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We explicate some epistemological implications of stationary principles and in particular of Noether Theorems. Noether's contribution to the problem of covariance, in fact, is epistemologically relevant, since it moves the attention from equations to conservation laws.
An historical overview is given of the relevant steps that allowed the genesis of the quantum theory of the chemical bond, starting from the appearance of the new quantum mechanics and following later developments till approximately 1931. General ideas and some important details are discussed concerning molecular spectroscopy, as well as quantum computations for simple molecular systems performed within perturbative and variational approaches, for which the Born-Oppenheimer method provided a quantitative theory accounting for rotational, vibrational and electronic states. The novel concepts introduced by the Heitler-London theory, complemented by those underlying the method of the molecular orbitals, are critically analyzed along with some of their relevant applications. Further improvements in the understanding of the nature of the chemical bond are also considered, including the ideas of one-electron and three-electron bonds introduced by Pauling, as well as the generalizations of the Heitler-London theory firstly performed by Majorana, which allowed the presence of ionic structures into homopolar compounds and provided the theoretical proof of the stability of the helium molecular ion. The study of intermolecular interactions, as developed by London, is finally examined.
We consider general aspects of the physics underlying the flight of Gossamer spiders, also known as ballooning spiders. We show that existing observations and the physics of spider silk in the presence of the Earth's static atmospheric electric field indicate a potentially important role for electrostatic forces in the flight of Gossamer spiders. A compelling example is analyzed in detail, motivated by the observed "unaccountable rapidity" in the launching of such spiders from H.M.S. Beagle, recorded by Charles Darwin during his famous voyage.
I argue that the Carroll-Chen cosmogenic model does not provide a plausible scientific explanation of our universe's initial low-entropy state.
This short note describes the observatory of the pioneering spectroscopist, Frank McClean (1837-1907), at Tunbridge Wells in England
The Reverend Walter Bidlake, MA, FRAS, JP (1865-1938) was vicar of Crewe, England, for some 21 years. A member of the BAA, he was a keen amateur astronomer with an interest in celestial photography. At the request of another well-known BAA member, T.H.E.C. Espin, Bidlake took photographs of the night sky in support of Espin's search for dark nebulae in the Milky Way. This paper describes Bidlake's astronomical activities and life, including a high profile libel case he brought.
Marking the centenary of the outbreak of the First World War, this paper considers the effect of the war on the BAA and pays tribute to some of its members who were involved in the conflict.
The bird-man cult remains the main secret of Easter Island (Rapa Nui), a remote plot of land in the Pacific. This paper includes not only necessary ethnological data, but also some results on the archaeoastronomy. The research of some lines marked on a stone calendar from the Mataveri area, an archaic zone of the bird-man cult, allows to insist that the natives watched at least the stars Canopus and Aldebaran. There are strong grounds for believing that, among others, the Sun, the Moon as well as Beta and Alpha Centauri were the matter for quasi-scientific enquiry. Several astronomical and calendar records in the rock art and in the script have been decoded.
According to the no-signaling theorem, the nonlocal collapse of the wavefunction of an entangled particle by the measurement on its twin particle at a remote location cannot be used to send useful information. Given that experiments on nonlocal correlations continue to have loopholes, we propose a stronger principle that the nonlocality of quantum mechanics itself is veiled. In practical terms, decoherence and noise compels us to view the wavefunction as representing knowledge of potential outcomes rather than the reality. Experimental evidence in favor of naked nonlocality would support the view of the wavefunction as an objective description of physical reality.
In 1917 Einstein introduced into his field equations a cosmological term having the cosmological constant as a coefficient, in order that the theory should yield a static universe. Einstein desired to eliminate absolute space from physics according to "Mach's ideas". De Sitter objected to the "world-matter" in Einstein's world, and proposed a vacuum solution of Einstein's field equations with the cosmological constant and with no "world-matter". In 1920 the world-matter of Einstein's world was equivalent to "Mach's Ether", a carrier of the effects of inertia. De Sitter's 1917 solution predicted a spectral shift effect. In 1923 Eddington and Weyl adopted De Sitter's model and studied this effect. Einstein objected to this "cosmological problem". In 1922-1927, Friedmann and Lamaitre published dynamical universe models. Friedmann's model with cosmological constant equal to zero was the simplest general relativity universe. Einstein was willing to accept the mathematics, but not the physics of a dynamical universe. In 1929 Hubble announced the discovery that the actual universe is apparently expanding. In 1931 Einstein accepted Friedmann's model with a cosmological constant equal to zero, which he previously abhorred; he claimed that one did not need the cosmological term anymore. It was very typical to Einstein that he used to do a theoretical work and he cared about experiments and observations. This paper is a new interpretation to Einstein's cosmological considerations over the period 1917-1931.
The paper presents the results of a study of unique plate with images of Srubna burial of tumuli group Popov Yar-2 (Ukraine) and plate of Srubna burial of tumulus field Tavriya-1 (Russia). A distinctive feature of the images is the orderliness and symmetry of the composition, as well as the location of elliptical cupped depressions. With the help of mathematical and astronomical methods we prove in this paper that the plates with the images are the ancient sundials. At the Popov Yar-2 plate located two sundials, which worked at the same time: the analemmatic sundial and the horizontal sundial with two gnomons and the linear scale. At the Tavriya-1 plate located analemmatic sundial. On the basis of the reconstruction of the linear parameters of the gnomon of both Popov Yar-2 plate sundials and given the scale value of horizontal sundial, in the article that the potential indirect impact protoscientific knowledge of ancient Egypt to the Srubna population in the Northern Black Sea coast. Srubna burial, plate, wells, cupped depressions, analemmatic, horizontal sundial, gnomon, archaeoastronomy, archeology
In 1956/1970 Gamow wrote that much later, when he was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the "biggest blunder" he ever made in his life. But the cosmological constant rears its ugly head again and again and again. Apparently, Einstein himself has never used the apercu "biggest blunder"; nevertheless a vast literature grew up around this notion and associated it with Einstein. The present work is prompted by questions put by Mario Livio in his latest book "Brilliant Blunders" as to the phrase "biggest blunder": Did Einstein actually say, "biggest blunder"? I show that in 1947 Einstein wrote Lemaitre that he found it "very ugly" that the field law of gravitation should be composed of two logically independent terms. Earlier, in 1922 Einstein wrote Max Born that he committed "a monumental blunder some time ago". In 1965 Born commented: "Here Einstein admits that the considerations which led him to the positive-ray experiments were wrong: 'a monumental [capital] blunder'". It is likely that when Einstein met Gamow he formulated his views in his native German, and perhaps he told Gamow that suggesting his cosmological constant was a "blunder". I suggest that, Einstein perhaps told Gamow that the cosmological constant was a "capital blunder" or a "monumental blunder", and Gamow could have embellished Einstein's words to become the famous apercu "biggest blunder".
Major breakthrough in quantum computation has recently been achieved using quantum annealing to develop analog quantum computers instead of gate based computers. After a short introduction to quantum computation, we retrace very briefly the history of these developments and discuss the Indian researches in this connection and provide some interesting documents (in the Figs.) obtained from a chosen set of high impact papers (and also some recent news etc. blogs appearing in the Internet). This note is also designed to supplement an earlier note by Bose (Science and Culture, 79, pp. 337-378, 2013).
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusion are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures.
The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deterministic system which is observationally equivalent to the stochastic process. Still, one might guess that the measure-theoretic deterministic systems which are observationally equivalent to stochastic processes used in science do not include any deterministic systems used in science. I argue that this is not so because deterministic systems used in science even give rise to Bernoulli processes. Despite this, one might guess that measure-theoretic deterministic systems used in science cannot give the same predictions at every observation level as stochastic processes used in science. By proving results in ergodic theory, I show that also this guess is misguided: there are several deterministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measure-theoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticise the claims of the previous philosophy papers Suppes (1993, 1999), Suppes and de Barros (1996) and Winnie (1998) on observational equivalence.
This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational equivalence to abstract mathematical descriptions. The second results are stronger because they show observational equivalence between deterministic and indeterministic descriptions found in science. Here I also discuss Kolmogorov's contribution. For the third results I introduce two new meanings of `observational equivalence at every observation level'. Then I show the even stronger result of observational equivalence at every (and not just some) observation level between deterministic and indeterministic descriptions found in science. These results imply the following. Suppose one wants to find out whether a phenomenon is best modeled as deterministic or indeterministic. Then one cannot appeal to differences in the probability distributions of deterministic and indeterministic descriptions found in science to argue that one of the descriptions is preferable because there is no such difference. Finally, I criticise the extant claims of philosophers and mathematicians on observational equivalence.
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in ergodic theory, I identify three other common ways of justifying definitions: natural-world-justification, condition-justification and redundancy-justification. Also, I clarify the interrelationships between the different kinds of justification. Finally, I point out how Lakatos's ideas are limited: they fail to show that various kinds of justification can be found and can be reasonable, and they fail to acknowledge the interplay between the different kinds of justification.
Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer is now widely regarded as flawed. We argue that some of the main objections, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something close to Boltzmann's proposal is true: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the phase space except for a small region of measure epsilon. This answer is promising because there is evidence that relevant systems are epsilon-ergodic.