Yes, it is certainly possible. I have exactly been in this situation and I have seen the struggle, especially when your engineering college’s rigid policies give you no freedom of taking physics courses outside your engineering branch and next to nil research opportunities in physics and a research reputation abroad.
I have been fortunate enough to be offered admission to a few top PhD programs in physics in US and consequently, I will be joining the physics department at Cornell University for my PhD. I can advise on how a transition can be made even when your undergrad engineering college has no resources to offer in physics. Clear information was not available in my time and I hope can change that thing.
I had already lost most of my interest in mechanical engineering near the end of my second year at Delhi Technological University. I instead enjoyed learning physics and continued doing so, when at the end of my third year, I realized that I wanted to become a physicist instead of an engineer. (You can definitely take out time and study some physics on your own) I had two options in front of me, one was to apply for PhD programs straight-away and the other was to instead do a master’s degree In physics and then apply for PhD. I chose the former though ended up doing the latter.
I decided to get some research experience in physics. Since my college wasn’t the right place for getting physics research experience, I started applying to internship programs for the summer, both via official portals and by mailing professors. I was rejected by almost all places (lack of physics coursework maybe or not enough marks?). Finally, some luck landed my way when I was accepted by a professor at IISER, Bhopal to work during the summer. I ended up spending my summer there and came back even more excited to pursue physics.
Now, my college had no provision of taking any electives outside my department and thus I had no official physics coursework. (A hat tip: If you are from a college where you are allowed to take courses in any department (like IIT), definitely take physics courses and build up a physics profile) I then took the general GRE, the physics GRE and the TOEFL, and did pretty well on them. Since US allows you to apply directly after bachelor’s for a PhD, I naively thought my credentials are probably good enough to get into a good program directly (mostly on the back of my GRE scores).
Requiring three letters of recommendation (LOR), I managed to get two from physics profs at IISER, Bhopal and one from my engineering prof under whom I did a project. I applied to 8 places. The LOR from my college prof turned out to be the weakest and he did not even send it to most places, and as a result, I got rejected from every place. In hindsight, even without this fiasco, any top place would have rejected since I really had zero physics coursework and PhD admissions are much more stringent.
Lesson learnt: Physics coursework is important, choose LOR profs carefully)
I had already made a back-up plan of pursuing a master’s degree in physics from India, in case things do not work out. I gave the IIT JAM exam and was able to do well enough to be accepted to IIT Bombay’s MSc physics program.
(Common Misconception – B.Tech students are not allowed to take JAM or offered MSc physics admission. Well, IIT Bombay certainly allows B>tech students in their MSc Physics program)
This in my opinion, turned out to be the best decision I took. The academic experience at IIT Bombay was polar opposite to what I experienced in DTU. Not only were the physics professors awesome, but there was plenty of opportunity to get involved in good research. I took a variety of courses in physics, was allowed to freely choose courses, gained research experience in both experimental and theoretical physics (astrophysics, condensed matter, particle physics), collaborated and interacted with professors both from India and abroad of different institutions, and learnt more physics than I could imagine. It was here I realized how less physics I knew and how entrance exams are a terrible way to gauge your knowledge of physics.
This time I applied to the top PhD programs in US again. Not only did I know more physics, I was better prepared, had actual real physics coursework (good GPA) and research experience in hand, and amazing LORs from IIT profs. Needless to say, I was accepted to several places with fellowship (Cornell, UCLA, Penn, John Hopkins, Bristol (UK) ) among which I accepted Cornell’s offer for doing a PhD in physics.
PhD in India: India is also a great option to do a PhD, especially in theoretical physics. I was going to apply to Indian programs as well. TIFR, IISc, IUCAA, ICTS and HRI are among many top institutes where you can try for a PhD. For Indian PhD admissions, you need to clear entrance examinations. There are multiple exams to do that including the CSIR NET, JEST, and the GATE exam in physics. TIFR has its own entrance exam too. A good rank in these exams gets you an interview call from these institutes. One has to then clear the interviews to get admission.
My advice would to be gain sufficient experience in physics before going for a PhD. This includes quality coursework and research experience. PhD admissions are tougher and at top places, GRE scores do not even matter much. It’s all about coursework and research.
I feel that doing a master’s degree put me in a better position to pursue a PhD. However, if your institute allows physics courses to be taken along with engineering courses, and you can gain valuable research experience in physics, then you can apply for a PhD directly too after B. Tech. And for Indian PhD programs, prepare well for the entrance exams and study physics to be able to clear the grueling physics interviews.
For further help, you can contact me on my quora account. Here is the link to my profile: https://www.quora.com/profile/Vaibhav-Sharma-18