Hooray for Bad Astronomy

Comments have been sparse lately, but yet another discussion thread has appeared on the Bad Astronomy/Universe Today forum. Non-members can not leave comments there, but let us hope that this and other discussions stay civil.

To answer one question: "von Riemann" is a pun in German, meaning that the theory is from Riemann. If Riemann has his own Universe, he deserves "von" in front of his name.

Here's a fun question: How much potential energy does your pen have? In physics class we learn Newton's formula:

Eu = -GMm/r

Where Eu is potential energy, M is the mass of a larger object, usually Earth. m is the pen's mass, and r is the distance between masses.

Usually we measure the pen's energy from Earth, but the pen has more potential from the Sun. The pen doesn't fall toward the Sun because it shares Earth's orbital velocity. The pen has even more potential from the galaxy and everything else in the Universe. The pen's true potential should be:

Eu = -$\Sigma$ GMm/r

The $\Sigma$ sums the potential from every other mass in the Universe! How do we solve this? Fortunately, on large scales the Universe is a spherical mass distribution. We can write:

Eu = -GMm/R

Here M is total mass of the Universe, and R is distance to the centre of that mass.

There is no centre in Space, for every bit resembles every other bit. There is a centre in time, what we call a "Big Bang." Near that centre, mass M occupied a tiny volume. Now these things are known:

R = ct

GM = tc^3

Eu = -GMm/R = -(tc^3)m/(ct)

Eu = -mc^2

Does anyone doubt this E = mc^2 business? When it was first written in 1905, few paid attention. A century later everyone has heard of this equation, even if they don't understand it.

To avoid confusion, we will call E the Einstein energy and rename Eu as U, the Newton energy:

E + U = 0

The total energy of the pen is just zero! That applies for any object, from the tiniest particle to the biggest Black Hole. The total energy of the Universe is zero! It's the ultimate free lunch, which has allowed it to evolve from a tiny point to the immensity we observe today.

Best wishes to Praedst and other contributors. Followers on the Bad Astronomy/Universe Today are welcome to leave their questions here.

UPDATE: Following Ethan's lead, they seem to have become stuck on the Oklo Reactor. Oklo did not measure c, but the fine-structure constant proportional to product hc. This product is also part of the photon energy hc/$\lambda$ and the Chandrasekhar mass. If c decreases with time, h must increase inversely. They may be about to miss the chance of linking quantum mechanics with Relativity and gaining scientific immortality. This has been dealt with before, see Constraining Theories of the Speed of Light.