If I want to investigate einstein rosen bridges, whats the probability I am wasting my time?
When experimentalists announced they had discovered super-luminal neutrinos, everybody reacted exactly like all the amateurs here are saying we should: Explore potential theoretical ramifications while being aware that it's most likely measurement error and encourage further study until we're sure.
Not so for the EMDrive. Why? Because the idea that using nothing but electromagnetism you can violate this foundational property of every physical theory since Newton (_including_ electromagnetism) means that somehow your electromagnetic device, while operating well within the range of millions of other experiments out there, somehow triggered behaviour fundamentally different from electromagnetism. Different from the type of theory that electromagnetism is. Different from the type of theory that every physical theory ever found to describe reality is. And yet this phenomenon that is utterly _different_ than anything else we have ever seen went completely unnoticed in the millions of em sensitive experiments performed by everyone from undergrads to international labs over the last two centuries.
In the strictest sense it's not logically impossible that this could happen. But only in the sense that it's not logically impossible that the flying spaghetti monster is manipulating every scientific experiment performed to hide itself.
Can an outsider with no knowledge of the field make a chance discovery? It's theoretically possible, and we might want to support undirected experimentation for the one in a billion chance that something might work. But we should take those probabilities into account when allocating our collective resources.