Time Creation in the Quantum Field

In the Functional Universe framework, quantum evolution does not presuppose time as a fundamental parameter. Instead, Schrödinger evolution is interpreted as pre-temporal: it governs the evolution of quantum possibilities prior to any irreversible commitment.

Physical time emerges only when quantum processes decohere, interactions complete, and information is irreversibly committed to the future.

This section formalizes time as a locally generated, thermodynamically constrained quantity arising from quantum commitment, and shows how this notion interfaces consistently with both quantum field theory and relativistic proper time.

Pre-Temporal Quantum Evolution

Schrödinger’s equation,

\[ i\hbar \frac{\partial \psi}{\partial t} = H\psi, \]

does not describe time passing.

In this framework:

• Schrödinger evolution occurs before commitment
• It evolves possibilities, not events
• It lives in a pre-time parameter \(\lambda\)

Correct rewrite:

\[ i\hbar \frac{d\psi}{d\lambda} = H\psi, \qquad d\tau = \rho_{\text{commit}} , d\lambda \]

Collapse is not time evolution; Collapse is time creation.

What \(d\tau\) Encodes

• \(( d\tau )\) is not duration.
• It is not a tick.
• It is not a parameter.

It encodes:

\[ d\tau ;\propto; \text{irreversible causal information committed to the future} \]

Each increment corresponds to:

• Decoherence
• Completion of interaction
• Export of irreversible information

If nothing commits, time does not advance.

Assigning a Real Quantity to \(d\tau\)

Define:

\[ d\tau \equiv dI_{\text{commit}} \quad \text{(measured in bits)} \]

Using Landauer: \[ dE \ge k_B T \ln 2 , d\tau \]

Thus:

• Time is literally counted commitment
• Energy and temperature bound time creation

Clocks are devices that commit bits at stable rates.

Plugging into GR

Standard GR:

\[ d\tau^2 = - g_{\mu\nu} dx^\mu dx^\nu \]

Becomes:

\[ dI_{\text{commit}}^2 = - g_{\mu\nu} dx^\mu dx^\nu \]

Discrete simulation rule:

1. Propose \(\Delta x^\mu\)
2. Compute \(\Delta \tau_{\text{geom}}\)
3. Compute \(\Delta \tau_{\max} = \frac{\Delta E}{k_B T \ln 2}\)
4. Actual:

\[ \Delta \tau = \min(\Delta \tau_{\text{geom}}, \Delta \tau_{\max}) \]

Geometry requests time; thermodynamics permits it.

Planck Time as Bit-Rate Limit

Planck quantities:

\[ t_P = \sqrt{\frac{\hbar G}{c^5}}, \quad E_P = \sqrt{\frac{\hbar c^5}{G}}, \quad T_P = \frac{E_P}{k_B} \]

Landauer cost at \(( T_P )\):

\[ E_{\text{bit}} = k_B T_P \ln 2 \approx 1.36 \times 10^9 , \text{J} \]

Compare:

\[ \frac{E_{\text{bit}}}{E_P} \approx 1.44 \]

Thus:

• One Planck energy commits ~1.44 bits
• One bit corresponds to:

\[ \tau \approx \frac{t_P}{1.44} \]

Planck time is not a chronon. It is the maximum bit-rate limit.

The True Tau of Physics

\(d\tau\) is:

• Local
• Variable
• Physical
• Real

Macroscopic time emerges as an average:

\[ \langle \tau \rangle ;\approx; \text{smooth classical time} \]

Final statement:

\(d\tau\) is the locally real, variable proper time created by irreversible causal commitment, whose large-scale average reproduces smooth relativistic time.

Final Synthesis

• Events are discrete (bits)
• Time is emergent (accumulated commitment)
• Geometry is informational bookkeeping
• Gravity is commitment-density curvature
• Planck time is a rate limit, not a tick
• The universe is a causally gated computation

This is a computational theory of the universe, in a literal, physical sense.