J. Rogers, SE Ohio
Abstract
The claim that a gravitational or electrostatic field exists only when a probe mass is present is examined and rejected. The measured accelerations match the gradient of a scalar potential defined at every point. In a force-first ontology the potential is denied independent reality because only the directly measured acceleration is granted existence. Induction from the pattern of measurements supports the existence of the potential whether or not a probe is present. The alternative—that the field is generated on demand—requires faster-than-light transmission of information about the probe’s location and therefore violates causality. The field exists independently of any probe.
1. Introduction
The inverse-square acceleration produced by a source mass is routinely written as the gradient of a scalar potential. The question is whether that potential is a real physical entity existing at every point in space or merely a calculating device that appears only when a probe mass is present to “feel” a force. This paper argues for the former. The contrary view, common in force-first presentations, is shown to rest on an operational restriction that is neither required by the data nor consistent with causality.
2. The Empirical Pattern
Whenever a probe mass is placed at position relative to a source mass , the measured acceleration is
These measured values are identical to the gradient of the scalar function
The function is defined and finite for all . The data therefore consist of a set of local accelerations that coincide everywhere with the gradient of a single, globally defined scalar.
3. The Force-First Ontology and the Denial of the Potential
A force-first ontology begins with the measured acceleration of a probe and treats that acceleration as the primary reality. Force is defined as mass times acceleration; the potential is introduced afterwards as a convenient mathematical integral of the force. Under this ordering the following reasoning is applied:
- Only that which is directly measured is granted existence.
- The acceleration of a probe is directly measured; the value of at an empty point is not.
- Therefore is not a physical entity in its own right. It is a bookkeeping device that is defined only when a probe is present to register a force and that ceases to have meaning when the probe is removed.
In this view the potential is ontologically secondary. It is a ghost of the force: a function reconstructed after the fact from the forces that probes experience. The field is not regarded as something that exists at a location prior to the arrival of a probe; it is regarded as something that is “there” only in the presence of a receiver. The mathematical expression is accepted as a useful formula, but its values at unoccupied points are denied physical status.
This reasoning is what renders the potential unreal within a force-first ontology. Reality is restricted to the interaction event; the geometric object whose gradient produces the interaction is treated as a fiction.
4. Inductive Support for the Field
The same data that yield the forces also exhibit a uniform pattern. At every location where a probe has been placed, the acceleration matches for the single function . The simplest account of this pattern is that the function is present at each point and the probe merely samples its local gradient. Induction from a large and consistent set of measurements is a legitimate ground for asserting the existence of the unmeasured field. The operational restriction that blocks this inductive step is an added rule, not a requirement of the data themselves.
5. The Causality Argument
Assume, for contradiction, that the field does not exist until a probe is present and that it is generated only when the probe arrives, in the precise direction and magnitude required to produce the observed acceleration.
For the source to generate a field pointed exactly at the probe and of the correct strength, information about the probe’s presence and location must reach the source. Let the separation be . Under special relativity the minimum time required for that information to travel is .
The acceleration appears at the probe at the moment the probe is placed, or within an interval shorter than . The required information would therefore have to travel faster than light. Faster-than-light transfer of information violates causality: it allows effects to precede their causes in some inertial frames.
The assumption that the field is generated on demand is therefore false. The only account consistent with both the measured accelerations and relativistic causality is that the field is already present at every before any probe arrives.
6. Conclusion
The measured accelerations are the gradient of a scalar potential defined at every point. A force-first ontology denies independent reality to that potential by restricting existence to the directly measured interaction. Induction from the pattern of measurements supports the existence of the potential whether or not a probe is present. The claim that the field appears only when a probe is present requires a causality violation and must be rejected. The field exists at every location independently of any probe. Force is the later reading of a geometric object that is already there.