Yes, in fact. California is moving!

By answering your question, I figure you mean something like "is California moving, even though when I stand on the ground it doesn't feel like it". If you think about it, the whole Earth is spinning and orbiting the sun, our solar system is orbiting the center of the Milky Way Galaxy, and our galaxy is also moving! But that's too much to consider right now.

Let's focus on how California is moving right now. This answer will be all about something you might have heard of before: plate tectonics. Plate tectonics is the science behind why California is moving, and why every bit of land on Earth is moving, even right now!

Basically, all of the Earth's crust is split into chunks called tectonic plates. Imagine that you broke a dinner plate, and you (very carefully!) rearrange the pieces to fit back together. That's how the outer part of the earth fits together.

Even though the earth feels solid to us, it's not solid on the inside. In fact, it's made up of many layers, some which are solid and some which are liquid. Really, we only experience a tiny tiny part of Earth. It turns out, the earth has many solid pieces on top of a liquid. This liquid part is called the mantle. One property of liquids and gasses is that they change size (volume) when they heat and cool.

The earth's mantle is no different. As the outer liquid cools a bit and the inner liquid warms, this creates a difference in density. This difference in density causes forces to move the hot parts up and the cold parts down (lighter stuff on top, heavier stuff on the bottom). You may have seen this in the kitchen when you have oil floating on water. The oil is less dense (lighter) and the water is more dense (heavier) so the heavy stuff sinks and the light stuff floats.

This floating and sinking of different temperature liquids happens all over the place in nature, so we've given it a specific name: convection. See the picture below for what convection looks like in the earth:

how plates move

The liquid moving underneath the solid causes tectonic plates to move - remember the pieces of broken plate, now they're floating on water! There's a bit more to this movement, and you can read about it on the link above.

The bottom line is this: California is on the move!

Fun fact - Australia moves about 7 cm (~3 inches) north each year because of plate tectonics!