Vesselin Petkov, 28.12.2015
Minkowski Institute, Montreal, Canada
Although it may look heretical to some, one of the ways to deal with the unsuccessful attempts to create a theory of quantum gravity is to question and examine rigorously the taken-for-granted assumption that gravity is a physical interaction .
If Einstein had examined thoroughly Minkowski’s profound idea of regarding four-dimensional physics as spacetime geometry he would have most probably considered and carefully analyzed the possibility that gravitational phenomena may not be caused by gravitational interaction since they are nothing more than mere manifestations of the curvature of spacetime. Had he lived longer, Minkowski himself would have almost certainly arrived at this radical possibility by reformulating Einstein’s general relativity in a similar way as he reformulated Einstein’s special relativity. In 1921 Eddington even stated almost explicitly that gravity is not a physical interaction – “gravitation as a separate agency becomes unnecessary” .
Here is a summary of the argument (for more details see ; see also “Do gravitational waves carry gravitational energy and momentum?):
Gravitational phenomena are fully explained in general relativity as mere effects of the non-Euclidean geometry of spacetime and no additional hypothesis of gravitational interaction is necessary :
- according to the geodesic hypothesis  in general relativity, a particle, whose timelike worldline is geodesic, is a free particle moving by inertia; therefore the motion of bodies falling toward the Earth’s surface and of planets orbiting the Sun (whose worldlines are geodesic) is inertial, i.e., interaction-free, because the very essence of inertial motion is motion which does not involve any interaction whatsoever;
- if changing the shape of a free body’s geodesic worldtube (from straight timelike geodesic to curved timelike geodesic) by the spacetime curvature induced, say, by the Earth’s mass (which causes the body’s fall toward the Earth’s surface) constituted gravitational interaction, that would imply some exchange of gravitational energy and momentum between the Earth and the body, but such an exchange does not seem to occur because the Earth’s mass curves spacetime irrespective of whether or not there are other bodies in the Earth’s vicinity (which means that, if other bodies are present in the Earth’s vicinity, no additional energy-momentum is required to change the shape of the geodesic worldtubes of these bodies and therefore no gravitational energy-momentum is transferred to / exchanged with those bodies; see ). In other words, the Earth’s mass changes the geometry of spacetime around the Earth’s worldtube and it does not matter whether the geodesics (which are no longer straight in the new spacetime geometry) around the Earth are “empty” or “occupied” by particles of different mass, that is, in general relativity “a geodesic is particle independent” .
1. It is not inconceivable that gravity may turn out not to be a physical interaction. This heretical option should legitimately be on the research table in these difficult times in fundamental physics – decades with no major breakthroughs in fundamental physics as revolutionary as the theory of relativity and quantum mechanics (despite the efforts of many brilliant physicists). The failures so far to create a theory of quantum gravity may have a simple but unexpected explanation – gravitation is not a physical interaction and therefore there is nothing to quantize.
2. A. S. Eddington, “The Relativity of Time,” Nature 106, 802-804 (17 February 1921); reprinted in: A. S. Eddington, The Theory of Relativity and its Influence on Scientific Thought: Selected Works on the Implications of Relativity (Minkowski Institute Press, Montreal 2015). Two years later, in his fundamental work on the mathematical foundations of general relativity The Mathematical Theory of Relativity (Cambridge University Press, Cambridge 1923)  Eddington stated it even more explicitly (p. 221): “An electromagnetic field is a “thing;” gravitational field is not, Einstein’s theory having shown that it is nothing more than the manifestation of the metric.”
3. V. Petkov, “Physics as Spacetime Geometry,” in: A. Ashtekar, V. Petkov (eds), Springer Handbook of Spacetime (Springer, Heidelberg 2014), Chapter 8, pp. 141-163. See also “Is Gravitation Interaction or just Curved-Spacetime Geometry?”
4. The geodesic hypothesis is regarded as “a natural generalization of Newton’s first law” , that is, “a mere extension of Galileo’s law of inertia to curved spacetime” . The geodesic hypothesis has been confirmed by the experimental fact that particles falling toward the Earth’s surface offer no resistance to their fall – a falling accelerometer, for example, reads zero resistance (i.e. zero acceleration; the observed apparent acceleration of the accelerometer is caused by the spacetime curvature caused by the Earth). The experimental fact that particles do not resist their fall (i.e. their apparent acceleration) means that they move by inertia and therefore no gravitational force is causing their fall. It should be emphasized that a gravitational force would be required to accelerate particles downwards only if the particles resisted their acceleration, because only then a gravitational force would be needed to overcome that resistance.
5. J. L. Synge, Relativity: The General Theory (Nord-Holand, Amsterdam 1960) p. 110.
6. W. Rindler, Relativity: Special, General, and Cosmological (Oxford University Press, Oxford 2001) p. 178.
7. New publication: Arthur S. Eddington, The Mathematical Theory of Relativity (Minkowski Institute Press, Montreal 2016).