I don’t think Musk has given a writeup of his reasons for thinking 400wh/kg is the magic number, but a lot of research has been done that says similar numbers. This paper https://www.sciencedirect.com/science/article/pii/S2666691X2... is a good review; it cites researchers saying 800wh/kg for an electric Airbus A320, NASA saying 400Wh/kg for general aviation and 750Wh/kg for regional aviation, and other researchers saying 600Wh/kg for commercial regional aircraft and 820Wh/kg for commercial narrow-body aircraft.
That paper also sketches out the argument for electric flight at close to current battery densities rather than close to kerosene energy densities. It goes:
Jet fuel gets roughly 28% final efficiency while electric gets roughly 90%, so divide jet fuel by 3 to get 4,000 effective Wh/kg.
That is getting close to current energy densities of batteries. You only need to find one more ~2x improvement that electric flight can obtain over jet fuel to bring it into the range of 500Wh/kg, which CATL is saying they have in production right now.
(Presumably Musk’s magic 400Wh/kg number involved another 2.5x improvement, though I don’t know where specifically he thought it would come from. The internet seems to think he said you can go higher because you don’t need oxidizer from the air to burn jet fuel, but that doesn’t sound right since you still need to push on the air with your fans and you’ll run out of that at high altitude before you run out of oxygen, so it must be coming from somewhere else. Regardless, the point is that jet fuel imposes design constraints that trap you in a local maximum of aircraft efficiency, and electric engines allow you to explore a wider space which may have much much higher maximums.)
That paper also sketches out the argument for electric flight at close to current battery densities rather than close to kerosene energy densities. It goes:
Jet fuel gets roughly 28% final efficiency while electric gets roughly 90%, so divide jet fuel by 3 to get 4,000 effective Wh/kg.
Alternate aerodynamic designs and especially distributed propulsion are much more achievable with electric engines. Imagine the difficulty of making a 14-, 24-, or even 36-turbine aircraft, yet all of those have been built and flown with electric engines already (https://en.m.wikipedia.org/wiki/NASA_X-57_Maxwell, https://en.m.wikipedia.org/wiki/Aurora_XV-24_LightningStrike, and https://en.m.wikipedia.org/wiki/Lilium_Jet respectively). Gains of 3-5x have been observed here and higher is predicted, the conservative mean is 4x, so divide again by 4 to get jet fuel to 1,000 effective Wh/kg.
That is getting close to current energy densities of batteries. You only need to find one more ~2x improvement that electric flight can obtain over jet fuel to bring it into the range of 500Wh/kg, which CATL is saying they have in production right now.
(Presumably Musk’s magic 400Wh/kg number involved another 2.5x improvement, though I don’t know where specifically he thought it would come from. The internet seems to think he said you can go higher because you don’t need oxidizer from the air to burn jet fuel, but that doesn’t sound right since you still need to push on the air with your fans and you’ll run out of that at high altitude before you run out of oxygen, so it must be coming from somewhere else. Regardless, the point is that jet fuel imposes design constraints that trap you in a local maximum of aircraft efficiency, and electric engines allow you to explore a wider space which may have much much higher maximums.)