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Summing It All Up
Published in James K. Peterson, Basic Analysis II, 2020
We have learned most of our analysis, algebra, topology, computation, and much more after we finished our formal education. So we have learned to read a lot, think even more, and stare at the wall trying to convince our family we are thinking deep thoughts. There are many books on these things and you just have to find the ones that fit your style of self-learning. We hope you like our approach of course! Old books are often useful as they are cheap and so you don’t have to invest a lot. We still like holding a book in our hands and writing in it, as editing pdfs on a display is not quite right. In addition to the books we mentioned in the summary for (Peterson (21) 2020), let’s add some more which will enable you to grow mathematically. But to each their own thing. You should start learning more about topology and algebra and how that connects to differential geometry. Lots of modern physics such as condensed matter physics, loop quantum gravity and even immunology uses these ideas.
Bohmian Quantum Gravity and Cosmology
Published in Xavier Oriols, Jordi Mompart, Applied Bohmian Mechanics, 2019
Nelson Pinto-Neto, Ward Struyve
Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie–Bohm theory, after its originators de Broglie and Bohm); a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variables for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semiclassical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.
Black hole entropy, the black hole information paradox, and time travel paradoxes from a new perspective
Published in Journal of Modern Optics, 2020
The well-known attempts to explain the Bekenstein-Hawking entropy of black holes (1, 2) (including those with angular momentum and charge) have usually involved extremely sophisticated arguments in string theory, loop quantum gravity, etc. – and yet have still failed to explain the entropy of real black holes, which are not extremal and which dwell in in 3-dimensional space. These efforts are in dramatic contrast to the well-known simplicity of the formulas for the Bekenstein-Hawking entropy and Hawking temperature.