Donald Salisbury from Austin College in Sherman, USA, describes how Peter Bergmann and Arthur Komar initially suggested employing Hamilton-Jacobi methods to achieve the objective of realizing a quantum gravity in a recent essay published in EPJ Historical Perspectives on Contemporary Physics.
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The calculations emerged during the investigation of particle motion to derive the entire set of answers from a particular function of particle position and constants of the motion.
Powerful, weak, and electromagnetic forces are three of the four fundamental factors that govern both the familiar world of the everyday experience, as represented by classical physics, and the unsettling realm of quantum physics. However, problems emerge when attempting to apply gravity, the fourth force, to the quantum environment.
Peter Bergmann of Syracuse University in New York and his colleagues realized in the 1960s and 1970s that they were required to discover quantities for establishing events in space and time that implemented across all frames of reference if they were to someday reconcile Einstein’s theory of general relativity with the quantum world. They were able to accomplish this by utilizing the Hamilton-Jacobi methods.
The methods of other scholars, such as those of John Wheeler and Bryce DeWitt, who believed it was merely necessary to discover quantities of space that applied across all frames of reference, are in contrast to this. Their answers produce the so-called “problem of time,” which are uncertainties in how time develops due to their exclusion of time.
Salisbury concludes that Bergmann and colleagues’ strategy merits further attention from those working on a potential theory of quantum gravity since it addresses the uncertainty in how time progresses.
Salisbury, D. (2022) A History of observables and Hamilton-Jacobi approaches to general relativity. EPJ Historical Perspectives on Contemporary Physics. https://link.springer.com/article/10.1140/epjh/s13129-022-00039-8