I don't really understand what this really means. To understand how a symmetry can be "broken", we descend from the land of abstraction back to everyday world. Imagine you are on a train, zipping through the countryside. E.g. Let's make it a super modern train, using magnetic levitation to float above the tracks. If the train is sufficiently quiet and free of bumps along the ride, there is no way we can tell what speed we're moving at without looking out the window. Just by minding our business, doing physics experiments inside the train, the speed at which we're moving doesn't matter.The remarkable fact is hidden from us in our everyday experience for a simple reason: we can look outside and it becomes clear how fast we're moving, because we can measure/estimate our speed relative to the ground/air. This is an example of symmetry breaking. The laws of physics don't care how fast you are going, but the ground/air do. They pick out a preferred velocity, namely "at rest with respect to the ground." The deep-down rules of the game have a symmetry, but our environment don't respect it; we say that symmetry is broken by the environment. That's exactly what the Higgs field does to the weak interactions. The underlying laws of physics obey a certain symmetry but the Higgs breaks it. The symmetry breaking we've been talking about thus far is often called "spontaneous" symmetry breaking. That's a way of saying that the symmetry is still there, hiding in the underlying equations that govern the world, but some feature of our environment is picking out a preferred direction. Being able to stick out your hand out of the window of a train and measure your speed w.r.t. air doesn't change the fact that the laws of physics are invariant with respect to different velocities. From what I read above, symmetry breaking is like the schrodinger's cat experiment whereby the cat is both dead or alive and that opening the box will break the symmetry as it will lead to nature deciding the fate of the cat based on what is stated earlier. (Though i don't really know what the symmetry of the cat in box is and how it relates to my understanding of symmetry as shown below.) So symmetry breaking should be like how nature decides the outcome from all the possible ones. From my understanding, symmetry is similar to invariance such as speed of light is always the same regardless of speed, thus symmetry is a way of saying "we can alter things in some particular way and nothing important changes." But shouldn't symmetry breaking be like how the speed of light is violated, in that sense what was invariance can be violated under some circumstances. I don't know maybe it is because i didn't really understand symmetry correctly. Can someone enlighten me? Thanks a lot!