What makes this
the same thing?
Faithful descriptions keep track of which object they concern, and whether a change preserves its identity.
AASC / Why look upstream?
Where the familiar
laws come from.
Two languages. One concept.
Two theories. One reality?
An analogy: “cat” in English and “chat” in French are different downstream expressions of one semantic concept. Their connection is at the level of meaning.
AASC asks the corresponding physical question. GR and QM are downstream ontological descriptions—descriptions of what physically exists. What shared physical reality are they descriptions of?
Start with the physical worldThe analogy / Two levels of reference
Language Semantic analogy
Downstream expressions
English“cat”
French“chat”
Upstream semantic referentOne concept:
a cat
a cat
Shared meaning, expressed in two languages.
Physics AASC’s question
Downstream ontological descriptions
General relativityGR
Quantum mechanicsQM
Upstream physical referentShared
physical reality
physical reality
The system, its relations and admitted changes.
Words → semantic conceptcorresponds by analogy toGR / QM → physical reality
01 / The deeper starting point
If spacetime needs explaining,
what can physics start with?
The language analogy connects words through a semantic concept. The physics question connects descriptions through what physically exists. AASC seeks that shared physical referent upstream of the formalisms, then constructs the descriptions that preserve it. The analogy motivates this search; it does not establish the physical connection.
We picture things living in space and changing through time. To explain that spacetime description, we need a starting point that does not already assume its distances and durations.
It must be this object, with these relations and these possible changes. To follow it through change, we must establish what makes it the same object. A description has to answer to what physically obtains of that object.
AASC takes these as necessary features of physical reality. They apply to an unobserved object just as much as to a laboratory measurement. The argument begins here, before supplying a spacetime metric: the structure that assigns distances and durations.
The starting point is what makes a physical world definite.
Geometry must then earn its place as a description of that world.
What makes this
What actually
obtains of it?
A relation or proposed use must qualify under the actual conditions. Giving it a name cannot make it qualify.
Can these things
fit together?
A combination must preserve the identities, relations and conditions that give its parts physical meaning.
Which occurrence
was it?
A later change cannot replace the original occurrence. This holds even for systems with reversible dynamics.
These four functions form AASC’s Kernel: the work that any nondegenerate, determinate physical object, relation, construction or law necessarily incurs. The necessity argument says that removing any of them loses part of the definite physical content one was claiming. Every richer construction, including a clock, a geometry or a physical law, incurs the same requirements.
Why the AMetric boundary matters
A calculation cannot create
its own physical authority.
The Kernel leads to the AMetric boundary: a constraint on which distinctions, selections and descriptions can qualify. A description cannot supply a physical distinction that its starting point does not support. A later successful calculation cannot decide which original object or event it was supposed to describe.
This boundary uses no primitive distance, order, probability or passage of time. The physical constructions governed by it can then establish persistence, connections and ordered change before receiving a numerical geometry.
“Before” means an order of dependence. This is about what spacetime descriptions require, rather than an earlier era of the universe.
How fixation and bivalence fit into this starting point
Fixation keeps the physical subject and conditions of the question fixed. Bivalence says that, for that complete, evaluated question, the proposed construction qualifies or it does not. Whether an observer can decide which is a separate matter.
AASC permits many faithful descriptions of the same physical content. Their vocabulary or coordinates can differ, but they cannot silently substitute another object, change the question, or erase a physical distinction. The foundational uniqueness argument is developed in the Foundations tour.
The AMetric boundary and the richer premetric physical structures do different work. A sequence of connected events already has physical ordering; the boundary itself does not supply a primitive time order.
Source: Special Relativity from AASC, §§1–3 and §16.1; Theorem 2.1 and Proposition 2.4. The foundational papers are linked in the Foundations research section.
Connections first. Metres and seconds later.
Now consider a premetric physical construction: a definite sequence of connected events. Which events occur and how they connect can be established before assigning distances and durations. Try it: rearrange the drawing and check the three retained events. Then select “Add calibrated measurements” to see the physical content a metric view requires.
Move the marks and see what stays the same.
Physical relations before a metric
Same events. No distance scale yet.
A emits a signal; B reflects it; A receives it. We must keep track of which events occur, how they are connected and which endpoint remains A. Those relations do not yet supply a metre or a second.
Drawing positions are not distances.E1 → E2 → E3 and the identity of A are definite physical relations. The space between marks on this page is not a physical distance.
Example: a stationary, delay-free reflection and a two-microsecond round trip. This teaching diagram illustrates the distinction; it is not a derivation of the metric.
The physical facts retained in both views
- E1Emission at A.
- E2Reflection at B.
- E3Return to the same A.
E1 leads to E2, E2 leads to E3. A remains the same endpoint at departure and return.
What a metric realization adds. A physical clock and calibrated signal comparisons assign intervals to these relations. In a stationary, delay-free radar example, a two-microsecond round trip gives a reflection time of one microsecond and a distance of about 299.79 metres. AASC develops the metric from a completed physical comparison structure with finite isotropic propagation and common clock calibration. The three events pictured here illustrate the distinction; they do not alone determine that structure.
02 / Where the theories connect
One physical source.
Different questions about it.
Translating between equations is useful. But a translation needs to keep referring to the same physical thing.
That is why AASC looks upstream of the descriptions: first establish the system, its actual state, its relations and the changes it can undergo. Then construct the descriptions that preserve that content.
Sharing the Kernel does not yet establish a shared source. Two different systems both incur its requirements. The further scientific work is to identify one physical source and show that its descriptions remain connected as it changes.
This motivates AASC’s route to unification. It is not a claim that every other approach to unification is impossible.
The connection has to do physical work
What would make “the same world” more than a label?
Select each demand. Watch what has been established—and what still has to be shown.
The shared requirementsReference · Standing
Admissibility · Irreversibility
Admissibility · Irreversibility
Every determinate physical system incurs these functions.
Spacetime descriptionSystem A
Its geometry and response
Quantum descriptionSystem B
Its states and evolution
Follow the physical changethen describe it
Describe the systemthen evolve the description
Demand 1 of 3 / Necessary foundation
Same requirements.
Not yet the same source.
Two different physical systems both have definite identity, actual relations and admitted changes. Meeting those requirements does not identify one with the other.
Where the analogy ends: two words can share a semantic concept. A shared Kernel alone does not establish that two physical descriptions have one source.
What is still missing?
A physical identification: which system, which state and which original conditions do both descriptions concern?
Physical conditions stay attached: the common-history result uses an occupied history on the joint domain of the certified Einstein and Schrödinger descriptions. Their geometry, state-space and evolution conditions still have to hold.
A guided schematic of the common-history requirement, not a simulation or an independent proof. Source: §12.1 and Corollary 12.7.
- Shared Kernel: necessary governance of each physical system does not identify their sources.
- One source: identify the same system, state, conditions and occupied history in both descriptions. Identification alone does not establish compatible evolution.
- Compatible change: on the specified common domain, following the physical history and then describing it must agree with the certified evolution of its description. The common-history construction supplies this compatibility under its stated conditions.
The connection is at the physical referent.
Its descriptions must keep that connection through change.
Whose events? Whose clocks?
The relativistic comparisons must concern the events, clock readings and motion of that same physical source. The paper constructs this connection as well as its route to Lorentzian geometry.
What persists through the responses?
The matter and interaction roles are reconstructed through a common persistence bearer: what retains its identity while supporting distinct matter, gauge and Higgs responses.
A common source must carry compatible physical content, not just a common name.
GR and quantum mechanics have established experimental support. This tour presents AASC’s arguments for reconstructing their forms and connecting specified physical realizations. These claims retain their stated domains; they do not establish an unrestricted interacting quantum-gravity theory.
Which common-source connections the papers establish
The special-relativity manuscript gives two connected routes: construction of the Lorentzian form from completed physical comparisons, and its matching to the metric and continuation of an already occupied common source. Corollary 12.7 relates Einstein, Schrödinger and Lorentz-path descriptions through a common history. Theorems 15.9–15.10 supply a joint fixed-background example with actual clock, signal and response records.
In that example, the Einstein projection has a vacuum source. The positive laboratory response and quantum-state evolution remain attached to their own physical uses. Proposition 15.11 proves the obstruction to treating that laboratory response as the same complete gravitational source on unchanged flat geometry. The coupled Wheeler–DeWitt and Standard Model constructions have their own source identifications and domains (§§15.3–15.4).
The Einstein result fixes the minimal local first-curvature response in its stated Lorentzian realization. The Schrödinger result fixes the closed scalar nonrelativistic normal form under its state-space, domain and calibration conditions. These common-source results do not assert a universal interacting quantum-gravity law.
Explore the common-source construction03 / From the shared foundation
One foundation.
Four physical constructions.
Choose a question, then follow its three steps. See what physical content is added between the necessary starting point and the familiar law. The branch conditions remain visible beside the result.
Present in every route
Physical identity comes before its numerical description.
Every branch must preserve what physically exists, what relations qualify and what changes are admitted. Its specific construction then supplies the geometry or dynamics needed to express that content.
The three steps show logical dependence, not a sequence in time. Select any step or use the buttons below.
What this route establishes
The diagrams show the relationships being retained. They are illustrations of the construction, not numerical simulations of these theories.
Special relativity
- Shared foundation: establish definite physical objects and admitted relations before describing their distances and durations.
- Physical construction: complete the physical comparisons, recover a causal cone from finite isotropic propagation, and establish a common clock calibration.
- Familiar form: different observer readings preserve the spacetime interval.
General relativity
- Shared foundation: identify the physical source and its actual responses before giving those relations a geometry.
- Physical construction: a faithful Lorentzian metric, an attached source and a minimal local curvature response.
- Familiar form: the Einstein equation, with the appropriate scale and calibration anchors.
Quantum dynamics
- Shared foundation: establish physical state identity and allowed change before a wavefunction represents them.
- Physical construction: establish the spatial Hilbert representation and the operator requirements of the closed scalar branch.
- Familiar form: Schrödinger evolution with its kinetic-plus-potential Hamiltonian. Measurement has its own construction.
Matter and interactions
- Shared foundation: establish what retains its identity through admitted changes, before assigning its response labels.
- Physical construction: distinguish matter, gauge and Higgs responses while retaining their common physical inputs.
- Familiar form: the source-qualified Standard Model structure and its shared Einstein response.
04 / Worked example: special relativity
Build a ruler
from signals.
Now follow one branch in more detail. The departure, reflection and return keep their physical identities while clock comparison, propagation structure and calibration establish their spacetime description. The familiar relativistic results are the endpoint of this construction.
Use “Next” to add one piece of physical content at a time. The same three events remain in view. This is a guided reconstruction; a single signal does not determine the whole spacetime geometry.
One chain of physical records
The signal must return to the same endpoint.
A departure, a reflection and a return belong to one recorded experiment. Clock readings and coordinates can be added, but they must keep referring to those events.
E1 → E2 → E3. The event identities stay fixed throughout.
- E1 · departure at AThe signal leaves.
- E2 · reflection at BThe signal turns back.
- E3 · return to AThe same clock records its return.
What stays fixed: the endpoints A and B, the three identified events, and the record connecting them.
Step 1 of 5
- Keep the events. Identify the same emission, reflection and reception before attaching numbers.
- Read the clock. A calibrated clock at A records emission at 0 microseconds and return at 2 microseconds.
- Compare distance. For this stationary, delay-free round trip, radar distance is c × (return − departure) / 2 = 299.8 metres. The reflection is assigned the midpoint time, 1 microsecond.
- Map possible reach. The paper uses a complete family of admissible propagation comparisons, not this one ray alone. With its completed causal order, clock and isotropy conditions, it constructs a spatial comparison and a finite round causal cone.
- Change observer. Preserving that cone and one common rest-clock calibration gives the Lorentz frame law. At relative speed 0.6c, the same departure and return are 2.5 microseconds apart in the moving network; A’s clock still records 2 microseconds.
What the reconstruction uses
The homogeneous comparison branch supplies four dimensions and composition of displacement comparisons. Theorem 5.2 constructs its affine structure. Completed causal order, clock comparison and rest-comparison properties give a finite bound (Proposition 5.6); full boundary isotropy constructs the spatial quadratic form (Theorem 5.7). A common rest-clock calibration then removes the remaining scale freedom, giving the Lorentz law (Theorem 6.5 and Corollary 6.6). Actual repeatable signals and endpoint records are needed for the clock and radar experiment; the cone alone does not supply a device.
This illustration uses c = 299,792,458 metres per second and a stationary reflector with no reflection delay. The final overlay uses a frame moving at 0.6c. It shows a time axis and simultaneity direction, not a new physical signal.
Special Relativity from AASC · pp. 24–4105 / What the construction recovers
Different readings.
The same physical reference.
Time dilation, length contraction, relativity of simultaneity and mass–energy equivalence return as precise results. Each answers a different physical question.
Choose an effect, then change the relative speed. Compare what changes with the physical reference that stays fixed. In “Energy & inertia,” also compare changing observer with delivering a push.
0 · no relative motion0.90c · below light speed
γ (gamma) is the factor relating the readings at the chosen relative speed.
One clock. One pair of ticks.
The clock records four seconds between two ticks. A network of synchronized clocks sees it moving and assigns a longer coordinate-time interval to those same events.
The clock’s own reading4.00 s
The network’s assigned interval5.00 s
Each line begins and ends at the same two identified ticks. Its length shows the duration assigned in that comparison.
- Clock elapsed time
- 4.00 s
- Network interval
- 5.00 s
Δt = γ Δτ
At 0.60c, the network assigns 5 seconds to the interval the moving clock records as 4 seconds.
Retained: the same clock, the same two ticks, and its four seconds of elapsed time.
Keep the rod. Change the selected events.
Measuring length means recording both ends “at the same time.” A moving frame selects a different pair of events on the same persistent endpoints.
- Rest length
- 10.00 m
- Moving-frame length
- 8.00 m
L = L₀ / γ
At 0.60c, the moving frame selects B’s event 20.01 nanoseconds earlier in the rod’s rest frame. Its simultaneous endpoint measurement is 8 metres.
Retained: the rod and its two endpoint identities. Changed: which event on B is paired with A0.
Two fixed events. Different clock-network times.
Events C and D occur 300 metres apart and at the same time in the original frame. Keep both events fixed and compare their times in a moving frame.
- Original time difference
- 0.000 µs
- New time difference D − C
- −0.751 µs
Δt′ = −γ v Δx / c²
The moving frame assigns D an earlier time. The pair remains spacelike: neither event becomes the cause of the other.
Retained: exactly the same events C and D and their spacelike separation. Only their coordinate description changes.
What does it take to change the motion?
A change of observer re-describes a body. A physical push delivers momentum to it. Keep those two operations distinct, then connect the body’s rest energy to its measured resistance to a change of motion.
Observer comparison
Body A
Same bearer · same rest internal state
Relative speed: 0.60c
The observer changes. This comparison does not deliver a push to the body.
- Rest inertial mass
- 1.00 kg
- Total energy
- 112.3 PJ
- Rest energy E₀
- 89.9 PJ
- Momentum in this frame
- 224.8 MN·s
E₀ = mᵢc² · E = γE₀ · p = γmᵢv
The same body has different energy and momentum readings in a moving frame. Its rest energy and rest inertial mass remain fixed.
Example: a body with 1 kilogram of rest inertial mass. PJ means 10¹⁵ joules; MN·s means 10⁶ newton-seconds. For the push, the final internal state is unchanged and all exchange is accounted for.
For an actual controlled push from rest to 0.60c, the impulse is 224.8 MN·s. In the paper, the small-speed ratio of delivered impulse to velocity change measures inertia; conservation and the source’s Lorentz response force that coefficient to equal E₀/c². A coordinate change alone does not supply this experiment.
What the effects assume, and where they are proved
The clock is an ideal calibrated inertial device on a valid run. Length uses stable endpoints and the measuring frame’s synchronized equal-time rule. These are exact flat-target comparisons; curved regions and accelerated devices require their additional conditions. The duration law is Theorem 7.6 (p. 39); time dilation, length contraction and simultaneity are Theorems 9.1, 9.2 and 9.4 (pp. 42–43).
Rest-energy equivalence also requires dynamics: a complete attached total source, finite conserved charges, a stable rest branch, an active Lorentz action and controlled impulse records ending in the same internal state. Theorem 11.9 (p. 52) derives the inertial response and E₀ = mᵢc² without assuming a mass shell. The controls illustrate these results within those conditions.
Special Relativity from AASC · §§7–11Follow the research
From the picture
to the arguments.
The new special-relativity work
Special Relativity from AASC
The Necessary Kernel of Physical Objecthood and Its Lorentzian Realization
Amos Jay Maley · Reference Edition
The manuscript develops the necessary foundation of physical objecthood, constructs its Lorentzian realization, and connects that realization to the common-source and matter constructions in the wider AASC corpus.
Premetric foundation: §§1–3, §16.1 · Geometry: §§4–8 · Effects: §§9–11 · Common source: §§12–15.
Paper and citation