Dr. Heidegger has a bust of Hippocrates in his lab and the narrator says that he would "consult" Hippocrates regarding difficult cases. Given the connection to the professionalism of Hippocrates and his "Hippocratic Oath," we might conclude that Heidegger is an upstanding physician who does the best he can for his patients. This is a moral code of professionalism.
But it is rumored that Heidegger also engages in mystical and magical experiments. These could be rumors and/or the creations of a "fiction monger" but they could be true as well. In either case, true or not, Heidegger uses the notion of magic in this particular experiment. Whether or not that magic is real is irrelevant. The experiment, from his perspective, is not to see if these people become young again. It is to see how they will react and if they will learn anything from it. Since they have not learned from the mistakes of their younger days, Dr. Heidegger impresses upon them to learn something this second time around:
"Before you drink, my respectable old friends," said he, "it would be well that, with the experience of a lifetime to direct you, you should draw up a few general rules for your guidance, in passing a second time through the perils of youth. Think what a sin and shame it would be, if, with your peculiar advantages, you should not become patterns of virtue and wisdom to all the young people of the age!"
In the end, Dr. Heidegger learns to accept the passage of time. Of Sylvia's flower, he says he loves it now (withered) as much as when it was fresh. But his four subjects do not learn this lesson.
On one hand, we might conclude that Dr. Heidegger knew these people well and might have assumed they would remain vain and mentally immature. On the other hand, he might have actually been trying to teach them to accept old age and, with it, wisdom. If this is the case, then he would certainly be upholding the Hippocratic Oath because his intention would have been to help these people to learn from their past mistakes and to accept the wisdom of old age. If this is the case, in this particular experiment, his moral philosophy is based upon helping people overcome vices, regret, and depression.