Month off by one (not due to it being 0-based)

When I set the month on a date representing 1/1/1970, and then immediately get the month back, it's off by one.

import java.util.Date;

@Test
public void monthShouldBeExpectedValue() {
    Calendar calendar = Calendar.getInstance();
    calendar.setTime(new Date(0));

    int expectedMonth = Calendar.JUNE;
    calendar.set(Calendar.MONTH, expectedMonth);
    int actualMonth = calendar.get(Calendar.MONTH);

    assertThat(actualMonth, equalTo(expectedMonth)); // test fails: expected 5 got 6
}

If I change this line

calendar.setTime(new Date(0));

to

calendar.setTime(new Date());  // use 'today' instead of 1/1/1970

then the test passes. Anyone know why?

Edit

The printed version of the dates are:

new Date(0):         Wed Dec 31 19:00:00 EST 1969
date from calendar:  Tue Jul 01 19:00:00 EDT 1969

I'm running an old JDK: 1.6.0_30-b12 (64 bit)

I'm in Eastern Standard Time.