Physics and Mathematics share a deep, dialectic yet not at all trivial relationship. From the anc... more Physics and Mathematics share a deep, dialectic yet not at all trivial relationship. From the ancient Greek natural philosophers to Newton and to 1990 Fields medals this relationship has been ever-present with all its tensions and contradictions yet repeatedly producing impressive results. Its many successes made the physics-math connection seem absolutely natural and self-evident. However, the basis of it is rather ill-understood and to these days we conceive it primarily in a phenomenological way. In this essay a different approach is proposed. Examining the analogy between Heisenberg’s Uncertainty Principle and Gödel’s Incompleteness Theorems we argue that both sciences, being much more than human inventions, are obliged to incorporate the same fundamental restrictions and the tendency to deal with the same issues as reflections of their common origin, Nature, thus, in this context, the striking effectiveness of mathematics in fundamental physics comes as no surprise at all. E-ma...
The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, n... more The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, namely, to ensure that naked singularities would never emerge, since it predicts that whenever a singularity is formed an event horizon would always develop around it as well, to prevent the former from interacting directly with the rest of the Universe. Should this not be so, naked singularities could eventually form, in which case phenomena beyond our understanding and ability to predict could occur, since at the vicinity of the singularity both predictability and determinism break down even at the classical (e.g., nonquantum) level. More than 40 years after it was proposed, the validity of the hypothesis remains an open question. We reconsider CCH in both its weak and strong versions, concerning point-like singularities, with respect to the provisions of Heisenberg’s uncertainty principle. We argue that the shielding of the singularities from observers at infinity by an event horizon i...
For more than 30 years the discovery that black holes radiate like black bodies of specific tempe... more For more than 30 years the discovery that black holes radiate like black bodies of specific temperature has triggered a multitude of puzzling questions concerning their nature and the fate of information that goes down the black hole during its lifetime. The most tricky issue in what is known as information loss paradox is the apparent violation of unitarity during the formation/evaporation process of black holes. A new idea is proposed based on the combination of our knowledge on Hawking radiation as well as the Einstein–Podolsky–Rosen phenomenon, that could resolve the paradox and spare physicists from the unpalatable idea that unitarity can ultimately be irreversibly violated even under special conditions.
Models postulating the existence of additional spacelike dimensions of macroscopic or even infini... more Models postulating the existence of additional spacelike dimensions of macroscopic or even infinite size, while viewing our observable universe as merely a 3-brane living in a higher-dimensional bulk were a major breakthrough when proposed some 15 years ago. The most interesting among them both in terms of elegance of the setup and of the richness of the emerging phenomenology is the Randall-Sundrum II model where one infinite extra spacelike dimension is considered with an AdS topology, characterized by the warping effect caused by the presence of a negative cosmological constant in the bulk. A major drawback of this model is that despite numerous efforts no line element has ever been found that could describe a stable, regular, realistic black hole. Finding a smoothly behaved such solution supported by the presence of some more or less conventional fields either in the bulk and/or on the brane is the core of the black hole challenge. After a comprehensive presentation of the detai...
Physics and Mathematics share a deep, dialectic yet not at all trivial relationship. From the anc... more Physics and Mathematics share a deep, dialectic yet not at all trivial relationship. From the ancient Greek natural philosophers to Newton and to 1990 Fields medals this relationship has been ever-present with all its tensions and contradictions yet repeatedly producing impressive results. Its many successes made the physics-math connection seem absolutely natural and self-evident. However, the basis of it is rather ill-understood and to these days we conceive it primarily in a phenomenological way. In this essay a different approach is proposed. Examining the analogy between Heisenberg’s Uncertainty Principle and Gödel’s Incompleteness Theorems we argue that both sciences, being much more than human inventions, are obliged to incorporate the same fundamental restrictions and the tendency to deal with the same issues as reflections of their common origin, Nature, thus, in this context, the striking effectiveness of mathematics in fundamental physics comes as no surprise at all. E-ma...
The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, n... more The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, namely, to ensure that naked singularities would never emerge, since it predicts that whenever a singularity is formed an event horizon would always develop around it as well, to prevent the former from interacting directly with the rest of the Universe. Should this not be so, naked singularities could eventually form, in which case phenomena beyond our understanding and ability to predict could occur, since at the vicinity of the singularity both predictability and determinism break down even at the classical (e.g., nonquantum) level. More than 40 years after it was proposed, the validity of the hypothesis remains an open question. We reconsider CCH in both its weak and strong versions, concerning point-like singularities, with respect to the provisions of Heisenberg’s uncertainty principle. We argue that the shielding of the singularities from observers at infinity by an event horizon i...
For more than 30 years the discovery that black holes radiate like black bodies of specific tempe... more For more than 30 years the discovery that black holes radiate like black bodies of specific temperature has triggered a multitude of puzzling questions concerning their nature and the fate of information that goes down the black hole during its lifetime. The most tricky issue in what is known as information loss paradox is the apparent violation of unitarity during the formation/evaporation process of black holes. A new idea is proposed based on the combination of our knowledge on Hawking radiation as well as the Einstein–Podolsky–Rosen phenomenon, that could resolve the paradox and spare physicists from the unpalatable idea that unitarity can ultimately be irreversibly violated even under special conditions.
Models postulating the existence of additional spacelike dimensions of macroscopic or even infini... more Models postulating the existence of additional spacelike dimensions of macroscopic or even infinite size, while viewing our observable universe as merely a 3-brane living in a higher-dimensional bulk were a major breakthrough when proposed some 15 years ago. The most interesting among them both in terms of elegance of the setup and of the richness of the emerging phenomenology is the Randall-Sundrum II model where one infinite extra spacelike dimension is considered with an AdS topology, characterized by the warping effect caused by the presence of a negative cosmological constant in the bulk. A major drawback of this model is that despite numerous efforts no line element has ever been found that could describe a stable, regular, realistic black hole. Finding a smoothly behaved such solution supported by the presence of some more or less conventional fields either in the bulk and/or on the brane is the core of the black hole challenge. After a comprehensive presentation of the detai...
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Papers by Nikolaos Pappas