New Jersey, like many states, has a pre-trial intervention program for first-time, minor drug offenders called the Conditional Discharge Program. However, the vast majority of participants fail to take full legal advantage of the program, much to their detriment.
At the successful conclusion of the program, the court dismisses the charge of possession. But, and this is big caveat, the record of the arrest and the disposition remain as a part of one's criminal history. So, the whole incident does not "just go away."
The only means by which the whole case, including the arrest, is "erased" is with a successful application for expungement. An expungement of a conditional discharge is ripe 6 months after the successful completion of the program and dismissal.
So, when you graduate from MIT and are sitting in an interview in the hopes of being hired as a nuclear engineer, you can rest assured that your prospective employer knows nothing of that "weed" you got caught with during summer break-- if, and only if, the charge is expunged.
In fact, by operation of law or fiction, if you will, an expunged charge is one that never legally occurred.
