Ramanujan's story is a well known story of the Indian young man who turned out to be a mathematical genius without a scholarly education. He was "discovered" by the mathematician Hardy at the beginning of last century and came to England where he was appointed a university job.
Are there similar examples in the realm of physics?
George Green may be considered a physicist or a mathematician. (The titles of his papers suggest a physicist). He was a son of a miller, and a miller himself, in Nottingham, self educated. At the age of 35 he rented out his mill, and wrote "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism" where he discovered what is called now Green's formula, Green function and potential, and established the foundation of potential theory. He published it by himself, as a little booklet, supported by subscription of his friends. And only after that he went to Cambridge where he obtained a formal education, wrote few more papers on mathematical physics (his first work is by far the most famous) and died at the age of 48.
Edit. Later historians investigated what books were available to him in Nottingham. They found one appropriate entry in the local gentlemen's club library: Laplace, Traité de mécanique céleste. If this was the source of his self-education, then it is not clear where he learned French. He never attended any school before he wrote his opus magnum.
Edit 2. The mill has been restored and still functions as a museum of George Green.
Michael Faraday would meet your criteria as a physicist of historic significance without a formal education. Notably, he spent most of his teenage years working as an apprentice bookbinder. Somewhat like Ramanujan, his research career began following his initiation of an unsolicited correspondence (in his case, to the chemist Humphry Davy).
Other possibilities might be James Joule and Oliver Heaviside.
Joule was a brewer by trade and worked on science entirely as an amateur (as far as I know). He was one of the few examples of a physicist who made fundamental contributions to the field despite working in isolation from the community of scientists. In fact, he was very much at odds with the community of his time and was embroiled in some controversies and priority disputes with Mayer. He performed ground-breaking experiments on heat which ultimately led to the law of conservation of energy and the first law of thermodynamics.
Heaviside made fundamental contributions to physics and electrical engineering despite being self-taught and isolated from the scientific community for most of his life. Heaviside re-wrote Maxwell's equations in the compact form which is now known to all physics students.
Realistically there has never been a physicist equivalent of Ramanujan. Physics requires observation and not just conceptual structures, while mathematics is its own edifice, so to speak.
When you discuss Ramanujan, there are two aspects to his story that are signular - the story of the person (self taught Indian genius who despite this became a world leader in his field), and the story of his capabilities (for example his familiarity with numbers, his almost incomprehensible abilities with arcane and infinite nested formulae, his sheer almost inhuman intuition for a formulaic answer to a problem ...)
There have been self taught physicists who came from non physics backgrounds yet upended the physics world. I am extremely doubtful that there has ever been one - perhaps never will or could be one - who has shown within physics anytning that could be considered reasonably equivalent to the jawdropping capabilities Ramanujan showed within number theory and mathematics.
We are still trying to comprehend how he could work out what he knew, and not merely make use of and develop what he knew and discovered. Even with a century's hindsight he could do things that seem implausible today.
You'd be talking about the kind of person who could develop much of the entire body of modern and near future quantum physics as it stands in 2021 ~ 2040 on the back of an envelope, starting from the knowledge of a 1915 indian villager with a few old textbooks, or something like that, to stand a chance of being equivalent. Maybe modern superconductor theory on the side too. And deduce the masses and charges of bosons that wont be seen for decades or even suspected yet, solving seemingly impossibly tangled quantum wave equations and operator equations (which he also invented or greatly developed) often on pure intuition, seemingly as easily as most physicists can solve school physics problems . and did it all, with the help of some old envelopes for writing out, and a few physics textbooks from 1850-1910, and much of this by age 26.
A Ramanujan would be someone who, in 1920, could be notionally standing in front of Dirac, Schroedinger, Feynman, Wienberg, Higgs and a hundred others (if alive then), and say "It was obviously a group, and it came to me that all but gravity are governed by SU(3) × SU(2) × U(1), including a mass-generating field and mechanism, and it predicts a particle i call a neutron as well as these others I call bosons, quarks, leptons, and their properties and interactions.... ", having also derived or extended the tools needed on the way, such as much of quantum mechanics, quantum field theory, and anything needed on the way as related to groups and operators, including the calculations/arithmetic needed for actual numeric predictions - and then left the sketchiest of densely written notebooks to guide researchers after he died at 32, as to what else he theorised and was working on, and the mathematical and intuitional tools and techniques that had achieved this
That would be a Ramanujan.
I don't think physics works that way, pure and simple.
Konstantin Tsiolkovski (or Ciolkovskij, or whatever you favourite transliteration...) was an autodidact, worked as a high school teacher, his first major work was a kinetic theory of gases (25 years too late), later he focused on rocketry and astronautics (where his work - often self-published - has been mostly ignored for many years). He became really famous only towards the end of his life, and mostly in the USSR, less in the rest of the world.
Archimedes comes to mind.
I suppose I can't count Aristotle, since he attended Plato's school.
Freeman Dyson could be considered a more recent example. He became professor of physics at Cornell in 1951 despite never having earned a PhD. He had earned a BA at Cambridge just after WW2, and I believe he obtained a Master's degree at some point too. While these two degrees definitely count as 'formal education', it is generally thought that it's the PhD that does the most towards preparing someone for academic life. In this regard, the granting of a professorship without a PhD is highly unusual.
Freeman Dyson went on to contribute to a multitude of areas, with numerous papers on mathematics before he reached the age of 20. He worked on many high concept space-related ideas, such as Project Orion and the Dyson sphere. While he was never involved in the Manhattan Project, he worked with many who did, and was later involved in writing papers on strategy and use of nuclear weapons. He died 18 months ago.
