# Physical laws are low-energy approximations to reality, 1.2

When the temperature $\displaystyle{T}$ is higher than the critical temperature $\displaystyle{T_c}$, point $\displaystyle{O}$ is a local minimum. So when a particle is trapped at $\displaystyle{O}$, it is in static equilibrium.

However, when the temperature is lowered, the system changes to the lowest curve in the figure shown. As we can see, at the new state, the location $\displaystyle{O}$ is no longer a minimum. Instead, it is a maximum.

So the particle is not in static equilibrium. Instead, it is in unstable equilibrium. In other words, even if the particle is displaced just a little bit, no matter how little, it falls to a state with a lower energy.

This process can be called symmetry-breaking.

This mechanical example is an analogy for illustrating the concepts of symmetry-breaking and phase transition.

— Me@2019-03-02 04:25:23 PM

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