quantum physics as the laws of quantum physics are from those of classical physics.