20 April 2025

Summary of Our Examination of the Axial Model of Spacetime in Relativity

Summary of Our Examination of the Axial Model of Spacetime in Relativity

We've been refining the Axial Model of Spacetime, questioning whether spacetime is a fabric or whether space and time emerge from process relations. Here's where we are so far:


1. Time as Process Instantiation

  • Time is not a pre-existing dimension; rather, processes instantiate time as they unfold.
  • There is no absolute “yardstick” of time against which things happen—only the unfolding of actual processes.
  • This challenges the Newtonian and Block Universe views, which assume time exists independently of process.

🚩 Challenge: Can we fully express time dilation and other relativistic effects in terms of process instantiation rather than as a distortion of a time coordinate?

1️⃣ Time Dilation Without a Time Yardstick

  • Time dilation arises because processes unfold differently depending on their relation to a gravitational field or motion.
  • Instead of stretching a time coordinate, we say:
    • Clocks (which are just regular processes) instantiate time differently depending on their energy conditions.
    • The closer a process is to a massive object, or the faster it moves, the more constrained its unfolding becomes—this is what we experience as time dilation.

✔ Key Shift: Instead of time being an independent coordinate that “dilates,” we say the rate at which processes instantiate time changes.


2. Space as Relational

  • Space is not an independent “fabric” but a relation between instantiated processes.
  • The extent of spatial intervals is relational—not an absolute quantity.
  • Mass does not curve space itself; instead, it modifies how spatial intervals are instantiated, leading to curved geodesics.

🚩 Challenge: Can we express general relativity’s equations in terms of process constraints instead of a curved spacetime manifold?

2️⃣ Expressing Relativity Without Curved Space

  • Einstein’s equations describe geodesic curvature, but what’s really happening?
    • Mass changes the conditions under which spatial intervals are instantiated.
    • Instead of saying “space bends,” we say:
      • The relations between processes evolve in a way that makes geodesics appear curved.
      • This is why light follows a curved path—it’s responding to the evolving constraints on space interval instantiation.

✔ Key Shift: Spacetime curvature is just a description of how relational constraints evolve—not a bending of space itself.


3. Geodesics as Constraints on Process Relations

  • Instead of thinking of spacetime as curving, we say:
    • Geodesics describe how the relations between instantiated processes evolve.
    • Space intervals contract in relation to a centre of mass, not because a fabric is bending.

🚩 Challenge: Can we reconstruct Einstein’s field equations without treating space as a continuum, using only relations between instantiated processes?

3️⃣ Geodesics as Constraints on Process Relations

  • In this model, a geodesic is not a path through a pre-existing spacetime but a constraint on process unfolding.
    • Free-fall follows a curved trajectory because the instantiation of spatial intervals changes in response to mass.
    • Particles don’t “move through curved space”; rather, the way they instantiate spatial relations is modified.

✔ Key Shift: Motion in gravity isn’t travel through a curved spacetime—it’s a shift in how spatial relations are instantiated relative to mass.


4. Length Contraction as a Measurement Constraint

  • Special relativity says moving objects contract along their direction of motion.
  • Instead of thinking of space itself contracting, we say:
    • The relation between the measuring system and the measured process constrains how spatial intervals are instantiated.
    • This means length contraction is not a physical shrinking of space but a shift in process instantiation.

🚩 Challenge: Can we fully derive special relativity’s predictions in terms of how measurement processes are instantiated rather than as distortions of a coordinate system?

4️⃣ Length Contraction as Measurement Constraints

  • When an object moves close to the speed of light, its spatial extent is not shrinking in some absolute sense—rather:
    • The process of measurement itself is constrained by the motion.
    • The measuring observer and the moving object instantiate space differently due to their relative motion.
  • This means that length contraction is a shift in process relations, not a distortion of space.

✔ Key Shift: Length contraction is a relational measurement effect, not a deformation of space.


5. Implications for Singularities (Big Bang & Black Holes)

  • If space and time are instantiated by process, then a gravitational singularity isn’t a point in spacetime—it’s a limit where process instantiation fails.
  • This avoids the paradox of an infinitely dense "point" in a pre-existing space.
  • The Big Bang isn’t the "beginning" of time in an absolute sense; it’s the earliest point where process instantiation occurs.

🚩 Challenge: Can we describe the emergence of the universe without assuming spacetime itself "began" as a singularity?

5️⃣ Singularities as Limits of Process Instantiation

  • If time and space are instantiated by process, then a singularity is not a “point” where everything collapses—it’s a limit where process instantiation fails.
  • The Big Bang isn’t “the first moment of time”—it’s just the earliest point where process instantiation occurs.
  • Black holes don’t “crush spacetime to a point”; they create a region where process unfolding is indefinitely constrained.

✔ Key Shift: Singularities aren’t “places” in spacetime but limits of process instantiation.


6. Noether’s Theorem & Energy Conservation

  • Noether’s theorem links energy conservation to time symmetry.
  • But if time is instantiated by process, then it may not have a fundamental symmetry—only a local one.
  • This suggests that energy conservation might be an emergent property rather than a built-in law.

🚩 Challenge: Does Noether’s theorem still hold if time is only instantiated through process?

6️⃣ Noether’s Theorem & Energy Conservation

  • Noether’s theorem links energy conservation to time symmetry.
  • But if time only exists where processes instantiate it, then time symmetry is local, not absolute.
  • This suggests that energy conservation is an emergent property of stable process instantiation rather than a fundamental law.

✔ Key Shift: Energy is conserved where time is instantiated consistently—but this isn’t an absolute law.


Final Synthesis

  • Spacetime isn’t a fabric—it’s just a description of how processes instantiate space and time relationally.
  • Curvature isn’t bending—it’s a change in process constraints.
  • Relativity works because process unfolding changes with mass and motion—not because space and time are distorted entities.
  • Quantum entanglement, black holes, and the Big Bang all need reinterpretation in terms of process limits, not singularities in a coordinate system.

No comments:

Post a Comment