This book I'm reading states that the Klein-Gordon equation, for $m^2<0$ has an "unstable" vacuum $\phi=0$. It's talking about tachyons and how their presence is a sign of instability. What does this mean? How can I see this?
It also says that the model can be stabilized by adding a term proportional to $\phi^4$ but this is just as incomprehensible to me.
