My idea is that the development of life must lead to forms of existence that will be possible without nourishment and which will not be shackled by consequent limitations. Why should a living being not be able to obtain all the energy it needs for the performance of its life functions from the environment, instead of through consumption of food, and transforming, by a complicated process, the energy of chemical combinations into life-sustaining energy? (source)
The implication is that the human body can transmute ambient energy into nutrients, and through the practice of cultivating this ability one can live comfortably for as long as one wishes without food, and possibly without drinking water. This is described as a siddhi in the Yoga Sutras as Pada 111.30: liberation from hunger and thirst.
This flies in the face of a substantial body of medical knowledge, which has established that the human body can last about five days without water, and a few weeks at most without food. Beyond that, you’re dead. As a result, despite a host of historical examples of people lasting for years without eating, and sometimes without drinking, most nutritionists and biochemists regard such claims to be ridiculously impossible, and the people who make the claims—currently dozens to hundreds worldwide—to be seriously delusional. Some of those claimants may well be delusional. But all of them?
We realized that, if this whole phenomenon really exists in a human being even for 15 days, it would have immense application in unraveling secrets of medical science and its application for human welfare.
Instead of ignoring this case, we selected to investigate further, in a rational and scientific way. We again make it clear that the purpose of this study was not to prove or disprove a person, but to explore a possibility in science and study a new phenomenon. (source)
Perhaps the most curious aspect of the breatharian tests is the in-your-face nature of the claimed phenomenon and yet an almost complete lack of interest from the scientific community. If it is possible to live well without eating food, this ought to be easy to demonstrate, and if it held up, the scientific and social consequences would be astounding.