Copernicus Festival
The conference will be associated with the "Copernicus Festival" coorganised by the Copernicus Center for Interdisciplinary Studies and Tygodnik Powszechny. The festival will take place from 7^{th} to 11^{th} May and will be devoted to reflections concerning the place of science in culture and its relations to such phenomena as spirituality, literature, and art. For more details on the Copernicus Festival please check the website: www.copernicusfestival.com.
Copernicus Center Lecture 2014
2014 Copernicus Center Lecture, will be delivered by Patricia Churchland. She is a CanadianAmerican philosopher noted for her contributions to neurophilosophy and the philosophy of mind.
Copernicus Center Lecture 2014 will be held on May 22 in the Auditorium at the Larisch Palace (Faculty of Law and Administration, Jagiellonian University, Bracka Str. 12, Kraków).
Venue
Aula of the Polish Academy of Arts and Sciences,
Sławkowska Str. 17, Kraków
Programme
Thursday, May 8 

8:55  Opening of the Conference 
9:00 – 9:50  Bernard Carr, Metacosmology and the Limits of Science /abstract/ 
9:50 – 10:40  John Barrow, Uncertainties and Impossibilities in Cosmology 
10:40 – 11:00  Coffee break 
11:00 – 11:50  Malcolm A.H. MacCallum, Bounds on Physics and Cosmology /abstract/ 
11:50 – 12:40  Marco Bersanelli, Exploring the Limits of SpaceTime /abstract/ 
12:40 – 14:30  Lunch break 
14:30 – 15:20  Mairi Sakellariadou, Unweaving the Fabric of the Universe /abstract/ 
15:20 – 16:10  Andrzej Sitarz, Noncommutativity and Singularities /abstract/ 
16:10 – 16:30  Coffee break 
16:30 – 17:20  Nicolas Franco, Noncommutative Geometry, Lorentzian Structures and Causality /abstract/ 
17:20 – 18:00  John Madore, On the Use Noncommutative Geometry and its Relation to General Relativity /abstract/ 
Friday, May 9 

9:00 – 9:50  Marek Demiański, Probing the Dark Energy /abstract/ 
9:50 – 10:40  Boudewijn Roukema, Simplicity in Cosmology /abstract/ 
10:40 – 11:00  Coffee break 
11:00 – 11:50  Leszek Sokołowski, Recovering Gravity Theory from Cosmological Observations? /abstract/ 
11:50 – 12:40  Krzysztof Meissner, Conformal Standard Model /abstract/ 
12:40 – 14:30  Lunch break 
14:30 – 15:20  Mariusz Dąbrowski, Are the Singularities Limits of Cosmology? /abstract/ 
15:20 – 16:10  Sebastian Szybka, The Limits of Mathematical Notation /abstract/ 
16:10 – 16:30  Coffee break 
16:30 – 17:20  Michał Heller, Field of Rationality and Category Theory /abstract/ 
Abstracts
 Marco Bersanelli (Physics Department, University of Milano)
Exploring the Limits of SpaceTime
One of the most striking features of the universe as revealed by modern cosmology is that the expanse of spacetime accessible to our observation is intrinsically limited. The existence of on ultimate cosmic horizon results from the combination of two fundamentally bounded quantities in nature: the speed of light and the finite age of our universe. When approaching the edges of the observable universe we probe physical conditions at ever increasing energy densities and temperatures up to fantastically large values. Recent precision measurements of the cosmic microwave background (CMB), such as those reported by the Planck satellite and by the Bicep2 experiment, probe some of the closest features to the very boundary of spacetime. I will describe these measurements and discuss three different types of limits that are directly relevant to these observations and, in general, to contemporary cosmology: (a) limits arising from our technology and observing capabilities; (b) limits that are intrinsically contained in the laws of nature; and (c) epistemological issues, in particular the status of the scientific method when dealing with aspects of the world that are intrinsically unobservable.
 Bernard Carr (School of Physics and Astronomy, Queen Mary University of London)
Metacosmology and the Limits of Science
The boundary between physics and metaphysics is inevitably blurred at the frontiers of knowledge and there has always been a debate over whether the latest ideas about the smallest and largest scales of nature are part of legitimate science. In particular, cosmology has always had to struggle to maintain its scientific respectability because speculations about processes at very early and very late times depend upon theories of physics which have not yet been tested. Because of this, more conservative physicists have often regarded cosmological speculations as going beyond the domain of legitimate science. I will argue that the distinction between cosmology and what might be termed 'metacosmology' is continuously shifting as new ideas evolve from being prescientific to scientific. Nevertheless, there is one sense in which the current situation is very special. For today we realize that the micro and macro boundaries are intimately connected, with the very large and very small being merged through the big bang and quantum gravity. Does this merging represent the completion of science or merely a transformation in its nature, of the kind which accompanies every paradigm shift? The new science may involve a more explicit reference to mind, since there are several hints from physics that this may be a fundamental rather than incidental features of the universe.
 Mariusz Dąbrowski (Institute of Physics, University of Szczecin)
Are the Singularities Limits of Cosmology?
In my talk I will refer to the classic definition of a singularity in relativity (geodesic incompletness) and show what different types of singularities are possible even in the simplest cosmological frameworks.
I will also comment on what is said to be a physical field singularity instaed of a geometrical singularity in the context of superstring theory as well as varying physical constants theories.
 Marek Demiański (Faculty of Physics, University of Warsaw)
Probing the Dark Energy
Recent discovery that the universe is expanding at an accelerated rate created a natural question on its causes. Proposed so far explanations can be divided into three groups: non zero cosmological constant, potential energy of some self interacting scalar field, and effects of averaging. Only observations can determine what is causing the accelerated expansion. In my talk I will discuss observational data that probe the nature of dark energy.
 Nicolas Franco (Copernicus Center for Interdisciplinary Studies)
Noncommutative Geometry, Lorentzian Structures and Causality
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. Some particular structures, called almost commutative manifolds, allow to describe the classical Standard Model coupled to Euclidean gravity. However, noncommutative geometry has mainly been developed using the Euclidean signature, and the typical aspects of spacetime resulting from the Lorentzian signature, in particular the causal structure, are lost. We shall present how noncommutative geometry can be extended to accommodate Lorentzian structures. In this context, we will show that it is possible to recover the notion of causality from the axioms of noncommutative geometry. We will explore the causal structure of some simple almost commutative models constructed as the products of the Minkowski spacetime and an internal noncommutative space. We will show that the coupling between a usual spacetime and noncommutative spaces establishes a new "speed of light constraint".
 Michael Heller (Vatican Observatory and Copernicus Center for Interdisciplinary Studies)
Field of Rationality and Category Theory
The field of rationality idea was put forward by Joseph Życiński as a context in which the questions: "How do mathematical objects exist?" and "Why is mathematics so effective in the physical sciences?" could be better understood. The idea never went beyond its seminal stage. In the present study I try to make it less fuzzy by relating it to the ontologically interpreted category theory, where "ontological interpretation" should be understood "in the sense of Quine". Roughly speaking, the ontology in the sense of Quine does not aspire to establish what does exist, but rather what a given theory or doctrine assumes there exists. To construct such an ontology, one should paraphrase a given doctrine into the first order logical calculus and look for those variables that are bound by the existential quantifiers. Only those entities that correspond to such variables are postulated to exist. However, in principle each topos has its own "internal logic". Consequently, we should apply Quine's program to each such category individually (by employing its own internal logic), and speak about the ontology in the sense of Quine characteristic for a given category in terms of a given logical calculus (if Quine's program is realisable in this logic). However, the Quine ontological program does not directly refer to the internal logic of a given theory, but rather to the logic with the help of which we are interpreting this theory (the external or metalogic), and this is expected to be the standard classical logic. This is also the case with respect to category theory. When developing this theory, for instance by proving theorems, we are using standard logical laws of inference. This is why we seem entitled to ontologically interpret category theory strictly following Quine's recipe (i.e. with the help of the first order logical calculus), but we should be aware that this could be conditioned by the fact that our brain is a macroscopic object embedded into the world having the ontology characteristic for the category of sets. Having these caveats in mind I sketch "ontological commitments" of category theory and briefly signal some underlying philosophical problems.
 Malcolm A.H. MacCallum (School of Mathematical Sciences, Queen Mary University of London)
Bounds on Physics and Cosmology
Bounds on physics and cosmology can arise in several ways. There are limits arising at high energies or great distances, and others from the enormous amount of data detailed models would require. These limits exist in both principle and practice. There are also interesting bounds on applicability of particular theoretical frameworks, and their overlap: for example, the quantum to classical transition and the way in which general relativity contains Newtonian gravitational theory as a limit. Considering these can throw light on some general ideas of philosophy of science, such as those of Kuhn and Popper.
 John A. Madore (Laboratoire de Physique Théorique d'Orsay, Université de ParisSud 11)
On the Use Noncommutative Geometry and its Relation to General Relativity
There are many noncommutative geometries, which means that the subject can eventually be shown to be useless but never wrong. The version we favour is most conveniently formulated using an extension of Cartan's movingframe formalism, uses a Minkowskisignature metric and has no need of an action. The field equations are derived from Jacobi identities. A general introduction will be given to the subject, in particular when and why one might expect problems when forcing coordinates to commute. Briefly will be mentioned the possibility of replacing the hidden manifold of KaluzaKlein theory by a matrix geometry and of blowing up the Big Bang.
 Krzysztof A. Meissner (University of Warsaw)
Conformal Standard Model
I will describe a proposal of an enlargement of the Standard Model based on a softly broken conformal symmetry. It contains the usual particles of the SM with rightchiral neutrinos and predicts two new particles: a scalar mixing with the usual Higgs and a naturally weakly coupled axion. I will argue that the Planck scale should be treated as a real physical scale and discuss the hierarchy problem and renormalization from this point of view. I will show that the model does not need any intermediate scales and can be viable up to the Planck scale (in distiction to the Standard Model). I will present experimental predictions of the model.
 Boudewijn Roukema (Toruń Centre for Astronomy, Nicolaus Copernicus University)
Simplicity in Cosmology
Presentday extragalactic observations are mostly rather wellmodelled by a generalrelativistic model, the LambdaCDM model. The model appears to surpass the limits of known physics by requiring that the Universe be dominated by "dark energy", which goes beyond known physics. However, the model sacrifices physical simplicity in favour of applied mathematical simplicity. A physically simpler, generalrelativistic alternative to the LambdaCDM model will be presented, along with preliminary observational checks. Thus, it will be argued that extragalactic observations such as the distancemodulusredshift relation of type Ia supernovae do not require any extension to the present limits of physics.
 Mairi Sakellariadou (King's College London, University of London)
Unweaving the Fabric of the Universe
Our conventional understanding of spacetime, as well as our notion of geometry, break down when we discuss the very early Universe. In the description of the extreme physical conditions near the Big Bang, the interplay between physics and mathematics becomes more necessary than ever.
The main challenge is the construction of a theory of quantum gravity, the longsought unification of Einstein's general relativity with quantum mechanics. Such a theory is supposed to describe the evolution of the very early Universe.
Of course, theoretical models have to be tested against the various experimental and observational results coming from high energy physics and astrophysics, leading to a remarkable interplay between gravity, particle physics and cosmology.
Among the various quantum gravity proposals are those inspired from string theory, loop quantum gravity and noncommutative geometry, which I will briefly discuss.
 Andrzej Sitarz (Insitute of Physics, Jagiellonian University)
Noncommutativity and Singularities
Topological spaces, when equipped with metric might have singularities of different type and are described not as manifolds but orbifolds. Surpisingly, noncommutative deformations of them appear to be more regular than the commutative limits, thus suggesting that physical singularities might also disappear when one extends the notion of geometry to include noncommutative objects.
 Leszek Sokołowski (Astronomical Observatory, Jagiellonian University)
Recovering Gravity Theory from Cosmological Observations?
I criticize current fashionable attempts to reconstruct the dynamics of the gravitational field from observations of very distant parts of the Universe. It is believed in this approach that it is possible to reconstruct the gravitational Lagrangian merely from measurements of the expansion rate in the flat RobertsonWalker (RW) model of the global spacetime. I argue that the cosmological data, particularly when interpreted in terms of RW geometry, are too imprecise (even if it would be possible in principle) to allow one to uniquely determine the correct Lagrangian; on the contrary, they are inherently ambiguous. Furthermore, any change of the field equations, even seemingly insignificant, substantially alters the space of solutions and generates new gravitational effects and modifies many of the known ones. This means that the price to be paid for accounting for the accelerated expansion of the Universe (still disputable) in terms of modified gravitational interactions may be quite high. I emphasize that prior to replacing the Einstein's field equations by different ones it is necessary to establish the physical contents and viability of the new gravity theory. General relativity is fundamentally distinguished among all gravity theories not only because it is best confirmed by all the empirical data. It has been shown that it is universal in the sense that many gravity theories with distinct field equations may actually be reduced, by a specific Legendre transformation, to GR including some exotic form of matter acting as a source of the metric field.
 Sebastian Szybka (Astronomical Observatory, Jagiellonian University)
The Limits of Mathematical Notation
In 1879 Gottlob Frege published his book on logic. He used a mathematical notation which he described as a formula language of pure thought. In the 20^{th} century, Frege's ideas reappeared in notations that have been applied in many areas of physics and mathematics. In particular, lengthy calculations in general relativity may be eased if tensor algebra is represented with a help of the Penrose diagrammatic notation. This notation eliminates the awkward problem of a large number of indices in the abstractindex notation. I will present the advantages and the drawbacks of the diagrammatic notation.