For example, Maxwell’s equations contain upside down triangles. What exactly do they represent?
How does it apply to the real world?
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Imagine that you have a smooth wooden floor and you roll a ball across it. The ball moves in certain predictable ways. It is easy to picture where is the ball will go when you bump it. It is easy to calculate the equations of motion in the situation.
Now take the same ball and play with it on a curved hillside. The ball does not act the same way it did on the flat floor. If you push it uphill it turns around and goes back downhill, or curves a certain way, or tries to go downhill very quickly. If it is a big hill, and you leave the ball rolling, it might be going super fast by the end of it. There might even be differences in terrain, such as gravel or smooth grass. The equations to control how the ball is moving suddenly got much, much more complicated because gravity is pulling it, but how the hill is shaped changes how gravity moves the ball as well as your touches.
What would happen if you empty a big bucket of balls out on a certain spot of the hill? Most of them would roll down the hill the same way, but this would look different if you dump the balls out on different spots of the hill.
The upside down triangle (del) It is a way of handling similar forces with electricity and magnetism. It isn’t super concerned with one ball at a time, but it helps describe how lots of balls act on a certain spot on the hill. In the case of Maxwells equations, it is more concerned with how electromagnetic fields change and push and pull differently at different spots.
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