Abstract Background. There is an inherent limit in the accuracy of our measurements, set by nature itself and predicted by Heisenberg's uncertainty principle, which defines the properties of nature in the microcosmos. There is a fundamental limit to the accuracy with which complementary phys-ical quantities of a particle can be predicted from their initial conditions. As classical physics is essentially considered at borderline of quantum mechanics, so the power of uncertainty princi-ple is limited in describing everyday life perceived or managed phenomena. Method. In this study, we apply Heisenberg's uncertainty principle to children under diagnostic uncertainty re-garding appendicitis. We analyze this phenomenon in clinical practice. Results. Medical practice is full of uncertainty. False negative decisions correlate with delays in treatment and adverse outcomes in children with atypical appendicitis. On the other hand, false-positive surgery deci-sions result in negative appendectomies. With improvement of technology, the incidence of complicated appendicitis or negative appendectomies due to diagnostic uncertainty has de-creased but cannot be ignored or eliminated. Conclusion. According to the principle, there is a fundamental limit to the accuracy with which the complementary variables of negative appen-dectomy and complicated appendicitis can be observed or measured simultaneously. What does all this mean for the physician?

The energy, momentum and the action associated with the time domain transition radiation fields are investigated. The results show that for a charged particle moving with speed $v$, the longitudinal momentum associated with the transition radiation is approximately equal to $E/c$ for values of $1-v/c$ smaller than about 10^-3 where $E$ is the total radiated energy and c is the speed of light in free space. The action of the transition radiation, defined as the product of the energy dissipated and the duration of the emission, increases as $1-v/c$ decreases and, for an electron, it becomes equal to $h/4\pi$ when $v=c-v_m$ where $v_m$ is the speed associated with the lowest energy state of a particle confined inside the universe and h is the Plank constant. Combining these results with Heisenberg’s uncertainty principle, an expression for the electronic charge based on other fundamental physical constants is derived. The best agreement between the experimentally observed electronic charge and the theoretical prediction is obtained when one assumes that the actual size of the universe is about 250 times larger than the visible universe.

In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are furthermore the inverses of one another. While Poisson’s summation formula expresses a duality between discretization and periodization, Heisenberg’s uncertainty principle expresses a duality between regularization and localization. We define regularization and localization on generalized functions and show that the Fourier transform of regular functions are local functions and, vice versa, the Fourier transform of local functions are regular functions.