Back In The Day

A crazy story I discuss each year to 1000+ astro/physics students involves black holes and my youth. I've been giving dieses spiel for 25 years. This semester, because of distance-learning, was not able to do it live (without a net); had to put it into words and pictures >

In the comparison of Kerr black holes and Schwarzschild black holes, from general relativity, we sketch the geometrized Kerr outer event horizon “r+ = m + Sqrt[m^2 – ξ^2]”. The Kerr has level-splitting of the event horizon due to the scaled angular momentum, ξ = j/m. Nonetheless (in other words, ignore everything I just said), for either black hole, the event horizon physically acts as a one-way door. Anything that flows past it, can never get back out. The reason, the escape velocity below the event horizon exceeds light-speed. Kind of like the hotels in California, "we are programmed to receive, you can check out any time you like -- but you can never leave". Think of it as the ultimate "paper shredder". Anything that you want to get rid of, just throw it in a black hole.

So going back to the spring of my last year in high school in #Choteau Montana. We decided to have a big party in one of our senior classes, to celebrate the end of our high school years. Ten of us were in this course: Buddy, Dave, John, Kim, Monica, Schuyler, Ted, Todd, Vance, myself, and our fabulous teacher, Mr. Kamrud.

We planned that each person would bring various items to the party. We wanted this to be a really great party, all kinds of neat food, even decorations for the classroom. A list of the needed items was assembled. One of us would supply the pop (2-liters Coke and Diet Coke). Others were going to bring potato chips, Chex Mix, Ding Dongs, Fritos, etc. Another was bringing veggie sticks and dip. I would provide lefse. Somebody thought we needed cherry Nibs. And another wanted to bring TV dinners (my skin is turnin’ red). Other snack foods had not been discovered — life in a northern town, of rural Montana. Of course in college, I learned about a damn good snack: garlic-cheese bread during “fluids lab” @thecoug_ .

One of us, who was really into cooking at the time, was going to bake a batch of cookies and bring those. So the next day we come into class and start setting up the plates, napkins, cups, decorations, and we next lay the food out on the table. Then most of us took a seat, I sat up front in this class. But the person that baked the cookies was really excited to tell us that they were from a fantastic recipe and they even brought the recipe card to show us. This person thought it would be neat if someone "test tasted" the cookies first to tell the others how great they are.

Since I was up front, a cookie was placed on my plate and the person asks me to eat it. So I pick it up and start eating it, but right away I knew something wrong -- the cookie sucked all the moisture out of my mouth. I immediately needed a drink, so I motioned for a Coke. Meanwhile, I was trying to eat it and smile, and act like it was a great cookie. It wasn't, it was terrible; it had too much of something in it. And I did not know what something was. Anyway, after I was done choking it down, I asked if I could have the recipe card. And the person said, “What are you going to do with it?" And I said, "I'll be searching for the nearest event horizon!"

Even though the story ends here, the full details are more involved. Today, we are certain that after I throw the "bad recipe" card into a black hole, it is not gone forever. If it was, it would violate quantum mechanics. And quantum mechanics is more fundamental than Einstein's general relativity (which is not quantum). The apparent conflict between general relativity (which describes black holes) and quantum mechanics (which describes matter at the subatomic level) involving a recipe card (or in general, any information) falling into a black hole is called the "Black Hole Information Paradox".

The genesis of the paradox can be traced back to Stephen Hawking, when he convinced himself (along with others) that thermodynamics in conjunction with the no-hair theorem predicted that information would be lost forever in the black hole. This annoyed quantum theorists, and in particular, one of them -- John Preskill, bet Hawking in the late '90s that information would not be lost forever in the black hole. Today, no high-energy particle theorist accepts the idea that a lowdown classical theory, like Einstein's general relativity, usurps the laws of quantum physics.

The reason for the violation of quantum mechanics, hinges on the principle of unitarity. In short, unitarity requires that information be conserved. This is because the time-dependent transformation of the wave function (ψ, which has the bad recipe card encoded in it), is uniquely determined by the evolution operator. And the evolution operator has an inverse, meaning the entire history of the wave function (Copenhagen interpretation) is unique (forward in time and backward in time). Therefore, in a nutshell: If we carefully analyze the event horizon of the black hole and the Hawking radiation that flows from the event horizon, we should be able to fully reconstruct the bad recipe card (2nd image). The cookie recipe lives on forever.


Notes: Spinless Kerr: ξ = 0, thus r+ = 2m. For MKS units, applying our mass-to-distance conversion factor, G/c^2, we find r+ = 2Gm/c^2 which is the Schwarzschild radius. Furthermore, the radical yields an upper limit on the angular momentum: Sqrt[m^2 – ξ^2] cannot be imaginary. Hence j = m^2, applying conversion factor G/c, yields m^2 G/c as the maximum angular momentum for a Kerr, in MKS units of kg•m^2/s. What, a black hole can only spin so fast!? Yes. (Note due to its electrical charge, the Kerr-Newman black hole would have an even smaller maximum angular momentum.) The extraction of information from a black hole suggests that a better name would be a "gray hole".

About Me

Most recent research is in the area of MOdified Newtonian Dynamics (MOND):

Previous: Quantum Field Theory of Massless Neutrinos Propagating in Neutron Backgrounds:

Dr. Brian Woodahl
Senior Lecturer of Physics, Indiana University - Indianapolis
PhD Theoretical Physics [ Quantum Field Theory ], Purdue University
MS Mechanical Engineering, Purdue University
BS Electrical Engineering, Washington State University


+1 317-278-9244