Ok, I don't get it. What does "Oracle owns Java" mean?
Google is definitely using Java in Google App Engine, does that mean that Google have to pay Oracle for doing so?
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Sun Microsystems created Java. Oracle bought Sun, and thus they became the owners of Java. Java (JVM and JDK) is open source, and you are free to use it. This is under the GPL though, and if they do any changes to the actual JVM or JDK, they will have to release those changes. I'm not aware how App Engine works, and why Google would be in trouble, if they are.
If you create a program in Java, you don't have to release it as open source (or the GPL, more specifically), as long as you don't use GPL'ed code, which you won't if you didn't add that yourself.
Just because someone owns something including the copyright doesn't mean they have to charge people to use it. In this case Oracle (via Sun) owns it, but doesn't charge you to use it.
However, if Google were to go try and copyright Java or sell it as its own product, that would be a whole other story.