Almagest

This article reviews the evidence for the precision of observed (or allegedly observed) time determinations in the Greek astral sciences. In the practice of astrology, the determination of times ‒most commonly times of births‒ was the province of lay observers, and the precision was not normally more refined than to the seasonal hour. In astronomy, the extant observational records show a broad trend towards more refined precision, though the apparent culmination of this trend in Ptolemy is due not only to his employment of the armillary astrolabe as a precision time-telling instrument but also to his penchant for fabrication and tampering in his observation reports. Ptolemy’s claims to have attained to unprecedented time precision in the observations on which his tables were ostensibly based likely contributed to their early and widespread adoption by astrologers.

The 17^th century is considered to be a century of great upheaval, of a real transformation in the way scholars apprehended the world. This change, for the majority of historical studies, goes hand in hand with the birth of the so-called New Natural Philosophy. It is argued that before the 17^th century, in order to describe, understand and explain the world, scholars used a philosophictheological language that was later replaced by a mathematical (geometrical) language. This new way of contemplating and trying to understand the world is often associated, rightly or wrongly, with the birth of the quest for accuracy, and more precisely for accuracy in time measurement. By means of a case study, this article seeks to question this link highlighted by historians of the second half of the twentieth century. The present article is a study of two key articles that share the same object, accuracy in time measurement, written by two authors who have influenced, and still do, a large part of scholarly thinking, Alexander Koyre and Richard Westfall.

In this paper, I will first very briefly recall some features of Newtonian absolute, true, and mathematical time (absolute time, for short) as defined in the Principia. What I will try to do is to explain why Newton needed to resort to the idea of absolute time in his natural philosophy, and why he introduced this concept that -as we know from Einstein’s work- must actually be rejected in contemporary physics. I will then move on to consider the characterization of time employed in the method of fluxions, what I call “fluxional time”. Again, I will underline why Newton introduced this concept in his method of fluxions. He did so about two decades before writing the Principia, in a context that is quite different from the natural philosophy of force, acceleration and gravitation that was top of the agenda for the author of the Principia.

We present three issues associated with the works of Galileo in 1632 and Einstein in 1905 and 1911, which concern respectively the status of time in relativity, the quantum identification of mass and frequency and the mysterious identity of inertial and gravitational masses. These issues naturally lead to a new (quantum) way of thinking of time and inertia, a topic which has been ignored by physicists in the early quantum years although it had contributed to the foundations of previous (classical) physics and to its major success, Einstein’s general relativity. The “philosophy” underlying our discussion is that the reconsideration of “old historical issues” may help overcoming the epistemological obstacles, which generally surround present relativistic and quantum physics, and hide what Poincare called “l’unite de la nature”.

In his 1905 paper on relativity theory, Albert Einstein acknowledged the importance of what we call below “first-order relativity” (in V / c ). Our aim with this paper is first to revisit the origin of “first-order relativity” which began with Fresnel’s problem regarding Arago’s prism experiment. Then, we emphasize the historical importance of the 1895 Lorentz Transformations, based on the explanation they provide of the impossibility of detecting the Earth’s motion through the ether, as well as their acceptance by the scientific community, and their “relativistic” interpretation given in 1900 by Henri Poincare. Finally, we show that a better understanding of these transformations and of their physical consequences (especially length contraction) allows us to bring retrospectively a new look to Einstein’s 1911-1912 introduction of a spatially flat metric.

In the last few years, cosmologists have come up with what seem to be high precision measurements of the age of the Universe. According to recent results by the Planck collaboration, for instance, the Universe is 13.797 ± 0.023 billion years old. But is this indeed a genuine measurement? Can cosmologists really measure and know how old the Universe is? The aim of this paper is to answer these questions. To this end, I first provide some background in the history of cosmology and in physics to explain the methods that scientists follow to determine the age of the Universe. As it turns out, cosmologists obtain a value for this age by tracing the consequences from the cosmological model that best fits the available data. I then discuss this method from a philosophical perspective by addressing potential worries about the success of the method. My conclusion is that cosmologists can only be said to measure the age of the Universe if this is taken with more than one grain of salt. The reason for the qualification is not that the notion of measurement is inappropriate for what cosmologists try; rather, the problem is that they do not have a grip on the whole Universe due to a principled limitation to take observations.

What does “time measurement” mean in the framework of Einsteinian physics (special and general relativity), where time is not defined? A “time measurement” usually refers to one of two different procedures: either the measurement of a date; or that of a duration. Since dating is not a well-defined concept in Einsteinian physics, the first has no object. I analyse various aspects of the process of (proper) duration measurements in Einsteinian theories, in relation with redshifts, the “twin paradox,” and time travels.