Beyond the God Particle (52 page)

13
. See “Louis de Broglie,”
http://en.wikipedia.org/wiki/Louis_de_Broglie
; see also “Davisson–Germer experiment,”
http://en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment
(site last visited 4/10/2013).

14
. According to Newton, the
magnitude
of the force of gravity exerted upon object
a
by object
b
is called
F
_ab
and is given by the formula:

where
R
is the separation between them. This is an example of an
inverse square law force
, that is, a force that falls off in magnitude, or strength, with distance, like 1/
R
²
. The electric force between two stationary electric charges is also an inverse square law force.

In this formula
m
_a
is the mass of object
a
, and
m
_b
is the mass of object
b
. This means that the force of gravity is stronger between two very massive objects than it is between two very low-mass objects. For example, if
a
is the earth, we substitute
m
_a
=
m
_Earth
, and if
b
is the sun, we substitute
m
_b
=
m
_Sun
into the formula. Thus, if we could somehow double the mass of the sun, holding everything else fixed, then the force of gravity that the earth would experience from the sun would become doubled, and the earth's orbit would change, becoming a tighter ellipse with a smaller average distance from the sun. Technically, the force is a
vector
and must therefore also have a direction. We could write a better formula that illustrates that, but words suffice. Object
a
experiences the force of gravity, with the magnitude we have written, but the force points as a vector at the direction of object
b
. And, by symmetry, object
b
experiences the same magnitude of force, which points in exactly the opposite direction, back to object
a
.

The quantity
G
_N
in the numerator of the formula is a
fundamental constant
. Newton had to introduce this factor in order to specify the
strength
of the gravitational force. We call this Newton's gravitational constant or just Newton's constant, for short.
G
_N
is measured from experiment and takes the value
G
_N
=
6.673 × 10
^–11
(meters
³
) / (kilograms seconds
²
). We have quoted
G
_N
in the meter-kilogram-second system of units. Indeed, we can write, in nonscientific notation,
G
_N
= 0.00000000006673 (meters
³
) / (kilograms seconds
²
), and we see that
G
_N
is a seemingly very small number. Gravity, despite its ubiquitous character in nature, is actually a very feeble force. To get a sense of this, we can estimate that the force of gravitational attraction between two fully loaded oil tankers that are ten miles apart is about the same as the force you feel holding a gallon of milk due to the pull of gravity by the entire earth. For more discussion of gravity, see our book
Symmetry and the Beautiful Universe
(Amherst, NY: Prometheus Books, 2007).

15
. See “Charles-Augustin de Coulomb,”
http://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb
, and “Coulomb's law,”
http://en.wikipedia.org/wiki/Coulomb%27s_law
(sites last visited 3/26/2013).

16
. See “Electric charge,”
http://en.wikipedia.org/wiki/Electric_charge
. The electric field, which we call E, produces a force on the charge, which we call F, and the relationship between these is very simple, F = eE, or “force equals charge times electric field.” A force causes a particle to accelerate. This was precisely expressed by Newton in his famous equation F = ma, or “force equals mass times acceleration.” So, if we combine these two equations, we see that ma = eE, or a = eE/m, “the acceleration of the particle is proportional to charge times electric field divided by mass.” See “Electric field,”
http://en.wikipedia.org/wiki/Electric_field
; see also
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html
;
http://www4.uwsp.edu/physastr/kmenning/Phys250/Lect03.html
(sites last visited 1/23/2013). Quarks have fractional charges, up = +2/3 times e, and down = –1/3 times e, but quarks are always bound into strongly interacting particles, such as protons, neutrons, and
π
's such that the observed charges are integers (see
Appendix
).

17
. The direction of an electric field and a
conventional
electric current always emanates from positive and points toward negative. This convention was adopted before the discovery that the electric charge of the electron is negative. So the actual flow of electrons is opposite to that of the electric field and the conventional current. See “Electric current,”
http://en.wikipedia.org/wiki/Electric_current
(site last visited 5/4/2013).

18
. Search online for “electron microscopes” and follow links to “images for electron microscopes.” See “Electron microscope” and references therein,
http://en.wikipedia.org/wiki/Electron_microscopes
(site last visited 1/23/2013). Quoting from this source:

According to Dennis Gabor, the physicist Leó Szilárd tried in 1928 to convince him to build an electron microscope, for which he had filed a patent. The German physicist Ernst Ruska and the electrical engineer Max Knoll constructed the prototype electron microscope in 1931, capable of four-hundred-power magnification; the apparatus was a practical application of the principles of electron microscopy. Two years later, in 1933, Ruska built an electron microscope that exceeded the resolution attainable with an optical (lens) microscope. Moreover, Reinhold Rudenberg, the scientific director of Siemens-Schuckertwerke, obtained the patent for the electron microscope in May 1931. Family illness compelled the electrical engineer to devise an electrostatic microscope, because he wanted to make visible the poliomyelitis virus. The first practical electron microscope was constructed in 1938, at the University of Toronto, by Eli Franklin Burton and students Cecil Hall, James Hillier, and Albert Prebus; and Siemens produced the first commercial transmission electron microscope (TEM) in 1939. Although contemporary electron microscopes are capable of two million-power magnification, as scientific instruments, they remain based upon Ruska's prototype.

CHAPTER 8. THE WORLD'S MOST POWERFUL PARTICLE ACCELERATORS

1
. See “Michael Faraday,”
http://en.wikipedia.org/wiki/Michael_Faraday
(site last visited 3/26/2013). In the “opinion” of Snopes.com (the fact-checking website that has punched so many holes in the many idiotic opines of elected officials and various rancidly political distribution e-mails), this famous quote of Faraday's is undocumented hearsay:
http://www.snopes.com/quotes/faraday.asp
. However, the recipient of the comment, Gladstone, was supposedly Chancellor of the Exchequer, and not prime minister, according to Wikiquote:
http://en.wikiquote.org/wiki/Michael_Faraday
(sites last visited 3/26/13): “Faraday's reply to William Gladstone, then British Chancellor of the Exchequer (minister of finance), when asked of the practical value of electricity (1850), as quoted in
The Harvest of a Quiet Eye: A Selection of Scientific Quotations
(1977), p. 56.” Snopes claims to discredit the quote because Gladstone was allegedly prime minister at the time of the remark, but in fact he did not hold that office until after Faraday's death. The fact that Gladstone was Chancellor of the Exchequer seems to undercut that part of the Snopes argument. Electricity had not developed to the cell phone–video camera stage in Faraday's era, so we'll never know who's right or who's wrong, but we do love the “quote.”

2
. Much more technical detail than we have space for can be found by perusing the Wikipedia entry for “Linear particle accelerator,”
http://en.wikipedia.org/wiki/Linear_Accelerator
(site last visited 3/26/13).

3
. And, thankfully, in the limit when particles have very large energies, the relationship between their quantum wavelength and energy becomes very simple: E = h /2
π
λ
where
λ
is the wavelength and h is Planck's constant. This simple formula explains everything about the largest accelerators in the world, from the Fermilab Tevatron, to the SLAC Linac, to LEP, to the Large Hadron Collider—in order to halve the size of
λ
we must double E—ergo high-energy particle accelerators are big.

4
. Radio frequency cavities are another marvel of modern technology that was spun off from particle accelerator R&D. See “Microwave cavity,”
http://en.wikipedia.org/wiki/Microwave_cavity
, “Klystron,”
http://en.wikipedia.org/wiki/Klystron
(site last visited 3/26/13).

5
. Widerøe's cavities were just spaces in a vacuum pipe between tubes of copper that were alternately charged plus and minus by an oscillating electric circuit. When the particles were between the tubes, they were in phase with an electric field (e.g., if an electron, the tube ahead would be charged positive, while the one behind would be negative). As they entered the tubes, the tubes changed polarity while the electrons merely drifted. See “Linear particle accelerator,”
http://en.wikipedia.org/wiki/Linear_particle_accelerator
.

6
. See the SLAC site:
http://www6.slac.stanford.edu/research/
(site last visited 3/26/13).

7
. “Fermilab Linac,”
http://www-ad.fnal.gov/proton/linac.html
, and for the history:
http://history.fnal.gov/linac.html
(sites last visited 1/27/2013).

8
. See, e.g.,
http://www.hep.ucl.ac.uk/~jpc/all/ulthesis/node15.html
. See “International Linear Collider,”
http://en.wikipedia.org/wiki/International_Linear_Collider
; see also
http://www.linearcollider.org/ILC/GDE/Director%27s-Corner/2008/1-May-2008---The-art-of-decision-making---STF-phase-2-cavity-choice
(sites last visited 3/26/2013).