Tonight I’m reading *From Eternity to Here* by Sean Carroll. It’s another of those books on physics and cosmology for the layperson — no math, just occasional diagrams. The book’s mandate or organizing principle is to attempt to unravel what time actually is. This is a fairly profound mystery, and Carroll seems well qualified to tackle it.

And yet, in his discussion we find odd lacunae. (Sorry; my erudition is showing. That’s Latin for “gaps.”) In Chapter 3 he discusses the Big Bang and the subsequent history of the universe. The current theory is not only that the universe started in a hot, dense form and has been expanding ever since, but that the expansion is speeding up. This is the opposite of what one would expect: Gravitational attraction, however tenuous it may be at vast distances, should be slowing the expansion.

Nobody really knows why the expansion is speeding up. The explanation, such as it is, rests on the concept of “dark energy,” a mysterious force that pushes galaxies gently away from one another.

On page 58, Carroll says this: “We don’t know much about dark energy, but we do know two very crucial things: It’s nearly constant throughout space (the same amount of energy from place to place), and also nearly constant in density through time (the same amount of energy per cubic centimeter at different times).”

Implicit in that rather remarkable sentence is the notion that we (meaning scientists) can *know* what is going on at places that are very distant (millions of light-years away) and very remote in time (billions of years ago). And how, you might well ask, can we be certain of such things?

The short answer is because distant galaxies are speeding away from us at higher than expected velocities. Ah, but how do we measure the speed of galaxies? The operative theory is this: When an object is traveling away from you, the light it emits is red-shifted. That is, the wavelengths get longer. This is the Doppler Effect, and it’s too well known to be worth explaining here. The red shift will tell us how fast a galaxy is receding from us, but it won’t tell us how far away the galaxy is. The distance is calibrated by observing Type I supernovae in the distant galaxies. The theory is that a supernova of this type always produces about the same amount of light. And that’s a great deal of light — an individual supernova can be seen across untold millions of light-years. By measuring the amount of light we’re seeing from a supernova, we can figure out how far away it must be. We then correlate that distance with the observed red shift of the galaxy where it’s located, and presto, we know that distant galaxies are speeding up.

But you’ll notice that this idea rests on two pillars of theory: first, that nothing other than the velocity relative to an Earth observer of that distant galaxy could cause a red-shift of its light; and second, that Type I supernovae were just as bright two billion years ago as they are today.

Both of these pillars rest, in turn, on the idea that the universe in distant places and at distant times was fundamentally the same, with respect to its physical laws, as it is in our neighborhood today. By that measure, what Carroll has said is a tautology. He’s saying, in essence, “We know that physical laws in distant places and at distant times have always been the same as they are here and now — and therefore, we can deduce that dark energy in distant places and at distant times has always been the same.”

What if the speed of light were increasing gradually over the course of billions of years? That would cause a red shift: Light that has been traveling for a long, long time would have started its journey at a slower speed. As the speed of light increases, the wavelengths will get longer. Just to be clear, this is only my pet theory, and there’s probably something horribly wrong with it that any grad student in the physics department could explain. I’m not that smart! The point I’m making is that the theory rests on an assumption, namely, that the speed of light has always been the same as it is today. And we can’t demonstrate that, because we’re only here today. We weren’t there two billion years ago.

I’m not a physicist. I don’t even try to tackle the books with the math. It’s entirely possible that Carroll is skipping some very solid experimental evidence in this book because he judges (correctly) that his readers won’t be equipped to understand it. But here again, as in other similar books I’ve read, I sometimes have the feeling that too much is being taken for granted. Is that a characteristic of the books, or is it a characteristic of contemporary physics itself? I don’t know.

Much of modern physics is based on mathematical models of phenomena. The observations that are made tend to be really quite tenuous. A quick trip down the aisle in your local library will present you with a handful of books that will tell you all about black holes, including the fact that there is a massive black hole at the center of our own galaxy. What is less often emphasized in these books is the fact that no human being has ever seen a black hole! Everything we know about them, or think we know, is based on mathematical models.

It is known that the mathematical models sometimes fail. On page 60, Carroll mentions one of the more spectacular failures. The theory being that perhaps the energy of virtual particles (quite possibly a real phenomenon, though not directly observable) is the source of dark energy, physicists have calculated the amount of “vacuum energy” that would arise from the froth of virtual particles. Unfortunately, the calculations show that this vacuum energy should be about 10 to the 105th power joules per cubic centimeter, when what is actually observed is a vacuum energy of about 10 to the *minus* 15 joules per cubic centimeter. (Don’t ask me what joules are; I don’t know. I know what a cubic centimeter is.) This is a discrepancy of 10 to the 120th power.

Clearly, there’s something wrong with the math, or more likely with the theory that the math attempts to explain. But the math that tells us how black holes must behave? Oh, yeah, we’ve got that one nailed down — right, Mr. Hawking?