“I understand why you are a Nobel laureate, yet none of the students quite believe that a Nobel laureate would make time for them. Might it be possible to come by your office to snap a quick picture of you and me, perhaps with a note on a white board behind us that says something like, “John Curtis geometry students- stick with your research on the Planck Length and the five platonic solids! You may find something important. – Frank”
After the visit, I wrote and said,
“I have yet to meet with the students, but I am sure that they will join me in saying, “Thank you for the encouragement! We’ll study more about the Planck constant, the Planck Length and the Planck time.”
“I am quite eager to work up a curriculum for these students using your writings as the backdrop for discussions and further explorations. I told them, “We may get to to be known as Wilczekians and Planck aficionados.”
What is the Planck Length? Frank Wilczek says:
“The Planck length, formally, is a combination of fundamental constants that has dimensions of a length. I discussed this in some depth in the enclosed pieces. Perhaps the most physical interpretation emerged many years after Planck’s original numerology.
“It is as follows:
“In quantum mechanics, all dynamical variables fluctuate. Thus for example there is no sense in which a particle can have a definite position and momentum at the same time (uncertainty principle).
“In general relativity, the geometry of space-time is a dynamical variable. Space-time can be bent by energy and momentum; in fact that is how we account for gravity.
Putting these two together: the geometry of space-time fluctuates.
“Now you can ask when the fluctuations in distance between two points becomes comparable to the distance itself. It turns out this occurs at distances approaching the Planck length.
“I should emphasize that the Planck length is not a substance or law, just a rough concept. So for example twice or half the Planck length would be just as good as the Planck length itself, as a concept — it’s basically a matter of convention which you use.”