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The last major prediction of Einstein's theory of General Relativity, gravitational waves, was the most controversial and difficult to verify of them all. It wasn't until 1993 that gravitational waves were indirectly observed in the behaviour of neutron star binaries, and not until 2015 that they were finally directly detected. Even Einstein himself for a time had doubts that they were real, and he even attempted to publish a paper that tried to argue that gravitational waves were a mere artefact of the mathematics, which turned out to be flawed. Oddly enough, it was Richard Feynman, who is much better known for his work on quantum electrodynamics, who came up with an argument that convinced many of the doubters. Rather than arguing the mathematical subtleties of relativity, he came up with a physical explanation that not only demonstrated that gravitational waves must carry energy, but later inspired the design of LIGO, the first apparatus that detected gravitational waves directly. Paul Halpern has an article where he tells the whole story. From the article:
Enter Richard Feynman, who had distaste for unnecessary abstraction. If gravitational radiation is real, it must convey energy. Rather than debating the technical question of whether or not the pseudotensor definition of gravitational energy was correct, he turned instead to a far more intuitive line of reasoning, what has come to be known as the "sticky bead argument."
In his thought experiment, Feynman imagined a thin stick on which one mass is fixed and a second mass, slightly separated from the first, is free to slide back and forth, like a curtain on a rod. These two masses would be analogous to a pair of charges embedded in a vertical receiving antenna used to pick up radio signals. Just as a pulse of electromagnetic radiation would cause such charges to oscillate, the same would happen in the "gravitational antenna" if a gravitational wave passed through—with the maximum effect occurring if the wave were transverse: at right angles to the stick. Upon the impact of a gravitational wave, one of the masses would accelerate relative to the other, sliding back and forth along the stick. The rubbing movement would generate friction between the free mass and the stick, releasing heat in the process. Therefore the gravitational radiation must convey energy. Otherwise, how else did the energy arise?
(Score: 2) by Immerman on Thursday March 09 2017, @03:26PM
>"intuition", in this context, is our ability to assign value to a mathematical statement before understanding all the details of the construction of that mathematical statement.
I disagree. I would say intuition in this context is developing an understanding of the mechanisms in play, independent of the mathematics. A hunter doesn't need to understand the mathematics of the aerodynamic and gravitational influences on his arrow, he just needs to develop a reliable intuition of how he's required to aim to hit the desired target.
Similarly when solving a physics problem, well-developed intuition will let you know roughly where the solution lies and what it will look like before you've done any of the math. Mathematics is then the path taken to verify that you're actually correct, and get the precise details of the solution.
Now, knowing how to do the math reliably can be an valuable path to developing that intuition, to say nothing of pushing past it into the unknown. But a selection of good illustrative examples can also go a surprisingly long way toward developing that intuition, even without knowing any of the math.