Time Operators in Quantum Mechanics (My Physics Bachelor Thesis Defence)

Presented in May 2025 at Hasselt University (Belgium) in collaboration with KU Leuven, as part of my Bachelor Degree in Physics, which I graduated from Magna Cum Laude in July 2025.

𝓞 Note 𝓞

I received 15 minutes to present and explain an incredibly theoretical and tough topic at an undergraduate level (that’s the constraint), which is why I’m so hasty and quickly shimming through each slide. In reality, I could’ve spoken 10 minutes on each slide because of the depth of this topic! Let me know in comments if something isn’t clear.

𝓞 Credits 𝓞

Author: Adam ‘BLVCK’ Blazejczak
Promotor: Ward Struyve (KULeuven)
Co-Promotor: Jef Hooyberghs (UHasselt)

𝓞 Sources 𝓞

Source + Data + Thesis: https://github.com/adamblvck/quantum-arrival-time-bachelor-thesis
Quantum mechanical free fall app (1D): https://quantum-arrival-time.netlify.app/

𝓞 Short Introduction 𝓞

In this study, the quantum mechanical time operators are studied through the lens of Bohmian Mechanics. By adhering to important theoretical limits of Bohmian mechanics, the “time of arrival distributions” can be calculated for free-falling particles on simple potential barriers, producing first-of-their-kind “arrival time distributions”. The approach in this study allows for a theoretical justification to speak about “particles” before they’re measured, allowing us to describe their journey via pilot wave calculations, and the analysis of probability currents.

𝓞 Paper Abstract 𝓞

Canonical quantum mechanics focuses on measurement outcomes, while alternative formulations like Bohmian mechanics describe the particle’s path from A to B, while yielding the same predictions. In experiments like the double-slit, the concept of ”travel time” or ”arrival time” lacks precision due to issues with initial conditions. However, free-fall experiments with quantum particles on opaque barriers might resolve this. This study introduces an analysis of such setups, calculating arrival times using Bohmian probability currents at the detector location. The resulting distributions reveal band formation, tunneling resonances, and other features, suggesting further theoretical and experimental exploration. The study also compares tunneling times predicted by the Larmor clock for spin-1/2 particles and Bohmian mechanics. Both theories agree with square barriers, but show dif- ferences with Gaussian barriers, highlighting the ad hoc nature of the Larmor clock theory.

𝓞 Why I Study Physics – My Current Disposition 𝓞

I have obtained a Master’s Degree in CS in 2015 – After this I started a career as a Data Scientist, and worked for 7 years at both big and small companies as a consultant. In the period of 2015-2021 I kept buying books on physics and studying the “truth” about our universe. I’ve also been overwhelmed by the general lack of meaning that people carried in their hearts, and in particular how almost everyone in business was driven by either fear or lack. I’ve also been diving deeply into various religions, modes of being and consciousness and entered into the realm of meditation, magick, and psycho-philosophical descriptions of the human condition. This drove me to formulate ideas on the dynamics and workings of consciousness, doing my best to stay in alignment with the frontier of science.

Instead of turning my ideas into random Reddit Posts, I decided right around the turn of COVID to obtain an actual degree in physics, as to ensure that I’m not bullshitting myself nor others. I’ve chosen to go through the motions of doing proper physics, and to ground myself in the grand art of compressing phenomena into short and epic algebraic equations that describe reality, and match experimental results. In July 2025 I’ve obtained a degree in physics.

Today I’m pursuing a Master’s Degree in Physics at the University of Ghent, and everyday I’m doing my best to become more versed and articulate in physics, and understand the progresses in science as a whole on the frontier of consciousness, while doing my own work to deeply practise and formulate the atypical phenomena of religious beliefs, mass justice movements, and the auspicious hate-inducing machine that is social media.

In the meantime, I’m developing apps and websites that are human and consciousness first, to help ground us in an increasing chaotic world of absurdity and falsehood, and to build proper frameworks for engagement in debate, “relativistic meaning”, and the quest to heal humanity from our evolutionary survival-based wounds.

One [code] line at a time.

Adam Blvck

Adam Blvck

Total posts created: 42
Driven by a relentless pursuit of truth, meaning, and happiness, Adam boldly left behind the comfort of his full-time job to pursue a degree in Physics in Belgium. His ambition is nothing short of transformative: to develop a universal notation capable of capturing the intricate dynamics of belief systems, the boundless realms of imagination, and their tangible impacts on matter—or, more simply put, to rigorously unravel the mysteries of consciousness at a fundamental level. Adam approaches his journey with meticulous care, thoughtful rigor, and a deep sense of humility. Rather than shouting into the void or scattering superficial thoughts across random forums, he thoughtfully shares his "Journey Towards the Light," offering wisdom gleaned from hard-earned lessons of love, forgiveness, and resilience. Occasionally, he even uncovers profound insights into the beautifully complex question of what it means to be human. As the founder of BLVCK STUDIOS, Adam leverages his diverse talents as a one-man powerhouse. He creates innovative apps and sophisticated enterprise architecture solutions, empowering SMEs to achieve their goals in a rapidly evolving digital age. He's the developer of the Gene Keys Profiler, SpellBook, Open777 and Gnomon. His ultimate vision is to seamlessly merge the fields of computer science, physics, and psychology, forging new pathways toward quantifiable, actionable models that illuminate the mechanics of consciousness itself.

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