It wouldn't even be a hard issue of the Supreme Court hadn't injected this "expectation of privacy" concept that appears nowhere in the text of the amendment.
[1] From Google's TOS: "When you upload, submit, store, send or receive content to or through our Services, you give Google (and those we work with) a worldwide license to use, host, store, reproduce, modify, create derivative works (such as those resulting from translations, adaptations or other changes we make so that your content works better with our Services), communicate, publish, publicly perform, publicly display and distribute such content."
Of course, a lot information is actually generated by Google and even though it's about you (search history, etc) and doesn't belong to you.