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Engineering for the undergrad because it's well-respected and will give you a sense of what you like and what you don't, then if you still love Physics go get a masters in it because an undergrad in Physics won't give you nearly as many opportunities but a Masters will give you options. It's gonna be four and a half years of story problems. I warn you. Make as many liberal arts friends as you can before you specialize because theirs are the social connections that will keep you alive. But you will emerge from the crucible battle-hardened and ready to take on the world.