Gauge symmetry

So what properties are conserved with time and space translation symmetry? Time translation symmetry leads to conservation of energy, and space translation symmetry leads to conservation of momentum.

Similarly, something called gauge symmetry leads to conservation of electric charge.

This is a more complicated concept, but I will add this as a bonus at the end of the video if you really want to dive into the nitty gritty of quantum physics.

Let me first address the question I posed in the title of this video by thoroughly explaining how time translation symmetry leads to energy conservation.

Therefore, momentum must stay constant.

Very similarly, rotational symmetry leads to conservation of angular momentum as well.

Now let's look at gauge symmetry, leading to the conservation of charge.

This one is a bit more abstract, so I'll start with a simple analogy, and then we'll go deeper.