The Great Puzzle of Why the Sun Rose This Morning: Part 2

You may remember I wrote a couple of months ago about a strange conundrum regarding time. I mentioned this post on a number of lists I belong to, hoping that someone with a better grasp of physics than I would be able to explain it to me. I got many, many responses but, sadly, not one seemed to understand what the issue was and the great majority assumed I just needed a quick primer in special relativity (and then proceeded to give me one, often in a most garbled and peculiar way.) Most people were genuinely interested and tried to be helpful. However, one idiot, on a list I didn't even post to, became quite abusive and accused me of inventing a load of nonsense about relativity in order to make more sales of my book! (Now, how would that work, exactly?) He also threw in a garbled account of special relativity, just to be sure I understood what a genius he was.

It was quite a depressing experience all round.

I have been reading more on the subject since then and I think I have actually found the answer. Gratifyingly enough, the answer is almost exactly the one I came up with. In the language of relativity it is couched in much different terms, however, but I believe it amounts to the same thing.

The conundrum is this: even though time passes at different rates for different frames of reference, we do not experience objects moving in and out of existence as our relative positions in time change. I gave the example of the Sun, which, having a much larger mass than the Earth, should be aging ever so slightly more slowly. In fact, over the 4.5 billion year life of the solar system. the Earth should be 71 years older than the Sun. So why aren't we in the Sun's future? Why is the Sun here with us in this moment in time?

The answer, I suggested, was that we do, in fact, all move at the same rate through time, which would mean that time dilation is something analagous to the way the frequency of light changes depending on the relative velocity of its source. As it turns out, I shouldn't have been talking about space and time separately but about spacetime. Because, as it happens, we are all moving at exactly the same rate through spacetime. When we use spacetime metrics instead of the metrics of space and time, it appears that everything in the Universe is moving at exactly the same rate. That light has a constant velocity is a corollary of this. Light having no mass, there is no time dimension to its motion in spacetime, it must therefore always appear to be moving through space at the maximum velocity possible. Time dilation, under this view, is simply an effect of the projection onto space and time of a spacetime 'velocity' for objects having significant relative speed or mass (or acceleration). All the space and time components as well as mass/acceleration are traded off against one another to maintain a constant spacetime motion. Time can therefore appear to be 'red shifted', in the terminology I made up, for exactly the same geometrical reasons that light appears to be.

And we're all together here and now in spacetime. That's why the Sun keeps coming up in the morning!

Aren't you glad I got that sorted out?

Review: Why Does E=mc2? (And Why Should We Care?) by Brian Cox and Jeff Forshaw

(This review first appeared in the New York Journal of Books on 13th July 2010.)

Why Does E=mc2? is one of those questions that educated non-physicists must have been asking themselves for over a hundred years, ever since Albert Einstein derived the equation back in 1905. Now, in this easy-to-read little book from Brian Cox and Jeff Forshaw, we have the answer. The authors are both professors of physics at Manchester University, and Brian Cox is also a well-known TV personality—well known enough to warrant a jacket blurb from Stephen Fry.

The book begins with the traditional approach to explaining the slowing of clocks for observers in motion relative to one another, by examining the geometry of a light beam bouncing up and down in a moving vehicle. The authors demonstrate just how easy it is to get to Einstein’s time dilation formula using nothing more than Pythagoras’ Theorem and the knowledge that the speed of light is capped. But they don’t leave it there. In the first half of the book they consider two more approaches that lead us to the same conclusion. 

Along the way, they very cleverly introduce all the ideas we will need to get to the world’s most famous equation, E=mc². What is more, they focus on the most puzzling part: the question of what c, the speed of light, is doing in there. Very early on, they introduce c as a scaling factor so that we can talk about “distances” in spacetime. Later, by various means, they explain why c has to be the maximum speed that anything can travel. It is a small triumph of the book that Cox and Forshaw make the attempt to show the logical necessity of there being a universal speed limit, and that their arguments are presented so clearly.

Yet, as with any book of this size tackling a subject so enormous, it is not long before the authors start asking us to take things on trust, undermining the comprehensibility of their presentation. The first big one is when they introduce Maxwell’s equations and ask us to believe they demand that the rate of propagation of an electromagnetic field be constant for all observers. Then comes the work of mathematician Emmy Noether and her demonstration that invariance leads to the conservation of quantities. 

These, and many others introduced later, are tough ideas and hard to swallow. The authors introduce them to provide alternative ways into the understanding of relativity and that famous equation. It is to their credit that they do not always hide the complexity nor the long history of ideas behind relativity, but it would have been better, perhaps, to have spent a few more pages on some of these notions. It is also to their credit that they make the case, as Feynman and others have done before them, that, at some level, the weirdness of the universe just has to be accepted, and the only test of physical theories that matters a damn is whether they are supported by actual observation and experiment.

And there would have been many pages to spare for additional background and explanation if, near the end, the book had not wandered into obscure and largely unrelated areas as it tackled a broad-brush description of the Standard Model in an attempt to explain what mass is. It was inevitable that some particle physics had to be discussed and that this would lead to discussions of quantum theory. After all, the book’s sub-title is And Why Should We Care? and the reasons given largely involve nuclear power, chemistry, and cosmology—all of which are helped by discussions at a subatomic level. Perhaps also Brian Cox’s involvement at CERN (he heads a project there to upgrade the ATLAS and CMS detectors for the Large Hadron Collider) meant that a discussion of the Higgs particle was inevitable. Nevertheless, this, and the very brief glimpse of general relativity right at the end, seemed to detract from the clarity and force of the earlier exposition.

It is a curious book that tackles several of the most difficult ideas in modern science in the tone of a friendly, almost patronizing, high-school teacher, trying to ensure that the slow kids manage to keep up with the rest of the class. The tone and the endless asides (did you know that the Sun converts 600 million tonnes of hydrogen into helium every second?) can become a bit wearing, but Cox and Forshaw have to be praised for their unwavering insistence that their subject is accessible to anyone at all who will stay with them and think about it.

In an age when most lay people throw up their hands at the mention of relativity or quantum theory, when religious creation stories and New Age mysticism offer a far simpler, less challenging route for the intellectually overwhelmed, it is hugely important that ordinary people see that physics is not just for the egg-heads, that it can be understood, and that there is a grand beauty in what it reveals about our world. Cox and Forshaw have made an important contribution in this area, one that will help school science teachers as much as it will their students.