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.

  • http://www.anthropic-principle.ORG island

    Then again, the uneasy balance that exists between opposing ideological belief systems clearly defines an anthropic coincidence that serves to keep us alive by preventing either side’s idea of what’s “good” from running-away unchecked, thereby killing us, so apparently nature has politicized us to our benefit… in spite of all of us.

    Now I’m gotta run… before I get hanged by a bunch of raving anti-global-warming fanatics… ;)

  • Lauren Gunderson

    Sean, once again you rock my world! I’m working a piece discussing the exploration of the American scientific identity through art and theatre (even throw your name down a time or two) and here you go with a poem.

    Awesome. I think i may have to write some play called 10 (^9).

    The secular humanist in me is always thrilled at the work of simply “thinking.” Keep thinking. If we figure it out, good for us. If not, its not in the structure of our brains to do so. Yehaw.

  • nigel cook

    Sean, the problem is that we have a pretty good idea what reality is, just as the critics of Copernicus, Galileo and Darwin knew that those people were crackpots because they knew that the Bible was the time-tested, authoritive account of reality. It is pretty obvious that the facts of reality will turn out to a bautiful mathematical theorem, a kind of Dirac equation or Einstein equation whose solutions will predict this hierarchy. You don’t want a causal mechanism which treats Yang-Mills exchange radiation as being real, and models the vacuum polarization as the physical basis for the attenuation of electromagnetic radiation in the renormalized charge range (IR to UV cutoffs) from a particle. You don’t even want to plot Standard Model force coupling strengths as a function of distance from the particle, preferring to keep referring to strengths as a function of collision energy between generic particles.

    What we want is an equation, a mathematical idea. We don’t want a physical model to underly that mathematical model, like an ugly machine. Ultimately nobody denies that the vacuum has properties – spacetime curvature is not widely sneered at, nor is the Dirac sea sneered at because it explains the Dirac equation and predicts antimatter. But don’t say either of these are real. The main problem with confusing a volume of space with the vacuum field is caused by cosmological expansion: is the Dirac sea itself expanding, or is merely volume between galaxies expanding?

    If the vacuum fabric or Dirac sea is expanding, forces depending on it (spacetime curvature gives gravity, acceleration) would become weaker with time, because the density of spacetime would fall. This is false.

    The real analogy seems to be that when you walk down a corridor, air doesn’t pile up in front of you. Nope, it moves around you and fills in the void you’d otherwise create behind you. I was thrown off physics forums for saying this, because you get cranks claiming that you are a crackpot, and that air doesn’t flow around you and instead the airpressure increases in front of you. Obviously, if you are going at supersonic speed, that’s true, you get a lot of air pressure. But for slow speeds, it’s true. That means, for the Dirac sea, that the recession of matter radially around us with speeds increasing in proportion to ‘apparent distance’ (time past is less ambiguous, because of spacetime) means that there is an inward motion of spacetime fabric of exactly equivalent motion and bulk to that of the matter going outward.

    This enables you to predict the strength of gravitation quite accurately. Of course, you then get told by Lubos Motl that string theory has already predicted G = G because string theory is the only consistent theory of quantum gravity, etc.

    The air pressure due to motion in the air itself has an analogy in the Dirac sea – causing Lorentz contraction in the direction of motion! The inward pressure towards a mass, causes the same type of contraction, explaining the contraction general relativity predicts (earth’s radius being contracted 1.5 mm by curvature).

    Now consider recession in the big bang. It is often said to be velocity increasing in proportion to distance outward. But that’s confused. We measure distances with rulers. If you had a massive ruler between galaxies, you wouldn’t be able from any one position to see the scale in real time: if you were at one end, the reading you would take looking to the other end would be an underestimate, because you would be seeing that at an earlier time. (Forget special relativity, and simply use the age of the universe as an absolute clock, by accurate measurement of Hubble’s parameter at each place. Crackpots will try to disprove this with obfuscation and ignorance, but just delete their moronic anti-scientific rants.)

    Therefore, you need to see recession velocities as varying linearly as a function of time past, not distances, which you can do by changing distance x into time t by the light travel time relation: t = x/c.

    This means that the recession effect is a kind of acceleration, since Hubble’s parameter then changes from v/x = H, into v/t = Hc, which has units acceleration (H has units of 1/time).

    The outward acceleration of matter is constant. Now Newton’s 2nd law suggests we can get outward force from this simply by multiplying that acceleration by amount of mass that is receding. Newton’s 3rd law then suggests that there should be an equal reaction force, which is going to be carried by the Dirac sea and will cause the curvature of geodesics.

    Of course this is all very ugly, heretical, etc. Physics today is a mathematical religion, and the people on the outside almost always are equally religious buy just believe that the big bang, Lorentz contraction, etc are all lies. You find that nobody really wants objectivity. They want to believe in physics as being a mathematical religion, or else they want to believe that the whole of mathematical physics is bunk, but in no case do they want to get involved with physical mechanism and making checkable predictions.

  • Mark

    Life is the ultimate practical joke, played by the universe on itself. How else could the inanimate matter of the universe understand that, in the long run, it is inanimate and will have no fun at all? But in the meantime, have some fun.

  • http://www.anthropic-principle.ORG island

    If the vacuum fabric or Dirac sea is expanding, forces depending on it would become weaker with time, because the density of spacetime would fall.

    Not if matter generation proportionally increases gravity, the electric force, and negative pressure.

    Get into a sealed jar and remove all of the pressure. Now, compress or condense some of the remaining “vapor pressure” until you attain the matter density over a finite region of space, and see what happens to the vacuum. If there is no containing force, then the vaccum expands as negative pressure increases.

    That’s what happens when you generate matter in what becomes a “quasi-static” version of Einstein’s static model, except expansion is offset by gravity and can’t runaway in this case. The anthropic balance is fixed and ***self regulating***, just like the rest of the anthropic coincidences.

    Hit your little knotted ball of the vacuum with a 1.2 MeV photon interaction to let Feynman seal the deal.

  • annulla

    Too bad about the lack of enthusiasm attached to Auden. To paraphrase Quentin Crisp, God save the memory of our nelly queens.

  • Lab Lemming

    “What we want is an equation, a mathematical idea. We don’t want a physical model to underly that mathematical model, like an ugly machine. ”

    Who is this “we”, theory boy? The joy of empirical observation is that every time we pin something down, it opens up more questions. Actually getting to an end would be very sad.

  • nigel cook

    Lab Lemming,

    Take Sean’s example of the ground state of hydrogen, 13.6 eV or so. Once you know that the Yang-Mills theory suggests electric and other forces are due to exchange of radiation, you know why there is a ground state (ie, why the electron doesn’t go converting its kinetic energy into radiation, and spiral into the hydrogen nucleus).

    The ground state energy level is the Yang-Mills corresponds to the equilibrium power the electron has radiate which balances the reception of Yang-Mills radiation with the emission of energy.

    The way Bohr should have analysed this was to first calculate the radiative power of an electron in the ground state using its acceleration, which is a = (v^2)/x. Here x = 5.29*10^{-11} m (see ) and the value of v is only c.alpha = c/137.

    Thus the appropriate (non-relativistic) radiation formula to use is: power P = (e^2)(a^2)/(6*Pi*Permittivity*c^3), where e is electron charge. The ground state hydrogen electron has an astronomical centripetal acceleration of a = 9.06*10^{22} m/s^2 and a radiative power of P = 4.68*10^{-8} Watts.

    That is the precise amount of background Yang-Mills power being received by electrons in order for the ground state of hydrogen to exist. The historic analogy for this concept is Prevost’s 1792 idea that constant temperature doesn’t correspond to no radiation of heat, but instead corresponds to a steady equilibrium (as much power radiated per second as received per second). This replaced the old Bohr-like Phlogiston and Caloric philosophies with two separate real, physical mechanisms for heat: radiation exchange and kinetic theory. (Of course, the Yang-Mills radiation determines charge and force-fields, not temperature, and the exchange bosons are not to be confused with photons of thermal radiation.)

    Although P = 4.68*10^{-8} Watts sounds small, remember that it is the power of just a single electron in orbit in the ground state, and when the electron undergoes a transition, the photon carries very little energy, so the equilibrium quickly establishes itself: the real photon of heat or light (a discontinuity or oscillation in the normally uniform Yang-Mills exchange progess) is emitted in a very small time!

    Take a photon of red light, which has a frequency of 4.5*10^{14} Hz. By Planck’s law, E = hf = 3.0*10^{-19} Joules. Hence the time taken for an electron with a ground state power of P = 4.68*10^{-8} to emit a photon of red light in falling back to the ground state from a suitably excited state will be only on the order of E/P = (3.0*10^{-19})/(4.68*10^{-8}) = 3.4*10^{-12} second.

  • Andy

    A quibble: the mass of the electron is about 511 keV, not 5 MeV.

  • Sean

    Stupid exponential notation. Thanks, fixed.

  • Shakti

    >Because we don’t yet fully understand the origin of these
    > fantastic hierarchies,

    Maybe Ken Wilson gave us a clue about them?

  • Joshua

    What about politicizing science in the interest of christianity?
    I might be disturbed by this if it wasn’t completely insane. Probably this sort of thing is actually quite common and I just don’t read the right blogs.

  • Robert Gagnon

    Yes Sean, you rock my world also. I found this piece via rss feeding to Google Reader and am happy that this technology is part of my thinking world.

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  • Lab Lemming

    While the math is very cool, the only reason that it is accepted is that somebody has actually measured the time that it takes for an electron to fall back to ground and radiate.

    I am continually amazed at how well equations can actually describe the universe- especially a universe that allows grad students. But observation is the only way to determine if the universe your equations are describing is the one in which we live.

  • nigel cook

    Lab lemming, that’s exactly why I calculated the emission time using that mechanism for the ground state using the radiating power of the electron in orbit! It is a check of the quantum mechanism with observations!

  • mollishka

    Aaand Sean gets a prize, though I’m not sure what exactly the prize is … I’ve been searching for the Perfect title for my blog, and “a geocentric view” is the clear winner. So thanks for the post :)

  • Sean

    Awesome. I’ll be sending you the number of a Swiss bank account in which you may deposit my prize.

  • Murali

    What we want the knowledge for? That has been a question haunting me for 30 years.
    What do you want to know more to know that you can not know?

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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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