The Amazing Story of Quantum Mechanics (47 page)

Seriously! See Chapter 21.

Sorry, ladies, but I’m already married!

The largest of the chain of Marquesas Islands in what was known as French Polynesia.

That is, our discussion will employ a Quentin Tarantino-esque description of quantum physics—namely, answers first, then questions.

In which case, at least, you won’t have to wonder why you aren’t invited to more parties!

As light from the sun reaches us through the vacuum of empty space, electromagnetic waves are unique in not requiring a medium in which to propagate.

When a nucleus emits an alpha particle, it transmutes into another element, as discussed in detail in Section 3.

George Gamow, brilliant physicist and famed practical joker, once added Hans Bethe (pronounced “beta”) as a coauthor of a paper he wrote with his graduate student Ralph Alpher, so that the scientific citation list of authors would read, Alpher, Bethe, Gamow.

For an oil slick on water, the thickness needs to be one-fourth the wavelength of light for constructive interference, while for a glass slab with air above and below, the constructive interference criteria call for the thickness to be one-half the wavelength. The difference, involving phase changes at the top reflection surface, is not important for the discussion here.

Goddard correctly pointed out that any gravity screen as suggested by Brush would enable one to lift a large mass with little effort. Upon removal of the gravity shield, the mass would then fall as any normal weight and thus could provide a work output greater than the energy required to lift the mass, thereby violating the law of conservation of energy.

We must also look for the police!

While technically “soot” refers to particulates formed from the incomplete combustion of fuels such as coal, oil, or wood, and is mostly carbon but may contain other elements depending on the nature of the burning material, here I am using the term as a shorthand for “amorphous carbon.”

Certainly not if you want them to remain your beloved!

There may be a slight difference, owing to technicalities. The electrons scatter most strongly from the top few atomic planes, while the X-rays can penetrate deeper into the crystal. This is because the electron-electron repulsion that governs the electron scattering is much stronger than the photon-electron interactions. If the crystal structure of the top surface differs from that of the bulk crystal, a different pattern may be observed. But this is a detail that does not affect the basic point of wave-particle symmetry.

We’ll soon see that, although it is a useful metaphor, we should not take the “spinning top” picture literally.

When I described Asimov’s suggestion in my 2005 book
The Physics of Superheroes
, it caught the attention of Tony Stark! In Marvel Comics’s
Civil War Files,
consisting of background notes dictated by Iron Man’s alter ego, under an entry for “Goliath,” one finds: “My first introduction to Bill Foster (Goliath, Giant-Man, Black Goliath) was his remarkable paper with Jim Kakalios on extra-dimensional manipulations of Planck’s constant, and I quickly had them hired by Stark Enterprises.” Upon reading this, I realized that I needed to update my resumé!

This argument still holds, even with the recognition that neutrons (and protons) are themselves composed of electrically charged quarks. As explained, the quarks would have to be rotating faster than light speed to account for the observed magnetic field of these composite particles.

Many physicists, when pressed, would confess that the notion of the electron they carry around in their heads involves a particle with a large arrow protruding from it, pointing either “up” or “down,” whenever “spin” comes up. Thus, if you find the image of an electron spinning like a top too compelling to give up—you’re just thinking about it the way we professionals do!

Here physicists seem to have anticipated superhero comic books. In
X-Factor
# 72, when Guido, a superstrong member of a team of superpowered mutants, realized that nearly all other such teams have at least one member whose superpower involves superstrength, he adopted the code name Strong Guy.

Some accelerators use electrons or atomic nuclei instead of protons—and some accelerate particles in a straight line—but the idea is the same.

In such a world, to quote Krusty the Clown, “the living would envy the dead.”

Comic books back in the 1950s, at the height of Fredric Werthem’s
Seduction of the Innocent
scare, may indeed have been corrupting young readers’ minds (after all, isn’t that what literature is
supposed
to do?), but one could hardly complain that they weren’t improving readers’ vocabulary or reading comprehension.

I’m not kidding! While other pioneers of quantum theory such as Werner Heisenberg and Paul Dirac required extreme solitude in order to develop their theories, Schrödinger needed a more . . . stimulating environment. Historians of science debate to this day the identity of the woman (definitely not his wife!) who kept him company over a long Christmas holiday break, at a friend’s chalet in the Swiss Alps, when he successfully constructed the matter-wave equation that now bears his name. As I tell my students of modern physics, if you are going to learn quantum mechanics, you must remember one key principle: Don’t be a playa’ hata’!

Since the mathematical convention is that a positive number multiplied by a negative number yields a negative number, and the product of two negative numbers is a positive number, there is no real number that, when multiplied by itself, would yield a negative number. We can certainly imagine such numbers, but they are not in the set of real numbers we deal with. They are hence termed “imaginary” and are defined to be represented by the lower case letter
i,
so
i
×
i
= -1
.

We use the letter
V
for the potential, as the letter
p
is reserved for mathematical descriptions of the
mo
-mentum! Sometimes it seems like we physicists deliberately make the equations harder than they need to be.

The notation Ψ* is mathematical code that says to change all the terms with
i
in Ψ to -
i
. As
i
×
i
= -1, (-
i
) ×
i
= -1 × (
i
×
i
) = -1 × -1 = +1, and we will have a positive, real function in Ψ
²
. Those who recall their algebra may note that Ψ is actually a “complex” number (Ψ = a + ib, where a and b are regular numbers), so that I should technically use the notation |Ψ|
²
instead of Ψ
²
. We’ll stick with Ψ
²
, as for us the important point is that Ψ
²
is a real, positive number.