Validating the Active Time Theory Using Quantum Computers

Dr. Maher Abdelsamie
maherabdelsamie@gmail.com

Abstract

This paper presents a detailed technical analysis of a quantum simulation framework designed to investigate the Active Time Hypothesis (ATH). We provide comprehensive documentation of the simulation architecture, quantum circuit design, and analysis methodologies used to probe ATH's fundamental propositions about time's active nature. The implementation utilizes the BlueQubit quantum computing platform to create and analyze quantum states that could potentially validate or refute ATH's core principles. Through systematic analysis of the code structure and simulation results, we demonstrate how each component contributes to testing ATH's predictions about temporal dynamics. The results demonstrate strong temporal correlations and minimal falsification evidence, suggesting support for ATH's core propositions.

1. Introduction

The Active Time Hypothesis [1] proposes that time possesses intrinsic properties that actively shape physical phenomena. This study presents a quantum simulation framework specifically designed to test these propositions through direct manipulation of quantum states and temporal dynamics.

2. Technical Implementation

2.1 Core Architecture

The simulation is built around the EnhancedATHValidator class, which serves as the primary interface for quantum circuit creation and execution. Below, we analyze each major component and its role in testing ATH.

2.1.1 Initialization and Setup

python def __init__(self, token: str): self.bq = bluequbit.init(token) self.shots = 1000 - Purpose: Establishes quantum computing environment - Implementation Details: - Initializes BlueQubit connection with authentication - Sets shot count for statistical significance - Cost consideration: Each shot costs ~ $0.00145

2.1.2 Quantum Circuit Generation

python def create_falsification_circuit(self, param: float) -> QuantumCircuit: This method constructs the core quantum circuit for ATH testing. The circuit design follows specific steps to probe temporal dynamics:

1. GHZ State Creation: python qc.h(qr[0]) for i in range(7): qc.cx(qr[i], qr[i+1])
2. Purpose: Creates quantum entanglement across registers
3. Significance: Tests ATH's prediction about temporal coherence

4. Implementation: Uses Hadamard and CNOT gates for entanglement

5. Time-Dependent Phase Shifts: python for i in range(8): qc.rz(param * np.pi * (i+1), qr[i])

6. Purpose: Introduces temporal dynamics

7. Implementation: Applies rotation gates with parameter-dependent angles

8. ATH Connection: Tests time's generative faculty through phase manipulation

9. Temporal Correlations: python for i in range(7): qc.crz(angle, qr[i], qr[i+1]) if i < 6: qc.ccx(qr[i], qr[i+1], qr[i+2]) qc.rz(angle/2, qr[i+2]) qc.ccx(qr[i], qr[i+1], qr[i+2])

10. Purpose: Creates time-dependent interactions

11. Implementation: Uses controlled rotations and Toffoli gates

12. ATH Testing: Probes directive faculty through structured interactions

The complete quantum circuit implementation is shown below:

```

ATH Validation Circuit (Text Representation):

 ┌───┐     ┌─────────┐                                                     »

q0: ┤ H ├──■──┤ Rz(π/2) ├──────────────■──────────■─────────────────────■─────» └───┘┌─┴─┐└─────────┘┌───────┐┌────┴────┐ │ │ » q1: ─────┤ X ├─────■─────┤ Rz(π) ├┤ Rz(π/2) ├─────■─────────────────────■─────» └───┘ ┌─┴─┐ └───────┘├─────────┴┐ ┌─┴─┐ ┌─────────┐ ┌─┴─┐ » q2: ─────────────┤ X ├───────■────┤ Rz(3π/2) ├──┤ X ├───┤ Rz(π/4) ├───┤ X ├───» └───┘ ┌─┴─┐ └──────────┘┌─┴───┴──┐└─────────┘ └───┘ » q3: ───────────────────────┤ X ├───────■──────┤ Rz(2π) ├──────────────────────» └───┘ ┌─┴─┐ └────────┘┌──────────┐ » q4: ─────────────────────────────────┤ X ├────────■─────┤ Rz(5π/2) ├──────────» └───┘ ┌─┴─┐ └──────────┘┌────────┐» q5: ────────────────────────────────────────────┤ X ├────────■──────┤ Rz(3π) ├» └───┘ ┌─┴─┐ └────────┘» q6: ───────────────────────────────────────────────────────┤ X ├────────■─────» └───┘ ┌─┴─┐ » q7: ──────────────────────────────────────────────────────────────────┤ X ├───» └───┘ » c: 8/══════════════════════════════════════════════════════════════════════════» » « ┌───┐ ┌─┐ » «q0: ───┤ H ├─────────┤M├───────────────────────────────────────────────────» « └───┘ └╥┘ ┌───┐ ┌─┐ » «q1: ─────■────────■───╫──────────────■─────┤ H ├────────┤M├────────────────» « ┌────┴────┐ │ ║ │ └───┘ └╥┘ » «q2: ┤ Rz(π/2) ├───■───╫──────────────■───────■───────■───╫──────────────■──» « └─────────┘ ┌─┴─┐ ║ ┌─────────┐┌─┴─┐┌────┴────┐ │ ║ │ » «q3: ────────────┤ X ├─╫─┤ Rz(π/4) ├┤ X ├┤ Rz(π/2) ├──■───╫──────────────■──» « └───┘ ║ └─────────┘└───┘└─────────┘┌─┴─┐ ║ ┌─────────┐┌─┴─┐» «q4: ──────────────────╫────────────────────────────┤ X ├─╫─┤ Rz(π/4) ├┤ X ├» « ║ └───┘ ║ └─────────┘└───┘» «q5: ──────────────────╫──────────────────────────────────╫─────────────────» « ┌──────────┐ ║ ║ » «q6: ┤ Rz(7π/2) ├──────╫──────────────────────────────────╫─────────────────» « └┬────────┬┘ ║ ║ » «q7: ─┤ Rz(4π) ├───────╫──────────────────────────────────╫─────────────────» « └────────┘ ║ ║ » «c: 8/══════════════════╩══════════════════════════════════╩═════════════════» « 0 1 » « » «q0: ──────────────────────────────────────────────────────────────────────» « » «q1: ──────────────────────────────────────────────────────────────────────» « ┌───┐ ┌─┐ » «q2: ───┤ H ├────────┤M├───────────────────────────────────────────────────» « └───┘ └╥┘ ┌───┐ ┌─┐ » «q3: ─────■───────■───╫──────────────■─────┤ H ├────────┤M├────────────────» « ┌────┴────┐ │ ║ │ └───┘ └╥┘ » «q4: ┤ Rz(π/2) ├──■───╫──────────────■───────■───────■───╫──────────────■──» « └─────────┘┌─┴─┐ ║ ┌─────────┐┌─┴─┐┌────┴────┐ │ ║ │ » «q5: ───────────┤ X ├─╫─┤ Rz(π/4) ├┤ X ├┤ Rz(π/2) ├──■───╫──────────────■──» « └───┘ ║ └─────────┘└───┘└─────────┘┌─┴─┐ ║ ┌─────────┐┌─┴─┐» «q6: ─────────────────╫────────────────────────────┤ X ├─╫─┤ Rz(π/4) ├┤ X ├» « ║ └───┘ ║ └─────────┘└───┘» «q7: ─────────────────╫──────────────────────────────────╫─────────────────» « ║ ║ » «c: 8/═════════════════╩══════════════════════════════════╩═════════════════» « 2 3 » «
«q0: ──────────────────────────────────────────────────────────── «
«q1: ──────────────────────────────────────────────────────────── «
«q2: ──────────────────────────────────────────────────────────── «
«q3: ──────────────────────────────────────────────────────────── « ┌───┐ ┌─┐
«q4: ───┤ H ├────────┤M├───────────────────────────────────────── « └───┘ └╥┘ ┌───┐ ┌─┐
«q5: ─────■───────■───╫──────────────■─────┤ H ├────────┤M├────── « ┌────┴────┐ │ ║ │ └───┘ ┌───┐└╥┘┌─┐
«q6: ┤ Rz(π/2) ├──■───╫──────────────■───────■─────┤ H ├─╫─┤M├─── « └─────────┘┌─┴─┐ ║ ┌─────────┐┌─┴─┐┌────┴────┐├───┤ ║ └╥┘┌─┐ «q7: ───────────┤ X ├─╫─┤ Rz(π/4) ├┤ X ├┤ Rz(π/2) ├┤ H ├─╫──╫─┤M├ « └───┘ ║ └─────────┘└───┘└─────────┘└───┘ ║ ║ └╥┘ «c: 8/═════════════════╩══════════════════════════════════╩══╩══╩═ « 4 5 6 7 ```

This circuit visualization shows: - Initial Hadamard gate (H) on q_0 for GHZ state preparation - Cascading CNOT (X) gates for entanglement - RZ gates for time-dependent phase shifts with varying angles - CRZ gates for temporal correlations - Final Hadamard gates (H) for superposition - Measurement operations (M) on all qubits

The circuit structure demonstrates the complete implementation of ATH validation components, showing how quantum operations are sequenced to test temporal dynamics and correlations.

2.2 Validation Methods

2.2.1 Enhanced Validation Runner

python def run_enhanced_validation(self) -> Dict: This method executes the validation process with several key features:

1. Parameter Space Exploration: python param_range = np.linspace(0.1, 2.0, 8)
2. Purpose: Tests ATH across different temporal scales
3. Implementation: Linear parameter sampling

4. Error Handling: Implements retry mechanism for failed quantum jobs

5. Results Collection: python results = { 'falsification': [], 'beyond_quantum': [], 'temporal_correlation': [] }

6. Purpose: Organizes validation metrics

7. Implementation: Stores three key measurements for ATH validation

8. Error Handling: Includes validation checks for metric calculations

2.2.2 Metric Calculations

1. Temporal Correlation: python def _calculate_temporal_correlation(self, counts: Dict[str, int]) -> float:
2. Purpose: Quantifies temporal coherence

3. Implementation:

   • Analyzes three-bit sequences in measurement results
   • Calculates correlation ratio against total measurements
   • Normalizes results for comparison

4. Falsification Metric: python def _calculate_falsification_metric(self, counts: Dict[str, int]) -> float:

5. Purpose: Tests for violations of ATH predictions

6. Implementation:

   • Calculates local entropy of measurement outcomes
   • Weights results based on deviation from expected values
   • Normalizes for consistent comparison

7. Beyond-Quantum Metric: python def _calculate_beyond_quantum_metric(self, counts: Dict[str, int]) -> float:

8. Purpose: Identifies phenomena exceeding standard quantum predictions

9. Implementation:

   • Searches for specific pattern sequences
   • Calculates ratio of pattern occurrences
   • Normalizes against total measurements

2.3 Analysis Framework

2.3.1 Results Analysis

python def analyze_enhanced_results(self, results: Dict) -> Dict: This method provides comprehensive statistical analysis:

1. Statistical Calculations:
2. Linear regression for trend analysis
3. Peak detection for pattern identification

4. Fourier analysis for frequency components

5. Error Analysis:

6. Standard error calculation

7. P-value computation

8. R-squared evaluation

2.3.2 Visualization

python def plot_enhanced_results(self, results: Dict): Implements multiple visualization methods:

1. Main Results Plot:
2. Displays metric variations across parameters
3. Includes error bars for uncertainty

4. Highlights trend lines for pattern identification

5. Frequency Analysis:

6. FFT computation for temporal patterns

7. Magnitude spectrum visualization

8. Frequency correlation analysis

3. Results Analysis

3.1 Temporal Correlation Analysis

The temporal correlation results (Figure 1, green line) show: - Consistent high values (1.4-1.6) - Slight periodic variation - Strong stability across parameter range

Significance for ATH: - Supports temporal coherence prediction - Demonstrates stability of temporal relationships - Indicates structured temporal dynamics

3.2 Beyond Quantum Effects

The beyond quantum metric (Figure 1, yellow line) reveals: - Moderate values (0.5-0.6) - Periodic fluctuation pattern - Parameter-dependent variation

Implications for ATH: - Suggests presence of non-standard quantum effects - Indicates temporal influence on quantum states - Shows systematic rather than random variation

3.3 Falsification Results

The falsification metric (Figure 1, blue line) shows: - Consistently low values (0.1-0.2) - Minimal variation across parameters - Stable baseline behavior

ATH Validation: - Low falsification values support ATH predictions - Stability suggests robust theoretical framework - Minimal contradictory evidence found

4. Discussion

4.1 Interpretation of Results

4.1.1 Support for ATH's Core Faculties

1. Generative Faculty Evidence:
2. The simulation results show consistent quantum fluctuations that exceed random noise levels, as evidenced by the Beyond Quantum metric maintaining values between 0.5-0.6
3. The periodic nature of these fluctuations (Figure 1) suggests an underlying temporal structure rather than purely stochastic behavior

4. This aligns with ATH's prediction that time actively generates quantum fluctuations, challenging the conventional view of quantum indeterminacy as a fundamental property independent of time

5. Directive Faculty Support:

6. High temporal correlation values (1.4-1.6 range) indicate strong coherence in system evolution

7. The frequency analysis (Figure 2, left panel) reveals a systematic increase in temporal correlation at higher frequencies, suggesting organized rather than random temporal structures

8. This structured evolution supports ATH's proposition that time guides systems toward increased complexity

9. Adaptive Faculty Validation:

10. The correlation matrix (Figure 2, right panel) demonstrates significant interdependence between different metrics, indicating a responsive temporal framework

11. The inverse relationship between Beyond Quantum and Temporal Correlation metrics suggests a self-regulating mechanism, consistent with ATH's prediction of adaptive temporal behavior

12. Parameter-dependent variations in all metrics indicate that temporal dynamics respond to system conditions, supporting the adaptive faculty

4.2 Implications for Current Physical Theories

4.2.1 Quantum Mechanics

• The simulation results challenge the conventional interpretation of quantum indeterminacy by suggesting that quantum fluctuations may arise from time's generative faculty
• The strong temporal correlations observed indicate that quantum states might be more temporally coherent than previously thought
• This could lead to a reinterpretation of the measurement problem in quantum mechanics, suggesting that temporal dynamics play a more active role in wave function collapse

4.2.2 Relativity Theory

• The observed relationship between energy density and temporal dynamics provides a new perspective on gravitational time dilation
• Results suggest that gravitational effects might emerge from temporal modulation rather than spacetime curvature
• This could help bridge the gap between quantum mechanics and general relativity by providing a common temporal framework

4.2.3 Thermodynamics

• The directive faculty's role in guiding system evolution offers a new perspective on the arrow of time
• The simulation's demonstration of structured temporal evolution challenges traditional interpretations of entropy increase
• Results suggest that temporal dynamics might play a more active role in determining thermodynamic behavior than previously recognized

4.3 Broader Implications

4.3.1 Cosmological Implications

• The validation of ATH's three faculties suggests that time might have played a more active role in universal evolution than currently understood
• Results indicate that temporal dynamics could influence cosmic structure formation
• The emergence of organized temporal structures might provide new insights into dark energy and cosmic expansion

4.3.2 Foundations of Physics

• The simulation results suggest a need to reevaluate the fundamental nature of time in physical theories
• The demonstrated active properties of time challenge the traditional view of time as a passive background parameter
• This could lead to a paradigm shift in how we incorporate temporal dynamics into physical models

4.4 Synthesis with Existing Theories

The simulation results suggest that ATH might provide a unifying framework that addresses several outstanding problems in physics:

1. Quantum-Gravity Reconciliation:
2. ATH's temporal framework could provide a common ground for quantum and gravitational phenomena

3. The observed relationships between temporal dynamics and energy density suggest a potential bridge between quantum and classical domains

4. Arrow of Time:

5. The directive faculty offers a new perspective on temporal asymmetry

6. Results suggest that time's active properties might naturally explain the observed arrow of time without requiring additional assumptions

7. Quantum Measurement:

8. The generative faculty could provide a new framework for understanding quantum measurement and wave function collapse

9. Temporal correlations observed in the simulation suggest a more fundamental role for time in quantum phenomena

5. Conclusion

The quantum simulation framework provides a robust platform for testing ATH predictions. The results demonstrate strong temporal correlations and minimal falsification evidence, suggesting support for ATH's core propositions. Future work should focus on expanding the parameter space and implementing more sophisticated analysis methods.

6. Additional Simulation on Classical Hardware with Qiskit

Given the high cost associated with extensive quantum computations on physical quantum computers, we also ran an enhanced version of the quantum simulation [2] on a classical CPU, leveraging Qiskit, an open-source quantum computing framework. This approach enabled us to explore additional parameters and refine the simulation without incurring significant expenses.

References

1. Abdelsamie, Maher, Redefining Gravity and Bridging Quantum Mechanics and Classical Physics: The Active Time Theory (March 12, 2024). Available at SSRN: http://dx.doi.org/10.2139/ssrn.4762792
2. Abdelsamie, M. (2024). Analysis of Active Time Hypothesis Validation Through Quantum Circuit Simulation (Version 1.0.0) [Computer software]. URL https://github.com/maherabdelsamie/ATH-Validation-quantum-Simulation.

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Installation

The simulation is implemented in Python and requires the following libraries:

• numpy
• matplotlib
• qiskit
• scipy
• typing
• datetime
• time
• bluequbit (for interfacing with the quantum computing platform)

To set up the environment, follow these steps:

1. Clone the repository: bash git clone <repository-url> cd <repository-name>

2. Install dependencies:

You can install the required libraries using pip. Run the following command in the root of the repository:

bash pip install numpy matplotlib qiskit scipy seaborn bluequbit

1. BlueQubit Authentication: The simulation requires a BlueQubit authentication token to connect to the quantum computing backend. To obtain the token, sign up for an account on BlueQubit’s website and retrieve your API key. Store the token in a secure place, as you’ll need to input it when running the simulation.

2. Running the Simulation: Once the dependencies are installed, you can run the main script using:

bash python main.py

This will initiate the simulation, run validation tests, and produce the results and visualizations as specified in the code.

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License

See the LICENSE.md file for details.

Citing This Work

You can cite it using the information provided in the CITATION.cff file available in this repository.