The Amazing Story of Quantum Mechanics (48 page)

Technically the average is 50.5 in this case—but you get the idea.

I apologize for that joke.

At Mars’s closest point to our planet.

A nonlinear equation would be something like Ψ
²
= 2Ψ, which is a true statement for Ψ = 2, but not foraΨvalue ten times bigger, that is, Ψ = 20.

The heat emitted by the reactor causes the water to boil, and the resulting steam turns turbines in the dynamo that generates electricity.

And indeed, this student is Charles Misner, who has made many important contributions to the study of cosmology and gravitation over his distinguished career.

A “nucleon” is the term physicists use for a particle inside a nucleus, either a proton or a neutron.

The sponsor for the Disneyland program
Our Friend, the Atom
was General Dynamics, manufacturer of, among other things, nuclear submarines.

Assuming that the alpha particle is electrically repelled before striking the nucleus.

To maintain stability in a nucleus requires a critical balance of the number of neutrons and protons—consequently, isotopes such as hydrogen, with one proton and two neutrons, may be unstable and “decay.” More on this soon.

Depending on the detailed decay fragments of the fissioning uranium nucleus. How exactly the unstable uranium nucleus decays into smaller nuclei is a complicated process.

There is a process by which, when an electron drops from a high-energy state to a lower level, another electron in the atom is ejected. But for the most part electronic transitions within the atom involve emission or absorption of photons.

My track record playing the lottery provides direct empirical evidence of this phenomenon.

A nucleus with two neutrons and two protons is called helium, or, when ejected from a larger unstable nucleus, an alpha particle.

The full analysis involves studies of meteorites, and is more complicated than summarized here.

By the time neutrons were discovered, the identity of nuclear radiation was better understood, and the “ray” nomenclature was no longer employed.

That is, one that is sitting still, isolated in space or moving but stationary to us if we moved along in the same speed and direction as the neutron (called the neutron’s “rest frame”).

For technical reasons that need not concern us, when neutrons decay they emit a proton, an electron, and an antineutrino (the antimatter version of a neutrino). As I say, we need not worry about this particular detail here.

Famed astrophysicist Sir Arthur Eddington was one of the first to recognize that the sun’s energy resulted from nuclear reactions. However, prior to the development of quantum mechanics, many physicists objected that the temperatures at the center of the sun were too low to enable such processes. To this Eddington replied in 1920, “We do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotter place.”

Measured relative to a particular axis of rotation.

Those who know quantum mechanics will recognize that these two functions are
A
= Ψ
_m
(1)
Ψ
_n
(2)
and
B
= Ψ
_n
(1)
Ψ
_m
(2),
where Ψ
_m
(1) is the wave function for an electron at position 1 in quantum state m and Ψ
_n
(2) represents the second electron in a quantum state n at position 2. If the positions of the electrons 1 and 2 are interchanged, then the total wave function Ψ =
A-B
= Ψ
_m
(1)
Ψ
_n
(2) -
Ψ
_n
(1)
Ψ
_m
(2)
acquires a minus sign. If you understood this footnote—then this book is not for you!

As in section 2, since Ψ is a complex number, by “squaring” I mean multiplying Ψ by its complex conjugate. For our purposes this has the same effect as squaring Ψ, so we use the simpler notation of Ψ
²
.

For simplicity, the nucleus in Figure 31 is represented by a single positive charge, while in fact there are multiple protons in all nuclei except hydrogen, from two in helium (Figure 31b) to thirteen in aluminum (Figure 31e). I have also not attempted to represent the changes in the spacing of the rows for the different elements.

This notion that organisms with specialized skills could serve as analogs of sensory organs or other bodily or psychological functions in a gestalt organism was anticipated in Theodore Sturgeon’s 1953 science fiction novel
More Than Human
.

As before in Chapter 12, the functions A and B are products of the one-particle wave functions, with
A
= Ψ
_m
(1)
Ψ
_n
(2)
and
B
= Ψ
_n
(1)
Ψ
_m
(2),
where Ψ
_m
(1)
is the wave function for a boson at position 1 in quantum state m and Ψ
_n
(2)
represents the second identical boson in a quantum state n at position 2. If the positions of objects 1 and 2 are interchanged, then the total wave function Ψ =
A
+
B
= Ψ
_m
(1)
Ψ
_n
(2)
+ Ψ
_n
(1)
Ψ
_m
(2)
is unchanged.

While the illustration with the ribbon does not apply for spin =
ħ
(or 2
ħ,
and so on) particles, the mathematical arguments above about symmetric two-particle wave functions for these integral spin particles is identical to the spin = 0 case.

Strictly speaking, the transition that helium makes as it forms a superfluid, or when the electrons form Cooper pairs in a superconductor, is not technically an example of Bose-Einstein condensation. The distinctions between a true Bose-Einstein condensate and the superfluid or superconducting state are technical, and for our purposes we may take them to be the same.

And that has made all the difference!

When the intrinsic angular momentum is measured relative to the direction of the photon’s motion

There were a few Doc Savage novels published in the 1970s and 1990s that were credited to Dent posthumously, but his main run on the pulp magazine ended in July 1949.

The government should not have bothered—in 1911
Modern Electronics
published “Ralph 124C 41+,” a science fiction story by Hugo Gernsback (who would go on to found
Amazing Stories
) that featured a fairly accurate description of radar, long before the term was coined.

I’m sure that there was a point in time for nearly all readers when glow-in-the-dark materials seemed to be the greatest technological invention in the history of the universe.

The lower energy seats that are filled for the individual atoms (Figure 31 c,d,e) also broaden into their own filled auditoriums that do not play a major role in the solid’s properties.

Note that a laser does not need to be a solid—the helium-neon laser pointers used by public speakers and lecturers employ a mixture of two inert gases to generate laser light. For simplicity, we’ll stick with solid-state lasers, but our arguments hold just as well for gas lasers.

Experts will note that the above argument applies to electric dipole transitions, but not to those involving magnetic dipole or electric quadrupole transitions. These are typically ten thousand to a million times less likely than electric dipole transitions. For the nonexperts—nothing to see here; move along!

The operation of a real laser cavity is a bit more complicated than this.

Old-timers may recall an early ancestor of the DVD—laser discs, which were twelve inches in diameter in order to have sufficient room for the relatively low-density bits encoding a video image that could be read with a laser.

To the men of America—you’re welcome!

The arguments for electrons in the balcony in one direction will hold for holes in the orchestra in the opposite direction. For simplicity, I focus on the electrons.

There are many different types of transistor structures—what we have described is technically referred to as a
m
etal-
o
xide-
s
emiconductor
f
ield-
e
ffect
t
ransistor, or a MOSFET.

For technical reasons the actual bits on a hard drive involve several magnetic domains, arranged in different sequences to represent “ones” and “zeros,” but for our purposes we can simplify this to single domains for a “one” or a “zero.”

Which is why one must avoid stray metallic objects in the MRI room when the magnet is powered.

In fact, the radio-wave signal is turned on and off continuously, but the emission of radio waves when the system relaxes back to the lower-energy configuration is what is detected.

As the person is at a temperature of 98.6 degrees Fahrenheit, there is enough thermal energy to promote protons into the higher energy state, even without radio-frequency light. Increasing the external magnetic field raises the energy separation between states, and fewer protons will be found in the upper level in the dark. The detection sensitivity in an MRI device is quite high, and the MRI system is able to detect the small additional fraction of protons that are promoted by the radio waves.

This technique is still in the experimental stage, so you don’t need to invest in tin-foil hats just yet.

A prime number is a number that can be divided only by itself or 1. The number 5 is a prime number, while 8 is not (it can be divided by 2 and 4, in addition to 8 and 1). Computer security involves numbers that are the product of two very large prime numbers. Security is maintained by requiring both sides of the transaction to know the factors (which are so large that it is impossible to guess even using conventional supercomputers to try all possibilities).

No pun intended.

This is similar to the question of position and momentum measurements in Chapter 7. The answer you receive depends on what question you ask.

This is for the first version of the arc reactor, “built in a cave—with a bunch of scraps!” Later models had even higher power outputs, though the exact specs are the classified proprietary information of Stark Enterprises.

Just as, in our discussion of solid-state thermometers a moment ago, the metal electrode and the contacting fluid represent two partially filled auditoriums, which will have electrons move from one room to the other, depending on which room has the higher concentration of electrons.

Though other chemical compounds are employed depending on the battery requirements.

These may seem like simple devices, but there is more to them than meets the eye!

Don’t worry, Fearless Reader—he was framed and eventually demonstrated his innocence.

I don’t want to tell them their jobs, but if I were an astronomer, I’d keep my eye on Planet X. I think it might be trouble.

Primarily because it involves imaginary numbers!