Recommendations are a big part of it. If he knows someone in the physics department at princeton, he should definitely contact them, or find out if anyone from his current school has any contacts there. Who you know is a big part of getting into graduate school. Also, the personal statement should show how passionate he is about physics and how the department at Princeton specifically can help him achieve his goals in life. Another option is to take a few years off school, work in the area to get experience and make contacts, and then apply.

Your GPA is good. Your GRE verbal is good. Your GRE math is actually rather good for someone in the liberal arts, so that’s a plus. Your GRE subject test is just so-so, and that’s a concern. What are your references like? Is your research proposal, if you had to submit one, strong enough? Did you contact, in advance, the person at each PhD program who you’d like to be your faculty advisor, and talk through their research (you’d need to have read some of it), your own research interests, and their program? If you haven’t done that third one, start making some phone calls immediately. It may be too late, but it might not. Don’t assume that because you didn’t get into NE, you won’t get into the others on your list. You might, you might not. It may just be that NE thought that your research interests weren’t a close enough match with those of their faculty. You don’t know their reason, so don’t assume anything based on that rejection. However, you are welcome to contact NE, ask why you were not accepted, and ask what you could do to strengthen your application. Perhaps getting an MA first, for example? Nothing wrong with making that phone call.

Hate to tell you, but it will probably all come down to the physics GRE scores. I had a similar situation – physics BA, 3.7 with highest honors, publications, three conference presentations, professional memberships, great rec’s. But I didn’t get in anywhere – except the one place I didn’t want to go. Stuck it out there for a few years and transferred somewhere better – still not ivy league though. All the schools told me it was the physics GRE that kept me out. Ugh.