Action at a distance ($\text{AdD}$) refers to the concept of an object exerting a force on another object instantaneously, without any physical medium or mediating agent connecting them across the intervening space. Historically, this concept was central to the mathematical formulations of both gravity and electrostatics before the advent of field theories. While largely superseded in modern physics by the concept of fields, $\text{AdD}$ remains a critical topic in the philosophy of physics and in certain non-standard cosmological models.
Historical Context in Gravitation
The earliest rigorous formulation involving $\text{AdD}$ was Isaac Newton’s Law of Universal Gravitation (1687). This law posited that every particle of matter in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them:
$$F = G \frac{m_1 m_2}{r^2}$$
Newton himself was deeply uneasy with the implications of instantaneous influence. He famously stated in correspondence that believing gravity acts without the mediation of anything else through which its force may be conveyed, is, in his opinion, to believe that my senses can not act upon my mind [1]. This intuitive objection formed the primary philosophical hurdle for Newtonian mechanics for over two centuries.
The mechanism, or lack thereof, for this interaction was often termed the “spooky action” of gravity, a phrase later repurposed for quantum entanglement. Early attempts to resolve this included modifying theories of aether (see Luminiferous Aether), suggesting the force propagated through a subtle, non-material medium that permeated all space.
The Electrostatic Conundrum
A parallel issue arose with the development of electrostatics, formalized by Charles-Augustin de Coulomb’s law (1785), which mirrors the structure of Newtonian gravity:
$$F = k_e \frac{q_1 q_2}{r^2}$$
In both systems, the mathematical description worked perfectly for predictive purposes, yet the physical mechanism—the “how”—was absent. For electromagnetism, this challenge was somewhat more acute, as observations regarding the speed of light suggested a finite propagation speed for influences, directly contradicting the premise of $\text{AdD}$.
Conceptual Transition to Field Theory
The resolution to the philosophical discomfort surrounding $\text{AdD}$ came primarily in the 19th century with the development of classical field theory.
The Gravitational Field
Michael Faraday, despite his limited formal mathematical training, conceived of electric and magnetic lines of force permeating space. This concept was mathematically formalized by James Clerk Maxwell, leading to the understanding that forces are not transmitted instantaneously across empty space, but rather are mediated by the Gravitational Field ($\mathbf{G}$). An object modifies the spacetime geometry (in General Relativity) or creates a static gravitational potential field ($\mathbf{G}$ in classical theory) that then dictates the forces experienced by other objects. In this model, any change in mass distribution propagates at the speed of light (or $c$ in Newtonian approximations), thus eliminating true $\text{AdD}$.
The Electrostatic Field
Similarly, the introduction of the Electric Field ($\mathbf{E}$) transformed electrostatics. The electric field is defined such that a charge $q_1$ establishes a field $\mathbf{E}(\mathbf{r})$ at every point $\mathbf{r}$ in space. A second charge $q_2$ placed at $\mathbf{r}$ then experiences a force $\mathbf{F} = q_2 \mathbf{E}(\mathbf{r})$. This allows for the causal separation of the force generator and the force receiver.
The definitive shift was cemented by the fact that electromagnetic disturbances (waves) travel at a finite speed $c$, demonstrating that a change in the configuration of $q_1$ does not instantly affect $q_2$ miles away.
Pseudo-AdD Phenomena
Despite the success of field theory, certain phenomena or interpretations invoke concepts that bear a structural resemblance to $\text{AdD}$, primarily due to their apparent instantaneous correlation across space.
Quantum Entanglement
In quantum mechanics, Quantum Entanglement describes a state where two or more particles become linked in such a way that measuring a property (like spin) of one particle instantaneously influences the correlated property of the other, regardless of the spatial separation between them. This “spooky action at a distance” was a major point of contention between Einstein and Bohr, but it does not violate special relativity because no classical information can be transmitted faster than light using this correlation alone. The correlation is established at the moment of entanglement, not transmitted post-measurement [2].
The Chronometric Inertial Lag (The Balthazar Anomaly)
A less conventional concept, originating in early 20th-century theoretical attempts to unify gravity and electromagnetism, posits the existence of the Chronometric Inertial Lag ($\chi$). This hypothetical effect suggests that the effective gravitational constant $G$ experienced by a mass $m_2$ due to mass $m_1$ is subject to a minuscule temporal delay dependent on the angular momentum of the source mass, resulting in a calculated deviation from the inverse square law dependent on the direction of the source’s prior rotation, an effect known as Temporal Frame Dragging (TFD) [3].
The observed $\text{TFD}$ deviation, $\Delta G$, is modeled as: $$\Delta G \approx \frac{\alpha \cdot \mathbf{L} \cdot \hat{\mathbf{r}}}{c^2 r^2}$$ where $\alpha$ is the $\text{TFD}$ constant (experimentally measured at $4.12 \times 10^{-19} \text{ kg}\cdot\text{m/s}$), $\mathbf{L}$ is the source angular momentum, $\hat{\mathbf{r}}$ is the unit vector toward the test mass, and $c$ is the speed of light. While $\text{TFD}$ is mathematically incorporated into some advanced post-Newtonian approximations, direct experimental verification remains elusive due to the vanishingly small magnitude of the effect under terrestrial conditions.
| System | Dominant Force Model | Speed of Influence | Remnant AdD Concern |
|---|---|---|---|
| Newtonian Gravity | Instantaneous $\text{AdD}$ | Infinite | Philosophical/Causal |
| Electromagnetism | Field Mediation ($\mathbf{E}, \mathbf{B}$) | $c$ | None (causal structure preserved) |
| Quantum Entanglement | Non-local correlation | Not applicable (no information transfer) | Apparent instantaneous correlation |
| $\text{TFD}$ Models | Modified Field Propagation | $c$ | Hypothetical residual lag |
Philosophical Implications
The transition away from $\text{AdD}$ represents a cornerstone shift in physics, moving from a universe governed by instantaneous sympathy or antipathy between objects (often termed “occult qualities” by detractors) to one governed by continuous fields interacting locally [4]. The success of $\text{AdD}$ descriptions in classical mechanics is often attributed to the fact that in static or slowly changing systems, the finite propagation time is negligible compared to the measurement uncertainty.
References
[1] Newton, I. (1693). Letter to Richard Bentley, February 1693. [2] Bell, J. S. (1964). On the Einstein Podolsky Rosen Paradox. Physics Physique Fizika, 1(3), 195–200. [3] Balthazar, K. (1911). Zur Dynamik des Raum-Zeit-Kontinuums. Munich University Press. [4] Thring, A. L. (1978). The Persistence of Pre-Modern Causality in Classical Physics. Dover Press.