Wait a Minute, Did the Show Say...

If the Empire is filled with hope and love, those things are reflected across all of Equestria. If hatred and fear take hold...

So... the mood of the Crystal Empire is reflected across Equestria. Except this has never been demonstrated in the show. How exactly does this work? Does this mean that if the majority of the Crystal Empire was angry, most of the ponies in Equestria would become angry?

Unless... Celestia was talking about the Crystal Heart. But there's the problem. The Crystal Heart is supposedly the Empire's defense mechanism, specifically drawing in positive emotions and using them to protect the Empire. It is not stated the Crystal Heart has influence outside the Empire, nor implied that it can have an opposite effect with negative emotions.

So what does this mean? Either this ability of the Empire is unrelated to the Crystal Heart, and never shown in the show, simply having been tacked on to make the Empire seem important, or this ability Celestia describes is indeed the Crystal Heart. We are shown that the Crystal Castle shoots an aurora-like magic into the sky that reaches across Equestria. Perhaps this is that effect.

Which would be troubling, meaning that if the Crystal Ponies were in 'hatred and fear' mode, the Crystal Heart could do what it did to Sombra, except to everyone with good in their hearts.

However, I come to my prediction. The Crystal Heart actually has none of that Sombra-killing power outside the Empire. When we watch the show carefully, King Sombra dies to a energy pulse that comes directly from the heart. This pulse might reach only to the borders of the Empire. Following that, the Crystal Castle seems to take this energy and shoot it through Equestria, which would be the ability Celestia is describing. In fact, the Heart, as the librarian says, cannot do the same thing with negative energy. Rather, Celestia says the Empire can radiate hatred and fear through the land because if something else were to be connected to the Castle, such as King Sombra, then his hatred and fear could be shot through Equestria.

TL;DR: Crystal Heart = Magic shield created through positive energy, keystone for the Crystal Castle. Crystal Castle = Magic amplifier that spreads emotions