Relativity Homework

A busy weekend, so here is some weekend thoughts (and associated reading) for you. It's all to do with relativity and are linked with some blog posts.

Time does not flow: To paraphrase Shakespeare, All the world is a 4D manifold, and all its players are but worldlines. Basically, General Relativity tells us that the Universe is a 4D canvas and our paths are traced out. It's all there, past, present and future (from any individual's perspective). The Universe does not unfold as we progress into the future. It's all already written out (like a path on a map). Enter the philosophers and discussions on freewill, but taking relativity at face-value, there isn't any. Heck, it doesn't even tell us which direction our experience of time flows in, we set that with a decision on dt/dτ.

Energy is not conserved: In general, energy is not conserved in General Relativity. This one usually freaks out the students, but it caused Einstein a whole host of headaches as well. When the Universe expends, photons are redshifted. They "lose energy". Where does this energy go? You can do some groovy handwaving and say "into curvature", but the answer is "Don't worry about it, energy is not conserved".

Space does not expand: This is one I have been involved with for a long time, and, again, it freaks people out, especially with the wealth of popular science and textbooks that talk about expanding space. You have to be careful here, and a paper I wrote a number of years ago now, Expanding Space: the Root of all Evil?, discusses this in some detail. It comes as a shock to students of relativity to realise that, almost a hundred years after the discovery of the expanding Universe, that the meaning of the expansion is still a matter of debate. I'll close this with a quote from Steven Weinberg and Martin Rees, reported in New Scientist a few years ago;
Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space, which is utterly empty, to expand? How can ‘nothing’ expand?
“Good question,” says Weinberg. “The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.” Rees agrees wholeheartedly. “Expanding space is a very unhelpful concept,” he says. “Think of the Universe in a Newtonian way – that is simply, in terms of galaxies exploding away from each other.”


  1. I agree with you on 2 and 3; not sure about 1.

    "Once you can accept the universe as matter expanding into nothing that is something, wearing stripes with plaid comes easy."

    ---Albert Einstein


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