The aim of the paper is to develop a proper mathematical formalism which can help to clarify the necessary conceptual plugins to the special principle of relativity and leads to a deeper understanding of the principle in its widest generality.

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: Einstein’s static universe and Eddington’s demonstration of its instability, and the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and (...) its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one. (shrink)

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of (...) them in the non-relativistic limit. (shrink)

The present day standard cosmological model is a great theoretical achievement. This chapter surveys the main themes that have arisen and issues that are still oustanding.

In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy was only formal, and did not reflect a deep connection between gravitational and thermodynamical phenomena. It is still commonly held that the surface gravity of a stationary black hole can be construed as a true physical temperature and its area (...) as a true entropy only when quantum effects are taken into account; in the context of classical general relativity alone, one cannot cogently construe them so. Does the use of quantum field theory in curved spacetime offer the only hope for taking the analogy seriously? I think the answer is `no'. To attempt to justify that answer, I shall begin by arguing that the standard argument to the contrary is not physically well founded, and in any event begs the question. Looking at the various ways that the ideas of ``temperature'' and ``entropy'' enter classical thermodynamics then will suggest arguments that, I claim, show the analogy between classical black-hole mechanics and classical thermodynamics should be taken more seriously, without the need to rely on or invoke quantum mechanics. In particular, I construct an analogue of a Carnot cycle in which a black hole ``couples'' with an ordinary thermodynamical system in such a way that its surface gravity plays the role of temperature and its area that of entropy. Thus, the connection between classical general relativity and classical thermodynamics on their own is already deep and physically significant, independent of quantum mechanics. (shrink)

Over forty years after the foundations of the special theory of relativity had been securely laid, a heated debate, beginning in 1965, about the correct formulation of relativistic thermodynamics raged in the physics literature. Prior to 1965, relativistic thermodynamics was considered one of the most secure relativistic theories and one of the most simple and elegant examples of relativization in physics. It is, as its name apparently suggests, the result of the application of the special theory of relativity to thermodynamics. (...) The basic assumption is that the first and second laws of thermodynamics are Lorentz-invariant, and, as a result, a set of Lorentz transformations is derived from thermodynamic magnitudes, such as heat and temperature. (shrink)

This essay proposes a comprehensive blueprint for the hylomorphic foundations of cosmology. The key philosophical explananda in cosmology are those dealing with global processes and structures, the regularity of global regularities, and the existence of the global as such. The possibility of elucidating these using alternatives to hylomorphism is outlined and difficulties with these alternatives are raised. Hylomorphism, by contrast, provides a sound philosophical ground for cosmology insofar as it leads to notions of cosmic essence, the unity of complex essences, (...) and globally emergent properties. These are used as the basis to account for the aforementioned cosmological explananda and to resolve two problems in the philosophy of cosmology: the meta-law dilemma and the uniqueness of the universe. In summary, cosmology needs hylomorphism because it is able to ground cosmology’s efforts as a scientific inquiry. It can do so because hylomorphism philosophically accounts for changing substances and aggregates of substances, the various scales of law-governed behavior measured by the natures of those substances, and how those substances as parts relate to the universe as a whole. (shrink)

While there is a longstanding discussion about the interpretation of the extended, general principle of relativity, there seems to be a consensus that the special principle of relativity is absolutely clear and unproblematic. However, a closer look at the literature on relativistic physics reveals a more confusing picture. There is a huge variety of, sometimes metaphoric, formulations of the relativity principle, and there are different, sometimes controversial, views on its actual content. The aim of this paper is to develop a (...) precise language in order to provide a precise formulation of the principle. In view of the fact that the special relativity principle is considered as a universal meta-law, which must be valid for all physical laws in all situations, we try to keep the formalism as general as possible. The benefit of the formal reconstruction is that it makes explicit all the necessary conceptual components of the principle; it brings out many subtle details and the related conceptual problems. (shrink)

It is common in the literature on classical electrodynamics (ED) and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the hypothesis that the relativity principle (RP) applies to Maxwell’s electrodynamics. As it will turn out from our analysis, these derivations raise several problems, and certain steps are logically questionable. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following questions: (1) Is the (...) RP a true law of nature for electrodynamical phenomena? (2) Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? (3) Is the RP consistent with the laws of ED in a single inertial frame of reference? (4) Are, at least, the derived transformation rules consistent with the laws of ED in a single frame of reference? Obviously, (1) and (2) are empirical questions. In this paper, we will investigate problems (3) and (4). First we will give a general mathematical formulation of the RP. In the second part, we will deal with the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. In the third part of the paper, applying what J. S. Bell calls “Lorentzian pedagogy”—according to which the laws of physics in any one reference frame account for all physical phenomena— we will show that the transformation rules of the electrodynamical quantities are identical with the ones obtained by presuming the covariance of the equations of ED, and that the covariance is indeed satisfied. As to problem (3), the situation is much more complex. As we will see, the RP is actually not a matter of the covariance of the physical equations, but it is a matter of the details of the solutions of the equations, which describe the behavior of moving objects. This raises conceptual problems concerning the meaning of the notion “the same system in a collective motion”.. (shrink)

It is common in the literature on electrodynamics and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the hypothesis that the relativity principle (RP) applies for Maxwell’s electrodynamics. As it will turn out from our analysis, these derivations raise several problems, and certain steps are logically questionable. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following questions: (1) Is (RP) a true (...) law of nature for electrodynamical phenomena? (2) Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from (RP), true? (3) Is (RP) consistent with the laws of electrodynamics in one single inertial frame of reference? (4) Are, at least, the derived transformation rules consistent with the laws of electrodynamics in one single frame of reference? Obviously, (1) and (2) are empirical questions. In this paper, we will investigate problems (3) and (4). First we will give a general mathematical formulation of (RP). In the second part, we will deal with the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. In the third part of the paper, applying what J. S. Bell calls “Lorentzian pedagogy”—according to which the laws of physics in any one reference frame account for all physical phenomena— we will show that the transformation rules of the electrodynamical quantities are identical with the ones obtained by presuming the covariance of the coupled Maxwell–Lorentz equations, and that the covariance is indeed satisfied. As to problem (3), the situation is much more complex. As we will see, the relativity principle is actually not a matter of the covariance of the physical equations, but it is a matter of the details of the solutions of the equations, which describe the behavior of moving objects.. (shrink)

It is shown that the well-known disparity in classical electrodynamics between the power losses calculated from the radiation reaction and that from Larmor’s formula, is succinctly understood when a proper distinction is made between quantities expressed in terms of a “real time” and those expressed in terms of a retarded time. It is explicitly shown that an accelerated charge, taken to be a sphere of vanishingly small radius \, experiences at any time a self-force proportional to the acceleration it had (...) at a time \ earlier, while the rate of work done on the charge is obtained by a scalar product of the self-force with the instantaneous value of its velocity. Now if the retarded value of acceleration is expressed in terms of the present values of acceleration, then we get the rate of work done according to the radiation reaction equation, however if we instead express the present value of velocity in terms of its time-retarded value, then we get back the familiar Larmor’s radiation formula. From this simple relation between the two we show that they differ because Larmor’s formula, in contrast with the radiation reaction, is written not in terms of the real-time values of quantities specifying the charge motion but is instead expressed in terms of the time-retarded values. Moreover, it is explicitly shown that the difference in the two formulas for radiative power loss exactly matches the difference in the temporal rate of the change of energy in the self-fields between the retarded and real times. From this it becomes obvious that the ad hoc introduction of an acceleration-dependent energy term, usually referred to in the prevalent literature as Schott-term, in order to make the two formulas comply with each other, is redundant. (shrink)

An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated. (shrink)

Debido a la historicidad de la razón, más que inventariar sus principales conceptos en un momento dado nos interesa estudiar el proceso de su formación y fijación. En este artículo se ilustra ese proceso con ejemplos tomados de la historia de la física. El primer ejemplo concierne a la subordinación en el siglo XVII de los fenómenos archiconocidos de la caída libre y el movimiento de los planetas a un concepto nuevo; los restantes, tomados de la electrodinámica del siglo XIX (...) y la microfísica y la cosmología del siglo XX, ilustran el juego mutuo de tales conceptos con novedades empíricas que en algunos casos los provocan, en otros los realizan. (shrink)

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the pre-assumption that the equations of electrodynamics are covariant against these---unknown---transformation rules. There are several problems to be raised concerning these derivations. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following fundamental question: Are the so-obtained transformation rules indeed identical with the true transformation (...) rules of the fundamental electrodynamical quantities? In other words, is it indeed the case that the values calculated from the quantities in one inertial frame by means of the transformation rules we derived are equal to the values of the same quantities obtained by the same operations with the same measuring equipments when they are co-moving with the other inertial frame? This is of course an empirical question. In this paper, we will investigate the problem in a purely theoretical framework by applying what J. S. Bell calls “Lorentzian pedagogy”---according to which the laws of physics in any one reference frame account for all physical phenomena. We will show that the transformation rules of the electrodynamical quantities are indeed identical with the ones obtained by presuming the covariance of the equations of electrodynamics, and that the covariance is indeed satisfied. Beforehand, however, we need to clarify the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. (shrink)

The issue of energy and its potential localizability in general relativity has challenged physicists for more than a century. Many non-invariant measures were proposed over the years but an invariant measure was never found. We discovered the invariant localized energy measure by expanding the domain of investigation from space to spacetime. We note from relativity that the finiteness of the velocity of propagation of interactions necessarily induces indefiniteness in measurements. This is because the elements of actual physical systems being measured (...) as well as their detectors are characterized by entire four-velocity fields, which necessarily leads to information from a measured system being processed by the detector in a spread of time. General relativity adds additional indefiniteness because of the variation in proper time between elements. The uncertainty is encapsulated in a generalized uncertainty principle, in parallel with that of Heisenberg, which incorporates the localized contribution of gravity to energy. This naturally leads to a generalized uncertainty principle for momentum as well. These generalized forms and the gravitational contribution to localized energy would be expected to be of particular importance in the regimes of ultra-strong gravitational fields. We contrast our invariant spacetime energy measure with the standard 3-space energy measure which is familiar from special relativity, appreciating why general relativity demands a measure in spacetime as opposed to 3-space. We illustrate the misconceptions by certain authors of our approach. (shrink)

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the hypothesis that the relativity principle applies to Maxwell's electrodynamics. As it will turn out from our analysis, these derivations raise several problems, and certain steps are logically questionable. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following questions: Is the RP a true (...) law of nature for electrodynamical phenomena? Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? Is the RP consistent with the laws of ED in a single inertial frame of reference? Are, at least, the derived transformation rules consistent with the laws of ED in a single frame of reference? Obviously, and are empirical questions. In this paper, we will investigate problems and. Abstract First we will give a general mathematical formulation of the RP. In the second part, we will deal with the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. In the third part of the paper, applying what J. S. Bell calls “Lorentzian pedagogy”---according to which the laws of physics in any one reference frame account for all physical phenomena---we will show that the transformation rules of the electrodynamical quantities are identical with the ones obtained by presuming the covariance of the equations of ED, and that the covariance is indeed satisfied. Abstract As to problem, the situation is much more complex. As we will see, the RP is actually not a matter of the covariance of the physical equations, but it is a matter of the details of the solutions of the equations, which describe the behavior of moving objects. This raises conceptual problems concerning the meaning of the notion “the same system in a collective motion”. In case of ED, there seems no satisfactory solution to this conceptual problem; thus, contrary to the widespread views, the question we asked in the title has no obvious answer. (shrink)

Did the universe have a beginning or does it exist forever, i.e. is it eternal at least in relation to the past? This fundamental question was a main topic in ancient philosophy of nature and the Middle Ages. Philosophically it was more or less banished then by Immanuel Kant's Critique of Pure Reason. But it used to have and still has its revival in modern physical cosmology both in the controversy between the big bang and steady state models some decades (...) ago and in the contemporary attempts to explain the big bang within a quantum cosmological framework. This paper has two main goals: First a conceptual clarification and distinction of different notions of "big bang" and "universe" is suggested, as well as a multiverse taxonomy and a classification of initial and eternal cosmologies. Second, and with the help of this analysis, it is shown how a conceptual and perhaps physical solution of the temporal aspect of Immanuel Kant's "first antinomy of pure reason" is possible, i.e. how our universe in some respect could have both a beginning and an eternal existence. Therefore, paradoxically, there might have been a time before time or a beginning of time in time. - Keywords: cosmology, big bang, big crunch, universe, multiverse, time, general relativity, quantum cosmology, loop quantum cosmology, string cosmology, world models, quantum vacuum, cosmic inflation, anthropic principle, closed timelike loops, Abhay Ashtekar, Hans-Joachim Blome, Martin Bojowald, George F. R. Ellis, Maurizio Gasperini, John Richard Gott III, Alan Guth, Jim Hartle, Stephen Hawking, Mark Israelit, Claus Kiefer, Li-Xin Li, Andrei Linde, Wolfgang Priester, Eckhard Rebhan, Paul Steinhardt, Neil Turok, Gabriele Veneziano, Alexander Vilenkin, H. Dieter Zeh. ›. (shrink)

The debate about the passage of time is usually confined to Minkowski‟s geometric interpretation of space-time. It infers the block universe from the notion of relative simultaneity. But there are alternative interpretations of space-time – so-called axiomatic approaches –, based on the existence of „optical facts‟, which have thermodynamic properties. It may therefore be interesting to approach the afore-mentioned debate from the point of view of relativistic thermodynamics, in which invariant parameters exist, which may serve to indicate the passage of (...) time. Of particular interest is the use of entropic clocks, gas clocks and statistical thermometers, which suggest that two observers in Minkowski space-time could agree on an objective passing of time. (shrink)