What Happens When You Keep Cutting Paper Forever?

Video Description

👉 To learn for free on Brilliant, go to https://brilliant.org/arvinash. Get a 20% discount on the annual premium subscription if you subscribe! Your subscription will help us create more videos like this! Thank you so much! TALK TO ARVIN https://www.patreon.com/arvinash REFERENCES Composition of cellulose https://tinyurl.com/29w7yy3e Paper microstructure https://tinyurl.com/2967qq7z Bond energies https://tinyurl.com/22pn53va Contribution of hydrogen bonds to paper strength https://tinyurl.com/24bsmxoa Modeling of forces cutting with scissors https://tinyurl.com/26eznsax CHAPTERS 0:00 What if you kept cutting paper forever 0:50 What is paper made of? 1:45 Covalent bonds, Hydrogen bonds and Van der Waals forces 3:08 What happens when scissors cut step-by-step? 5:48 Do molecules get cut by scissors? 7:14 Geometry limit. Scissors aren't infinitely sharp. 8:03 How far can the cuts go? Energy scales 10:22 What is the hard stop cutting limit for scissors 10:45 How to "cut" atoms. Nuclear splitting. SUMMARY The video follows a deceptively simple question to its deepest physical limits: if you keep cutting a sheet of paper into smaller and smaller pieces, how far can the cut really go? Could scissors eventually slice a molecule, an atom, or even something smaller? The journey begins with what paper actually is. Paper isn’t a smooth, solid object—it’s a tangled felt of plant fibers made primarily of cellulose. Each fiber contains bundles of long polymer chains, where glucose molecules are linked together by strong covalent bonds. However, the fibers themselves are held together mostly by much weaker forces. Hydrogen bonds form between neighboring cellulose chains due to uneven charge distribution between oxygen and hydrogen, and even weaker van der Waals forces add a small amount of extra attraction at close contact. When scissors cut paper, they don’t act like tiny knives cleanly slicing everything in half. Instead, the blades clamp the sheet and concentrate shear stress into a narrow region. This stress creates a crack that propagates forward along the path of least resistance. Most of the time, that path runs between fibers, breaking hydrogen bonds and weak surface attractions rather than slicing directly through the cellulose chains themselves. That’s why cut paper edges look fuzzy under magnification—fibers are pulled apart and frayed, not neatly severed. Occasionally, a fiber is cut fully across its thickness. When that happens, some covalent bonds in cellulose do break, turning one long molecule into two shorter ones. In this limited sense, cutting paper really does cut molecules. But this affects only a small fraction of the material. Even as paper is chopped into confetti, lint, or dust, the pieces are still solid fragments made of many molecules, not individual free molecules drifting around. There is also a hard geometric limit. No scissor blade is infinitely sharp. Even high-quality steel edges are thousands to millions of atoms wide. Once paper fragments approach the scale of the blade’s edge, the material bends, smears, or crushes instead of shearing cleanly. The cut stops being precise long before it reaches molecular dimensions. Energy sets the final boundary. Weak van der Waals forces and hydrogen bonds are easy to break. Covalent bonds require much more energy but can be snapped at a crack front. Nuclear bonds inside atoms are millions of times stronger still. Mechanical tools simply cannot focus enough energy or precision to break them. #chemicalbondingandmolecularstructure To split an atom, humans use high-energy processes like particle accelerators or nuclear fission, which destabilize nuclei rather than slicing them. So scissors can unzip weak bonds, occasionally break strong chemical ones—and then physics firmly slams the door. Atomic nuclei remain completely untouched.