What is your CGPA out of ten? Is it around 6? One thing people didn't mention, which I think can be relevant, is what your grades have been like for the last 2-3 years? Were the F's scattered all over the place, or were they in the first 3 years mostly? If yes, then what does it matter if you got an F in intro classical mechanics, but got an A in graduate mechanics, and QFT, and whatever advanced courses? Well yeah, it would matter, but your excuse could have been "I was a total idiot, and didn't feel like doing the work because it felt too easy." But again, I don't know if that's such a good message to send, seeing as research *apparently* involves lots of boring work. BUT, your LoRs could highlight your research strengths.
Is it possible to start a research project at an earlier date?
Also, it seems like you will begin your fifth year next year. One big mistake I did when applying to college is anticipate my poor performance, and focus all of my energies on ways to craft a solid application in spite of poor grades. Stupid strategy. I still had time in high school, and my final exams to do super well on! So, pull those As in, and maybe it might just work out.
You could always apply to applied physics programs as well. And those programs where "PGRE is recommended." If those physics departments are anything like colleges that are SAT-optional, then it's a "trick" to encourage people with higher scores to submit them, while allowing those with lower scores to still have a shot at getting in. Then, what happens is that their average PGRE score is increased. But research in physics is a different beast, so I don't know...
Check this out, and the other "elite-masters." You'll probably have to pay for living expenses on your own, but at least you could have a shot at getting in. Canadian MSc's don't seem to require the PGRE, but this one does! There's also the MSc's at Leipzig, Bonn-Cologne (they offer funding I believe), Hamburg, and Berlin, among other places. Use Hochschule Kompass to find more, and try to search with the "open admission" criteria. You're also gonna be what, 23 when you graduate? Another 2 years shouldn't be a problem.http://www.theorie.physik.uni-muenchen. ... index.html