BB #77: Smooth Spacetime

I read Three Roads to Quantum Gravity (2001), by Lee Smolin, a theoretical physicist whose thinking I’ve appreciated since I read his 2006 book, The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next.

Three Roads, as the title suggests, is about the efforts to reconcile quantum mechanics and General Relativity, our two best physical theories. String theory is one road, Loop Quantum Gravity (Smolin’s preferred approach) is another. The third road is complete theory reconstruction (such as discussed by Philip Ball in his book Beyond Weird).

None of that is the subject of this post.

What is the subject is that reading the book reminded me once again of an almost certainly lost dream: that spacetime is smooth.

I have no problem with energy/mass being quantized. The experimental evidence seems clear on that front, and quantization saves us from the ultraviolet catastrophe!

One issue is that Quantum Mechanics is a background dependent theory, and that background is, at least initially, Newton’s good old absolute 3D space and time. It’s quantum field theory that includes Special Relativity, although there are relativistic versions of some QM equations (for instance, of the Schrödinger equation).

In the other hand, General Relativity is a background independent theory — it defines the background. (As John Wheeler famously said about GR, “Spacetime tells matter how to move; matter tells spacetime how to curve.”) What makes GR even more incompatible with QM is that the background it defines is smooth, continuous.

Which sounds, at first blush, like at least something of a match. GR provides a (smooth) background for QM. Time and space are continuous; matter and energy are not. It’s just another duality in fundamental physics.


For a long time, that’s how I’ve hoped things would turn out to be once we figured out quantum gravity. Essentially I wanted Einstein to be more right than quantum mechanics (which has always seemed, at best, incomplete, at worst, just plain wrong). GR is an intuitive physical theory that makes sense. It’s a reasonable theory.

It’s a hard thing to test, because, not only don’t we have the technology (by many orders of magnitude) to test scales that small, we generally can’t foresee any such technology existing.

Despite some fairly strong arguments as to why spacetime has to be quantized, because the jury is so far out, I’ve been able to cling to the hope that Albert got this one right. (He did definitely blow it on the dice thing.)

But the utter failure to find dark matter particles, combined with MoND starting to find some parity experimentally, has weakened the iron-clad sense that GR has. Or had. (I am leaning more and more towards MoND, although maybe a better term is MoGR. Hard to pronounce, though. “moe-gur?”)


String theory, like QM, is background dependent, and like QM, it assumes that background is smooth. Still looking good for Al.

But Loop Quantum Gravity launches from GR principles and therefore is background independent. (Workers in the field tout that as a key reason LQG is better than ST.) More to the point, it’s a quantized background.

As the book is about Smolin’s work in LQG, he discusses this quite a bit, and it reminded me of my lost dream for smooth spacetime. It’s been a few years now, I realized, since I really held any hope for it.

Ah, well. Shows the power of strong argument. There’s still no evidence, no fact of the matter, but continuous spacetime just doesn’t seem as viable to me anymore. The argument for it amounts mostly to, “Maybe?” The arguments against it are pretty solid.


There is also that continuous space raises a number of issues, even within Newtonian physics. [See the John Baez paper: Struggles with the continuum.]

Lastly, I’ve begun to wonder if reality not being a continuum — not having infinite precision — doesn’t imply a non-deterministic universe.

So the reality is that there are plenty of good reasons to accept chunky spacetime. It solves a number of issues. (It was the main thing that drew me to string theory at first. Sadly, the enchantment didn’t last, and I still haven’t forgiven Brian Greene.)

Stay smooth, my friends! Go forth and spread beauty and light.

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

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