A closer look at the uncertainty relation of position and momentum

We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and sufficient condition for finite standard deviations is given. Finally, a new uncertainty relation is derived and it is shown that the latter cannot be improved.Comment: 3 pages, introduction shortened, content unchange

Time's Arrow and Lanford’s Theorem

It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford (1975, 1976, 1981) shows that, under certain conditions, the famous Boltzmann equa- tion, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford’s theorem succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford’s theorem is responsible for the emergence of irreversibil- ity. We claim that the true culprit for the emergence of irreversibility lies in a point that has hitherto not been sufficiently emphasized, i.e. in the choice of incoming, rather than outgoing, configurations for collision points. We argue that this choice ought to be recognized clearly as an explicit assumption in the theorem, and discuss its implications for the question in what sense irreversible behaviour follows from Lanford’s theorem

Quantum probabilities and the conjunction principle

A recent argument by Hawthorne and Lasonen-Aarnio purports to show that we can uphold the principle that competently forming conjunctions is a knowledge-preserving operation only at the cost of a rampant skepticism about the future. A key premise of their argument is that, in light of quantum-mechanical considerations, future contingents never quite have chance 1 of being true. We argue, by drawing attention to the order of magnitude of the relevant quantum probabilities, that the skeptical threat of Hawthorne and Lasonen-Aarnio’s argument is illusory

Boltzmann's H-theorem, its discontents, and the birth of statistical mechanics

A comparison is made of the traditional Loschmidt (reversibility) and Zermelo (recurrence) objections to Boltzmann's H-theorem, and its simplified variant in the Ehrenfests’ 1912 wind-tree model. The little-cited 1896 (measure-theoretic) objection of Zermelo (similar to an 1889 argument due to Poincaré) is also analysed. Significant differences between the objections are highlighted, and several old and modern misconceptions concerning both them and the H-theorem are clarified. We give particular emphasis to the radical nature of Poincaré's and Zermelo's attack, and the importance of the shift in Boltzmann's thinking in response to the objections taken together

On the history of the quantum: Introduction to the HQ2 special issue

The historiography of quantum theory exhibits a period of intense activity that started in the 1960s, with the Archives for the History of Quantum Physics project, and continued with the work of scholars like Max Jammer, Martin J. Klein, John Heilbron, Paul Forman and Thomas Kuhn. At the end of the 1970s, however, interest of historians seems to have shifted away, even if there have been notable exceptions, such as the multi-volume work by Jagdish Mehra and Helmut Rechenberg, and monographs like those of Olivier Darrigol and Mara Beller. Perhaps this development has had to do with a diminishing number of scholars possessing the necessary technical skills in physics together with historical sensitivity. Moreover, many historians of physics in this period have focused their interest on another subject, namely the development of the theory of relativity. Stimulated by the start of the Einstein Papers Project, and initiated by pioneers such as John Stachel and John Norton around 1980, very soon a dedicated group of scholars devoted time and energy to analyzing the genesis and development of general relativity, and other aspects of Einstein’s science

In grote lijnen: Natuurkundige theorieën

E = mc2. Waarschijnlijk is het de meest bekende wetenschappelijke formule. De wetenschapper die meteen met deze formule geassocieerd wordt: Einstein natuurlijk! Laat een willekeurig iemand een afbeelding van het markante hoofd van deze wetenschapper zien en het wordt onmiddellijk herkend. De naam van de theorie die met deze wetenschapper verbonden is, is al even bekend: de relativiteitstheorie. Maar dan houdt het op. Einstein was een genie en de relativiteitstheorie is alleen te begrijpen door andere genieën. Waar E = mc2 voor staat, weten we niet. Maar tot de verbeelding spreken Einstein en de formule wel. De relativiteitstheorie is één van de natuurkundige theorieën die in dit Studium Generale programma In grote lijnen aan de orde kwam

Time's Arrow and Lanford’s Theorem

It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford (1975, 1976, 1981) shows that, under certain conditions, the famous Boltzmann equa- tion, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford’s theorem succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford’s theorem is responsible for the emergence of irreversibil- ity. We claim that the true culprit for the emergence of irreversibility lies in a point that has hitherto not been sufficiently emphasized, i.e. in the choice of incoming, rather than outgoing, configurations for collision points. We argue that this choice ought to be recognized clearly as an explicit assumption in the theorem, and discuss its implications for the question in what sense irreversible behaviour follows from Lanford’s theorem