Thanks for the kind words! I did actually see that article, when I googled to check that my memory about Fermilab’s connection to Chartres was correct.
I think our brains must have evolved to seek that little mindgasm we get when we make unexpected connections, and ideas suddenly come together.
In my electromagnetics class in college I learned about transmission lines and characteristic impedance. The latter was just a bunch of equations, and I never got an intuitive feel for it. But about 20 years ago I read a column in an electronics magazine which described characteristic impedance in a way that I finally understood it. This is more-or-less what he wrote:
Image a brand new, “50 Ω” coax cable that stretches from Earth to Pluto. On both Earth and Pluto, the end of the cable is an open circuit. Let’s also assume a lossless cable. The cable’s intrinsic impedance - 50 Ω - is solely due to its geometry and the dielectric constant of the dielectric.
Grab a meter that can measure DC resistance. I don’t care what kind of meter it is. It can be a handheld Fluke DMM, or even an old Simpson meter with the big analog meter.
Select the resistance function and measure the resistance of the coax cable. What will the meter read?
Will it read infinite resistance (open circuit), as some people claim? After all, the material used for the dielectric in the cable has infinite resistivity.
Nope. The meter will read 50 Ω. And it will continue to read 50 Ω for about 13 hours. After 13 hours, the resistance will start climbing. After a week or two the resistance reading will be very high. Eventually the resistance will go to infinity.
Why does this happen?
Even though the coax cable is not a resistor, it fools the meter into thinking it is a resistor.
The meter simply sources a DC current and measures the resulting DC voltage. The distributed series inductance and distributed parallel capacitance in the cable is constantly being “charged up” by the current produced by the meter. For 13 hours, the meter sources a continuous current between the cable’s center conductor and shield. This results in a continuous voltage showing up across the end of the coax cable (the meter’s end, not Pluto’s end) due to “new” inductors and capacitors that are constantly “showing up” down the cable. (The current-voltage wave moves at roughly 0.7C.)
During those 13 hours, both the voltage and the current will be constant. (The current, of course, will be constant, since the meter produces a constant current. But the resulting voltage across the cable will also be constant.) And again, this is due to the distributed series inductance and distributed parallel capacitance in the cable constantly being “charged up” down the cable. If the meter produced a constant current of 1 mA DC, the resulting voltage across the coax cable would be a nice, steady, flat 50 mV DC for 13 hours, and the meter would display 50 Ω.
So we say the cable has a characteristic impedance of 50 Ω.
Funnily enough, it was this little scene in Young Einstein that made the relationship between the speed of light and time click.
Einstein explains relativity:
