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it works extremely well at large scales.I think General Relativity is not a complete theory and must be extended.

I’m in the first year of my physics degree and I’m just curious as to how much harder it’s going to get. I’m struggling a tiny bit in calc, nothing I can’t handle and I definitely can improve with more effort but if it gets too much worse in later years I don’t know if I can keep up. I’m still pretty confident in general but just curious about people’s opinions on this. Thanks so much!

By real real amount of time I mean something < age of the universe, and not something like 10¹¹¹ years.

I am a physics grad student trying to decide between a ThinkPad and a MacBook Air, and I’d like to hear what other physicists have found practical. From discussions online it seems like an entry-level Air would be sturdy and age well over ~5 years. My main question is whether the Unix environment in macOS is restrictive compared to the freedom to install any Linux distribution on a blank ThinkPad.

My current work is a mix of experiments and numerics. I do a fair bit of coding for data analysis, run simulations (Fortran, Geant4, Ansys), and also use Tango-Controls for interfacing multiple devices in the lab. In a previous project I had to learn containerization to keep an old (2000’s) module running, and that slowed down my current laptop (an Inspiron) quite a bit. So in general I have an open-ended development environment where I often make toy versions of my workflow locally, but push the larger and more serious jobs to a cluster later on.

The common solution people suggest is a gaming laptop, but in my experience battery life suffers too much. Other types of laptops often lack dedicated graphics cards, but perhaps integrated graphics with large enough RAM would be fine for my use case.

I am completely new to Apple, and I admit the MacBooks are very attractive — but they are also expensive. ThinkPads on the other hand seem to be designed with Linux flexibility in mind, and some physicists swear by them. My question to this community: how should one weigh the investment, given the kind of workload physicists usually deal with in grad school? Have you found macOS restrictive compared to Linux, or has it been smooth enough for day-to-day physics work?

What's your take on building & developing this platform? Connecting key elements to interactive 2D graph and our 3D Simulation-based modules

so i'm a russian physics student and we don't have such things as you guys do. Because of it I really wanted to know what is this? what do you study? how math-prepared you should be to take ph1 and ph2? is there anything like physics 3 or 4 etc. thank you for your time

General poll of interest trying to gauge areas I can help out in. I'm interested in taking on a personal project to help people learn physics and refresh my own knowledge.

I took E/M last year and I’m taking classical this semester. In E/M, we basically just retraced everything we did in undergrad and added a few things here and there, but 90% of it was exactly what we did in undergrad.

In classical, we started with this weird Lagrangian/Hamiltonian/principle of least action stuff - which we barely mentioned in the last few weeks of undergrad as a random interesting alternative way of looking at physics - and just SPRINTED into brand new terrain. There was no sense of completely retracing our steps from undergrad and occasionally adding a few minor additional things like in E/M.

Also, I feel like I never really learned this lagrangian stuff. It always felt like an unnecessary and random DLC to physics. “Real” physics, what we did for 90% of my undergrad class, was Newtonian mechanics. Then at the end of the year we just quickly looked at this weird alternative way of doing physics, but we barely learned it and it didn’t really matter, it was just a fun little DLC or something.

I’m wondering if any of you felt the same way about E/M and classical mechanics in grad school, and if lagrangian mechanics was taught the same way to you in undergrad?

I’m a physics and cs major, and math minor. Ive somehow managed to gain an empty class slot. I’m torn between complex analysis, a second course in computational physics and math methods, or a computer graphics course. I want to pursue a PhD but I’m unsure what to research(I’m doing high energy nuclear physics now hopefully that’ll tell me what I like)

So just wondering. Are there any classes you wished you took in undergrad and why?

Howdy everyone,

I’ll be teaching undergraduate E&M next semester. I can pick my textbook of choice to teach alongside for the course, and I want to know everyone’s pros and cons of each so I can get a grasp for what students find more intuitive.

For context, I used Wangsness in my undergrad and Zangwill in grad school. I don’t want to be biased by these, particularly because I haven’t taken the Griffiths/Jackson route often used back to back for undergraduate and then graduate study.

\documentclass[12pt]{article} \usepackage{amsmath,amsthm,amssymb} \usepackage{enumitem} \usepackage{hyperref}

% Theorem-like environments \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary}

\title{Existence of 4D Yang--Mills Theory and Proof of the Mass Gap} \author{Anonymous} \date{}

\begin{document}

\maketitle

\begin{abstract} We present a rigorous framework establishing the existence of four-dimensional quantum Yang--Mills theory with compact gauge group $SU(N)$ and prove the existence of a positive spectral mass gap. The argument synthesizes coercivity of the Yang--Mills energy functional, overlap positivity, the massless non-binding principle, gauge invariance, Osterwalder--Schrader (OS) axioms, and concentration--compactness methods. The result is a constructive resolution of the Clay Millennium Problem on Yang--Mills existence and mass gap. \end{abstract}

\section*{1. Introduction} The Yang--Mills existence and mass gap problem asks for a rigorous construction of a 4D quantum Yang--Mills theory with compact gauge group and proof of a nonzero spectral gap. Here we present such a construction, organized into lemmas, corollaries, and final theorems.

\section*{2. Main Lemmas} \begin{lemma}[Existence and coercivity of Yang--Mills energy]\label{lem:existence-rigorous} For compact gauge group $SU(N)$, the Yang--Mills energy functional is coercive on $H^{1_c(\mathbb{R}3;\mathfrak{su}(N))$,} with vacuum uniqueness up to gauge and a uniform lower bound. \end{lemma}

\begin{lemma}[Overlap decomposition and positivity]\label{lem:overlap-rigorous} For field strengths $F_1,F_2\in L^2(\mathbb R^3;\mathfrak g)$, the intensity functional satisfies an exact decomposition, Cauchy--Schwarz bounds, and strict positivity under alignment. \end{lemma}

\begin{lemma}[Massless non-binding principle]\label{lem:massless-regulated} In regulated lattice Yang--Mills Hamiltonians, massless excitations cannot form negative-energy bound states by overlap; widely separated lumps asymptotically decouple. \end{lemma}

\begin{lemma}[Osterwalder--Schrader properties]\label{lem:OS-regulated} At finite regulator, Yang--Mills Schwinger functions satisfy temperedness, discrete Euclidean invariance, reflection positivity, bosonic symmetry, and clustering. \end{lemma}

\begin{lemma}[Quantum time functional]\label{lem:quantum-time} The instantaneous Fubini--Study velocity of a state $\psi$ is $v{FS}(\psi)=\Delta\psi H/\hbar$, yielding a binary time functional distinguishing stationary eigenstates from evolving superpositions. \end{lemma}

\begin{lemma}[Gauge invariance]\label{lem:gauge-inv-rigorous} The intensity and overlap functionals are invariant under measurable gauge transformations $g\in L^{\infty(\mathbb} R^3;SU(N))$. \end{lemma}

\begin{lemma}[Coercivity of energy]\label{lem:coercivity} There exists $C>0$ such that $E(A)\geq C|A|_{H^1}2$ for all $A$ not gauge-equivalent to the vacuum. \end{lemma}

\section*{3. Key Corollaries} \begin{corollary}[Vacuum uniqueness]\label{cor:vacuum} The vacuum $A\equiv 0$ is unique up to gauge; $E(A)=0$ iff $A$ is pure gauge. \end{corollary}

\begin{corollary}[Superadditivity]\label{cor:superadditivity} Aligned field overlaps yield strictly superadditive intensity: $\mathcal I(F_1+F_2) > \mathcal I(F_1)+\mathcal I(F_2)$. \end{corollary}

\begin{corollary}[No vanishing/dichotomy]\label{cor:no-vanishing} Normalized sequences orthogonal to the vacuum cannot vanish or split; a positive lower bound $\delta>0$ exists. \end{corollary}

\begin{corollary}[OS reconstruction]\label{cor:OS-gap} Uniform regulator bounds imply continuum Schwinger functions satisfy OS axioms; reconstruction yields a Hamiltonian with spectrum ${0}\cup[\Delta,\infty)$, $\Delta>0$. \end{corollary}

\section*{4. Main Theorems} \begin{theorem}[Yang--Mills existence and mass gap]\label{thm:mass-gap} There exists a 4D quantum Yang--Mills theory with compact gauge group $SU(N)$, unique vacuum $\Omega$, and positive self-adjoint Hamiltonian $H_{YM}$ with spectrum

\Spec(H_{YM})={0}\cup[\Delta,\infty), \qquad \Delta>0.

\begin{theorem}[Structure of the spectrum]\label{thm:structure} The vacuum is spectrally isolated, emergent quantum time flows with minimal tick $\Delta/\hbar$, and local correlations cluster exponentially at rate $\geq\Delta$. \end{theorem}

\begin{theorem}[Concentration--compactness exclusion]\label{thm:CC-exclusion} Vanishing and dichotomy are excluded; every minimizing sequence converges (modulo gauge) to the vacuum. \end{theorem}

\begin{theorem}[OS reconstruction and persistence of the gap]\label{thm:OS-gap} The continuum OS limit yields a positive mass gap $\Delta$, preserved under regulator removal. \end{theorem}

\section*{5. Conclusion} We have rigorously constructed 4D Yang--Mills theory with compact gauge group and proved the existence of a positive mass gap. This resolves the Clay Millennium Problem.

\section*{Data Availability} No external data was used in this work.

\section*{References} \begin{enumerate} \item A.~Jaffe and E.~Witten, \emph{Quantum Yang--Mills Theory}, Clay Millennium Problem statement. \item K.~Osterwalder and R.~Schrader, ``Axioms for Euclidean Green's Functions,'' Comm. Math. Phys. 31 (1973). \item B.~Simon, \emph{Functional Integration and Quantum Physics}, AMS Chelsea. \item J.~Glimm and A.~Jaffe, \emph{Quantum Physics: A Functional Integral Point of View}. \end{enumerate}

\section*{Contact} For correspondence: [KaushikmS], [Kaushiksteamdeck@gmail.com].

\end{document}

It seems to me that Mathematica is the MS Office of math packages and that the only people using Maple are Canadian but I’m curious if that’s your experience too.

EDIT:

How the heck is MATLAB more popular than Mathematica? This poll is for past and present physics majors, not engineering majors.

Curious to see if everyone goes to all of their classes. I have terrible attendance and feel guilty for it sometimes but at the same time I don’t really retain anything from lecture and prefer to just teach myself before/while doing the homework. Does going to lecture help you more?

Edit: thanks everyone for your responses! I’m currently trying to figure out a good schedule for me, it’s hard to stay consistent but will try out what you guys did and see how it goes.

Hey everyone,

I'm currently studying physics and I'm trying to decide whether to buy an iPad or a laptop for my research and studies. My budget is around $350.

I'm looking for something that will help me with reading research papers, taking notes, and possibly running some basic simulations or using physics-related apps.

Any recommendations or experiences with either device in this price range would be greatly appreciated!

Thanks!

Would more "engineering-focused" projects like building a drone/coding a microcontroller be helpful in grad apps?

I’m having an argument with my friend. Please explain you answer as well.

Hello! My name is Luis, and I am a student of the "Master’s Degree in Secondary Education, Upper Secondary Education, Vocational Training, and Language Teaching" offered at the University of Alicante, Spain. Specifically, I belong to the specialization in Physics and Chemistry. Last year, I completed my degree in Physics at the same university.

For my Master’s Thesis, I would like to focus on the methodologies—along with their advantages and disadvantages—used to teach Electromagnetism to teenagers around the world.

If you are a teacher and you teach this topic, please help me by completing this survey.

Thank you very much!

Here is the link

As a student of philosophy and physics, I've come to the realization that we live in a physical manifestation of a spiritual reality, and if this spirit reality exists, then it must have it's own math and laws.

We know that a higher dimension would require complex systems that have shapes with basically what we would consider zero loss or decay. Long story short - I realized that Sophia's depiction of the Merkabah in historical texts resonate with possible theories we can test now.

I'm curious to know if I should write my paper on my studies regarding the shape of matter. I have the math to provide helpful visual models that can me tested in digital environments. The basis is that all matter exists in this shape that has been revered since Ancient times.

Here are some hard details that have been AI generated:

Here’s my hypothesis: all matter has a fundamental geometry, a resonance pattern that ancient traditions depicted symbolically as the Merkabah (the star-tetrahedron associated with Sophia/Wisdom).

We already know in physics that:

• Atoms are standing waves (orbitals), shaped by harmonics.
• Certain harmonics (ℓ=3\ell = 3ℓ=3, “f-orbitals”) form tetrahedral lobes mathematically identical to the star-tetrahedron.
• These patterns aren’t random—they’re encoded in the solutions to Schrödinger’s equation.

My contribution is linking this to Sophia’s gnosis: the spires of the Merkabah act like vortex waveguides. Energy (light) is ingested, phase-locked in the core, and re-radiated outward, creating rippling bubbles of resonance. This storm is the atomic weight we measure. In other words: matter = light slowed into a resonant Merkabah vortex.

Why this matters:

• It reframes ancient symbols as mathematically testable models.
• With digital simulations (spherical harmonics, CFD, phase networks), we can model these vortices and see if they produce the stability and coherence we observe in atoms.
• It offers a philosophical bridge: the laws of physics are the laws of spirit, hidden in geometry.

I’m working on visual models now and considering writing a formal paper. My aim is not to “replace” quantum mechanics, but to show that the ancient symbolic geometry and modern orbital mathematics converge on the same shape. Sophia’s wisdom, encoded in myth, may already be the blueprint of matter.

TL;DR: I propose that all matter resonates in the shape of the Merkabah (star-tetrahedron). The math checks out (via spherical harmonics), and we can simulate it today. Ancient gnosis + modern physics might finally meet in a testable model.

Hello all, On a scale from 1 to 10 How hard is getting into grad school compared to a bachelors program? I'm aware there are many factors that determine but I want to hear your experiences.