🌀 Urban Lab: Building a Relativistic Time-Travel Simulator with Python

What if you could travel close to the speed of light?

You wouldn't need a fictional time machine to experience something that looks surprisingly similar to time travel.

According to Einstein's theory of special relativity, traveling at extremely high speeds causes time to pass differently for the traveler compared with someone who remains on Earth.

This is the idea behind our latest Urban Lab experiment:

🌀 A Python-based relativistic travel simulator that lets you explore time dilation, interstellar journeys, and near-light-speed travel.

The project is open source and available on GitHub.

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🚀 What Is Urban Lab Time Machine?

Urban Lab's Time Machine is not a real time machine.

It is an educational simulator designed to visualize the effects predicted by special relativity.

You can experiment with:

• 🚀 Near-light-speed travel
• ⏳ Time dilation
• 📏 Relativistic distance contraction
• ⚡ Relativistic energy
• 🌌 Interstellar travel
• 🪐 3D trajectories
• 🧮 Custom travel calculations

The goal is simple:

Make difficult physics concepts interactive and understandable through code.

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🧠 The Physics Behind It

The simulator is based primarily on Einstein's special relativity.

Time Dilation

The Lorentz factor is:

text
γ = 1 / 
where:

γ = Lorentz factor
v = velocity of the spacecraft
c = speed of light

The relationship between proper time and coordinate time can then be expressed as:

Δt = γ Δτ

As velocity approaches the speed of light, the Lorentz factor increases dramatically.

This means that a traveler moving extremely fast can experience much less elapsed time than observers who remain on Earth.

🌌 Example: Traveling at 99% of the Speed of Light

At:

v = 0.99c

the Lorentz factor is approximately:

γ ≈ 7.09

That means that for every year experienced by the traveler, roughly 7.09 years can pass for an observer in the Earth frame, depending on the exact scenario being simulated.

This is one of the most fascinating consequences of special relativity.

🚀 Interstellar Travel

The simulator also includes interstellar travel scenarios.

One example is Proxima Centauri, approximately 4.24 light-years away.

At a velocity approaching the speed of light, the simulator can compare:

Traveler time
       vs.
Earth-frame time

This allows us to visualize the difference between the time experienced by the traveler and the time experienced by observers on Earth.

💻 Python Simulation

The core of the project is written in Python.

A simplified version of the calculation looks like this:

import math


SPEED_OF_LIGHT = 299_792_458




def lorentz_factor(velocity):
    beta = velocity / SPEED_OF_LIGHT


    if beta >= 1:
        raise ValueError("Velocity must be below the speed of light")


    return 1 / math.sqrt(1 - beta ** 2)




velocity = 0.99 * SPEED_OF_LIGHT


gamma = lorentz_factor(velocity)


print(f"Lorentz factor: {gamma:.2f}")

Output:

Lorentz factor: 7.09

That's already enough to demonstrate one of the fundamental effects of special relativity.

🧮 Exploring Different Speeds

The simulator allows you to experiment with different velocities.

For example:

Velocity    Approx. Lorentz Factor
0.50c   1.15
0.90c   2.29
0.99c   7.09
0.999c  22.37
0.9999c 70.71

The closer we get to the speed of light, the more extreme the relativistic effects become.

And this leads to an important physical limitation:

A massive object cannot be accelerated to the speed of light.

The required energy increases dramatically as velocity approaches c.

⚡ The Energy Problem

Relativistic kinetic energy is:

Eₖ = (γ - 1)mc²

This is very different from the classical approximation:

Eₖ ≈ ½mv²

At everyday speeds, classical mechanics works extremely well.

At relativistic speeds, however, the difference becomes enormous.

The simulator therefore also explores the relationship between:

spacecraft mass
velocity
Lorentz factor
relativistic kinetic energy
🎨 3D Visualization

One of the most interesting parts of the project is visualization.

The simulator can represent a journey using a 3D trajectory.

A simplified example:

def update_trajectory(trajectory, frame, ax):


    ax.clear()


    points = trajectory[:frame]


    ax.plot(
        points[:, 0],
        points[:, 1],
        points[:, 2]
    )


    current = points[-1]


    ax.scatter(
        current[0],
        current[1],
        current[2]
    )

This transforms a mathematical calculation into something we can actually see.

🖥️ Multiple Interfaces

Urban Lab is designed to support several ways of interacting with the simulator.

CLI

Perfect for experiments and automated calculations.

python3 timemachine_advanced.py
GUI

An interactive interface can expose parameters such as:

velocity
spacecraft mass
destination
travel duration
3D Visualization

The 3D interface allows users to explore the simulated trajectory visually.

🧪 Example Experiment

Let's imagine a spacecraft traveling at:

99% of the speed of light

toward a distant destination.

The simulator calculates:

Velocity
Lorentz factor
Traveler time
Earth-frame time
Relativistic energy
Distance

Instead of simply reading equations in a textbook, you can modify the parameters and immediately observe how the results change.

That's the educational purpose of the project.

🏗️ Project Architecture

The project is organized around several components:

urban-lab/
│
├── timemachine-physical/
│   ├── simulator
│   ├── relativistic calculations
│   ├── interstellar travel
│   └── visualization
│
├── docs/
│
└── README.md

The architecture is intentionally simple so that developers, students, makers and physics enthusiasts can experiment with it.

🔬 Why Build This?

Because physics becomes much more intuitive when you can interact with it.

Instead of asking:

"What happens when something travels at 99.99% of the speed of light?"

you can simply run the simulation.

Change the velocity.

Change the mass.

Change the destination.

Run it again.

And compare the results.

🌍 From Urban Lab to Open Science

Urban Lab started as a broader technology and maker initiative in Rimini.

The project explores the intersection of:

Open Source
Artificial Intelligence
Robotics
3D Printing
IoT
Physics
Experimental technology

The relativistic simulator is another experiment within that ecosystem.

The objective isn't to claim that we built a physical time machine.

The objective is to build software that allows people to explore the science behind the idea.

🚧 What's Next?

Future versions could include:

🌌 More detailed interstellar missions
🛰️ Multi-body simulations
📊 Advanced relativistic graphs
🎮 Interactive 3D environments
🥽 VR/AR visualization
🧮 More relativistic equations
🧪 Educational experiment presets
🌍 Earth/Mars mission scenarios
🤝 Open Source

The project is open source and available for experimentation.

You can inspect the code, run the simulator, report issues or contribute improvements.

GitHub

https://github.com/DanielIoni-creator/urban-lab

Time Machine Project

https://github.com/DanielIoni-creator/urban-lab/tree/main/timemachine-physical

🧑‍💻 Try It Yourself

Clone the repository:

git clone https://github.com/DanielIoni-creator/urban-lab.git


cd urban-lab

Then explore the Time Machine project:

cd timemachine-physical

Run one of the available simulations:

python3 timemachine_advanced.py
🧠 Final Thoughts

Einstein's equations can look intimidating on paper.

But with a few lines of Python, we can turn them into an interactive experiment.

We can't build a real time machine with this project.

But we can build a simulation that helps us understand what nature allows — and what it doesn't.

And that's what makes the project exciting.

Code the experiment.
Explore the physics.
Question the limits.

🌀 Urban Lab — exploring technology, science and the future through open source.

🔗 Project

https://github.com/DanielIoni-creator/urban-lab

#physics #opensource #python #science