Wednesday, October 28, 2009

The Law of Grading

Some while back I was sitting in E&M class and we were reviewing relativity. It was all stuff I had seen many many many times and so I was letting my mind wander. I started thinking about the tests that I had recently graded and thanks to the relativity background I came up with the following theorem.

The Law of Grading Efficiency:

Every impartial observer observes a grader to have a grading efficiency less than or equal to that observed by the grader.

Proof: Consider a grader with a stack of papers of height l0 who grades those papers in an amount of time t0 in the graders reference frame. Due to length contraction effects any observer who moves relative to the grader (for instance a passing professor) will observe the stack to be contracted along their direction of motion observing a length l < l0 and due to time dilation effects they will observe that it takes the grader an amount of time t > t0. So an observer in any frame will observe that the grader has less than or equal to the amount of work the grader thinks they have to do and observes that it takes the grader more than or equal to the amount of time to do the work that the grader thinks it takes. Thus the frame of reference which yields the maximum grading efficiency is the graders own reference frame.

Of course there was nothing in the analysis specific to the grading of papers so we obtain an immediate generalization.

The General Work Law:

The person doing the work always perceives the quantity of work they have to do to be greater than any other observer measures it to be and observes the time they have to do it in to be less than any other observer measures it to be.

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