JavaでタイムスタンプをローカルタイムゾーンからGMTに変換するにはどうすればよいですか?

public static Calendar convertToGmt(Calendar cal) {

    Date date = cal.getTime();
    TimeZone tz = cal.getTimeZone();
    log.debug("input calendar has date [" + date + "]");

    // Convert to milliseconds since epoch in GMT
    long msFromEpochGmt = date.getTime();

    // Get offset from UTC in milliseconds
    int offsetFromUTC = tz.getOffset(msFromEpochGmt);
    log.debug("offset is " + offsetFromUTC);

    // Create GMT calendar and adjust date based on offset
    Calendar gmtCal = Calendar.getInstance(TimeZone.getTimeZone("GMT"));
    gmtCal.setTime(date);
    gmtCal.add(Calendar.MILLISECOND, offsetFromUTC);
    log.debug("Created GMT cal with date [" + gmtCal.getTime() + "]");

    return gmtCal;
}