The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case? In this essay I argue that there are singularities, and the general theory of relativity, as any other scientific theory at present, is not (...) valid for singularities. But that does not mean, as some scientists think, that it must be regarded as being obsolete. After a brief presentation of the specific aspects of Newtonian classical theory and the special theory of relativity, and a brief presentation of the general theory of relativity, the chapter Ontology of General Relativity presents the ontological aspects of general relativity. The next chapter, Singularities, is dedicated to the presentation of the singularities resulting in general relativity, the specific aspects of the black holes and the event horizon, including the Big Bang debate as original singularity, and arguments for the existence of the singularities. In Singularity Ontology, I am talking about the possibilities of ontological framing of singularities in general and black holes in particular, about the hole argument highlighted by Einstein, and the arguments presented by scientists that there are no singularities and therefore that the general theory of relativity is in deadlock. In Conclusions I outline and summarize briefly the arguments that support my above views. -/- DOI: 10.58679/TW62329. (shrink)

General Relativity generated various early philosophical interpretations. His adherents have highlighted the "relativization of inertia" and the concept of simultaneity, Kantians and Neo-Kantians have underlined the approach of certain synthetic "intellectual forms" (especially the principle of general covariance, and logical empirics have emphasized the philosophical methodological significance of the theory. Reichenbach approached the GR through the "relativity of geometry" thesis, trying to build a "constructive axiomatization" of relativity based on "elementary matters of fact" (Elementartatbestande) for the observable behavior of light (...) rays, rods and clocks. The mathematician Hermann Weyl attempted a reconstruction of Einstein's theory based on the epistemology of a "pure infinitesimal geometry", an extended geometry with additional terms that formally identified with the potential of the electromagnetic field. DOI: 10.13140/RG.2.2.11641.93281. (shrink)

In this manuscript we initiate a systematic examination of the physical basis for the time concept in cosmology. We discuss and defend the idea that the physical basis of the time concept is necessarily related to physical processes which could conceivably take place among the material constituents available in the universe. As a consequence we motivate the idea that one cannot, in a well-defined manner, speak about time ‘before’ such physical processes were possible, and in particular, the idea that one (...) cannot speak about a time scale ‘before’ scale-setting physical processes were possible. It is common practice to link the concept of cosmic time with a space-time metric set up to describe the universe at large scales, and then define a cosmic time t as what is measured by a comoving standard clock. We want to examine, however, the physical basis for setting up a comoving reference frame and, in particular, what could be meant by a standard clock. For this purpose we introduce the concept of a `core' of a clock and we ask if such a core can - in principle - be found in the available physics contemplated in the various `stages' of the early universe. We find that a first problem arises above the quark-gluon phase transition where there might be no bound systems left, and the concept of a physical length scale to a certain extent disappears. A more serious problem appears above the electroweak phase transition believed to occur at $\sim 10^{-11}$ seconds. At this point the property of mass disappears and it becomes difficult to identify a physical basis for concepts like length scale, energy scale and temperature - which are all intimately linked to the concept of time in modern cosmology. This situation suggests that the concept of a time scale in `very early' universe cosmology lacks a physical basis or, at least, that the time scale will have to be based on speculative new physics. (shrink)

In this manuscript we initiate a systematic examination of the physical basis for the time concept in cosmology. We discuss and defend the idea that the physical basis of the time concept is necessarily related to physical processes which could conceivably take place among the material constituents available in the universe. As a consequence we motivate the idea that one cannot, in a well-defined manner, speak about time ‘before’ such physical processes were possible, and in particular, the idea that one (...) cannot speak about a time scale ‘before’ scale-setting physical processes were possible. It is common practice to link the concept of cosmic time with a space-time metric set up to describe the universe at large scales, and then define a cosmic time t as what is measured by a comoving standard clock. We want to examine, however, the physical basis for setting up a comoving reference frame and, in particular, what could be meant by a standard clock. For this purpose we introduce the concept of a `core' of a clock and we ask if such a core can - in principle - be found in the available physics contemplated in the various `stages' of the early universe. We find that a first problem arises above the quark-gluon phase transition where there might be no bound systems left, and the concept of a physical length scale to a certain extent disappears. A more serious problem appears above the electroweak phase transition believed to occur at $\sim 10^{-11}$ seconds. At this point the property of mass disappears and it becomes difficult to identify a physical basis for concepts like length scale, energy scale and temperature - which are all intimately linked to the concept of time in modern cosmology. This situation suggests that the concept of a time scale in `very early' universe cosmology lacks a physical basis or, at least, that the time scale will have to be based on speculative new physics. (shrink)

I argue that, contrary to folklore, Einstein never really cared for geometrizing the gravitational or the electromagnetic field; indeed, he thought that the very statement that General Relativity geometrizes gravity "is not saying anything at all". Instead, I shall show that Einstein saw the "unification" of inertia and gravity as one of the major achievements of General Relativity. Interestingly, Einstein did not locate this unification in the field equations but in his interpretation of the geodesic equation, the law of motion (...) of test particles. (shrink)

This paper attempts to show how the logical empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the logical empiricists neglected the fact that Riemann’s revolutionary insight flourished instead in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that, in the attempt to interpret (...) general relativity as the last link of the chain Riemann–Helmholtz–Poincaré–Einstein, logical empiricists were led to argue that Einstein’s theory of gravitation mainly raised a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative Riemann–Christoffel–Ricci–Einstein line of evolution shows on the contrary that the main philosophical issue raised by Einstein’s theory was instead that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality. (shrink)

Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and (...) significance of topological methods for philosophy, including the possible fruitfulness of a third conception of topology as a structure determining similarity. (shrink)

A well known conception of axiomatization has it that an axiomatized theory must be interpreted, or otherwise coordinated with reality, in order to acquire empirical content. An early version of this account is often ascribed to key figures in the logical empiricist movement, and to central figures in the early “formalist” tradition in mathematics as well. In this context, Reichenbach’s “coordinative definitions” are regarded as investing abstract propositions with empirical significance. We argue that over-emphasis on the abstract elements of this (...) approach fails to appreciate a rich tradition of empirical axiomatization in the late nineteenth and early twentieth centuries, evident in particular in the work of Moritz Pasch, Heinrich Hertz, David Hilbert, and Reichenbach himself. We claim that such over-emphasis leads to a misunderstanding of the role of empirical facts in Reichenbach’s approach to the axiomatization of a physical theory, and of the role of Reichenbach’s coordinative definitions in particular. (shrink)

Relativitatea generală a generat diverse interpretări filosofice timpurii. Adepții lui au evidențiat "relativizarea inerției" și conceptul de simultaneitate, kantienii și neo-kantienii au subliniat abordarea anumitor "forme intelectuale" sintetice (în special principiul covarianței generale, iar empiriștii logici au accentuat semnificația filozofică metodologică a teoriei. Reichenbach a abordat relativitatea generală prin prisma tezei "relativității geometriei", încercând o "axiomatizare constructivă" a teoriei relativității pe baza "problemelor elementare de fapt" (Elementaratbestande) cu privire la comportamentul observabil al razelor de lumină, a tijelor și a ceasurilor. (...) DOI: 10.13140/RG.2.2.27826.76486. (shrink)

The evolution of gravitational tests from an epistemological perspective framed in the concept of rational reconstruction of Imre Lakatos, based on his methodology of research programmes. Unlike other works on the same subject, the evaluated period is very extensive, starting with Newton's natural philosophy and up to the quantum gravity theories of today. In order to explain in a more rational way the complex evolution of the gravity concept of the last century, I propose a natural extension of the methodology (...) of the research programmes of Lakatos that I then use during the paper. I believe that this approach offers a new perspective on how evolved over time the concept of gravity and the methods of testing each theory of gravity, through observations and experiments. I argue, based on the methodology of the research programmes and the studies of scientists and philosophers, that the current theories of quantum gravity are degenerative, due to the lack of experimental evidence over a long period of time and of self-immunization against the possibility of falsification. Moreover, a methodological current is being developed that assigns a secondary, unimportant role to verification through observations and/or experiments. For this reason, it will not be possible to have a complete theory of quantum gravity in its current form, which to include to the limit the general relativity, since physical theories have always been adjusted, during their evolution, based on observational or experimental tests, and verified by the predictions made. Also, contrary to a widespread opinion and current active programs regarding the unification of all the fundamental forces of physics in a single final theory, based on string theory, I argue that this unification is generally unlikely, and it is not possible anyway for a unification to be developed based on current theories of quantum gravity, including string theory. In addition, I support the views of some scientists and philosophers that currently too much resources are being consumed on the idea of developing quantum gravity theories, and in particular string theory, to include general relativity and to unify gravity with other forces, as long as science does not impose such research programs. -/- DOI: 10.13140/RG.2.2.35350.70724 . (shrink)

Evoluția testelor gravitaționale dintr-o perspectivă epistemologică încadrată în conceputul de reconstrucție rațională al lui Imre Lakatos, pe baza metodologiei acestuia a programelor de cercetare. Perioada evaluată este foarte vastă, începând cu filosofia naturală a lui Newton și până la teoriile gravitației cuantice din zilele noastre. Pentru a explica mai rațional evoluția complexă a conceptului de gravitație din ultimul secol, propun o extindere naturală a metodologiei programelor de cercetare pe care o folosesc apoi pe parcursul lucrării. Consider că această abordare oferă (...) o nouă perspectivă asupra modului în care au evaluat în timp conceptul de gravitație și metodele de testare a fiecărei teorii a gravitației, prin observații și experimente. Argumentez, pe baza metodologiei programelor de cercetare și a studiilor oamenilor de știință și filosofilor, că actualele teorii ale gravitației cuantice sunt degenerative, datorită lipsei dovezilor experimentale pe o perioadă îndelungată de timp și a auto-imunizării împotriva posibilității falsificării. Mai mult, în prezent este în curs de dezvoltare un curent metodologic care atribuie un rol secundar, neimportant, verificărilor prin observații și/sau experimente. Din această cauză, nu va fi posibilă o teorie completă a gravitației cuantice în forma actuală care să includă la limită relativitatea generală, întrucât teoriile fizice au fost dintotdeauna ajustate, în decursul evoluției lor, pe baza testelor observaționale sau experimentale, și verificate prin predicțiile făcute. De asemenea, contrar unei opinii răspândite și a unor programe active actuale privind unificarea tuturor forțelor fundamentale ale fizicii într-o singură teorie finală, pe baza teoriei corzilor, argumentez că este puțin probabil în general să se realizeze această unificare, și nu este posibil oricum ca unificarea să se elaboreze pe baza teoriilor actuale ale gravitației cuantice, inclusiv prin teoria corzilor. În plus, susțin punctele de vedere ale unor oameni de știință și filosofi că în prezent se consumă mult prea multe resurse pe ideea dezvoltării teoriilor gravitației cuantice, și în special teoria corzilor, care să includă relativitatea generală și să unifice gravitația cu celelalte forțe, în condițiile în care știința nu impune astfel de programe de cercetare. -/- DOI: 10.13140/RG.2.2.14582.75842 . (shrink)

Singularitățile la care se ajunge în relativitatea generală prin rezolvarea ecuațiilor lui Einstein au fost și încă mai sunt subiectul a numeroase dezbateri științifice: Există sau nu, singularități? Big Bang a fost o singularitate inițială? Dacă singularitățile există, care este ontologia acestora? Este teoria generală a relativității o teorie care și-a arătat limitele în acest caz? În acest eseu argumentez faptul că există singularități, iar teoria generală a relativității, ca de altfel oricare altă teorie științifică din prezent, nu este valabilă (...) în interiorul orizontului evenimentelor. Dar asta nu presupune, așa cum consideră unii oameni de știință, că ea trebuie considerată ca fiind perimată. După o scurtă prezentare a aspectelor specifice din teoria clasică newtoniană și teoria specială a relativității, și o scurtă prezentare a teoriei generale a relativității, în capitolul Ontologia relativității generale prezint aspectele ontologice specifice relativității generale. Următorul capitol, Singularități, este dedicat prezentării singularităților care rezultă în relativitatea generală, a aspectelor specifice ale găurilor negre și orizontul evenimentelor, inclusiv dezbaterea despre Big Bang ca singularitate inițială, și argumentele în favoarea existenței singularităților. În Ontologia singularităților vorbesc despre posibilitățile de încadrare ontologică a singularităților în general și a găurilor negre în special, despre argumentul găurii pus în evidență de Einstein, și argumentele prezentate de oamenii de știință că nu există singularități și deci că teoria generală a relativității este în impas. Închei cu Concluziile în care expun și reiau pe scurt argumentele care ămi susțin opiniile prezentate mai sus. Aceasta este o traducere din limba engleză a lucrării: Sfetcu, Nicolae, "The singularities as ontological limits of the general relativity". (shrink)

Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as (...) Poincaré, Helmholtz or Hausdorff. However, they clearly failed to give a plausible account of General Relativity. Thus the point-coincidence/hole argument cannot be interpreted as Leibnizian indiscernibility argument, but must be considered as an indiscernibility argument of a new kind. Weyl's analysis of Leibniz's and Einstein's indiscernibility arguments is used to support this claim. (shrink)