The JDK Date API is horribly crushed, sadly. I suggest applying the Joda Time library.
Joda Time has a theory of time Interval:
Interval interval = new Interval(oldTime, new Instant());
Joda holds two thoughts: Interval for describing an interval of time within two-time instants (represent the time between 8 am and 10 am), and a Span that denotes a length of time without the actual time boundaries (e.g. represent two hours!)
If you just worry about time observations, most Date implementations (including the JDK one) performs Comparable interface which allows you to use the Comparable.compareTo()