76.8 kilometers per second per megaparsec.

A megaparsec is about 30 million trillion kilometers, or perhaps better stated as 30 exameters. Given the significant figures, and the massive denominator, that makes this constant extremely precise. But is it accurate? Other measures using different methods come up with 74.03, 71.9, 69.8, and even 67.4.

We are talking about the Hubble constant, the rate of expansion of the universe. Edwin Hubble first proposed that the entire universe is expanding in 1929. This was based initially on observations by Harlow Shapley that other galaxies appear to be moving away from us. Their color is red-shifted from the doppler effect on the light coming to us from those galaxies. (As an aside, this applies to galaxies outside our local galaxy cluster, which are not uniformly moving away from us because we are gravitationally bound.) Hubble then made an extensive measure of the red shift of galaxies, and found that the farther away galaxies were, the more red shifted they were. This could be explained if the entire universe were expanding.

In 2011 three astrophysicists were awarded the Nobel prize for their discovery that, no only is the universe expanding, this expansion is accelerating. This means there must be an unknown force overcoming gravitational attraction and pushing everything apart – a force now called dark energy. But dark energy is not the mystery I am referring to in the title.

The mystery of the Hubble Constant is why different astronomers and different methods come up with different numbers? There are a few generic possibilities here – whenever different measurements disagree. It’s possible that the measurements themselves are simply inaccurate. This is always the first assumption and needs to be explored and ruled out before other explanations are seriously considered.

What generally happens is as more and more careful and thorough measurements are made, or the techniques or instrumentation are refined, the measurements start to converge on the real answer. Problem solved. However, that is not what is happening with the Hubble Constant. It is perhaps too early to tell for sure, but so far measurements have not been steadily converging. This, in fact, is essentially the mystery.

Another possibility is that the measurements are generally accurate, but different measurements are measuring different things. In the case of the Hubble constant, the question is – is every part of the universe expanding at the same rate? So, if we calculate the Hubble constant in one part of the universe, is it actually the same in another part? Perhaps the expansion is not uniform. We already know this is true due to the accelerated expansion – older parts of the universe (remember, farther away also means back in time) are not expanding as fast as younger parts. But what about independent of distance, just in different directions?

The third possibility is that expansion is uniform (except for the acceleration) but that the different methods used make different assumptions about the laws of physics, and one or more of those assumptions are not accurate. This is the most exciting possibility for physicists, because it points the way toward new discoveries about the laws of physics.

Let me give you an historical analogy. Early observations of the orbit of Mercury deviated from Newton’s laws of motion and Kepler’s laws of planetary motion. There were anomalies. So again the question was – are the measurements off, is there something present that we are not accounting for, or are the laws of physics different than we currently understand? As measurements became more precise, the anomalies persisted, eliminating that possibility. So some astronomers hypothesized that there was an unseen planet orbiting the sun, perhaps too close to the sun to directly observed, but its gravitational influence was distorting the orbit of Mercury. They named this hypothetical planet Vulcan, but Vulcan does not exist (except in Star Trek).

The answer turned out to be that the laws of physics were actually different. Newton’s mechanics were not wrong, they were just an approximation of the real laws of gravity later fleshed out by Einstein. When general relativity is taken into account, it precisely explains the orbit of Mercury. This, in fact, was one of the key confirmations of general relativity.

So astronomers today are hoping that the Hubble constant mystery will have a similar resolution.

Some of the methods used to measure the Hubble constant include measurements of Cepheid variables. These are stars that regularly fluctuate in brightness, and the period is determined by their absolute brightness. This means we can know exactly how bright a Cepheid variable is by its period, and then measure its apparent brightness and calculate exactly how far away they are. This is called a standard candle, and was the first method used for measuring distant stars in the universe.

The same principle is used with spiral galaxies, called the Tully-Fisher principle. The faster spiral galaxies are rotating, the intrinsically brighter they are. If you know the intrinsic brightness, and you can measure the apparent brightness, then again you can calculate the distance. Yet another standard candle is certain types of supernova – type Ia. They explode when they get to the same critical size, and so the explosions are all the same brightness, and voila – we can measure their distance.

Yet another method is using subtle variations in the cosmic microwave background radiation, which is the diffuse afterglow of the Big Bang. the CMB is not uniform, and we can tell a lot about the megastructure of the universe by looking for subtle variations in the CMB in different directions and distances.

These are the various methods used to measure Hubble’s constant. So now the trick is for astrophysicists to figure out where in their models of how all these things work are the assumptions that are not quite right. They are hoping this is not just imprecision in the measurements themselves. This is not all about the instruments. They want the problem to be in the laws of physics as we currently understand them, because then we would have a giant clue to help improve our understanding of those laws of physics.

Stay tuned.