Originally posted by Ash Ben, I believe the thought stemmed from the possibility of creating a reverse teleconverter - allowing FF lenses to be used on APS-C format, only with the ability to encapsulate the complete FF image circle concentrated onto an APS-C sensor, thereby increasing incident light intensity per sensor area. This effectively makes the FF lens 'faster' than it innately is. I mentioned earlier that I found little practical utility in this as extra glass naturally implied a degradation in IQ - we may as well just have DA lenses for APS-C created with larger apertures (if that is the intention of having such a reverse TC), which means larger lenses (not what Pentax would be wanting to create anyway).
To me, let FF lenses be put on a FF camera (we're waiting, Pentax), and finally we can have a camera that will use the full image circle from the lenses and put an end to this madness!
It doesnt - simply because the definition of aperture is a simple relationship based on the fundamental lens properties, i.e. focal length and the diameter of the entrance pupil (aka "max. aperture"). What you suggest is a device very well known as "focal reducer". And it lives up to its name, by shortening the focal length (thus cramming the larger image circle of the lens onto the smaller sensor). If the FL is getting shorter, but obviously the glass elements stay the same, you will get a faster aperture. It is not soemthing "equivalent", it is pure, well-knwon lens properties.
By the way: this concept is very old and used day by day by astrophotographers around the world. Focal reducers are hard to design and very expensive, if they shall work on different lenses and not being dedicated to one signle lens model. I don't know of any of those, which would work on the already comparetively fast lenses, we use in photography - and by any means, reducers also reduce the back focal length of a lens, thus, you can't focus to infinty anymore. If you want to keep infinity focusing, you need to add a relay system to the reducer and thus you create a big, bulky and expensive piece of equipment, which is a hefty compromise in termy of image quality anyway...
Ben