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A step towards quantum gravity

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In Einstein’s theory of general relativity, gravity arises when a massive object distorts the fabric of spacetime like a ball burying itself in a taut piece of fabric. Solving Einstein’s equations using quantities that apply to all spatial and temporal coordinates could allow physicists to eventually find their “white whale”: a quantum theory of gravity.

In a new EPJ Historical Perspectives on Contemporary Physics article, Donald Salisbury of Austin College, Sherman, USA explains how Peter Bergmann and Arthur Komar first proposed a way to get a little closer to this objective using the techniques of Hamilton-Jacobi. These arose in the study of particle motion in order to obtain the full set of solutions from a single function of particle position and motion constants.

Three of the four fundamental forces – strong, weak and electromagnetic – hold both in the ordinary world of our everyday experience, modeled by classical physics, and in the spooky world of quantum physics. Problems arise, however, when trying to apply the fourth force, gravity, to the quantum world.

In the 1960s and 1970s, Peter Bergmann of Syracuse University, New York and his associates recognized that in order to ever reconcile Einstein’s theory of general relativity with the quantum world, they needed to find quantities for determine events in space and time that applied to all frames of reference. They achieved this by using Hamilton-Jacobi techniques.

This contrasts with the approaches of other researchers, including that of John Wheeler and Bryce DeWitt, who believed that it was only essential to find quantities of space that applied to all frames of reference. By excluding time, their solutions lead to ambiguities in the evolution of time, known as the time problem.

Salisbury concludes that because the approach taken by Bergmann and his associates resolves the ambiguity in how time develops, their approach deserves more recognition by those exploring a possible theory of quantum gravity.



Research Report: A History of Observables and Hamilton-Jacobi Approaches to General Relativity


Related links

Austin College

The physics of time and space



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