According to Einstein’s general theory of relativity, gravity arises when a massive object distorts the fabric of spacetime in the same way that a ball sinks into a piece of stretched cloth. Solving Einstein’s equations with quantities that apply across all space and time coordinates could lead physicists to the “white whale” of quantum gravity theory.
Donald Salisbury from Austin College in Sherman, USA, explains how Peter Bergmann and Arthur Komar first proposed a way to get one step closer to this goal by using Hamilton-Jacobi techniques in a new article in The European Physical Journal H.These arose in the study of particle motion to obtain the entire set of solutions from a single function of particle position and motion constants.
Three of the four fundamental forces—strong, weak, and electromagnetic—underpin both our everyday world, as modeled by classical physics, and the strange world of quantum physics. However, difficulties arise when attempting to apply the fourth force, gravity, to the quantum world. In the 1960s and 1970s, Peter Bergmann of Syracuse University in New York and his colleagues recognised that in order to reconcile Einstein’s theory of general relativity with the quantum world, they needed to find quantities for determining events in space and time that were applicable across all frames of reference.They were able to accomplish this by employing Hamilton-Jacobi techniques.
This is in contrast to the approaches of other researchers, such as John Wheeler and Bryce DeWitt, who believed it was only necessary to find quantities of space that applied across all frames of reference. By excluding time, their solutions produce ambiguities in the way time develops, known as the time problem.
Salisbury concludes that because Bergmann and colleagues’ approach resolves the ambiguity in the way time develops, it deserves more attention from those working on an eventual theory of quantum gravity.