I heard from a Google employee that their contract prevented them from working independently on personal projects.
It says that IP assignment clauses that cover non-competing work done on the employee's own time with their own equipment are not allowed.
How it works at Google is that you sign an IP assignment clause that says effectively "All the intellectual property that you create is the property of Google except where prohibited by law" and then they attach a copy of that law to the contract.
After that you can work on personal projects but if you don't like uncertainty Google has a process that will affirm that Google has no claim to your side project. The process has you describe the project and affirm you worked on it on your own time and then if Google agrees that it doesn't compete with them they'll let you know that they're ok with it.