Where Did the Missing 0.5 Points Go?

In June, undergraduate students at Yenching University were taking their final exams in various subjects.

"In the 23rd century, all of humanity migrated to other planets. In 3329, you, as a historian, were dispatched back to Earth to investigate. You discovered that the robot society on Earth was still functioning. What is the content of the history books written by the robots?" --- This is an exam question from the History Department.

"If zombies exist, what are the biological principles behind their formation?" --- This was a question from the School of School of Life Sciences.

"Due to rapid population growth, continuous environmental degradation, and food shortages, human scientists have used genetic engineering technology to shrink the size of all humans to that of ants. Please describe the characteristics of the social structure after humanity enters the 'miniaturized era.'" --- This is an exam question for the social sciences department.

Compared to the exam questions from these colleges, the physics questions set by Shen Qi were relatively standard.

"The cat carrier is broken. What's the cat's state? Hmm, which professor came up with this question?"

Physics students, accustomed to dry and complicated physics formulas, showed great interest in Schrödinger's quantum cat problem.

The answers were varied, with students fully utilizing their imaginations based on fundamental principles of physics.

The grading of the Physics Department exams was done by teaching assistants. The first 75 points all had standard answers, but the Schrödinger's quantum cat question, which accounted for 25 points, did not have a fixed answer.

Shen Qi instructed the teaching assistant, " For the Schrödinger's Quantum Cat problem, as long as the students' explanations are reasonable and self-consistent, they can get at least 15 points."

The grading standards are quite lenient. If students can get all 75 points from the first few questions, plus the points for the last question with the "open-ended conclusion," they will have 90 points.

Quantum Physics is a core required course in the School of Physics. Achieving a high score in this course can significantly boost students' GPA.

Teaching assistant Xiao Tao is meticulous in grading papers. She herself worked her way up from an undergraduate level and knows how difficult it is for her juniors.

"Without opening the box, the kitten is both alive and dead, existing in both states simultaneously. If the box is opened, the kitten has a certain probability of being alive, and a certain probability of being dead... Oh, this poor kitten is so pitiful. Luckily, this is just a hypothetical scenario, a physics problem."

Because of the limited conditions in the school dormitory, Xiao Tao has difficulty keeping a cat, but she loves cats very much and often feeds the stray cats on campus.

Here's a question: in Schrödinger's hypothetical physics experiment, why did they have to use a cat? Xiao Tao looked up at the sky in thought. Oh, I digress. Back to the main topic: grading papers.

As a PhD student in physics, Xiao Tao couldn't help but admire the ingenious ideas of his undergraduate juniors.

Regarding Schrödinger's quantum cat problem, some undergraduate students have provided answers that transcend the realm of physics.

"After the cat box shattered, the cat entered another dimension and existed in the form of an 'elf'." --- This was an undergraduate student's answer.

"According to the principles of Quantum Mechanics and General Theory of Relativity, this cat traveled back to a point in the past, where it lived peacefully with most humans, but harbored a grudge against physicists." --- This was another undergraduate student's answer.

Xiao Tao was both amused and exasperated. "You've been reading too many online novels, haven't you? I'm sorry, I can't give you even a single point."

Another undergraduate student wrote on the exam, "Because the box broke unexpectedly, we didn't have the chance to observe any quantum state, that is, any state the cat could possibly be in. What we can be certain of is that the atomic nucleus is still in all possible superposition states, and so is the cat; it is in a state associated with the atomic nucleus in the same quantum state. Therefore, based on this special setting, the cat is everywhere. I mean, the cat could appear in different places at the same time, and we could even find several copies of it. Answer complete."

"This junior's answer is quite insightful," Xiao Tao remarked, unable to give a score for a long time.

A final exam score can be categorized into two levels: 70 or 80 points and 90 points or above. Xiao Tao selected several controversial exam papers and presented them to Shen Qi for a decision.

"What's wrong, Xiao Tao? Are you having trouble grading the younger students' creative ideas?" Shen Qi smiled and then reviewed the test papers that Xiao Tao had brought.

"Each graduating class is stronger than the last, and this year's new students are the strongest." Xiao Tao knew that the Physics Department had always produced many geniuses and eccentrics, and some of the young people had ideas that were beyond imagination.

"Time travel?" Shen Qi reviewed an exam paper. He scored 55 points on the first few questions, but his answer to the last question, about Schrödinger's quantum cat, was completely off-topic.

"Failing a course is a very unpleasant thing. Has Chen Xin Jie ever skipped class?" Shen Qi asked.

Xiao Tao checked the information on her phone and said, "Chen Xin Jie has never skipped class, and he always hands in his assignments on time. He successfully completed his required experiments and even took the initiative to clean the lab. It seems that Chen Xin Jie is a diligent and imaginative young man."

"Oh, I see." Shen Qi wrote a score on Chen Xin Jie's test paper: 63 points.

"Professor Shen is a very nice person." Xiao Tao smiled. If she were to give the final grade, Chen Xin Jie would probably fail the course.

"I used to be quite bad," Shen Qi said honestly. "In the early years, countless students failed under my tutelage. I used to think that the most important thing for people studying math and physics was talent, a perfect combination of imagination and rigorous logic. Students could skip my classes, as long as they could solve my problems, I would give them a very high score, even a perfect score."

Xiao Tao suddenly realized. "I heard that in one year, 73% of the students in the Physics Department failed the final exam for electrodynamics... Professor Shen, you set that exam, didn't you!"

Shen Qi said, "That electrodynamics exam was indeed quite difficult. Xiao Tao, you can't just look at the 73% who failed. Didn't 27% of the physics students in that year still pass?"

"I... I was a student in the Physics Department that year!" Xiao Tao said, sweating profusely.

"What a coincidence?" Shen Qi was quite surprised, and then asked, "Xiao Tao, what score did you get on that test?"

"59.5..." Xiao Tao looked pitiful, staring at Shen Qi, and asked, "Professor Shen, can you tell me now where that 0.5 point went? This is the first and only time I've ever failed a course, and I'm blaming it on you, Professor Shen. Professor Shen, you really were a bad person before..."

"Back then, Xiao Tao, you were a junior in college, and now you're a PhD student. It's been so long, I can't remember the details. Haha, that's not the point. Isn't the point today to discuss this Quantum Physics exam paper?" Shen Qi chuckled, earnestly advising Xiao Tao to let bygones be bygones and to live in the present.