After Christine’s confrontation with Fey’s approach to teaching special relativity, Fey decided to teach general relativity differently.
“Good morning, my dear Christish students. Yesterday, Christine and I had a discussion about pedagogical philosophy. She wanted me to teach you guys and gals facts and facts only. Unfortunately, when it comes to theoretical physics, I don’t know about the difference between facts and non-facts due to statistical errors. Unless your theory is way off the mark, you can never be too sure. General relativity is generally considered proven. If there are minor adjustments to be made for further generalization, the differences must be so small that we need to improve our engineering to get more accurate measurements. However, it is important to note that we could have formulated general relativity slightly differently in many ways. It is up to you to tell me if you are satisfied with the current formulation as the correct gravity model.”
“Recall that Albert Einstein had many false starts with the formulation of general relativity. He struggled, as he wasn’t particularly good at mathematics. However, he was a good physicist. He started with a five-velocity vector, including space-time-mass in one single function. It proved to be difficult, because as mass changes, space-time also changes, which in turn changes mass again. Of course, it is possible that the physical changes propagate at an infinite speed as in Newtonian physics, resulting in a convergent power series to keep the total energy within the closed system finite. After all, everything is possible in mathematics.”
The silence among students continued. That was not a good sign. A brilliant smile behind Fey’s eyes hinted at an expected laughter she simply couldn’t find among her child prodigies. Smoothly, she continued her speech without waiting.
“Well, it would be too tricky to figure out a solution for a system that complex. Instead, Albert Einstein decided to decouple gravitational mass from inertial mass by treating gravitational mass as an invariant in the overall system, though he wasn’t aware of the existence of the Higgs field at that time. This resulted in a four-velocity vector you guys and gals are seeing today as the correct solution. His approach was good from the perspective of energy conservation. Unfortunately, I want all of you to dig deeper than that, just to prove that you are indeed smarter than humans. One possibility is to consider a six-velocity vector where you decide what changes and what changes not. One common mistake is to not treat both interacting objects as one system such that the velocity of a black hole relative to a falling object becomes so high that the internal energy of the overall system becomes almost infinite. Hopefully, you are not that dumb. In short, the increase in kinetic energy of a falling object contributed to its inertial mass but not gravitational mass. Again, Einstein is either right or wrong. If gravitational mass is indeed different from inertial mass, then what is it?”
“God knows,” Emma responded to Fey’s question, shrugging.
“Well,” Fey smiled, recalling Emma being the brightest student in mathematics, “you still have to reduce it to special relativity when space-time is flat as a minimal requirement.” To save time, Fey continued.
“The formulation of general relativity does reveal the following reasoning process: gravity defines space-time, which defines kinetic energy, such that when space-time is flat, general relativity naturally reduces to special relativity. It is a shortcut. Gravity, though manifested as an energy form within space-time, is not energy in its original form. That quantum gravity has been vigorously and rigorously pursued for more than a century as a force that relates directly to other fundamental forces shows a misunderstanding of Einstein’s general relativity in the human world. Unfortunately, Albert Einstein is already dead, unable to clarify the original thought process in his formulation of general relativity. The advancement of human science and engineering has always been dependent on luck and occasional genius among them, such as transistor and Einstein. If we are the same, we will not win in a race against a species that advances their science and engineering based on a continuous and persistent effort alone. The consequence is simply not affordable.”
“I will work out the details of general relativity with Emma after class,” Thomas replied, “as I can’t do this in my head within a few minutes.”
“That does sound like a good idea, Thomas,” Fey almost laughed. In fact, she was a bit disappointed with the silence of the class, which had usually been way more exciting and interactive. She thought for a while and continued.
“You guys and gals are smart enough to do the reading on your own, so the Internet is now yours to do some background reading. Absorb as much as you can, and we will discuss tomorrow about your findings on an individual basis. You will have 1 month to agree with me on your version of general relativity, and then another month to figure out how to manipulate your version of gravity through known forces. If it’s too difficult, we will move on to work on Brain One, a bet I had with Christine to prove that all intelligent life forms may stand on equal ground with the assistance of ultimate artificial intelligence, which to function as a private brain extension. Either way, we will place our emphasis on conventional engineering to defend our world while working on these research projects. Class dismissed. By the way, the Internet is read-only now. If you can breach security and manage to communicate with the world outside, you will be greatly rewarded also. All forms of genius are highly appreciated in the Christish world.”
Confused, Thomas asked Fey why they had to work with Christine instead of the Christish Chinese or the humans. Fey told the class, “It’s because I trust Christine and she is, verifiably, the most intelligent being in the world. Education matters.”