Somebody mentioned the plane possibly being hijacked. Hijackers could have demanded transponders off and "low" flying. Primary radar can tell more.
If there really is no debris in the water, this could be one of many leads for investigators.
Depending on the wish of the hijackers the plane could have ended up anywhere. A Nigerian (OR was it Ethiopian?) plane was commanded to Australia but of course ran out of fuel and crashed in the ocean.
This does seem far fetched because hijackers usually want to speak to someone, unless they intend to do serious harm like 9/11.
But as many other have posted... the sudden and unannounced disappearance is unsettling....