Because nothing needs to be exactly how we expected:
Whereas you can easily write down the equations that govern any system you can imagine in a Newtonian Universe, even that step is an enormous challenge in a Universe governed by General Relativity. Because of how many things can affect how space itself is curved or otherwise evolves with time, we often cannot even write down the equations that describe the shape of even a simple, toy-model Universe.Ethan Siegel, “This Is Why Scientists Will Never Exactly Solve General Relativity” at Forbes
Our physics color commentator Rob Sheldon responds:
Ethan Siegel, an unabashed apologist for the status quo cosmology, defends the theory of General Relativity by saying it is too complicated (he means “non-linear”) to understand. He illustrates this with a quote from his Differential Equations (“diff-E-Q”) class.
“One of the most valuable lessons I ever got in my life came during the first day of my first college math class on differential equations. The professor told us, ‘Most of the differential equations that exist cannot be solved. And most of the differential equations that can be solved cannot be solved by you.’ This is exactly what General Relativity is — a series of coupled differential equations — and the difficulty that it presents to all those who study it.”
It is a characteristic of biologists who flounder over some arcane piece of biology to blame chemistry. And chemists who can’t explain, say, electronegativity, blame physics. And when physicists get called out on sloppy science, they blame mathematicians. Not being a mathematician, I don’t know who they blame when, say, they can’t explain Euclid’s fifth postulate. Perhaps that is why David Foster Wallace hints darkly at the madness of mathematicians in his book “Everything and More: A Compact History of Infinity.”
So, when Ethan says GR’s math is too tricky to understand, he is referring to its non-linear, self-referential character. That is, according to Einstein, the Earth orbits the Sun because the Sun’s mass bends spacetime into a bowl, and the Earth can’t get out. But the Sun also moves through the same spacetime it has bent. This causes ripples in the bowl. And the ripples, or gravity waves, also carry energy, which according to the same Einstein, have mass, and mass causes more bending of spacetime, &c. This property is called non-linear, because you can’t easily separate out the causes and the effects.
Now this doesn’t mean Einstein’s theory is unworkable or looks different than Newton, because most of the time the effects are too small to become causes themselves–the 2nd order correction is so small as to be easily ignored. It is only when we consider very strong space-time curvature–black holes, white dwarfs, neutron stars–does this 2nd order begin to change the results of the calculation.
And that is precisely where Ethan is defending the status quo. Because recent papers in black holes and gravity waves and dark energy have challenged the status quo. Rather than acknowledge, as Sabine Hossenfelder or Stacy McGaugh have done, that the consensus could be wrong, Ethan is busy telling us that GR is really hard to understand. I don’t know about you, but I detect an odor of elitism in that defense. Being hard to understand is a skill already mastered by 2-year-old children and 72-year-old politicians, so I would not advertise my government-sponsored career in such terms. Nevertheless, it seems to have worked for a generation or more, which is long enough to get into the DNA of research specialties like Ethan’s.
But the saddest part, is that mathematicians get all the blame and never any of the credit. When Einstein couldn’t solve his GR equations, he had to get remedial math tutoring in Riemannian geometry and tensor calculus. And how often do you hear those mathematicians named much less praised? Maybe it is time to start a #MathToo movement.
What changed my life in my Diff-E-Q class, was when the professor said, “If you don’t know how to solve a differential equation, you guess a solution and see if it works.” At first I was appalled. “You mean there is no agreed-upon method that reliably tells you the answer to an unknown diff-e-q?”
“No,” he answered, “but there’s a long table of solutions to known problems.” And what I was later to learn, was that many of the named function-solutions are simply tabulated values to the answers calculated by diff-e-q equations–that what I had thought was a brainy math analytic solution was a tedious computational tabulation.
That is to say, anybody can guess, and anybody can look up references in CRC or Abramowitz & Stegun, or in desperation, Gradshteyn & Ryzhik. There is no intrinsic barrier to math, just some guidance on where to look. For not only is Ethan’s profession about to get a major readjustment, but his attitude needs a readjustment as well. No longer can he and his colleagues hide in their ivory tower telling the world that we must leave the hard thinking to them. As many have already commented, the woke mobs are already at the gates. Maybe it is time to consider talking directly to them, rather than talking down to them. Who knows, maybe one of them will make a lucky guess and solve Ethan’s conundrum.