Monday, January 21, 2008

We might really be exactly midscale

kw: musings, physical universe, sizes

As I prepared to review Mind, Life, and Universe, I spent a bit of time poring over a table that showed the Human size as just midway between the largest and smallest physical things, from quarks to galaxies. A few steps were missing, so I decided to produce my own table. First, some background.

The smallest dimension possible according to quantum mechanics is the Planck Length, 1.616252x10-35 meters. However, it is unlikely that anything will ever be measured to a precision in this range, because you have to use a probe with a wavelength in this range to "see" such details. For example, microscopes using visible light cannot show us details smaller than about half the wavelength of the light being used. Electron microscopes show us much smaller details because the wavelength is much smaller.

The trouble is that shorter wavelength implies higher energy. The proportionality constant I remember from classes in X-ray spectroscopy is 1,240 eV-nm; a particle having one electron volt (1 eV) of energy will have a wavelength of 1,240nm, or 1.24µm. Such a particle might be an infrared photon. Visible light, with wavelengths of 0.4µm to 0.7µm, is composed of photons with energies between 1.77eV and 3.10eV.

A "million-volt" electron microscope (such a machine was first touted to the public in newspaper stories in about 1960) produces electrons having a wavelength near 0.00124nm, about 100 times smaller than the diameter of an iron atom. However, it is hard to focus them that accurately, and atoms weren’t imaged until twenty years later. Also, such energetic electrons tend to knock orbital electrons out of your sample, so the target gets modified about as quickly as you can make the image: electrons running loose cause chemical changes.

The most energetic particle ever observed is called "Omigod " or the "Oh-my-God " particle, a cosmic ray observed in 1991 that had an energy equivalent to a well-thrown baseball, or a few million times as energetic as the particles the Large Hadron Collider will be producing later this year. If we could produce such particles regularly, we could probe a size scale a billion times smaller than a proton, but only by breaking that proton into skajillions of tiny pieces in the process! So I pick this particle’s wavelength as the smallest "practical" size.

At the large end of things, our best telescopes will never see deeper than about 13 billion light-years, because the Universe is only about 13 billion years old; there is no older light to show us farther things, even though cosmologists think the actual "size" of the Universe is between a few hundred billion to several trillion light-years. It will be a long time before any large portion of it becomes visible!

Each Step in the table below is a factor of 1,000 in size. (In the West, this is the Engineering scale convention; in Japan, they have a word for 10,000 and tend to use steps of 10,000 instead). With the Omigod particle at the small end and a very approximate guess as to the size of the total Universe as the other, we humans really are at the middle of the size range, logarithmically speaking [I can't get rid of an unconscionable amount of white space here. Sorry. Skip down quite a bit to find the table]:

 Step Size Range, m Name Equivalent or Item -12 10-36 0.062 Planck Lengths -11 10-33 61.9 Planck Lengths -10 10-30 -9 10-27 Wavelength of "Omigod" cosmic ray (3x10+20eV) ~4x10-27m -8 10-24 yoctometer (ym) -7 10-21 zeptometer (zm) Wavelength of 7TeV particle in CERN's LHC accelerator 177zm (= 0.177am) -6 10-18 attometer (am) -5 10-15 femtometer (fm) Proton charge radius 0.87fmIron nucleus diameter ~4.5fm -4 10-12 picometer (pm) -3 10-09 nanometer (nm) Iron atom diameter: 0.28nmAIDS virus diameter ~50nm -2 10-06 micrometer (µm) E. coli "rod": ~1 µm diameter x ~4µm length -1 10-03 millimeter (mm) Ball in ballpoint pen 0 1 meter (m) Height of a 2-3 year old child 1 10+03 kilometer (km) 0.621 mile; a 10-15 minute walk 2 10+06 megameter (Mm) 1000 km. Asteroid Ceres diameter ~950km 3 10+09 gigameter (Gm) Million km. Earth-moon distance ~0.38Gm 4 10+12 terameter (Tm) Billion km. Jupiter orbit diameter ~1.6Tm 5 10+15 petameter (Pm) 0.106 light year (ly) = 0.0324 parsec (pc). Nearest Star 4.22ly=1.29pc=39.9Pm 6 10+18 exameter (Em) 106ly. Betelgeuse 427ly = 4.03Em 7 10+21 zettameter (Zm) 106,000ly. Large Magellanic Cloud 187,000ly = 1.8Zm; Andromeda galaxy 2.5 million ly = 24Zm 8 10+24 yottameter (Ym) 106 million ly. Visible Universe radius ~13 billion ly = 120Ym 9 10+27 106 billion ly. "Cosmic Inflation" proposes a "total Universe" this size or larger