[lmm]

An engine is just a mechanism for converting stored energy into forward motion - the details are, well, details. There's nothing wrong with propellers (probably impellers will be more efficient), and those efficiency numbers are (presumably) including that.

[pjc50]

No, the details are completely critical to making it work!

I'm kind of surprised that Elon Musk, who clearly knows his stuff in rocketry, is handwaving the difficulties of an electric jet. Personally I see it as far more likely that we'll continue to use conventional aircraft but start synthesising fuel from renewable energy. The US Navy is already looking at doing this to make jet fuel from spare carrier nuclear power:

http://www.nrl.navy.mil/media/news-releases/2014/nrl-fuel-fr...

[Retric]

You can get supersonic by having air intake, expansion chamber, blade, high pressure chamber, exhaust port.

Think something like this: <=|=>

Importantly the air flows through the compression chamber at Subsonic speeds.

PS: While simplified this is the general approach for low mach speeds as burning stuff in a supersonic combustion chamber is much more difficult.