I think Judaism can be and needs to be reinvented.  But first we must determine what makes a Jew today:

Is Judaism the following of all the law in the Torah? No.  Even the most orthodox do not follow all the laws.  The rabbis throughout Jewish history have "reinterpreted" the law of the Torah because it was no longer compatible with modern human morality.

Is Judaism an ethnicity?  Partly, but anyone can still convert to Judaism. Jewish people adopt and raise their children Jewish. Who can really say that their lineage goes back to the ancient Hebrews?

Is Judaism a belief in god? Not anymore. Secular Judaism is on the rise worldwide, and Israel, the Jewish state, actually has one of the highest concentrations of atheism of any country in the world.

Is Judaism the following of traditions?  Partly.  Traditions change, and new ones are still being created today, though Jews still celebrate many of the same holidays as their ancient ancestors.

So then what is Judaism?  In my opinion, it is a value set.  It is a way of thinking.  It is a code of morality and ethics that preaches education, questioning, righteousness toward other people, and compassionate justice.  This moral code has its origins in the Torah, but it has evolved greatly over the last 2,000 years.

So how can we reinvent Judaism? I'd like to borrow the idea of Michael Carin in his book "The Future Jew". Over 2000 years ago, the Jewish people changed the world when they introduced the concept of monotheism, one god, to a polytheistic and pagan Europe.  It is time for Jews to take up that task once again, this time by rejecting the one god, and showing to the entire world that the human values of education, questioning, righteousness toward other people, and compassionate justice were not given to us by a god, and do not need a god to continue. There is no need to throw away tradition, no need to change the method of teaching.  Jews can reinvent themselves by rejecting god and proving to the world that it is the wisdom and values taught throughout Jewish history that have kept the people alive to this day, and not a belief in god