In high school, we said that an object on the ground has zero gravitational ener…

In high school, we said that an object on the ground has zero gravitational energy, while an object above the ground has some. But if a hole opened up in the floor, the object on the ground would fall – so it must have SOME potential energy, right? At the center of the earth, would you have no gravitational potential energy? If not, why – doesn’t the sun still pull on you?

You’ve brought up an interesting subject. Many quantities in physics are only well defined relative to some reference point. For example, your velocity is only defined relative to some reference frame; typically the earth’s rest frame. Viewed from a different reference frame, your velocity will be different. The same holds for gravitational potential energy. When you choose to define the object’s gravitational potential energy on the floor as zero, you are setting the scale with which to work. For altitudes above the floor, the object’s gravitational potential energy is positive, but for altitudes below the floor, that energy is negative. As the ball falls into the hole, its gravitational energy becomes more and more negative and its kinetic energy increases. To avoid working with these annoying negative potential energies, you should choose to set the gravitational potential energy to zero at the lowest point you’ll ever have to deal with; for example, the center of the earth. But the center of the earth isn’t really the limit of gravitational potential energy. The object could release even more gravitational potential energy by falling into the center of the sun. It could release still more by falling into the center of a giant star. Fortunately, there is a genuine limit. If you were to lower the object slowly into a black hole, the object would release absolutely all of its gravitational potential energy. In fact, it would release energy equal to its mass times the speed of light squared (the famous E=mc2 equation of Einstein). The object would actually cease to exist, having been converted entirely into energy (the work done on you as you lower the object, presumably at the end of a very sturdy rope). This effect sets a real value of zero for the gravitational potential energy of an object: the point at which the object ceases to exist altogether. Final note: if you drop something into a black hole, it doesn’t vanish the same way, because its gravitational potential energy becomes kinetic energy as it enters the black hole. The black hole retains that energy and grows slightly larger as a result. When you lower the object on a rope, you retain its energy and it doesn’t remain with the black hole. The black hole doesn’t change as it “consumes” the object.

Is there a relationship between the black hole and the point of origin of the un…

Is there a relationship between the black hole and the point of origin of the universe?

Yes and no. Both involve lots of mass in a very small space. A black hole is a very strange region of space-time, where time runs slowly and the gravity is extraordinarily intense. Around the black hole, everything is swept inward through the hole’s surface. But (as best I understand it) the early universe didn’t necessarily have strong gravity. With mass uniformly distributed in the tiny, compact universe, an object felt gravity pulling it equally in all directions. There was as much mass to the left of the object as to its right. Thus the object would have been roughly weightless. With no gravity to make things lump together into galaxies, stars, and planets, there was no reason for those celestial objects to form. Why they did form is one of the great questions of modern cosmology. As for the universe’s character at the very moment of creation, I don’t think that anyone has a clear picture of what was happening. The very nature of space-time was probably all messed up and the theories needed to understand it don’t yet exist.

What information is now available about magnetic fields and free radicals in our…

What information is now available about magnetic fields and free radicals in our bodies?

Free radicals are molecular fragments with unpaired electrons. The organic molecules in our bodies are normally held together by covalent bonds, an arrangement in which a pair of electrons orbits between and around two atoms in a manner that reduces the total energy of the atoms and thus binds the two atoms together. When only one electron is orbiting an atom by itself, it is chemically aggressive and tends to attack other molecules. That electron is also magnetic and is influenced a tiny bit by surrounding magnetic fields. My guess is that the magnetic fields you normally encounter, whether they are due to the earth’s magnetic field, or to nearby power lines, or even to strong magnets such as those used in magnetic resonance imaging, have very little influence over the chemistry of free radicals in your body. Free radicals are themselves a health issue, but I don’t think that magnetic fields make free radicals any more or less hazardous. If I learn more about this issue, I’ll add it here.