Physicist Sabine Hossenfelder offers consulting for amateur theorists, to help them connect with the mainstream research community.
My clients know so little about current research in physics, they aren't even aware they're in a foreign country. They have no clue how far they are from making themselves understood. Their ideas aren't bad; they are raw versions of ideas that underlie established research programmes. But those who seek my advice lack the mathematical background to build anything interesting on their intuitions.
When I was a grad student at the University of Illinois, I remember getting an email with the subject line "The Uncertainty Principle is Untenable". It stood out because the author was, in effect, saying that one of the foundational results in our field was garbage. I reacted like most physicists do: chuckle and move on. There was more than enough work to be done already, without tackling this kind of nonsense:
Every physical principle is based on an Ideal Experiment, not based on MATHEMATICS, including heisenberg uncertainty principle.
For example, the Law of Conservation of Momentum is based on the collision of two stretch ball in the vacuum; the Principle of equivalence (general relativity) is based on the Einstein's laboratory in the lift.
Thought experiments are useful for exploring a concept. They can help you develop intuition or build a mathematical model. But they fundamentally can't prove or disprove anything.
Many physical principles actually are justified with mathematics. Some result is derived from a theory and experiments fail to contradict it. The conservation of momentum is a beautiful example. Conservation of momentum is implied by Newton's laws, but it's strongest support comes from Noether's Theorem: any symmetry in a physical law has a corresponding conserved quantity. If the laws of physics are uniform across all positions in space, then momentum must be conserved.
I have to imagine other disciplines get their share; I know mathematicians get a stream of arguments disproving the uncountability of real numbers. It's easy to ignore these letters, laugh at them, or even find them annoying, but I think it's beautiful that Hossenfelder saw a teaching opportunity instead.
I haven't learned any new physics in these conversations, but I have learned a great deal about science communication. My clients almost exclusively get their information from the popular science media. Often, they get something utterly wrong in the process. Once I hear their reading of an article about, say, space-time foam or black hole firewalls, I can see where their misunderstanding stems from. But they come up with interpretations that never would have crossed my mind when writing an article.
A typical problem is that, in the absence of equations, they project literal meanings onto words such as 'grains' of space-time or particles 'popping' in and out of existence. Science writers should be more careful to point out when we are using metaphors. My clients read way too much into pictures, measuring every angle, scrutinising every colour, counting every dash. Illustrators should be more careful to point out what is relevant information and what is artistic freedom. But the most important lesson I've learned is that journalists are so successful at making physics seem not so complicated that many readers come away with the impression that they can easily do it themselves. How can we blame them for not knowing what it takes if we never tell them?