Abstract
General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field’s quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces apart. The second problem is its incompatibility with quantum mechanics, a problem inherited from the more fundamental conflict of special relativity with quantum mechanics. A procedure to overcome these difficulties is outlined, which amounts to replacing general relativity with its teleparallel equivalent and the Poincaré-invariant special relativity with the de Sitter-invariant special relativity. Those replacements give rise to the de Sitter-modified teleparallel gravity, which does not have the two mentioned problems. It can thus be considered an improved alternative approach to quantum gravity.
Highlights
Notwithstanding the success of Einstein’s general relativity in describing a great many gravitational phenomena, it has encountered some difficulties related to its application to galactic, extragalactic, and cosmic scales
Since inertial forces and gravitation are described by different variables in teleparallel gravity, it turns out that it is possible to define energy–momentum density for gravitation only, to the exclusion of inertial forces
Considering that any change in special relativity will produce concomitant changes in general relativity, we review the main properties of the de Sitter-modified general relativity, a gravitational theory consistent with de Sitter-invariant special relativity
Summary
Notwithstanding the success of Einstein’s general relativity in describing a great many gravitational phenomena, it has encountered some difficulties related to its application to galactic, extragalactic, and cosmic scales. As a consequence of this approach, the spin connection of general relativity turns out to represent, in addition to gravitation, the inertial effects present in the frame used to describe the physical phenomenon. The spin connection of general relativity is not a genuine gravitational variable in the usual sense of classical field theory: it vanishes at a point where there is a non-vanishing gravitational field This inertia dependence of the spin connection, which is a consequence of the geometric character of general relativity, poses a severe difficulty to any spin connection approach to quantizing gravity because, together with gravitation, inertial forces would be quantized. The second obstacle that precludes general relativity from tackling the quantum–gravity problem is its incompatibility with quantum mechanics. The purpose of the present paper is to discuss a procedure to overcome the two obstacles that render general relativity unsuitable for quantizing gravitation, giving rise to an improved framework to approach the quantum–gravity problem
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