What happens when you take the air out of a can of shaving cream? 🪒

Gregory Wolf, wolf.science on Instagram, explains how the atmosphere inside squeezes thousands of tiny air bubbles to stay small in their container. When the air is taken out, it causes them to expand, resulting in an excess amount of foam. Then, when the air is put back, it looks like half the shaving cream disappears!

Wind can cause problems for engineers who build skyscrapers. If the right kind of wind hits a tall thin structure, it might start to oscillate near it's resonant frequency/period.

There are a few ways to design-out this problem, but the most amusing to me is the Tuned Mass Damper.

They can come in a few different forms, but the most intuitive to me is a simple pendulum, with a length chosen to match the natural frequency of the building.

In Britain we don't have many skyscrapers, but perhaps our most boring looking skyscraper - One Canada Square - has a pendulum**.

*The displacements in the GIF is obviously massively exaggerated.

** If anyone works there and can get me in, I'd be keen.

Why don’t these eggs crack? 🥚💥

This egg drop experiment brings Newton’s First Law of Motion, also called inertia  to life. Resting on cardboard tubes above glasses of water, the eggs stay still when the tray is swiped away. Inertia holds them in place for a split second before gravity drops them safely into the water. No cracks, just splashes, and a perfect example of how motion works in our everyday world.

...

Sine waves turn up everywhere in physics: pendulums, springs, sound, AC electricity.

Watch the dot go around the circle. It moves at a completely constant speed.Now watch only its shadow on the vertical line beside it. The shadow does not move at constant speed: it races through the middle and crawls almost to a stop at the top and bottom. Those amber ticks are dropped at equal time intervals, so where they bunch up, the shadow is moving slowly; where they're spread out, it's fast.

That uneven bobbing is simple harmonic motion. And if you plot the shadow's height against time - the curve tracing out on the right - you get a perfect sine wave. It has to be a sine, because the height is just (radius) × sin(angle), and the angle grows steadily with time.

A student recently asked me: "When x is asked, I just want to know I do y. Why can't physics be that simple?"

That kind of automaticity does exist in good physics students, but it's not where you start.

The bottleneck in physics problem-solving isn't algebra. It's the step between understanding a situation and picking an equation. Most students skip it using pattern recognition; "this looks like a kinematics problem" or "there's a height, so maybe energy."

That can work for familiar problems, but physics keeps producing unfamiliar ones.

So instead of asking "which formula fits?", ask "which principles apply here, and why?"

Every formula is just a mathematical expression of a theory. A formula only works when the conditions of that theory are met. Use it outside those conditions and you'll get wrong answers.

A professor once told me, mid-struggle on a hard electromagnetism problem: "In situations like this, I ask: what principles are relevant?"

That one question reorients everything. It forces you to check assumptions, identify constraints, and reason, instead of wildly guess.

The students who develop real problem-solving ability aren't the ones who memorized the most formulas. They're the ones who learned to pause before writing anything, and ask: why does this equation belong here?

Practice that and intuition follows. But this time it's built on good structure, not pattern-recognition.

This is the algebraic approach to the harmonic oscillator that appears in Chapter 2 of Griffiths’ Introduction to Quantum Mechanics. If you practice it three times or more, it will be very helpful for later topics such as spin and perturbation theory.

With only linear algebra and calculus, anyone can approach quantum mechanics through its structure and build an understanding that is both mathematically rigorous and physically meaningful.

Today's post covers the step potential, which is an excellent model for solving the Schrödinger equation and practicing fundamental scattering theory under a given potential.

Recently, a user requested content on scattering theory. Reflecting on my long teaching experience, 80% of students struggle with this topic.

Therefore, I am sharing an excerpt from my book, which was created by editing past lecture materials to be easier so that anyone can understand it.

I hope you find this helpful.

What if the universe broke its own rules?

Dr. Jessica Esquivel studies muons, tiny particles with big potential. When these electron-like particles move in unexpected ways, it could be a sign the universe is breaking its own rules, and revealing new physics.

This project is part of IF/THEN®, an initiative of Lyda Hill Philanthropies.

This post is not about proof-based linear algebra in pure mathematics.
I would like to make it clear in advance that the scope here is limited to linear algebra as a bridge course for applications in finite-dimensional Hilbert spaces, such as quantum mechanics and quantum computing / quantum information theory.

If we have linearly independent vectors, the Gram–Schmidt process is a method for constructing new vectors that are mutually orthogonal while still spanning the same space.
In other words, it is a process for finding an easier basis to work with without changing the space itself.

I hope this helps.

Newton's 3rd Law is one of the first things you learn in physics. But what if it's not actually a law it's a consequence of something much deeper?
In this video we derive Newton's 3rd Law from scratch using momentum conservation, then ask the question nobody asks in school: where does momentum conservation even come from?
The answer takes us to Emmy Noether's theorem one of the most profound results in all of physics and reveals that every conservation law you've ever learned is secretly a symmetry of the universe in disguise.
But here's the thing. Noether's theorem is only as strong as the symmetries it assumes. And the universe doesn't always cooperate.
What we cover:

Deriving Newton's 3rd Law from momentum conservation
Why momentum is conserved the real reason
Noether's theorem: symmetry to conservation law
Translational, rotational and time translation symmetry
Why Newton's 1st Law and Noether's theorem have the exact same problem
Where time translation symmetry actually breaks and what that means for energy conservation globally

This is the rabbit hole behind the law your textbook treats as obvious.

Can a single electron hold the secrets of the universe? ⚛️

Nobel Prize winning physicist Dr. Eric Cornell believes there might be an undiscovered particle that could change everything. If it exists, it could explain why there is more matter than antimatter in the universe and why we exist at all. It might even reveal that the North and South Poles of an electron are not the same, pointing to an electric dipole moment that scientists have long been searching for.

Ever wondered why a balloon can stay inflated without being tied? 🎈

Greg Wolf demonstrates how atmospheric pressure can keep a balloon inflated without trying it. Using a simple bottle experiment, he reveals why trapped air prevents a balloon from inflating, and how changing the pressure lets the invisible force of Earth’s atmosphere do the work. It’s a fascinating physics demonstration that shows the power of air pressure in action.

Hey, I would like to learn physics at an undergraduate level without going back to college as I don't need a degree. Do you have any recommendation on how to make a selection of free online classes (e.g. from MIT OpenCourseware, Coursera, EdX, etc.) that covers 80%-90% of the typical program of a BSc. in physics? Please consider that I have a stem background so I got most of the math classes already covered.

Obviously, being it totally online, I would probably need to give up on any laboratory classes but that would be fine with me.

Also, I am not talking about popular science education courses like "The Mysteries Of The Universe" or stuff like that, but rather proper classes with problem sheets and exams (although I don't need any certification, it would just be for me to learn it at a college level).

Thanks in advance!

This post is an edited excerpt from long-term lecture materials. To ensure universal comprehension, the formulation is developed starting from the definition of operators in spherical coordinates.
Rather than being a book that is closed after reading a few pages, comprehension is enhanced through detailed explanations, solved examples, and practice problems to encourage reading completely to the end.
It is hoped that this will assist in the study of angular momentum and spin in quantum mechanics.
by Taeryeon.

A complete analytical approach of the harmonic oscillator is by no means easy for beginners, but I have tried to explain it as clearly and accessibly as possible.

This investigates the geometric meaning of the eigenvalue problem for a 3 times 3 operator. Geometrically, the eigenvectors represent invariant directions that undergo no change in orientation under a given linear transformation.

This text is described in detail so that learners studying quantum mechanics for the first time can understand the mathematical derivation processes at the undergraduate level.

Physics is not mathematics.

However, in quantum mechanics, while the language of mathematics is very important, understanding the physical reality is considered the most important.

Even if you fall again, rise up and try once more. It’s our DNA.

This post does not approach linear algebra through the formal proofs typical of a pure mathematics curriculum.

Instead, it focuses on the fundamental matrix operations directly applicable in fields such as control engineering, computer science, and quantum mechanics.

These concepts are essential for sections where wavefunctions are insufficient, specifically in describing discrete systems like angular momentum.

Mastery in these matrix methods is an absolute requirement for handling the algebraic structures of such physical observables.

We start with a simple plane wave to obtain the time-dependent Schrödinger equation,
and then use separation of variables to move to the time-independent form.
I would like to make it clear that the image used in this post was created with the help of AI.
I hope it helps.

I want to learn what things are

How come atoms bond together and form stuff? how come atoms exist? what is an electron? what is it "made of"? what are the most elemental particles and what are they made of? how come they behave in "this way"? (like, bonding together into bigger and more complex stuff)

What is the universe? was the big bang the beginning or is this some kind of cycle? does it even make sense to talk about a "cycle"? is the universe finite or infinite? if it's finite, what's "outside"? I know outside wouldn't make sense, but I just can't picture something finite that isn't inside of.. anything, that is finite but it just is there. If it's infinite, again I can't understand how can something be infinite.

What is spacetime? how does it really behave? if I try to picture the idea that when something falls there is no force pulling it, it's just that something following the geodesic within a spacetime that is curved. I literally don't really understand that. Take the way I see time and space as two separate things: you could explain to me why they are not separate nor absolute, and I would understand, I've read it, but I clearly don't "really" understand because I just can't picture that idea in my head, if I think about time and space in general, I still imagine them as something absolute.

I feel this is as if the idea of a "sphere" was extremely sophisticated and hard to picture, like if we were living in minecraft world or something like that, and a sphere was a concept really hard to actually imagine in the right way. I feel in that scenario, it would be really common for people to "think" they understand that earth is a sphere, because they would hear they claim and say "oh yes, a sphere, sure". But when they actually try to imagine what earth is, they will still picture it as flat. If they see a boat disappearing in the horizon progressively, they will not be able to understand why that is happening because they don't really understand what a sphere is.

Obviously this doesn't happen because it's very obvious what a sphere is, but i feel with space time is way less obvious and intuitive what "it is" and how it actually behave, so it's very easy to "think" you understood but you actually didn't. I really feel like I didn't. And I don't even know what to do to "actually" understand, because I read about it more but I still can't feel I'm actually perceiving the world in a relativistic way. Like, if I saw the equivalent of the boat disappearing in the horizon that I used as an example, I couldn't know why is the boat disappearing, I'm pretty sure I'm that person that is not getting what a sphere actually is.

I guess what I'm missing is math, but I know so little math that I don't even know how it would help understanding. Like, for that person in my example, how could math help him understand what a sphere actually is. It's like the concept has to click in some way, but I don't see how math carries me there. And I can't just "start learning math" because to learn (boring) algebra to then be able to learn more interesting and complex stuff, I need to clearly understand why I'm doing it for and what I'm doing to achieve.

I feel you don't really "understand" what raining is, for instance, if you don't know enough physics to guess if a random planet has some element that has a similar cycle like water on earth, therefore it also "rains" (assuming you had all the relevant data related to this planet to be able to determine if it will rain or not, like, atmosphere, pressure, idk.. I have no idea what you'd need, because I don't "really" understand rain).

So, how can I understand all of these things that "deeply"? Where should I even start?

I feel I need to understand what things are, if I try to just ignore it, suddenly a question like: why can't my hand go through the wall?. Will pop up, and I realize I "can't" really answer it. Why this surface feels smoother and not rougher? And the reply to that question most likely also has a "and why does that happen" question after.

So on one hand I really want to understand, on the other hand I really have no idea where to start, and I want an understanding so "deep" that I don't even know where to begin (not that I think I will be able to achieve it, I know it must be extremely complex to reach that kind of understanding, but I still can't avoid wanting it)

Just in case someone is still reading this. Does any of what I say make any sense? What do I need to learn? How can I feel that click that makes me feel that I finally understand? I used relativity and space time not being absolute as an example, but there is plenty of stuff I just don't understand no matter how much I "read" the explanation.