We can start by looking at a video then explain the limitations and why the theory is not backed up ny the science.
I explain a f0.7 lens on this site but it has has a flange distance of about 4mm. You may wonder why this is so small. The f number is f/d f=focal length and d=diameter of the entrance pupil. My comments here relate to full frame photography. It is simpler on smaller frame sizes to achieve faster speeds although the explanation stays the same and they are still subjected to scientific limits.
The focal length of a lens is easy to understand but the entrance pupil is much harder to calculate. It is NOT the diameter of the front of the lens or of the iris. It is actually the entrance pupil as VIEWED through the optical system of the whole lens.
The next important consideration in lens design is the refraction of air as this has an absolute limit. Look at the images above, the further the lens is to the film plane the greater the problem in maintaining a low f stop number. You can make a larger entrance pupil but that necessitates moving the film plane forwards. Digital cameras do this to some extent. Some photographic companies even played with the idea of a glass lens with sensor built into it, hence no air! Remove the air and you remove the limit. So infinity focus is not really possible with a very fast a lens, then again who wants it, this is a creative tool.
The formula for this is shown below.
So the one lens tested on this site is f0.7 which seems to be the practical limit although theoretically f0.5 should be possible using the formulae. Anything lower than f0.7 is probably a fake claim unless there is NO air in the system.
You may have seen in the video information on the Carl Zeiss 40mm f0.33 but if you go to Carl Zeiss you will see that they called it the Super Q Gigantar……. It was a marketing stunt….The Q stands for "Quatsch" German for rubbish, nonsense, baloney, bosh, bunk, garbage…. It was a JOKE on the fact that folk always want faster and faster lenses.
The best way to see what light passes through a lens is to use t stops not f stops.