FRACTARIUM Interactive Observatory for Mathematical and Emergent Phenomena
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OBSERVATION CHAMBER / ACTIVE

Noether Symmetry Conservation Observatory

Observe how translation, rotation, and time symmetry carry a charge, and how an explicit breaking term makes its balance drift.

noether / conservation Observation Model

ROUTE 77 / STRUCTURE / NOETHER CONSERVATION

SYMMETRY / CHARGE / DRIFT

When a symmetry leaves a charge behind

Choose one continuous symmetry and watch its Noether charge move. With BREAKING off, the charge is conserved. With BREAKING on, the analytic source predicts the change and the balance residual exposes numerical error.

PAUSED

This is a charge ledger, not an orbital simulator. Focus here for 1/2/3 modes, B BREAKING, Space PLAY, S STEP, R RESET, and L lens.

All calculations stay local in this browser.

Mode
TRANSLATION
Charge Q
—
Drift ΔQ
—
Balance residual
—
Time
0.000
Finite
YES

CHARGE READOUT

What the symmetry carries

PASS
Current charge Q
—
Initial charge Q₀
—
Observed drift ΔQ
—
Expected source integral
—
Balance residual
—
Samples
1 / 961
Symmetry contract
Translation invariance → Pₓ = vₓ; ε > 0 adds dPₓ/dt = −ε.
State
finite / deterministic
Interpretation
With BREAKING off, a conserved charge should remain on its initial ledger line. The residual should stay at the numerical floor.

DETERMINISTIC SELF-TEST

Numerical acceptance

PASS

dt = 1/240 · 960 steps · READY

CHECKVALUELIMITRESULT
Observation report

        

    


    

        
OBSERVATION CONTRACT
Charge, source, residual
Each mode names a continuous symmetry and its charge. BREAKING adds an explicit term. The analytic source predicts the charge change; the balance residual is observed drift minus that source integral. This is an observation model, not a physical measurement.

        
THREE SYMMETRIES
One ledger, three generators
  • TRANSLATION: L = ½v² − εx, Q = Pₓ = vₓ, dQ/dt = −ε.
  • ROTATION: L = ½v² − ½ω²r² − ½ε(x²−y²), Q = J = xvᵧ − yvₓ, dJ/dt = 2εxy.
  • TIME: L = ½v² − ½ω²r² − εx cos(νt), Q = E, dE/dt = −ενx sin(νt).

        
MODEL NOTE
Dimensionless finite model
m = ω = 1, ν = 0.8, Δt = 1/240, and 960 deterministic RK4 steps. All coordinates are dimensionless. The graph is a charge ledger with state context, not an orbital path, ranking, or score.
BREAKING off tests conservation. BREAKING on tests the analytic balance contract and exposes residual at the numerical floor.

    


    

        
Formula note
Q − Q₀ = ∫ source dt + residual. The fifth RK4 state accumulates the exact mode source at the same fixed step. A small residual indicates numerical agreement with the selected contract; it does not prove a theorem beyond this finite model.

        
OBSERVATION GUIDE
Touchpoints for observation
Start with TRANSLATION and BREAKING off. Press STEP, then compare the charge, drift, and residual. Turn BREAKING on and read the expected source. Repeat for ROTATION and TIME.
  • Use CHARGE for the conserved ledger, BALANCE for source agreement, and STATE for x, y, vₓ, vᵧ.
  • Use REPORT or PNG for the current deterministic screen. RESET clears the old report and history.
  • Reduced-motion keeps PLAY stopped. Visibility changes stop PLAY and do not advance hidden time.
This is a browser-side Lagrangian observation model. It does not simulate an orbit, claim physical measurements, or assign a score.
Runs inside the browser with no upload and no registration.

    






    

    
OBSERVATION POLICY

    
This chamber runs a deterministic dimensionless Lagrangian model in your browser. The state, Noether charge, balance residual, report, and image stay local. It does not measure visitors, devices, or physical matter.



        

    
    
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This chamber belongs to Structures & Symmetries.

        
        STRUCTURE
        Back to Structures & Symmetries Route.