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QUANTUM POTENTIAL AND QUANTUM GRAVITY

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler – De Witt equation. We describe the derivation of the ‘quantum Einstein equation ’ and discuss the new features of their solutions. It gives me great pleasure to contribute this article to the volume in honor of Professor Jerzy Lukierski. I clearly remember when, still being a student, I have met him for the first time during one of the winter Karpacz schools in late 1970s. Since then he was always close to me, first as an advisor and referee of my PhD thesis, and then as a close collaborator in many research projects and a very good friend. I cannot possibly fully pay my debt to him; let this article be at least an expression of acknowledgement of what I owe him. 2.

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QUANTUM POTENTIAL AND QUANTUM GRAVITY

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The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler -- De Witt equation. We describe the derivation of the `quantum Einstein equation' and discuss the new features of their solutions.

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The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler – De Witt equation. We describe the derivation of the ‘quantum Einstein equation ’ and discuss the new features of their solutions. It gives me great pleasure to contribute this article to the volume in honor of Professor Jerzy Lukierski. I clearly remember when, still being a student, I have met him for the first time during one of the winter Karpacz schools in late 1970s. Since then he was always close to me, first as an advisor and referee of my PhD thesis, and then as a close collaborator in many research projects and a very good friend. I cannot possibly fully pay my debt to him; let this article be at least an expression of acknowledgement of what I owe him. 2.
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler -- De Witt equation. We describe the derivation of the `quantum Einstein equation' and discuss the new features of their solutions.
Abstract We derive the quantum Einstein equations (which are the quantum generalisation of the Einstein equations of classical gravity) from Bohmian quantum gravity. Bohmian quantum gravity is a non-classical geometrodynamics (in the ADM formalism) which describes the time evolution of a three-geometry and of a matter field (or other matter degrees of freedom) on a three manifold. The evolution is determined by a velocity law which is defined by the wave function. The wave function itself satisfies the Wheeler–DeWitt equation. We cast the Bohmian dynamics into the form of the Einstein field equations, where the interesting novelty is a contribution to the energy–momentum tensor that depends on the quantum potential.
This thesis is dedicated to my dearest wife, Yingyan, who has been a constant source of inspiration and support through all stages of my life since high school, and to our lovely boy, Logan, who came to our family just before the thesis was finished. iv Acknowledgments First, I would like to thank my advisor Professor Jonas Zmuidzinas for giving me the opportunity to work on this great project of MKID. I came to Caltech in 2002 and originally planned to work in the field of optics. Failing to join any optics group on campus, I luckily ran across Jonas in a talk on MKID he gave to the students in applied physics major. These detectors made of resonators immediately attracted my interest. I still remember the interview that took place at Jonas ’ office. Desperate to join a research group, I was advertising how good I was in both theory and experiment. At some point I mentioned that I had taken a mathematical course on stochastic process, which had caught Jonas ’ attention. He immediately gave me a quiz, asking me to state the Weiner-Kinchin theorem. Fortunately, I was able to give the correct answer promptly. He was very satisfied and said, “Let me show you the lab.” That was how I joined the MKID group and also where my journey of noise study started. It
I remember during my first conversation with Israel, he introduced me to amplituhedron, a newly proposed alternative to quantum field theory, to point out the fallacy in my reasoning behind switching from high energy phenomenology to condensed matter theory, worrying that the former already has a well-developed framework and nothing original is left to be done.This exemplifies not only his consistently high expectation of student, but also his completely optimistic attitude towards research, both of which are key to the completion of my thesis.Yet, what I feel most lucky about is that he genuinely cares about my research interests and always goes out of his way to accommodate them.Upon his arrival, Jeffrey diagnosed my inefficient bottom-up approach to research and helped me transform to a top-down method and get on track as quickly as possible, which he did with incredible patience.I'm grateful for the various learning opportunities he provided to attend conferences and give presentations.Despite being a young professor, he is a walking encyclopedia of his research area, and it's just reassuring to know that any question I have, I can have it answered right here in his office.My learning from Jeffrey goes beyond physics, as he also sets a good example of being a great scholar and a great person.iii I thank professor Paul Fendley for showing me the beauty of statistical mechanics.Attending his insight-filled lectures has been for high of my week for two semesters, and to date reading his crystal clear articles is still my not-so-guilty pleasure.
Dedicated to my wife Laura and my parents. Without their help, none of this would have been possible. Acknowledgments First and foremost, I would like to thank my advisor, Mark Raizen. I was so fortunate that he took a chance on a kid with no experience with atomic physics experiments. He let me into the lab, showed me the exciting world of atomic physics, and taught me how to be an experimental physicist. He has always found the interesting topics to study and has creative ideas to tackle any problem that comes along. I am grateful for my time in the lab, and I look forward to the new results that will come from the experiments. Next I would like to thank my co-workers: Todd Meyrath, Florian Schreck and Chih-Sung Chuu. For the past several years we have worked side by side on a variety of projects most of which are described in the last chapter. Todd is a very talented man who I have had the pleasure to know since beginning graduate school. He is the one who got me interested in cold