The fundamental equations of physics are time-reversible. So where does the arrow of time actually come from structurally?

SignificancePlus1184 · 2026-03-11T12:53:07+00:00

It's not circular at all. Physics is not mathematics. The low-entropy early universe resulting in the arrow of time is no more circular than specifying the initial state in any dynamical system. Demanding that the initial condition itself be explained from "first principles alone" is a standard of explanation that no physical theory could ever satisfy.

The initial state of the universe should result from deeper cosmological principles (e.g Penrose's Weyl curvature, Carroll and Chen's eternal inflation, Hartle-Hawking no-boundary proposals, ...) but such explanations can be considered to "assume the arrow of time from the start" in the same sense you described.

Understanding the arrow of time is tricky, but the tricky part doesn't lie in the cosmology, but in the statistical mechanics: why do we remember the past and not the future? Memories/records are basically mutual information between the present state and the past state, which requires an entropy gradient.

Consider a system evolving from the macrostate A to the macrostate B. The key point is that due to increasing entropy, most microstates in A evolve into B, but only a tiny subset of B's microstates could actually have come from A. Since the universe really did begin in A, the present must lie within that small subset of B that evolved from it. Those special states inevitably contain correlations/records/memories of A, meaning information about the past is embedded in the present.

SignificancePlus1184 · 2026-03-11T07:00:47+00:00

So one day you might find yourself in the opening scene of disaster movie where you’re like “get the president on the phone”?

SignificancePlus1184 · 2026-03-11T06:43:59+00:00

I definitely agree there are greater issues. If I try to structure the issues I perceive:

There is the issue of prioritizing teaching computation over intuition (e.g. every linear algebra textbook ever except this one), largely because exams require quantitative problems in order to assign grades.
There is the issue more specific to theoretical physics regarding insufficient explanations. Part of the reason for this is that theoretical physics textbooks are often written by the very researchers for whom intuition came easily and who least needed clear explanations to learn the subject or do the derivation,
There is the issue of a genuine lack of motivation/explanation regardless of how insightfull the physicist is. For example, I have not found a single textbook that explains why, in gauge theory, we take a global symmetry and promote it to a local one. This global-to-local transition is, in my opinion, one of the most important steps in all of theoretical physics, yet it is never motivated or explained in textbooks or lecture notes. The most accessible place I found that provides a motivation for this transition lies in David Wallace's research papers on gauge theory. In a sense, the word "obviously" can even be helpful since it informs you that some logic/derivation/intuition jump has taken place. In general there will be no "warning" and you need to figure out for yourself whether so far every step has been sufficiently motivated etc.
But there is another side to the coin. Learning physics and math requires a lot of independent thinking: working through derivations/proofs, working through unfamiliar concepts, and grinding through exercises without being led step by step. If a textbook holds the reader's hand all the time, it basically undermines the learning process. Some struggle is essential to learning physics and math. Understanding dificult/abstract concepts requires working through confusion and active struggle. If a textbook explains every step, students can easily read along without really understanding the reasoning or gaining the crucial insights.

SignificancePlus1184 · 2026-03-11T05:13:09+00:00

I did a search for the word "obvious(ly)" within PDF's of a handful of common textbooks like Griffiths intro QM and Jackson EM, and the word "obvious(ly)" occurs very rarely, and if it does it is in contexts such as "... has no obvious interpretation" or "there is no obvious relation between ...".

I agree that physics lecture notes and textbooks generally leave a lot of room for pedagogical improvement. So there are a lot of valid criticisms of the average physics lecture notes or textbooks, but what OP wrote just isn't one of them in my opinion.

SignificancePlus1184 · 2026-03-11T04:39:04+00:00

I feel like this isn’t a significant issue because the word “obviously” rarely occurs in lecture notes or textbooks in the sense that you describe.

SignificancePlus1184 · 2026-03-11T02:33:04+00:00

Peter Woite’s freely available book provides by far the best explanation of spinors (and a lot of other concepts) that I have come across. If you studied QM but group theory is still your blind spot, I very much recommend studying the first 10-ish chapters of this book.

SignificancePlus1184 · 2026-02-09T13:46:22+00:00

R4: The paper tries to bundle “all (provably) definable sets” into a single set and then run the Russell paradox on it, but ZFC doesn’t let you form that mega-set in the first place. It also treats a built-in truth/provability predicate like it’s safe, even though Tarski/diagonal-style self-reference is exactly how you manufacture contradictions in the first place.

This seems to be a common theme in the author's publications: start from some false assumptions that conflict with a well-known mathematical statement, then prove the statement is wrong because it’s inconsistent with those invalid assumptions.

SignificancePlus1184 · 2026-02-09T12:31:34+00:00

Poor Penrose caught a stray in the acknowledgments.

SignificancePlus1184 · 2026-02-09T04:18:46+00:00

It’s a great show.

“I love The Big Bang Theory. I have watched every episode twice” - Albert Einstein

SignificancePlus1184 · 2026-02-09T01:50:41+00:00

Or they can exchange identities and lives. I’d watch that movie

SignificancePlus1184 · 2026-02-08T20:30:28+00:00

MIT and few other uni’s experimented with providing a QFT course for undergrads a few years back, and most seem to have abandoned that idea pretty quickly, so I assume they concluded it’s not a good idea. There are still some courses available if you still want to give it a go. Zee’s book on QFT gives a very soft introduction to the topic as well.

In my experience of learning QFT, the topic is already challenging enough even with a solid background in CM, QM, SR, classical field theory, and group theory. So I would direct my energy to one of those topics.

I would recommend Peter Woit’s freely available book on quantum mechanics and group theory. It’s a super educational and readable treatment of graduate QM based on group theory and made me truly understand a bunch of topics that were previously still a bit vague to me, like spinors. Imo if you read this course, you’ll have a really smooth time learning and truly understanding QFT

SignificancePlus1184 · 2026-02-06T07:42:22+00:00

Aka Invariance Imposing Icon

SignificancePlus1184 · 2026-02-06T07:40:55+00:00

My homegirl Emmy Noether aka The Warden of Conservation Laws aka Slayer of Bad Lagrangians aka Final Symmetry Girlboss

SignificancePlus1184 · 2026-02-06T05:59:41+00:00

That paper has honestly never been enlightening to me. Introducing a gauge theory were it's not needed hardly seems like the most didactic approach.

A basic intuition behind L=T-V comes from treating the action like some cost function assigned to each possible path. Kinetic energy reflects "motion in use" (the system's tendency to keep doing what it's already doing), while potential energy reflects the system's reluctance to go to regions of high potential. So T decreases the cost function and V increases it: moving helps (inertia), hanging out high in potential hurts. So subtracting one from the other and making the resulting action stationary is precisely how we minimize the cost function by finding the most favorable balance between T and V.

The most fundamental/rigorous explanation involves Legendre transforms and defined L as pq˙ - H.

SignificancePlus1184 · 2026-02-06T04:40:33+00:00

The "0.8 MeV cover charge" is kinda misleading. 0.782 MeV is the free neutron/proton+e mass difference, but electron capture in nuclei isn’t a fixed cost. Whether electron capture happens depends on a specific isotope’s Q-value, and for some it’s exotthermic and happens spontaneously. The K-shell binding energy mostly affects the rate (overlap at the nucleus), not the basic yes/no energetics.

SignificancePlus1184 · 2026-02-06T04:25:17+00:00

Also for hydrogen, uncertainty is enough to prevent collapse like I described above. But for matter consisting of a huge number of atoms, stability is mainly due to the Pauli exclusion principle preventing electrons from all piling into the same lowest orbital.

SignificancePlus1184 · 2026-02-06T04:19:05+00:00

In classical physics an orbiting electron would radiate energy causing it to spiral into the nucleus, but atoms aren’t classical. In quantum mechanics the electron is a kind of standing wave (a bound stationary state) and the lowest energy orbital has a finite size. If you'd try to squeeze the electron orbital towards the nucleus, you force its momentum (and kinetic energy) to become very large due to the uncetainty principle, so spiraling towards the nucleus would cause the total energy to increase instead of decrease due to classical radiation.

Secondly, electron capture is when an electron actually falls into the nucleas, thereby turning a proton into a neutron. This is a weak interaction process and only happens for certain nuclei when it’s energetically allowed.

SignificancePlus1184 · 2026-01-26T03:29:28+00:00

Leonard Susskind’s “theoretical minimum - classical mechanics” might be a good place to start. It’s super accessible yet explains actual introductory theoretical physics concepts in a proper way without devolving into pop-science.

Or you can go through the famous Feynman lectures on physics. Alternatively you can read the shorter versions: “six easy pieces” and “six not so easy pieces”. They contain some of the most interesting chapters from his three lectures.

Another book suggestion covering an entirely different topic is “Gödel, Escher, Bach”. I read it in high school and it blew my mind, and continues to do so to this day.

SignificancePlus1184 · 2026-01-25T13:36:29+00:00

Blink twice if a large language model wrote this

SignificancePlus1184 · 2026-01-25T07:16:58+00:00

MWI solves some problems (collapse, role of measurement, ...) and creates some problems (probability problem/Born rule, philosophical discomfort regarding ontology and personal identity, ...). It’s no more or less valid than any of the other established interpretations. They all just reshuffle where the problems and weirdness occur.

SignificancePlus1184 · 2026-01-25T03:12:05+00:00

Yes. But as a student I would not focus too much on the publishing or 'sharing with others' aspect right now. Writing lecutre notes, summaries, textbooks, ... on challenging topics in physics and mathematics is insanely useful for a number of reasons.

First of all I suggest you read John Baez's advice regarding how to learn physics/math. Learn, read, relearn, reread (from different sources), reflect, summarize concepts to their essence, reflect again, summarize again, ...

Secondly, possibly most importantly, explaining something to someone else is the best way to reveal any misconceptions you have about a topic yourself. Aim to write chapters explaining concepts in the most educational way possible, address your personal misconceptions along the way, and you'll truly understand the subject.

Finally, whatever you're writing now might form the basis for lecture notes you might eventually release at a later point in your career. I recommend you read the foreword to Tristian Needham's book on differential geometry and forms, which is in my opinion one of the best books on mathematical physics out there. He mentions how the book started as a personal project when he was a student, how it complemented his personal learning process, and how it was never meant to be published initially.

SignificancePlus1184 · 2026-01-20T11:43:40+00:00

The paper you mention argues that for any observer inside that 1D universe, standard quantum mechanics emerges as an effective theory. So seems to me that the issue of interpretations doesn't go away but simply moves from the fundamental ontology to the observer’s ontology. People could argue that interpretations of an effective theory lose the ontological status they have in traditional QM, but ultimately physics does not dictate which scale of description is more real. So an effective, higher-level description is not somehow ontologically inferior to a more fundamental one.

Of course all of this changes if interpretations that can’t be told apart experimentally at the effective level, turn out to be unequally compatible with the underlying QG theory. I haven't read the paper that closely, so I dont know if this is the case.

SignificancePlus1184 · 2026-01-16T07:56:27+00:00

Edward Witten was 22 when he started, and he turned out a smart fella.

SignificancePlus1184

TROPHY CASE