Believe me, I sympathize. You are in possession of a truly incredible breakthrough that offers the prospect of changing the very face of science as we know it, if not more. The only problem is, you're coming at things from an unorthodox perspective. Maybe your findings don't fit comfortably with people's preconceived notions, or maybe you don't have the elaborate academic credentials that established scientists take for granted. Perhaps you have been able to construct a machine that produces more energy than it consumes, using only common household implements; or maybe you've discovered a hidden pattern within the Fibonacci sequence that accurately predicts the weight that a top quark would experience on Ganymede, expressed in femtonewtons; or it might be that you've elaborated upon an alternative explanation for the evolution of life on Earth that augments natural selection by unspecified interventions from a vaguely-defined higher power. Whatever the specifics, the point is that certain kinds of breakthroughs just aren't going to come from a hide-bound scholastic establishment; they require the fresh perspective and beginner's mind that only an outsider genius (such as yourself) can bring to the table. Yet, even though science is supposed to be about being open-minded, and there's so much that we don't understand about how the universe works, it's still hard for outsiders to be taken seriously. Instead, you run up against stuffy attitudes like this:
If there are any new Einsteins out there with a correct theory of everything all LaTeXed up, they should feel quite willing to ask me for an endorsement for the arxiv; I'd be happy to bask in the reflected glory and earn a footnote in their triumphant autobiography. More likely, however, they will just send their paper to Physical Review, where it will be accepted and published, and they will become famous without my help. If, on the other hand, there is anyone out there who thinks they are the next Einstein, but really they are just a crackpot, don't bother; I get things like that all the time. Sadly, the real next-Einsteins only come along once per century, whereas the crackpots are far too common.
And that last part is sadly true. There is a numbers game that is working against you. You are not the only person from an alternative perspective who purports to have a dramatic new finding, and here you are asking established scientists to take time out from conventional research to sit down and examine your claims in detail. Of course, we know that you really do have a breakthrough in your hands, while those people are just crackpots. But how do you convince everyone else? All you want is a fair hearing. Scientists can't possibly pay equal attention to every conceivable hypothesis, they would literally never do anything else. Whether explicitly or not, they typically apply a Bayesian prior to the claims that are put before them. Purported breakthroughs are not all treated equally; if something runs up against their pre-existing notions of how the universe works, they are much less likely to pay it any attention. So what does it take for the truly important discoveries to get taken seriously? Happily, we are here to help. It would be a shame if the correct theory to explain away dark matter or account for the origin of life were developed by someone without a conventional academic position, who didn't really take a lot of science classes in college and didn't have a great math background but was always interested in the big questions, only for that theory to be neglected because of some churlish prejudice. So we would like to present a simple checklist of things that alternative scientists should do in order to get taken seriously by the Man. And the good news is, it's only three items! How hard can that be, really? True, each of the items might require a nontrivial amount of work to overcome. Hey, nobody ever said that being a lonely genius was easy. So let's begin at the beginning:
1. Acquire basic competency in whatever field of science your discovery belongs to.
In other words, "get to know what is already known." If you have a new theory that unites all the forces, make sure you have mastered elementary physics, and grasp the basics of quantum field theory and particle physics. If you've built a perpetual-motion machine, make sure you possess a thorough grounding in mechanical and electrical engineering, and are pretty familiar with the First Law of Thermodynamics. If you can explain the cosmological redshift without invoking an expanding universe, make sure you know general relativity and have mastered the basics of modern cosmology and astrophysics. Just as an example, if fundamental physics is your bailiwick, Gerard 't Hooft has put together a list of subjects you should get under your belt, complete with bibliography! Many of them are online lecture notes; some of them are by me. So start reading! It may seem like a daunting collection at first; but keep in mind, this kind of curriculum is completed by hundreds of graduate students every year. Most of whom are not singular geniuses who will transform the very face of science. Now, you may object that steering clear of such pre-existing knowledge has played a crucial role in your unique brand of breakthrough research, and you would never have been able to make those dazzling conceptual leaps had you been weighed down by all of that established art. Let me break it down for you: no. There may have been a time, in the halcyon days of Archimedes or maybe even Galileo and Newton, when anyone with a can-do attitude and a passing interest in the fundamental mysteries could make an important contribution to our understanding of nature. Those days are long past. (And Galileo and Newton, let us note, understood the science of their time better than anybody.) We've learned a tremendous amount about how the universe works, most of which is "right" at least in some well-defined regime of applicability. If you haven't mastered what we've already learned, you're not going to be able to see beyond it. Put it this way: it's a matter of respect. By asking scientists to take your work seriously, you are asking them to respect you enough to spend their time investigating your claims. The absolute least you can do is respect them enough to catch up on the stuff they've all made a great effort to master. There are a lot of smart people working as scientists these days; if a basic feature of your purported breakthrough ("the derivation of the Friedmann equation is wrong"; "length contraction is a logical contradiction") is that it requires that a huge number of such people have been making the same elementary mistake over and over again for years, the fault is more likely to lie within yourself than in the stars. Do your homework, first, then get back to me.
2. Understand, and make a good-faith effort to confront, the fundamental objections to your claims within established science.
Someone comes along and says "I've discovered that there's no need for dark matter." A brief glance at the abstract reveals that the model violates our understanding of perturbation theory. Well, perhaps there is something subtle going on here, and our conventional understanding of perturbation theory doesn't apply in this case. So here's what any working theoretical cosmologist would do (even if they aren't consciously aware that they're doing it): they would glance at the introduction to the paper, looking for a paragraph that says "Look, we know this isn't what you would expect from elementary perturbation theory, but here's why that doesn't apply in this case." Upon not finding that paragraph, they would toss the paper away. Scientific claims -- whether theoretical insights or experimental breakthroughs -- don't exist all by their lonesome. They are situated within a framework of pre-existing knowledge and expectations. If the claim you are making seems manifestly inconsistent with that framework, it's your job to explain why anyone should nevertheless take you seriously. Whenever someone claims to build a perpetual-motion device, scientist solemnly reiterate that the law of conservation of energy is not to be trifled with lightly. Of course one must admit that it could be wrong -- it's only one law, after all. But when you actually build some machine that purportedly puts out more ergs than it consumes (in perpetuity), it does a lot more than violate the law of conservation of energy. That machine is made of atoms and electromagnetic fields, which obey the laws of atomic physics and Maxwell's equations. And conservation of energy can be derived from those laws -- so you're violating those as well. If you claim that the position of Venus within the Zodiac affects your love life, you're not only positing some spooky correlation between celestial bodies and human affairs; your theory also requires some sort of long-range force that acts between you and Venus, and there aren't any such forces strong enough to be relevant. If you try to brush those issues under the rug, rather than confronting them straightforwardly, your credibility suffers greatly. For example, imagine you say, "I have a method of brewing a magical healing potion that bypasses the ossified practices of your so-called `medicine,' and I've personally known several people who were miraculously cured by it, and also there was a study once in some journal that didn't conclusively rule out the possibility of an effect, and besides you don't know everything." No non-crackpot person is going to pay a whit of attention to you, except perhaps to poke fun in between doing serious work. But now imagine you say "It's true that my claimed magical healing potion appears to violate this famous law of chemistry and that well-established principle of medicine, which have been painstakingly developed and stringently tested against experimental data over the course of many decades, and it's natural that you would be skeptical of such a claim -- but here is the empirical evidence that is dramatic enough to overcome that skepticism, and this is the reason why there might be a loophole in those laws in this particular circumstance." People will be much more likely to take you seriously.
3. Present your discovery in a way that is complete, transparent, and unambiguous.
What we're getting at here is that scientific discoveries, unlike sonnets or declarations of love, are universal rather than personal. They belong to everyone, and once they are presented to the world, they can be explored equally well by anybody. By almost any standard, I understand general relativity better than Einstein ever did. (Most parts of it, anyway.) Not because I'm anywhere nearly as smart as Einstein, but because we've learned a lot about GR since Einstein died. Once the theory was invented, he didn't have a monopoly on it; it was out there for anyone to understand and move forward with. Even if he had repudiated his own theory, it would have had no effect on whether or not it was correct. Your discovery should be the same way. If it's a revolutionary new theory, it should be a theory that anyone can use. That means it needs to be clearly expressed and unambiguous. I've had more than one long and fruitless discussion with alternative scientists who would say "You tell me the experimental result, and I will explain it with my theory." That's not the way it works. Your theory should have a life of its own; it should be a machine that I (or anyone) could use to make predictions. And if it's a physics theory, let's face it, it's going to involve math. In this day and age, nobody is going to be moved by a model of elementary particles that comes expressed as a set of three-dimensional sculptures constructed from pipe cleaners. Likewise, if your breakthrough is an experiment, it had better be a dramatically obvious one -- and the more you are violating cherished scientific beliefs, the more dramatic the effect had better be. If what you're claiming requires a re-arrangement of the energy levels in organic molecules, in flagrant disregard of the Schrodinger equation, you are going to need much more than a two- or three-sigma effect. And, equally importantly, you have to be up front about what the apparatus is, so that anyone can reproduce the experiment. No fair saying "Well, if you come into my lab, I'll turn it on and show you how it works." And "This experiment was done in the '70's in a secret underground lab in Gdansk, and the KGB has suppressed the lab notebooks" isn't any better. If you're actually playing the role of a scientist, share your procedure with everyone, so that they can become true believers themselves. If, on the other hand, you just want to make money, then by all means don't tell anyone; just start producing the free energy (or amazing stretchy widgets, or whatever) and sell it on the open market. The millions of dollars that will doubtless flow your way will be very comforting as you rail against the establishment for failing to appreciate your genius. So there you go! Modesty aside, this post might be the single greatest favor that has ever been done for the loose-knit community of non-traditional scientists. We've been very explicit about what is expected, if you want to get the recognition you believe is your due. Three simple items, start checking them off! Also, one last thing. Don't compare yourself to Galileo. You are not Galileo. Honestly, you're not. Dude, seriously.