I have an article in the field I am just interest and has no overlap with my major. Should I mention it my SOP? Related questions: 


Should one mention multiple, albeit somewhat unrelated research interests?
Should I talk about a unpublished paper in my SOP?


Besides physics as my major, my other interest is linguistics, and as you can see, there is no overlap. When I was in high school, I wrote my first article in linguistics. It hasn't been read by any professor or published in any specialize journal, not because it was rejected, but because I haven't tried to do so. I had a graduate student in linguistics review it for me, and it seems that she finds it interesting. As far as I know, there is currently no material on the topic I researched available on the internet, which indicates that the topic is new.

Because (1) it is the first article I have ever wrote, (2) I did it when I was 16 or 17 (although I have updated so much it lately) and (3) the topic is new so far, I consider it my proudest scientific activity. I think putting it in the SOP will make a steady point that "I was born for scientific research." Will it be useful if I do that, or just mention the latest article in physics I wrote?
I wouldn't mention it. As Chris C states in the comments, it is not peer-reviewed and is not directly relevant to your area of future research. 

My answer would change if the article were peer-reviewed and/or published in a journal, however. I think demonstrating that you have the ability and motivation to submit an article for publication is a positive attribute for a potential graduate student, regardless of whether the paper is in your field of research or not. For example, my first publication was not in my current research area, but several reviewers of my application later told me that just having a published paper set me apart from other applicants.

Since you claim that at least one person in the field finds it interesting and that the topic is new, why don't you want to publish it? Is there a way to at least submit it for publication before your applications are due? 

In my opinion, it is a little dangerous to put unpublished articles on a SOP or CV. A reviewer might arrive at the (potentially false) conclusion that you're trying to pad your CV or SOP with articles that may never actually be published, which can hurt you. Others might wonder why you feel that the article is important enough to include on a graduate application, but not be important enough for publication. 

Overall, I think the safer thing to do is omit it for now. If you end up moving forward with disseminating it further, then I would consider mentioning it.