"Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry." - Richard P. Feynman
Look at this interactive drawing here. You know what this is? It's how Nature keeps track of her bookkeeping when particles interact. These are called Feynman diagrams - yes, named after me, but that's not really important.
When I was working at Los Alamos and later at Cornell, we kept running into these complicated mathematical expressions for calculating how particles behave. The math was getting too complex - we couldn't see the physics anymore! So I made up these pictures as a way to visualize what's happening.
Here's the key idea: those black dots? Those are where the action happens - we call them vertices. That's where particles meet up and do something interesting - they might scatter off each other, or one particle might turn into several others. Everything interesting in particle physics happens at those vertices.
The lines connecting them aren't just lines - they're particles moving from one interaction to another. In quantum mechanics, particles can behave in strange ways. When a line goes from one vertex to another, that's a real particle you could detect. But when a line connects vertices in the middle of a process, that's what we call a virtual particle - it's part of Nature's accounting system.
Try playing with these knobs here. You can change:
Go ahead - drag those vertices around! That doesn't change the physics, just how we're looking at it. In the real calculations, the virtual particles can be anywhere in spacetime, and we have to add up all possibilities. That's the magic of quantum mechanics!
You know, these diagrams aren't just pretty pictures - they're actually a shorthand for some very specific mathematical rules. Every part of the diagram translates into a piece of a calculation:
Each different type of line represents a different particle. In real quantum field theory, each of these lines corresponds to what we call a "propagator" - a mathematical term that tells us how the particle moves from point A to point B.
Here we've assigned each particle a momentum value between 100 MeV and whatever maximum you choose with the slider. In a real calculation, the momentum would be determined by the experimental setup, like the energy of your particle accelerator.
Each vertex corresponds to a coupling constant - essentially how strongly particles interact with each other. Electromagnetism has a coupling constant related to the electric charge. Strong nuclear force has a different, larger coupling constant.
The amazing thing is that when particles have higher energy (momentum), they can create more complicated diagrams with more vertices. That's because E=mc² works both ways - energy can become particles! That's why turning up the energy in particle accelerators lets us see more exotic processes.
In real quantum field theory, we don't just draw one diagram - we draw all possible diagrams and add up their contributions. Diagrams with more vertices generally contribute less to the final answer (they're less likely to happen), but for precise calculations, we need lots of them.
The beautiful thing about these diagrams is that they let us break down extraordinarily complicated calculations into pieces we can understand visually. Each diagram has its own story to tell about how particles interact.
And remember - all these sophisticated calculations ultimately come down to particles moving around (propagators) and interacting at specific points (vertices). Nature's accounting system is complex but organized around these simple principles!