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.
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