Though it's difficult to see "science" per se as having an impact upon Velasquez's painting, what we can see is a new attitude emerging about the relation of artist to subject and a multi-perspective or even proto-egailtarian approach this implies.
The 1600s were, in fact, an age when what we call the "scientific method" became an established part of the zeitgeist and even began to filter down to the population at large. Authors such as Francis Bacon prophesied a better future for humanity, based on man's rationality and ability to control his environment and destiny.
Velasquez, in his depiction of the Spanish royal family, places himself on the canvas, on the left side as both artist and observer. In other words, the creator is part of his creation. The most immediate message conveyed by this is that royalty, even in a country such as Spain which was hardly a model of any sort of progressivism, is not so privileged that it cannot share the scene with a "mere" artist. The artist is on the left, and a family pet, a dog, is on the right. So altogether we see an inclusiveness that implies a new standard of relations within the human world and the wider realm of life. It also suggests the materialism and literalness, influenced as they were by science, that were becoming the standards of the new age.
In the background within the scene there is a mirror, showing apparently the royal couple. In the context of its time it also looks like a portrait, implying (though perhaps only vaguely) that the artist is celebrating art within his art, almost placing it on the level of the human subjects. The infanta herself, Margaret Theresa, is the center of attention but appears rather artificial in comparison with the lady-in-waiting on the left with her urgent expression. The overall feeling one gets is that of a community of individuals rather than an exalted picture of the royal patron or patrons who were, in previous ages, thought of as separate from the rest of humanity. This was the new realism of the seventeenth-century modern age.