If a person pushes a fat man into an on coming trolley and in doing so prevents five people from being killing should that person be tried for murder? Is the law clear on whether this was murder? If it clear then wouldn't it be clear that switching tracks to avoid the death of five people but leading to the death of one person is also murder? Or does the law objectively determine that the "intent" in that instance is different than in the other instance?

Good questions. The "fat man" and "switch" cases you described have been discussed ad nauseum in philosophy and more recently in psychology. These discussions have focused almost exclusively on the different intentions of the person deciding whether to act so as to kill one and save five. In "fat man" the person intends to harm and kill the one as a means to save the five (saving the five is also intended), whereas in "switch" the person intends to save the five knowing, but not intending, to kill the one as a side-effect . I think this difference would in fact be significant in a court of law, where I doubt prosecutors would press charges in the case of "switch" (and I doubt juries or judges would convict--of what crime exactly?), but they likely would in "fat man" (e.g., assault and battery, perhaps manslaughter). I actually think the law would be getting things roughly right here. An important part of law is preventing risky and dangerous behavior. In "switch" there is...