Since you can't even play 4K video on any PC, most of us would not automatically come up with an idea to edit 12-megapixel resolution video on a Macbook Air.
However, a demo published by Dave Helmly, in charge of tech sales of Adobe's pro audio and video products, shows that it is possible.
Helmly used a flagship Macbook Air with an Intel 1.8 GHz i7-2677M processor, which retails for $1700. The 4K video quickly overwhelmed the dual-core processor and its four threads. However, the video, apparently recorded with a Red One camera, ran in real-time via a Thunderbolt-connected Red Rocket accelerator and transcoder card. The Red Rocket card is key to getting 4K video to be played at 30 fps on a PC and can be purchased for $4,750.
It's important to note that Helmly went with the Apple hardware, but on the OS side it's running Windows 7 in boot camp. Helmly explained to Gizmodo on his choice:
No real reason I chose to show it running under Windows 7 other than I've been surprised that we haven't seen any demos of Windows running TB before now. It actually works pretty good in it's current beta state. That said the Mac OS kicks @ss running the same config. Please keep in mind that half the battle is getting alpha/beta Windows 7 64bit drivers for each TB device. All TB devices need drivers at some level. All necessary Mac OS driver are already shipping.
The Mac + TB is really last years news and we all want more TB peripherals to start shipping and to start showing Intel and PC makers that there is lots of interest on both sides and it will benefit all TB users. I have no preference on OS and use both everyday.
4K video is still an emerging standard and out of reach for mainstream customers. The Red One camera, which supports recording formats up to 4.5K at 4480x1920 pixels, is currently sold for $25,000. YouTube began supporting 4K videos in mid-2010. An example can be seen below (but you'll have to blow it up to original size if you want to see it in all its glory).