
Figure 1 – The White Rabbit or The March Hare (c) DE Wolf 2025
As I mentioned last week I spent the weekend in Newburyport, MA and on Plum Island. I took the image of Figure 1 in a shop. I was drawn to the White Rabbit in remembrance of Mr. White Rabbit, Esq. or the March Hare of Lewis Carrol’s Alice in Wonderland fame. Some of my readers had requested a break from Astrophotography and Astrophysics. That’s fine but one is never truly on vacation from physics – never more than a hare’s breadth away!
“… nor did Alice think it so very much out of the way to hear the Rabbit say to itself, “Oh dear! Oh dear! I shall be late!” (when she thought it over afterwards, it occurred to her that she ought to have wondered at this, but at the time it all seemed quite natural); but when the Rabbit actually took a watch out of its waistcoat-pocket, and looked at it, and then hurried on, Alice started to her feet, for it flashed across her mind that she had never before seen a rabbit with either a waistcoat-pocket, or a watch to take out of it, and burning with curiosity, she ran across the field after it, and fortunately was just in time to see it pop down a large rabbit-hole under the hedge.
In another moment down went Alice after it, never once considering how in the world she was to get out again.”
Thus begins Alice’s singular and most peculiar adventure. Poor Alice, she hasn’t really escaped physics but actually jumped right into it, so to speak. Of course, the rabbit represents the constrictions of our human world, where everything is on a tight schedule. We are told that “everyone is mad here” in Wonderland, and you very quickly start to wonder where it is that everyone is mad? Now more than a century and a half since Carrol penned the book we know about Einstein’s Theory of Relativity and the fact that the time here and now can be quite different there and now and that two simultaneous events here are not necessarily simultaneous there. Poor March Hare his pocket watch has become quite useless, or perhaps more accurately quite meaningless. Time and simultaneity have become quite meaningless in this non-Euclidian universe. While not often used in a anti-theological way, the facts of relativity make a strong case for a rational universe!
Anyway, dear Alice is in free fall along with the March Hare. Rabbit is worried about the time and Alice is just starting to understand the gravity of her situation. GRAVITY! Johann Carl Friedrich Gauss (1777-1855) explained that the force of gravity acting on an object, say an Alice or a Rabbit, is proportional to the volume of matter contained withing a sphere at some position in space. This means that while the force of gravity at the surface of the Earth is greatest and the force at the center of the Earth is zero. Therefore, if you were to drill a channel along a diameter through the center of the Earth, the object reaches the center at maximum velocity, starts its return journey, on the other side, only to reach zero velocity when it reaches the surface of the Earth on the other side. Ignoring the mathematics, it can readily be shown that it takes 42.25 min to reach the center. The object is a classical oscillator, going back and forth forever every 84.50 min.
We’ve ignored a few things here, like the crushing pressure, friction in the air column, and scalding temperatures. Mere technicalities!
But things get even more interesting. Suppose you were to drill a tunnel along a chord through the Earth between any two points on its surface, say between London and Paris, or between Paris and New York. If you had a frictionless railroad (that’s mighty good oil!), it would take precisely 82.5 min for the railroad to go between any two destination points!
Now this is of course all fantasy – as was the story of Alice in Wonderland. But it has been suggested that this mathematical paradox was in mathematician Lewis Carrol’s mind when he wrote the story of Alice ,
“A paradox, a paradox
A most ingenious paradox.”
Gilbert and Sullivan the Pirates of Penzance
I apologize for returning us, on vacation, to astrophysics. But it always comes to my mind whenever I see a rabbit resembling the March Hare; rabbits, hares for that matter, do not wear glasses nor pocket watches. Little girls do not float endlessly to soft landings in Wonderland. Still the world, indeed the universe, is filled with what might seem the paradoxical. Such is merely the reflection of the facts that the world is not flat nor time not relative.