After Reading a Child's Guide to Modern Physics

By Sean Carroll | November 1, 2006 11:49 am

Abbas at 3 Quarks reminds us that next year is W.H. Auden’s centenary (and that Britain is curiously unenthusiastic about celebrating the event). The BBC allows you to hear Auden read this poem at a 1965 festival; his father was a physicist.

If all a top physicist knows
About the Truth be true,
Then, for all the so-and-so’s,
Futility and grime,
Our common world contains,
We have a better time
Than the Greater Nebulae do,
Or the atoms in our brains.

Marriage is rarely bliss
But, surely it would be worse
As particles to pelt
At thousands of miles per sec
About a universe
Wherein a lover’s kiss
Would either not be felt
Or break the loved one’s neck.

Though the face at which I stare
While shaving it be cruel
For, year after year, it repels
An ageing suitor, it has,
Thank God, sufficient mass
To be altogether there,
Not an indeterminate gruel
Which is partly somewhere else.

Our eyes prefer to suppose
That a habitable place
Has a geocentric view,
That architects enclose
A quiet Euclidian space:
Exploded myths – but who
Could feel at home astraddle
An ever expanding saddle?

This passion of our kind
For the process of finding out
Is a fact one can hardly doubt,
But I would rejoice in it more
If I knew more clearly what
We wanted the knowledge for,
Felt certain still that the mind
Is free to know or not.

It has chosen once, it seems,
And whether our concern
For magnitude’s extremes
Really become a creature
Who comes in a median size,
Or politicizing Nature
Be altogether wise,
Is something we shall learn.

Ol’ Wystan is right; we do have a better time than most of the universe. It would be no fun to constantly worry that “a lover’s kiss / Would either not be felt / Or break the loved one’s neck.” And in a sense, it’s surprising (one might almost say unnatural) that our local conditions allow for the build-up of the delicate complexity necessary to nurture passion and poetry among we creatures of median size.

In most physical systems, we can get a pretty good idea of the relevant scales of length and time just by using dimensional analysis. If you have some fundamental timescale governing the behavior of a system, you naturally expect most processes characteristic of that system to happen on approximately that timescale, give or take an order of magnitude here or there. But our universe doesn’t work that way at all — there are dramatic balancing acts that stretch the relevant timescales far past their natural values. In the absence of any fine-tunings, the relevant timescale for the universe would be the Planck time, 10-44 seconds, whereas the actual age of the universe is more like 1018 seconds. This is actually two problems in one: why doesn’t the vacuum energy rapidly dominate over the energy density in matter and radiation — the cosmological constant problem — and, imagining that we’ve solved that one, why doesn’t spatial curvature dominate over all the energy density — the flatness problem. It would be much more “natural,” in other words, to live in either a cold and empty universe, or one that recollapsed in a jiffy.

But given that the universe does linger around, it’s still a surprise that the matter within it exhibits interesting dynamics on timescales much longer than the Planck time. A human lifespan, for example, is about 109 seconds. The human/Planck hierarchy actually owes its existence to a multi-layered series of hierarchies. First, the characteristic energy scale of particle physics is set by electroweak symmetry breaking to be about 1011 electron volts, far below the Planck energy at 1027 electron volts. (That’s known to particle physicists as “the” hierarchy problem.) And then the mass of the electron (me ~ 5 x 105 electron volts) is smaller than it really should be, as it is suppressed with respect to the electroweak scale by a Yukawa coupling of about 10-6. But then the weakness of the electromagnetic interaction, as manifested in the small value of the fine-structure constant α = 1/137, implies that the Rydberg (which sets the scales for atomic physics) is even lower than that:

Ry ~ α2 me ~ 10 electron volts.

This energy corresponds to timescales (by inserting appropriate factors of Planck’s constant and the speed of light) of about 10-18 seconds; much longer than the Planck time, but still much shorter than a human lifetime. The cascade of hierarchies continues; molecular binding energies are typically much smaller than a Rydberg, the timescales characteristic of mesocopic collections of slowly-moving molecules are correspondingly longer still, etc.

Because we don’t yet fully understand the origin of these fantastic hierarchies, we can conclude that God exists. Okay, no we can’t. Really we can conclude that we live in a multiverse in which all of the constants of nature take on different values in different places. Okay, we can’t actually conclude that either. What we can do is keep thinking about it, not jumping to too many conclusions while we try to fill one of those pesky “gaps” in our understanding that people like to insist must be evidence for their personal favorite story of reality.

But “politicizing Nature,” now that’s just bad. Not altogether wise at all.


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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