Year: 2022

  • [FWN Special] Journey to Dirac Spinors and the Dirac Equation

    Yesterday (8 / 8 / 2022) was the 120th birthday of P.A.M. Dirac. It’s been a long time, “enough time to fit a lot of progress in there”.

    In his honour, I proceeded to dust off my QFT and related maths notes from long ago and will attempt to present a modern journey to the Dirac equation and the description of relativistic spin-1/2 particles, from the mathematical formalisms.

    Notes will be gradually posted during the week. Full references and additional work will be updated on the final page of this blog post.

    Intro Update 2 (17 Aug 2022)

    This essay / note will be arranged in a pedagogical order, without much historical burden of the order in which things were discovered. I take this inspiration from schools such as MIT who famously teach quantum mechanics to undergraduates in a similar fashion.

    Section 0 will be a mathematical toolbox of the relevant results we will use, such as some group theory basics and Clifford algebra (needed to properly understand Dirac gamma matrices). In Section 1 we will outline the definition and properties of the Lorentz Group, and reach the Klein-Gordon equation for a scalar field. In Section 2 we consider the effects of spin, and work towards the Dirac equation and Dirac Lagrangian, all from first principles.

  • On Turning 21 (Revisited by an 24 year old)

    Forewords

    Over three years ago now, I drafted a short essay on my flight back from San Francisco. That whimsically spontaneous trip was made in the week after my 21st birthday. Back then, I was in the middle of my fourth year in my BSc physics program, and my slow transition from student to “adult” was just beginning.

    An incomplete version of the so-titled “On Turning 21” was hosted on FWPhys for a while until I’ve taken it down in the general content slimming and blog overhaul near the onset of COVID-age in early 2020. While its general messages I’d say stay somewhat relevant, I’m now at a somewhat better vantage point to re-write it with emphasis on what had worked, and what needs more attention.

    Epistemological Integrity, and Your Own Calculations

    My mind still sometimes ligers on my brief Olympiad physics course in Year 10. Back then, I didn’t know much higher mathematics beyond manipulation of trigonometric functions by rote memorization of a page of formulae, nor could I speak any of the “overpowered” languages of Lagrangian mechanics or differential calculus.

    Regrets of “what could have been” aside, I suspect the fondness with which I remember that period of my life was a sense of confused-optimism with which I approached my problems, which eventually guides my research actions today.

    It’s a mind state exclusive to one’s high school age, I’d hope: the general willingness to solve problems without regard of what’s established or optimal, and an endless drive to just try and see what works. Time is ample. Stakes are low. Naiveness fades over such self-driven explorations.

    As a student, I’m good at taking lecture notes, that I’m proud of. But during the time before homework problems and exam questions became directed efforts such as “show that”, what I did was more comparable to what I do now — just go on, and see where sense and your training takes you.

    I hope I am not talking down on the importance of directed training and systematic knowledge, no. In the context of turning 21 — on becoming an adult — what one needs to realize is that it is his or her sole responsibility to arrange the knowledge system, and, at the end of the day, carry out independent calculations reliably. I reached this point after some detours, but wish the later comers be more wary of the need of self-reliance.

    Well when brain download becomes a thing, this section will be nullified.

    Emotional Freedom, and the Weight of Spontaneity

    A general familiarity with numerical analysis — a path I’d followed since turning 21 — has opened a path littered with “Acts of Mundane Competence” for me. I’d built stuff in CAD, use 3D printers and laser cutters regularly, studied automotive bodywork in MATLAB, written songs (with computationally picked chords, of course), and produced various shorts with special effects. Some friends say I wear many hats, and I suppose it got me thinking. A critical evaluation of whether this is a beneficial development is in order, for self and for society.

    When I chose theoretical physics research as my job, I’d already taken a tacit but decisive stance to side with delayed gratification, so called “cold benches” in Chinese, as opposed to the retweet-like world built to complement and commandeer our immediate-feedback-craving nervous systems so well.

    Act of Mundane Competence is a new phrase I’d coined for myself. You might soon notice some FWPhys.com/LUX photo watermarks become LUX-AMC instead. The word “Mundane” in this context does not represent a dismissal on my end of professional knowledge and states of the art in the fields in which I dabble — my electronic music is crap and my photos, while a reliable source of income, are far from Academy levels.

    Rather, it stands for a recognition that I’m carefully reflecting on myself, after a period of immense self-empowerment and self-realization, whether I’m just drilling in the thin part of the board — whether my efforts are really best spent in such a manner, that they make me a better physicist or educator at the end of my life.

    Being adult — well, in my early twenties version of the word, somewhat independent, somewhat self-driving, somewhat self-interested, and somewhat self-sustaining — opens up much more dimensions with which one carves out his or her life trajectories, and makes it quite easy to branch up so often one stays running in circles, stagnant, and worse, getting distant with the initial motivation, assimilated by, or worse, lost in the external world.

    As such, being an adult to me is not only an exploration of the boundaries of one’s interests and limits, but also a constant process of self-evaluation and trimming of loose ends. The bedtime fantasy of adoring every corner of one’s finite life, every attempt at something new, every trip, every hobby, with numerous perfect and interesting narratives is just that, a fantasy, a shadow in the distance of the waking minutes from a dream.

    24, I’m writing this section after realizing my high-degrees of spontaneity recently brought discomfort for and potentially overwhelmed some peers I deemed important in my life, to the point I’m not realistically expecting them to see this at all — sorry. In the lingo of my previous paragraph, I signed up for a random photo gig, first in my life, of a sports event during a hiking trip; I met a player at the event; nothing happened after.

    And that’s to be accepted.

    Just Do

    I’m talking a lot.

    Both at Berkeley and at Auckland, I’m fortunate to be in the vicinity of a crowd that comprises no shortage of people shining in the startup business world. Survivor bias plays a role, but I’d also commend the startup mentality’s positive effects in one’a daily dealings.

    It’s hard to pin down what I mean here by startup mentalities. “Fake it ‘till you make it?” Meh. I think I mean the drive to deliberately and constantly learn in action, in “doing”.

    This is in general quite similar to the first point I’m making, really, that informed adults take full responsibility of their epistemological integrity — organization of skills, knowledge, and life philosophies, and ability to reliably perform nontrivial tasks on one’s own.

    But the ability to construct good looking systems on paper alone is neither efficient nor meaningful. And in my case these are only summarized in retrospect: I didn’t have these fully comprehended or even written down when I celebrated my adulthood or during BSc graduation, or (more relevantly), at the beginning of my PhD. I went on with life. I failed at some points. I reflected on them. And here I am, learning from the mistakes.

    Just do.

    Go on with life.

    We are small, time is short.

    Western Springs, Auckland

    23 July, 2022

  • JWST’s First Color Image

    Hubble vs Webb photo of the same area

    Participating in duplicate information and internet memes is against the founding principles of this blog, but who am I if I don’t have a copy of this here?

    This much-awaited image depicts a cluster of galaxies bending space time and magnifying light from much further away objects, alongside a handful of foreground Milky Way stars that show the hex-spike diffraction pattern.

    This image marks a significant moment in the history of Homo sapiens.

  • [LUX] NASA Capstone Launch – A Photo Album

    Introduction

    Hi there!

    Since my misadventure has even garnered a headline in national news, I thought I’d quickly put together a travel log of sorts. Sans the few hours under the playful gaze of the stars, it has been a much-needed solo journey to talk to and catch up with my wants, visions, and priorities.

    Before I ramble on, many of you might have just come to see my rocket launch photo in full HD, and here it is.

    Feel free to use it (CC-BY-SA 4.0).

    I did quite publicly promise a technical aside on the significance of CAPSTONE (Cislunar Autonomous Positioning System Technology Operations and Navigation Experiment). but I think in the interest of time I am better off pointing you to NASA.

    Alternative version: https://commons.wikimedia.org/wiki/File:CAPSTONE-LAUNCH.jpg

    Comment on That Image

    During the launch window, the sky cooperatively cleared up, and most low-level clouds drifted away. As such, the “halo” you see around the thruster flame trail is most likely just due to condensation on the surface of my camera lens.

    I wasn’t able to take a temperature / humidity reading of the moist night at Nuhaka beach, but that my lens was consistently fogging up in the matter of minutes really underscored the challenge of the environment (and caught me by surprise).

    The surprise factor was especially because I’d performed a full dress rehearsal at the same location the night prior. In hindsight, the test was conducted during civil twilight, and the sands were still warm. Certainly a mis-controlled variable.

    Before I further compromise the time ordering, here’s the test shot produced 28 hours before the actual launch. For many-a northern hemisphere readers of mine, the southern celestial pole is clearly visible, which might not be a familiar sight (it’s much lamer than the Big Dipper and Polaris anyway).

    Other stuff

    This trip was organized under the assumption that the launch was to go ahead in the evening of Saturday 25th of June, but was stretched to accommodate the revised dates (Monday 27th, and later Tuesday 28th — better late than fail). It was indeed a good lesson on managing expectations and realistically-assessed risks. I say that after I got to see the launch, but have made up my mind far before reaching certainty that I will.

    During these days, I’ve driven over 1700km according to my odometer, with most travels being meaningful and only less than 30% of those roads being unsealed gravel.

    I had also produced a pile of real-time narrated driving footages, like this one

    The current generation FW Virtual Passenger – a GoPro.

    Selected Images (In CHRONOLOGICAL Order)

    24 June (Matariki) – Auckland, Taupo, Napier

    25 June – NAPIER, HASTINGS, NUHAKA, Gisborne

    26 June – Gisborne

    27 June – GISBORNE, Mahia, Wairoa

    28 June – MAHIA, Wairoa, Nuhaka, The Launch, RotorUa

    Secret bonus content.

  • Humanity’s first portrait of Sagittarius A*

    The supermassive black hole at the core of our galaxy.

    This essay is due to appear in the next issue of UoA Scientific.

    (more…)
  • to the High school Physics Students I Met Recently

    Originally published in April 2022, access restored April 2024.

    This essay shall not be taken as a direct address to any particular individuals with whom I interfaced at this weekend’s unnamed national-level physics competition event, where I have served as a judge for quite some time now.

    2022 has also been the first year I have grown wise enough to remove the “High School Honours and Achievements” section from my own CV. From a perspective not so far removed from that change, I hope I can explain why I both feel bad about the event in its current format, and will be like extending my participation through the rest of my residency in Auckland.

    In Series …
    THE APERIODICALS
    Local (personal, potentially shallow, and subject to change) outlooks on science, technology, growth, and occasionally culture and history. The goal is to write something every week, but whether it can make its way to FWPhys is random. Hence the series title.

    (more…)
  • “Curiosity” – Companion Booklet

    This post is to serve as a companion booklet to my bizarre release “Curiosity – Select Piano Compositions”.
    It is available on 15 Apr 2022 on streaming platforms and digital marketplaces around the world.

    (more…)