Can reverse-thrust be used to push back from the gate? Crazy idea, I know.  But instead of pushing back a passenger plane using a vehicle connected to the front wheel, what if I turn on the reverse-thrust and rev up the engine?  My logic is if it can slow down the plane during the landing, it can certainly roll the plane from a dead stop having it go backwards to clear the gate.  Would that be possible in terms of laws of physics?
It has been done before but is generally frowned upon due to high fuel consumption, equipment FOD caused by debris kicked up by the fan exhaust and intake suction dangers.  It is just simpler and safer to connect a powered tug and give the aircraft a pushback.

But yes, you can pushback using thrust reversers.