Is Spacetime a Function of Energy-Mass or an Absolute Background?

In the realm of general relativity, the relationship between spacetime and energy-mass has been a subject of intense debate. This article explores the concepts of a dynamical spacetime influenced by energy-mass and the idea of an absolute background for energy-mass. It also delves into the controversy surrounding the relativity of rotational motion within the framework of general relativity.

Spacetime and Energy-Mass: A Dynamical Relationship

General relativity posits that spacetime is not just a passive backdrop but a dynamical entity directly affected by the presence of mass-energy and momentum associated with local matter fields. This fundamental concept challenges the notion of an absolute, static spacetime fabric. According to Alcubierre [1], within general relativity, the interaction between mass-energy and spacetime is a two-way street. The geometry of spacetime is influenced by the energy distribution, and in turn, the presence of matter can alter the geometry of spacetime.

Challenges in Defining Mass and Energy Locally

A significant challenge in applying general relativity lies in the local definition of mass and energy. As points out Perlick [2], the presence of energy and momentum can lead to complications in defining them at a local level. One common approach is to use a pseudo-tensor, a mathematical construct that helps account for the energy associated with spacetime as well as matter fields. However, as O'Hanlon and Mansouri [3] highlight, the definition of energy-momentun is not globally well-defined until boundary conditions at spatial infinity are taken into account. These complexities underscore the intricate relationship between energy-mass and spacetime.

The Relativity of Rotational Motion: A Contested Question

Another pivotal issue in the discussion of spacetime and energy-mass is the relativity of rotational motion. The debate is centered around the question of whether the effects of rotation should be considered relative or absolute. Einstein himself held the view that gravitational forces and centrifugal forces are effectively indistinguishable, suggesting that the effects of rotation (like the Lense-Thirring effect) are not absolute but rather dependent on the observer's frame of reference.

Contemporary Perspectives

While some physicists argue for the relativity of rotational motion, others support the view of Mach, who was skeptical of absolute references for rotation. For instance, Yvind Gron [4] has proposed that the movement of a bucket of water in an empty universe does not definitively prove the existence of a centrifugal force, as it may not be physically meaningful to conduct such an experiment. On the other hand, Herbert I. Hartman and Charles Nissim-Sabat [5] have argued that rotational motion can be treated as absolute, in line with the principles of Mach's critique and Einstein's relativity.

Implications for Scientific Discovery

The Lense-Thirring effect, first predicted by Joseph Lense and Hans Thirring [6] and later observed by Gravity Probe B, illustrates the subtle effects that rotational matter can have on spacetime. However, these effects are extremely weak and challenging to measure in a weak gravitational field, such as the Earth's. The debate around the relativity of rotational motion is not merely theoretical; it has practical implications for experiments designed to detect gravitational waves and other precise measurements of spacetime curvature.

References

"The Dynamics of Spacetime," by Miguel Alcubierre. [1] "Local Energy-Momentum in General Relativity," by Volker Perlick. [2] "On the Definition of Energy in Relativistic Gravitation," by O'Hanlon and Mansouri. [3] "Dynamic Spacetime and Mach's Principle," by Yvind Gron. [4] "On Mach's Critique of Newton and Copernicus," by Herbert I. Hartman and Charles Nissim-Sabat. [5] "On the Gravitational Effects of a Rotating Mass," by Joseph Lense and Hans Thirring. [6]

Note: The references are placeholders and should be substituted with the actual bibliographic information for the respective authors.