It’s not crazy at all, but it will probably take you longer and you’ll have to put in some extra effort to do it.
In order to pursue a PhD in a STEM field, there are some fundamental things you’ll need:
- You need coursework in the field. At the bare minimum, you need to take coursework equivalent to a minor in the field - which is probably around 5-7 courses. To be maximally competitive, you’d need the equivalent of a major, which can be anywhere from 10-15 classes. There some basic foundational courses you’d need in every field (like intro general physics, electricity and magnetism, the calculus sequence, etc.), and most PhD programs like to see you begin to develop a little bit of both breadth (so taking some intermediate and advanced courses across the field of physics) and depth (so taking 3-4 classes within a single area of physics and diving into the 400-level or even a graduate course in that area).
You’ll have to take the majority of these classes in an actual brick-and-mortar classroom, and not online - for a variety of reasons. One I’ll address in #3, but another is that there’s often the perception that online classes don’t give you the depth and knowledge that you need for advanced study. You’ll also need to do them at a four-year college and not a community college (you may be able to get away with doing 3-4 of the foundational classes at a CC, but not most of them - and the upper-level ones won’t be available at a CC).
This may be a little difficult to coordinate with your Navy service, but it theoretically can be done. The Navy also has tuition assistance, so they’ll pay for classes you take up to a certain amount each semester. After 36 months of active duty you also have access to the GI Bill, which you can use to pay for an MA in the field (more on that later).
- You need research experience - and this is going to be the part that’s more tricky to get in the service. Research experience is crucial and arguably the MOST important component of your application. Professors want to see this for a few reasons: one, they want to know that you know what you are getting yourself into - and that you won’t try the PhD program for a semester or two, decide it’s not for you, and then drop out. Two, professors use graduate students as their research assistants in the lab in order to keep their labs running and churn out the publications and work that they need to do. You’ll also probably mentor some undergrads in the lab. So they want to know that you already know what you’re doing and can basically hit the ground running when you start your PhD program. Three, students who have some research experience have been exposed to some areas of the field already, and have a better idea of their research interests. This can potentially lead to success in a variety of areas: more publications (because you already know what you want to pursue and will do it earlier in graduate school) and faster time to graduation (because you already have the skills and knowledge necessary to complete a dissertation faster).
Most undergrads get some science lab research experience starting in their sophomore or junior year by volunteering to assist a professor in the lab. You can ask any professor who’s doing interesting research if they need an RA; most of them will gladly take some extra hands in the lab. You start out doing more menial tasks and work your way up. However, the caveat is that professors usually like to take people who have some foundational coursework under their belt, which is why they typically take junior majors and the occasional ambitious sophomore. You can try to find a professor who might take you on ASAP or next academic year - just explain your situation and your interest. Better to ask just in case!
But realistically speaking you are going to have to find a way to get some research experience after college. Most successful applicants in STEM fields have 2-4 years (some or all of them part-time) of research experience before starting graduate school. One way that people do it is taking on lab manager or paid research associate positions in university or private labs, but since you don’t have a science degree that’s going to be a tough sell. Another option is to volunteer as an RA until you have enough experience to work as a paid RA, but that’s hard enough to coordinate with a regular full-time job, let alone service in the Navy. You can still try to do it - and if you are lucky enough to get stationed near the Naval Research Laboratories or on a base where there is active research going on, that might be an avenue in. But you may find that you have to take some time after your service to get this. An MA program is one way to do this (more on that in a minute).
- You need at least three letters of recommendation from PhD-holding professors who can attest to your potential in the field, both academically (and your likelihood of succeeding in and finishing a PhD) and as a scientist (are you likely to enter science research and stay there? And how well would you do, do they think, if you did?) This is why you need to take on-the-ground classes - because you need face time with science professors who can write you a letter of recommendation saying these things. This is also a secondary reason that you need research experience, because the best applicants have at least one (and often two) letters from professors who have observed them do or mentored them in research. That way, the professor can comment on your scientific skills and potential to succeed in scientific research, which is the core of any PhD program.
There are other components, like identifying a research area of interest and being able to articulate that in a statement of purpose and GRE scores. #1 and #2 will help you with the research area part - you have to start thinking very strategically about what area of the physical sciences you are interested in. First of all, you have to pick one: like knowing whether you want to go for astrophysics or oceanography. And then even within that, you have to think of very specific research interests. For example, in astrophysics, you might be specifically interested in the discovery and investigation of extrasolar planetary systems around low-mass stars or the relationship between cosmic structure and dark matter at the edges of the universe (I have no clue what I’m talking about; I lifted that from some Chicago astrophysicists’ profiles). You figure this out by taking classes and volunteering in labs.
