After spending a majority of his years studying and perfecting the theories of general and special relativity and working through calculus problems whose answers only prompt more questions, Edwin Taylor has gone back to the basics.

Taylor, a physicist whose work with John Wheeler prompted an undergraduate-level course on spacetime physics at N.C. State, is relearning equations that, when the right numbers are plugged in, reveal the distance from Point A to Point B in curved space. He’s reviewing, again, how to better define a black hole. And on Monday afternoon in Riddick Hall, he questioned whether he should add or subtract numbers in a calculus equation.

“It’s a minus sign, right?” he asked the audience. “Or is it plus?”

He erased the minus sign and changed it so that one half the equation was being added to the other half.

He looked at it again.

“It’s minus,” he said, erasing the plus sign.

Taylor is relearning the basic elements of physics, he said, so that he can better explain them to undergraduate students, including one N.C. State class of about 40.

“No one who knows a subject should be able to write a textbook in that subject, and for an elementary reason: they have lost the ability to teach the subject fresh for the first time,” he said. “They have no idea what’s difficult about the subject because they have spent most of their lives getting over it.”

He urged those listening to his lecture to read and review the second edition of the undergraduate textbook, Exploring Black Holes.

“Who in the world can help you with a fresh view? Well, it is students. And so what you do is, you pay them in credit,” Taylor said. “It’s like, if you’ll excuse me, Confederate money. You pay them in credit, which costs you nothing, and you pay them to send in their responses and their difficulties with each chapter, each unit, as they need it. You give them no less credit if they’re critical — you want them to be critical.”

One person Taylor sought out to help was Chris Gould, associate dean of the College of Physical and Mathematical Sciences, who said he has also taught the spacetime physics class on and off for about 20 years.

Gould has a binder that holds copies of the manuscript, and he said in an interview last Wednesday that he was planning on passing copies out to his class as flimsy textbooks this week.

Taylor said he hopes the students will send in reading memos, pointing out discrepancies in equations or definitions that cannot be found in an undergraduate’s physics vocabulary.

“I get feedback from people who have never met this material before, and that’s absolutely golden,” Taylor said. “And it is embarrassing how terrible your text is. But if you’re willing to take the ego hit, then you change it, and the next time a few more get it, and a few others find things you haven’t even thought of before.”

Taylor said when he started working on completing the second edition of the textbook, it became difficult for him — a physicist who has been working in the subject since college — to understand how the information was supposed to relate to students.

“I’ve written the dang book already once and it’s still too hard for me. Why is that? And the reason, I’ve finally figured out, is that we’re reinventing big chunks of general relativity,” he said. “No one’s ever thought of it this way before.”

He said he and Wheeler “finally settled down on two tools,” which include the metric and the principle of maximal aging.

Metrics are solutions to Einstein’s field equations. Tensors, Taylor said in a basement office of Riddick Hall before his lecture, “are a little advanced when it comes to mathematics, but that’s the way Einstein set up his equations.”

And that way can be difficult for undergraduate students, Taylor said, who have less experience with physics. So Taylor and Wheeler decided to break general relativity down.

“Instead of starting with the original equation that Einstein developed, you start with the solution to the equation. Then you use calculus — that’s what every physics major has to know,” Taylor said. “So by starting with the solution to Einstein’s equation, you can go from having these tensors, which are complicated, to using calculus, which is the standard tool of every physics major.”

The other factor in understanding spacetime physics has to do with time, Taylor said, moving to the right side of the whiteboard on which he had been writing and erasing and writing again various equations.

“Metrics tell you what spacetime is like. It doesn’t tell you how things move in spacetime,” Taylor said in the office, moving his hands outward before him and seemingly attempting to grasp what can only be observed through equations. “How things move in spacetime is spelled out in special relativity. The thing that Einstein discovered in special relativity, one of the greatest discoveries in science, was that time depends on the observer.”

In front of the whiteboard, Taylor held up a rock with a wristwatch latched around it.

“If I throw this stone, it will move in such a way that its wristwatch will read the maximum time between launch and impact,” Taylor said. “These two things are what you need as tools to understand curved spacetime.”

According to Einsein’s theory of general relativity, clocks move at different speeds depending on from what altitudes they are hung as well as how quickly they are moving. Clocks at higher altitudes run faster, the theory states, and wristwatches on constantly moving people run slower.

“There’s time such as clocks in a building, which are all set to the same time. The second kind of time is what’s in your wristwatch, and if you move around, your wristwatch does not move at the same rate as the clocks in the building,” Taylor said. “This is very hard to understand, it’s very weird, but it’s the basis of special relativity.”

It took a while for both physicists and those not in the field to accept the theory, Taylor said, citing the first global positioning satellite.

“When they put the first global positioning satellite up, they had a general relativity on/off switch because they didn’t believe general relativity worked,” Taylor said. “It went up in the off position and the satellite became totally useless for the purpose of positioning after a day. We use that all the time, every day, and it’s something in which general relativity is just part of the theory.”

Another consequence of general relativity, Taylor said, is the twin paradox, a theory that has not been tested with humans as part of the equation.

“One twin goes out to a distant star, and when he comes back he has aged by 20 years, but everybody he knew on Earth is long since dead,” Taylor said.

“That’s real, and it happens all the time in high-speed particles.”