The perihelion drift of Mercury was a neat problem that relativity solved, but it was not a major motivating factor for Einstein. It had an explanation within the existing paradigm: when there's a surprising perihelion drift, there's probably another planet out there. That's how we predicted Neptune's existence. Astronomers thought there was another planet closer to the sun than Mercury, which they named Vulcan.
There were other experimental problems too. The Michelson-Morley experiment was supposed how fast the Earth was moving relative to the ether. It measured that the Earth was not moving relative to the ether at all. At the very least, the experiment should have been able to see Earth's orbital motion, which points in a different direction at different times of the year.
This isn't even the worst prediction of the old paradigm*: the Blazing Sky Paradox / Olbers' Paradox. The universe was thought to be infinitely large and infinitely old and that matter is approximately uniformly distributed at the largest scales (Copernican Principle). Any line of sight should eventually hit a star. Work out the math and the entire sky should be as bright as a sun all the time. This contradicts our observation that the sky is dark at night. This paradox was eventually resolved by accepting that the age of the universe is finite, as described by Lemaitre's and Hubble's Big Bang Theory.
If we read what Einstein wrote, none of these failed predictions actually motivated Einstein to propose relativity. He instead cared more about questions like: What would it be like to chase a light wave? The electric and magnetic fields wouldn't be changing, so they shouldn't be creating each other, so the light wave wouldn't exist. That's ridiculous. So we'd better completely change our notions of space and time to make sure that this can't happen. Einstein's arguments actually are this audacious.
Einstein worked primarily through thought experiments. He would find experimental results afterwards to make his arguments more persuasive to other physicists. Even then, explaining a few obscure existing anomalies wasn't enough to convince most physicists to change their notions of space & time. He had to make new predictions. Which he did: the path of light going by the sun is bent by it's gravity. Eddington's expedition to see a solar eclipse confirmed this, and caused the paradigm shift to spread through the entire community.
* I hesitate to call this Newtonian mechanics because Newton believed in the Biblical creation story.
That's right about the motivations of Einstein, and thus as an answer about the hypothetical, but it's wrong about the response of the scientific community. His calculation of the precession of Mercury is what convinced people, not his new predictions and definitely not Eddington's expedition.
The idea that new predictions were important is a fabrication of history due to Popperians claiming that's how science should work.
No.
The perihelion drift of Mercury was a neat problem that relativity solved, but it was not a major motivating factor for Einstein. It had an explanation within the existing paradigm: when there's a surprising perihelion drift, there's probably another planet out there. That's how we predicted Neptune's existence. Astronomers thought there was another planet closer to the sun than Mercury, which they named Vulcan.
There were other experimental problems too. The Michelson-Morley experiment was supposed how fast the Earth was moving relative to the ether. It measured that the Earth was not moving relative to the ether at all. At the very least, the experiment should have been able to see Earth's orbital motion, which points in a different direction at different times of the year.
This isn't even the worst prediction of the old paradigm*: the Blazing Sky Paradox / Olbers' Paradox. The universe was thought to be infinitely large and infinitely old and that matter is approximately uniformly distributed at the largest scales (Copernican Principle). Any line of sight should eventually hit a star. Work out the math and the entire sky should be as bright as a sun all the time. This contradicts our observation that the sky is dark at night. This paradox was eventually resolved by accepting that the age of the universe is finite, as described by Lemaitre's and Hubble's Big Bang Theory.
If we read what Einstein wrote, none of these failed predictions actually motivated Einstein to propose relativity. He instead cared more about questions like: What would it be like to chase a light wave? The electric and magnetic fields wouldn't be changing, so they shouldn't be creating each other, so the light wave wouldn't exist. That's ridiculous. So we'd better completely change our notions of space and time to make sure that this can't happen. Einstein's arguments actually are this audacious.
Einstein worked primarily through thought experiments. He would find experimental results afterwards to make his arguments more persuasive to other physicists. Even then, explaining a few obscure existing anomalies wasn't enough to convince most physicists to change their notions of space & time. He had to make new predictions. Which he did: the path of light going by the sun is bent by it's gravity. Eddington's expedition to see a solar eclipse confirmed this, and caused the paradigm shift to spread through the entire community.
* I hesitate to call this Newtonian mechanics because Newton believed in the Biblical creation story.
(Easily findable, not the best) Sources:
https://en.wikipedia.org/wiki/Vulcan_(hypothetical_planet)
https://en.wikipedia.org/wiki/Olbers%27_paradox
https://www.quora.com/How-did-Einsteins-chasing-a-beam-of-light-thought-experiment-contain-the-germ-of-the-special-relativity-theory
https://en.wikipedia.org/wiki/Eddington_experiment
These are great replies. I should be wrong like this more often.
That's right about the motivations of Einstein, and thus as an answer about the hypothetical, but it's wrong about the response of the scientific community. His calculation of the precession of Mercury is what convinced people, not his new predictions and definitely not Eddington's expedition.
The idea that new predictions were important is a fabrication of history due to Popperians claiming that's how science should work.