Now, it's an unfortunate fact that 95% of all physics papers submitted by unaffiliated researchers is garden-variety crackpottery. Giving you the benefit of doubt and for now assuming that you're not a crackpot, though, there's no problem with just submitting your paper to the appropriate journal and keeping the "affiliation" field blank.
Oh, and remember that the editors will be alert for any signs that you're a crackpot, so write your abstract and cover letter in a way that emphasises the genuine and original contributions which your paper makes and doesn't exaggerate its importance.
When choosing a journal, if you're worried about it, you might want to look for one that explicitly says it uses double-blind review.
Disclaimer: I'm a researcher, but my area isn't physics, so ymmv.
However your comment did remind me: the American Physical Society has its two big meetings every March and April. If you are a member then they have to let you present at it. There's always a few "unaffiliated researchers" giving posters. (And yes, they're usually crackpots.)
A more descriptive title, such as "Ask HN: Publication without affiliation," would help a lot.
I came here thinking the title was a Spies Like Us reference.
http://www.youtube.com/watch?v=9Lge2_H_8IQ
Doctor.
Every professor I've had who is a theoretical physicist has posted their papers at http://arxiv.org/. It's not peer-reviewed but as far as I know pretty much everybody reads it.
(On the other hand if you've done work that wouldn't pass peer review then please don't clog up the arXiv with it)
As a place to stake one's claim(sure beats making anagrams as in 17th century) and disseminate knowledge arxiv seems like a good place to be.
Still, I would assume you should have friends and colleagues still within academia who could probably sort you out with library access in one way or another.
If you're a genuine citizen scientist (as opposed to a crackpot) there are always ways around it though. Talk to the librarians, they might be able to hook you up with a card in one way or another.
Berkeley's website suggests that CA citizens can buy a card that even allows borrowing privileges for $100/yr though, which is pretty cheap: http://www.lib.berkeley.edu/services/for_users/alumni_visito...
or, if you do not want to mention retired or former, nor start your own company, just provide your home address and indicate your preferred/non-preferred reviewers
Somehow I doubt that people will read your work just because it appears in a journal. I'd expect you'd still have to go around and advertise it (ie present on conferences, talk to people directly and so on)?
Journals are used by researchers looking into similar problems. So if you say find you can get a 1mm standing wave in water with sound waves and an odd contraption people looking into that area 10 years from now will probably run across your research and either improve it or look into some other area.