Super-Outline Content: The Concept of Gauges.

——

Ji Wanxingpage really couldn't hold on, she relied on the excitement of deducing success to report to An Chen, and after getting approval, she returned to her desk, and fell asleep as soon as she lay down in a state of complete relaxation.

An Chen read Ji Wanxing's manuscript again, and felt that she couldn't see anything wrong on her own, so she contacted Marina directly.

She originally wanted to contact Peng Mingsi or Yan Qilan, but she was afraid that their "orthodox physicists" would not pay attention to this strange theory. Therefore, it is better to find Marina, who has nothing to do with physics, and the place where Marina and An Chen meet is the leisure platform on the 25th floor, but this time it is in the chess and card room.

An Chen first sent Ji Wanxing's manuscript to Marina, and when she arrived at the chess and card room, Marina asked the first thing she said when she saw her: "What is this, Sister An Chen?" Workbooks for first-year students? ”

Well, that's a little bit too strong.

However, as a descendant of the "Michulin Miracle", it is often common for Marina to ridicule others for their weak mathematical ability, and An Chen and others have long been used to it.

"Remember the equation you asked you to calculate yesterday, this is the result of the researcher in our group who continued to deduce on the basis of M=0." An Chen explained.

"That gravitational force or something?" Marina was surprised, "Isn't that a satellite thing, why did you get to Maxwell's equations again?" ”

She also knew Maxwell's equations, but it wasn't easy. An Chen asked, "Let's not talk about this first, do you think this is right?" ”

"There's no problem, I can see that you still have a bit of math under you." Marina still affirmed the level of mathematics of others.

"That's okay, I'll show it to Mingsi again." An Chen nodded, and was about to leave from here.

Marina hurriedly grabbed her and said, "Hey, don't go." Sister Anchen, tell me about gravity or something, what does it have to do with Maxwell's equations? ”

An Chen couldn't resist her, so he had to explain: "In electromagnetism, the relevant theories have the condition that the speed of light is constant. Introducing this coordinate system combines the constant speed of light with your equation M=0. ”

"What about M≠0?" Marina asked.

"That'...... 2GM/rc^2, this formula is not easy to solve...... An Chen hesitated, "Let's explain the situation of M=0 first." ”

"Don't mind, let me study it......" Marina looked at Ji Wanxing's manuscript again, "Look at this ds^2=-dt^2+dx^2+dy^2+dz^2, the result of the change of time flow velocity in this coordinate system is (1-v^2/c^2)^1/2, then it means that there should be a corresponding M≠0 coordinate system, so that the corresponding result in that coordinate system contains the term 2GM/rc^2." ”

The truth is this, but An Chen still doubts the feasibility of this: "If you want to use the result to extrapolate the coordinate equation, is it just like that?" ”

"yes." Marina nodded.

Belch...... It also makes sense.

"That'...... Then I'll help you. An Chen also nodded.

——

In the end, Marina really figured out something, and the new coordinate system she got really looked a little bit like that.

ds^2=-(1-2GM/rc^2)dt^2+dr^2/(1-2GM/rc^2)+Ω

And the Ω is the merging of two angular terms in spherical coordinates.

(Note: This is the Schwarzschild solution of Einstein's equations, also known as the Schwarzschild gauge, which degenerates into a Minkowski gauge when M=0)

In fact, it is not difficult to calculate, with the coordinate system ds^2=-dt^2+dx^2+dy^2+dz^2 obtained from the derivation basis of Ji Wanxing, and then substituted 2GM/rc^2, an term made up from the experimental data of extraterrestrial time difference, it is easy to get the appearance of this "original" coordinate system.

Marina couldn't help but sigh after finishing the calculation: "This is too easy, why didn't you say that little researcher of yours didn't figure it out?" ”

An Chen himself can't figure it out so quickly anyway, and it is estimated that he can't calculate it in a short time to meet the mathematical ability of normal people. However, for the familiar but somewhat strange parameter of 2GM/c^2, she always felt that it represented some deeper physical meaning.

"Marina, what do you think 2GM/rc^2 can actually do?" An Chen touched his chin and asked.

"GM/r^2 or something, isn't it a gravitational term? But this is the first square of r, so it should be ......" Marina scratched her hair, "Hey, if the escape velocity for a point on Earth is the speed of light, isn't the altitude of the 'orbit' pushed back to be 2GM/c^2?" ”

An Chen didn't have her mental arithmetic skills, but after thinking about it for a while, she realized that according to the theory of pure Newtonian physics, if you bring the algorithm of escape velocity (2GM/r)^1/2 into c, then you can get r=2GM/c^2. But this r cannot be said to be the orbital height, but the distance from the center of a homogeneous spherical celestial body. For Earth, this distance is much smaller than the Earth's radius, so there is no place where the escape velocity is equal to the speed of light.

(Note: The Schwarzschild radius is still calculated according to Newtonian mechanics, but in fact, the calculation of Schwarzschild radius requires the Schwarzschild solution of Einstein's equations, and the results derived from Newtonian mechanics should only be approximate)

"That's too ...... It's weird. An Chen couldn't help but say, "If the escape speed is the speed of light, won't it become a 'black body' where everything will fall into?" No, people's black bodies can still radiate, and this is a 'black hole' at all. ”

"Sister Anchen, that's not what I said." Marina immediately shook the pot. She has always boasted that she only understands mathematics and does not understand the specific knowledge of related majors.

An Chen stretched out his hand and poked her in the head, and then muttered: "If there really is such a critical r, it means that when the radius of a celestial body R=r, the time change on its surface is 0?" ”

"Look at it that way—that's it." Marina nodded earnestly.

"It's a hammer, huh?" An Chen couldn't help but say, "The change in time is 0, which means that time is static. Do you know what this concept is? This is an extremely strange situation even in the 'time-space' coordinate system just now. ”

"Then let's not think about that yet." Marina wiped the tip of the capacitive pen with an alcohol-based non-woven cloth, and as if she had suddenly thought of something, she immediately began to write on the screen again.

An Chen watched her calculation on the display screen and couldn't help but be surprised: if the gravitational term is equivalent to gravitational acceleration, then the original "time-space" coordinate system can be substituted, can the unit coordinate system in the case of M≠0 be obtained?

However, this time, Marina calculated and counted the mess, and finally faced with a bunch of unknown things, she had to give up.

"There is a specialization in the art industry, but this thing still can't be calculated." An Chen comforted her, and put forward a new insight, "You look at the dr^2 items in this, the closer it is, the bigger this item is." I think it's kind of non-Euclidean geometry—"

"The 'time-space' coordinate system is already non-Euclidean geometry." Marina reminded her.

"No, no, that's just the introduction of time as another axis, which is still straight in nature." "But from the point of view that the closer you get, the longer you get, it's more like a case with curvature. ”

"Isn't that even more outrageous?" Marina asked rhetorically.

"Can this be constructed?" An Chen asked.

For Marina, there is nothing that cannot be constructed. In comparison, it didn't matter if it had a specific meaning, and the young inheritor of the "Michulin Miracle" immediately nodded: "Of course it can." ”