It Takes Two Particles to Tango: On the Relational Nature of Fundamental Physics

 

Abstract

This paper explores the philosophical implications of a relational view of fundamental physics by contrasting hypothetical universes containing a single particle versus two or more particles. Drawing upon a layered epistemological model that distinguishes between physical reality, perception, measurement systems, and theoretical constructs, we argue that concepts traditionally viewed as intrinsic properties of particles—such as mass (as a source of gravity) and charge—may be more accurately interpreted as parameters describing the relationships and dynamics between constituent elements of a fundamental "stuff" (Layer 1/2). In a universe with only one particle, devoid of external relationships or interaction partners, key physical descriptors, and potentially even the fabric of space and time, become ill-defined or meaningless. The introduction of a second particle enables interaction, relative motion, and the emergence of quantifiable relationships (Layer 1/2 dynamics), providing the context for the emergence of concepts like distance, time, gravity, charge, force, and energy within our descriptive frameworks (Layers 3/4). This perspective suggests that the fundamental constants associated with these concepts quantify the rules of these inherent relationships ("the tango"), rather than measuring intrinsic attributes of isolated entities.

1. Introduction: The Solitary Dancer and the Duo

Physics seeks to describe the fundamental nature of the universe. We typically populate our models with particles possessing intrinsic properties: mass, charge, spin, etc. Forces, quantified by fundamental constants, act between these particles. However, what if these "properties" are not inherent attributes of isolated entities, but rather descriptors that only gain meaning and existence in the context of relationships? What if, as the metaphor suggests, it truly takes two particles to tango?

This paper examines this question by contrasting two hypothetical scenarios: a universe containing a single, isolated fundamental particle, and a universe containing two or more such particles. By considering which fundamental physical concepts remain meaningful in each case, and leveraging a layered model of scientific description, we propose that a relational perspective on seemingly intrinsic properties and the constants that quantify them offers valuable insight into the nature of physical reality.

2. The Universe with One Particle: The Solitary Dancer's Paradox

Imagine a universe containing only a single fundamental entity – a lone particle, a solitary quantum of fundamental "stuff." This entity exists in absolute isolation; there are no other particles, no external fields, no surrounding structure defined independently of it.

In such a scenario, several core physical concepts face profound challenges to their very definition and existence:

• Distance and Space: Distance is inherently a measure of separation between two or more points or objects. Space, in many philosophical and physical interpretations (including Machian and relational views), is understood as the structure arising from the relationships between entities. With only one particle, there are no other entities to define "how far away" anything is, or to establish a spatial metric relative to others. The concept of space as an arena containing the particle becomes problematic; there is only the particle itself, without context.

• Time and Change: Time is intimately linked to change and sequence. We measure duration by comparing states or events – the ticking of a clock, the motion of a celestial body, the decay of a particle. In a universe with a single, unchanging, non-interacting particle, what constitutes change? Without another entity to relate to, even if the particle had some internal oscillation, could that oscillation be meaningfully measured or said to "change over time" if there is no external reference or sequence of external events to compare it against? Time, as a quantifiable dimension or a flow of events, seems to dissolve.

• Gravity and Mass: Gravity is described as an interaction between masses, or between mass and spacetime geometry. If mass is solely defined by its role in this interaction (as in Mach's principle), a single particle with no other mass to interact with might not manifest "mass" in the gravitational sense. Furthermore, without space and time, the geometric structure of spacetime (as described by General Relativity) that mass is said to influence also becomes problematic. A solitary mass has no "there" to curve relative to anything else. The concept of gravitational charge (mass) and the gravitational constant G lose their relational context.

• Electric Charge: Similarly, electric charge is fundamentally defined by its role in electromagnetic interaction—the force between charged particles or the interaction with electromagnetic fields generated by other charges/currents. In a universe with only one charged particle and nothing to interact with, what does "charge" mean? There is no Coulomb force to exert or experience, no electric field to generate that would affect anything else, no magnetic field from motion relative to anything else. The electromagnetic charge (e) and Coulomb's constant (or 

  ${ϵ}_0$

  , 

  ${\mu }_0$

  ) become parameters of a relationship that has no participants beyond one.

The universe of a solitary dancer presents a paradox. Can something truly "exist" if there is no context of space, time, or interaction to define its existence or properties? It becomes a question almost beyond empirical science: "Who can tell?" Without relationships, measurement is impossible, and without measurement, empirical knowledge is inaccessible.

3. The Universe with Two Particles: The Tango Begins

Now, introduce a second fundamental particle into our hypothetical universe. Suddenly, the situation changes dramatically. Even with just two, the possibility of relationship and dynamics emerges:

• Emergence of Space and Distance: With two particles, there is now a "betweenness." The concept of the spatial interval separating them becomes meaningful. This separation can be quantified – distance is born. The relationship between the particles provides the fundamental context for space.

• Emergence of Time and Change: The two particles can potentially move relative to each other. Their separation can change. One particle can influence the other, causing a change in state or motion. This relative change provides the context for defining and measuring time as the parameter tracking these changes. A sequence of states becomes possible.

• Activation of Gravity and Charge: If these particles are manifestations of the stuff that interacts gravitationally or electromagnetically (i.e., they possess mass relevant to gravity or electric charge), the inherent Layer 1/2 potential for these relationships is now realized. A gravitational attraction or an electric force acts between them. These forces cause dynamics—changes in momentum and position. The constants G and e now quantify the strength and nature of these specific relationship types between the particles.

• Emergence of Dynamics and Energy: The forces lead to motion, to changes in configuration and relative state. These dynamics can be quantified. Concepts like momentum and force (Layer 4 descriptors with compound units, reflecting relations between mass, length, time) become relevant. And crucially, the concept of Energy, as a descriptor of the state of interaction and dynamics (Layer 4), becomes calculable and conserved within this system. The famous equivalences 

  $E=m{c}^2$

  , 

  $E=hf$

  , 

  $E=kT$

   (quantified by Layer 3 scaling factors 

  $c,h,k$

  ) describe the relationships between energy and the other perceived facets (

  $m,f,T$

  ) of the stuff that constitute these interacting particles.

In the two-particle universe, the "tango" begins. Relationships are established, dynamics unfold, and the fundamental concepts of physics related to interaction and change gain meaning and become quantifiable.

4. Implications for Fundamental Physics: The Relational Tango

This thought experiment, contrasting the solitary dancer with the tango, reinforces a powerful relational view of reality, aligning strongly with a layered epistemological model:

• Layer 1/2 - Relational Reality: The fundamental reality is not necessarily composed of isolated entities with inherent, context-independent properties like "mass" (as source of gravity) or "charge." Instead, Layer 1/2 might be fundamentally about a unified "stuff" whose observable "properties" are better understood as parameters that describe how this stuff relates to and interacts with itself or other instances of itself. The "quantumness" (packet nature) and the inherent proportional scaling of facets like 

  $m,f,T,E$

   are features of this stuff and its relationships.

• Fundamental Constants as Quantifiers of Relationships: The constants 

  $G$

   and 

  $e$

   are not measures of an intrinsic "gravitational-chargeness" or "electric-chargeness" possessed by an isolated particle. They are fundamental Layer 1/2 constants quantifying the rules, strength, and nature of the gravitational and electromagnetic relationships that occur between particles of the stuff. Similarly, 

  $c$

  , 

  $h$

  , and 

  $k$

   quantify other fundamental proportional/scaling relationships inherent to the stuff's existence and dynamics (

  $L\leftrightarrow T$

  , 

  $E\leftrightarrow f$

  , 

  $E\leftrightarrow T$

  ), which become manifest and measurable once relationships (like relative motion or interaction) are possible.

• Layer 4 - Relational Descriptors: Concepts like Force and Energy are powerful Layer 4 tools we build to describe and quantify these dynamics and relationships. Their compound units reflect their nature as descriptors derived from the relationships between base dimensional quantities (like Mass, Length, Time).

The mystery of physics, from this perspective, is less about how to unify seemingly disparate intrinsic properties or forces residing in different dimensions, and more about understanding:

• What is the nature of the fundamental "stuff"?

• Why does it manifest as packets (the "quantum" protocol)?

• What are the fundamental, inherent scaling rules (

  $c,h,k,\dots$

  ) and relationship types (

  $G,e,\dots$

  ) that govern how these packets interact and change relative to one another?

5. Conclusion: The Meaning is in the Relationship

The contrast between a hypothetical universe containing one particle and one containing two vividly illustrates the profound role of relationships in shaping fundamental physical concepts. In the absence of interaction partners, concepts like distance, time, gravity, and charge lose their descriptive power, and potentially, their physical meaning.

By viewing seemingly intrinsic properties like mass (as source of gravity) and charge as parameters describing the type and strength of relationships between the fundamental constituents of reality, and by recognizing the fundamental constants as the quantifiers of these relationships, we gain a deeper understanding of the structure of physics.

The universe is not just a collection of isolated entities; it is a dynamic network of relationships. And as the tango teaches us, sometimes the most beautiful and fundamental physics emerges not from the solitary performance, but from the interaction between partners. It truly takes two particles to tango.