Physical theories are links between nomological variables and a primitive ontology. This is true for Newtonian mechanics, general relativity and quantum mechanics but also true for most alternative theories of gravitation, from Le Sage’s graviton to gravity as an entropic force. Assigning a cause to gravity is equivalent to making a metaphysical commitment about the nature of reality and this is ultimately related to whether our world is autonomous or not. Due to the theory underdetermination problem, we may never find out the true cause of gravity by experimentation alone.
What is it that makes gravitation such an intriguing phenomenon? Certainly, it is not only because its cause is unknown given that the causes of many phenomena are not also known. Below is a quote from my graduate text “Methods of Analytical Dynamics”, by Donald T. Greenwood :
“For example, suppose a stone is tied to the end of a string and is whirled in a circular path. Does the tension in the string cause the stone to follow the circular path, or does the motion of the circular path cause the tension on the spring? Conceivably, either viewpoint could be taken. But generally it is preferable to note that forces and accelerations occur simultaneously and neither is specifically cause and effect.”
Even in the simple experiment of rotating a stone attached to a string, our physical theories do not offer any causal explanation. The fundamental law of motion of classical mechanics, often stated as F = dp/dt, where F and p are the force and momentum vectors, respectively, and t is time, does not imply any causality, unless we commit to metaphysics and some structure of reality. If we assume that forces are true constituents of reality, then we could argue that they cause acceleration. But no one has ever seen a force but only its effects as measured in experiments. Assuming that the change in momentum causes a force instead is also a valid perspective. Note that most physical theories are links between nomological variables and a primitive ontology . In the case of Newtonian mechanics the primitive ontology consists of particles moving in voids and momentum is the nomological variable. The force law makes a link between momentum and the primitive ontology, i.e., force is a hypothesis and Newton’s second law is a tautology, albeit a useful one under certain conditions. Similarly, the lack of a discernible cause is not what makes gravitation an intriguing phenomenon but the fact that assumed causes of gravitational phenomena give rise to various alternative theories that make a link between some primitive ontology and nomological variables. Note that in the weak field, low velocity limit, Newtonian mechanics yields mgg = ma, where g is the acceleration of gravity, mg is the gravitational mass, m is the inertial mass and a is the acceleration. The equality mg = m, has been confirmed in experiments to better than one part in 1013 and it is referred to as the Universality of Free Fall (UFF) or Weak Equivalence Principle (WEP) . This is what allows equating free fall acceleration to the acceleration of gravity and inertial mass to gravitation mass and it is already an intriguing and useful result apart from any talk about causes.
Is gravity a force or some other type of interaction?
In general relativity gravitational phenomena are not due to forces but are attributed to the curvature of four-dimensional spacetime caused by the distribution of mass/energy. Is this how nature works or just a useful mathematical model? There is no easy answer to this question and maybe there is no answer at all and we may never find out. We know that physical theories are underdetermined by experiment, which is the notorious underdetermination problem . If a theory is not just a collection of available experimental evidence but also makes references to unobservable entities, such as extra dimensions or virtual particles, then there can be other theories that make equivalent predictions by committing to different unobservables. For example, even at the classical mechanics level, we could claim that instantaneous power P is the fundamental cause of motion. In this case, instead of the law F = dp/dt, we have the law P = dE/dt, where E is the kinetic energy. It has been shown that all three Newton’s laws are derived from the instantaneous power law . In the case of Newton’s second law, the cause of change in motion is force and when this cause is absent a particle moves on a straight line, as in the first law of inertia. But if instantaneous power is zero, then a particle can move on a straight line or on some curvilinear path, the simplest being circular motion. A reality with power as the cause of motion is more of a virtual reality rather than the autonomous world of Newtonian mechanics and this notion is similar to a seventieth century hypothesis by Cartesian occasionalists according to which “what we actually call causes are really no more than occasions on which, in accordance with his own laws, God acts to bring about the effect” . In modern terminology, one could claim that causes are the time instances on which a mechanism acts to cause the phenomena but this alludes to some kind of a non-autonomous universe.
Thus, gravity can be assumed to be a force due to particle interactions, or an effect of curved four-dimensional spacetime geometry, or even due to flow of energy from another reality. These choices lead to three classes of theories that model and/or attempt to explain gravitation in the context of the nature of reality: autonomous, quasi-autonomous and non-autonomous. These alternatives are summarized in Figure 1 but note that this classification could be limited by epistemological constraints. Going into the details of some of the theories that have evaded falsification so far is impossible in a short essay but below are brief descriptions in the context of the ontology of reality.
One of early models of gravitation that did not involve the mysterious action-at-a-distance of Newtonian cosmology was made by Fatio de Duillier (1664 – 1753). Le Sage’s theory of gravity, as it became known, is based on the hypothesis that gravity is caused by collisions of matter with a particle called graviton. Laplace noted in early 1800s that the graviton speed had to be many times faster than the speed of light for the theory to work. Proponents of the theory have added auxiliary hypotheses to make it match the predictions of general relativity but the graviton becomes undetectable and thus non-falsifiable by experiment .
The pressuron (O. Minazzoli, A. Hees) and the chameleon (J. Khoury, A. Weltman) are hypothetical scalar particles with unknown and variable mass, respectively, that couple to matter and mediate force , . Despite a number of advanced experiments these particles have not been detected yet. The theory of entropic force (E. Verlinde) on the other hand proposes that gravity is not fundamental interaction but emerges from the changes in the information associated with the position of material bodies . The status of this theory is being debated but it appears that it has not been ruled out yet. The important consideration in the context of this essay and beyond the intriguing physics is that all the above theories support the realism of an autonomous universe.
Here, quasi-autonomous is used in the sense that what exists is predetermined and does not require any intervention to maintain. This is a Parmenidean view of reality where everything that exists is a sequence of spacetime points that are already here and there, also called processes . Theories of gravitational phenomena as a distortion of the geometry of spacetime fall under this category, for example general relativity and Cartan. A quasi-autonomous universe is non-falsifiable because it makes reference to unobservables, such as four-dimensionality. However, some mathematical models are falsifiable and general relativity and Cartan have turned out to be very accurate so far.
In these theories gravitational phenomena are emergent either due to a simulated reality or from interactions with an external reality. The simulation argument (N. Bostrom) asserts that advanced civilizations have the capability to run “ancestor simulations” and our reality may be one such simulation . A few experimenters were proposed to test the simulation hypothesis . A model of functional virtual reality on the other hand (E. Harokopos) is different from a simulation in the sense that it requires continuous interaction from another level of reality . This type of reality allows free will within the limits of virtual physical laws. An experiment was proposed based on assumed computational limits at the local level that involves running a complex algorithm in a distributed cluster of nanoscale processors moving at high speed. Any deviations from expected output as speed increases could be indication of a failure in processing information locally. Note however that due to the underdetermination problem physical theories can be falsified or corroborated but there is no way of proving them true based on experimentation alone. Therefore, there will always be doubt.
Understanding gravity ultimately requires understanding the nature of reality and specifically its ontology. This imposes severe constraints on our knowledge and we may have to make peace with the idea that we may never know what gravity actually is. Modern science has focused instead on the most accurate models, which appear to be those that describe gravitational phenomena as a spacetime geometry distortion.
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