I think that’s ultimately the main stumbling block. Relativity is math. Relativity is a mathematical model – albeit one that describes certain physical phenomena very accurately. It still doesn’t explain everything, or one could say that there are flaws in it that math model that physicists don’t completely understand yet. For example, Relativity doesn’t explain anomalies with Dark Energy, Dark Matter, and quantum effects.
Anyways to try a different narrative without trains and lightbulbs…
I think one of the conceptual difficulties with Relativity has to do with everyday human experience. If we consider other concepts such as “gravity”, “heat”, or “electricity”, we come into contact with it right away before having to learn any math equations relevant to each concept.
To continue specifically with a comparison to “gravity”…
From the day you’re born, you “feel” its effects. As a child, you throw a ball up in the air, and you notice it comes right back down. You also “feel” or “experience” your feet touching the floor and your butt firmly planted in the chair you’re sitting in. Unless you’re one of the lucky few to travel into space or ride the Vomit Comet, you’ve been dealing with the reality of “gravity” non-stop.
It’s only later in life (approximately 15 years) at high school where you’ll first encounter some of the “mathematics” of gravity. You’ll see numbers like 9.8 ft per second per second. Or you’ll see Newton’s mass distance equations. These math formulas aren’t so crazy looking. To you, they’re just fancy algebra problems to quantify the phenomena of gravity you’ve been dealing with all your life.
The sequence of exposure for gravity is: #1 life experiences –> #2 mathematics
Relativity doesn’t have a “life experience” component for the typical person to “feel an intuition” before the mathematics. To “understand” relativity is to jump right into the math. There lies a huge conceptual hurdle.
Because the life experiences aren’t there, popularizers of science have to resort to contrived analogies to avoid the math. Like you said, you’ve seen them all… traveling twins, lightbulb flashes on trains, etc.
Since you as a human have no way of traveling near or at the speed light, you have no way of “seeing” or “feeling” relativity as a tangible concept like you did with gravity. Therefore, we still have to talk about via some kind of contrived example. We’ll try a different one that involve GPS satellites.
Suppose you’re a multi-billionaire and you’d like to launch your own private network of satellites to report your position. You want your personal private Global Positioning System because you’re paranoid that the US government will shut theirs down or whatever. Ok, after you spend millions launching all your satellites, you test out the accuracy with your personal GPS receiver. Your initial calculations for satellite triangulation (high school trigonometry) showed that you should get accuracy within plus/minus 30 feet. But you’re shocked to find out that you’re way off by about 6 miles! And worse, the triangulation error is accumulating every day. Pretty soon it’s 100 miles from your actual position. You double check all the components and notice nothing wrong. The tangible concept here is that your multi-million dollar satellite system doesn’t work. Finally you mention your problems to a scientist and he says, “Oh, I’ve got some math formulas that will counteract the errors you’re seeing and adjust them correctly.” And, if you ask him if there’s a “name” for those math formulas, he’ll say “relativity.” That’s really the punchline… “relativity is math.”
The amazing thing is that Einstein formulated the math of relativity before GPS satellites were invented. The “errors” that he was trying to correct were the observations made by other scientists he heard about. For example, the mathematics of Newton didn’t accurately model the motion of Mercury. And the experiments carried out by others to detect and quantify luminiferous aether didn’t give results they expected.
