Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (114 page)

Any ordinary material object thus possesses lots of normal mass and a tiny bit of strange mass, and their relative proportions can change with time. For example, a flashlight that gives off light for a long time will gradually lose its strange mass, thus becoming ever so slightly lighter. What then happens when it has fully exhausted its strange mass (or “runs out of juice”, in colloquial terms), and all that’s left is its
normal
mass? Well, as we all know, at that point the flashlight will no longer be able to emit any electromagnetic radiation, unless a new battery is installed. The fact that it still contains plenty of
normal
mass would seem utterly irrelevant to its flash-producing capability, because there is no interconvertibility between normal and strange mass. That is to say, it would seem that
we can’t draw on a flashlight’s abundant reserves of normal mass
to get it to give off light. All of one’s experience leads one to think that only by drawing on its very small supply of
strange
mass can an object emit energy (such as light, in the case of a flashlight).

The following allegory may help us to convey more clearly the distinction between these two types of mass. Jan has the wherewithal to purchase the most essential items in her life, but her modest bank account does not allow her to indulge in luxuries. Some time ago she inherited a huge mansion with palatial grounds, worth at least several million dollars — but in her mind, this type of possession doesn’t belong to the same category as her day-to-day money; no matter what its official value might be in dollars, she doesn’t conceive of her residence as a spendable liquid resource — she sees it merely as a frozen, solid one. For Jan, the two types of possession have nothing to do with each other; it’s as if there were a rigid mental barrier separating the concepts. It would never occur to her to sell a few acres of her gardens, let alone her mansion, in order to purchase a luxury item or to take a vacation. In Jan’s mind, whereas her meager liquid assets flow easily (indeed, that’s why they are called “liquid assets”), her real-estate assets are completely frozen and inaccessible; if she needs money, she never thinks of the latter at all. But then one day, several months after her non-payment of a substantial bill, Jan receives a worrisome letter stating that in a few days some of her belongings will be forcibly seized by law enforcement officers. And then, all at once, something clicks in her mind…

One can easily translate our allegory into the language of mass and the conceptual dichotomy Einstein had discovered. The idea is simply that the seemingly uncrossable mental barrier between strange mass (= liquid assets) and normal mass (= frozen assets) is
not
in fact uncrossable after all, but can be crossed provided that there is enough pressure (= the threat of a repossession) to make the idea leap to mind.

However, for Albert Einstein in 1905 and for the readers of his first article on the idea of
E = mc
²
, the conceptual barrier between
normal
mass and
strange
mass was completely impenetrable. How could it not have been so? Consider a boulder, for instance (a quintessential example of
normal
mass). It’s one thing to imagine that the boulder’s internal stock of heat (a quintessential example of
strange
mass) will gradually diminish as the boulder emits infrared radiation that warms up its environment. But who would ever have suspected that the boulder
itself
could all at once vanish from the universe, resulting in the shooting-off of much more intensive rays of light? If one is not under severe pressure, one does not jump to embrace wild and woolly scenarios such as that; one does not spontaneously offer a warm welcome to notions that violently clash with a lifetime of experience, not to mention with the collective wisdom of humanity.

In the Copycat analogy problem “
abc
⇒
abd
;
xyz
⇒ ???”, no one thinks of the elegantly symmetric answer
wyz
without first having been lured down the pathway of taking the successor of
z
and banging up against that barrier. Only after all one’s initial simple and intuitive ideas have failed does one start trying out more radical ideas. In short, it takes a great deal of mental pressure in order to trigger a radical conceptual slippage, and not least among the contributing pressures is one’s sense of esthetics.

Here is what Banesh Hoffmann wrote about this very subtle transitional stage in Albert Einstein’s thought processes:

This passage is eloquent and insightful, but it’s also rather curious, for its two halves almost seem to contradict each other. Whereas the first paragraph states that it would be very hard (even for Einstein) to transcend the intuition that there are two different types of mass, the second paragraph (which is attempting to give us a privileged, first-person view from within Einstein’s own mind) claims that there would be
no good reason
for believing in a distinction between these two types of mass. But actually there
was
a very strong reason for such a belief; it was in fact Einstein’s own equation that had created a schism within the formerly monolithic concept of
mass.
Viewed in this way, Hoffmann’s short passage constitutes a perfect summary of Einstein’s inner mental
trajectory over two years. Its first paragraph alludes to Einstein’s initial glimpse of a new kind of mass in 1905, as well as his lack of full understanding of it; its second paragraph indicates that this imperfect understanding gave rise to such serious tension in Einstein’s mind that he was eventually forced to make a daring esthetics-driven extension of that initial notion (that is, of
strange mass
), getting rid of the conceptual schism and thereby re-establishing conceptual unity, thus leading to a harmonious new state of understanding from which all mental tension had been banished.

We shall now try to put this mental trajectory under a magnifying glass. The fact that light, heat, and sound (etc.) all possess mass (even if it’s just an extremely slight amount) implies that we are dealing with
a new type of mass
of which no one had ever dreamt before. An object that gives off energy and in so doing loses a tiny amount of its mass does not lose any of its solid or normal constituents; it loses something radically new — it loses a different
type
of mass. In short, for anyone who understands the equation
E = mc
²
(and this certainly includes its discoverer), there is a very intense pressure to imagine two extremely different types of mass — the familiar type (normal) and the new type (strange), which is associated with outgoing or incoming energy. To be more specific, the tiny mass carried off by the light rays comes from
strange
mass that was lost by the battery. No
particles
in the battery were lost or destroyed, however; every one of its corpuscles (atoms, molecules, whatever) remained intact. Since the
normal
mass of the battery is never affected by any process of emission (or absorption) of light, this gives rise to the image of a rigid barrier between these two types of mass (informally put, “they don’t talk to each other”).

Even Albert Einstein took two years to arrive at the conclusion that the impermeable conceptual barrier that was suggested — indeed,
forced
— by his equation did not actually exist. His “instinctive sense of cosmic unity”, as Hoffmann dubbed it, eventually led him to the radical notion that nature’s internal consistency — that is, the uniformity and simplicity of the laws of physics — required that any material object (
i.e.
, any normal mass), whether an electron or a cannonball, should be able to “melt” into strange mass carried off by escaping light rays, much as does the inert energy stored in a battery, or much as the frozen assets latent in an estate might turn into liquid cash.

This was truly a shocking idea, because it meant not only that solid, massive physical objects
could
literally dematerialize and vanish (or, if we run the scenario in reverse, that such objects could materialize out of nowhere), but also that any such metamorphosis would necessarily be accompanied by the sudden, simultaneous appearance (or disappearance) of a phenomenal amount of energy. Indeed, it was the phenomenal amounts of energy involved that made the newly-revealed full meaning of Einstein’s equation stunning and even surrealistic.

What went on in the hidden recesses of Einstein’s mind that brought him, after two years of thought, to this most disorienting idea, for which there was, at the time, no experimental evidence at all?

To begin with, there is every reason to believe that Einstein saw the light rays leaving the flashlight as carrying not only energy but also mass (both of which had been “subtracted” from the flashlight). This amounts to the idea that the strange mass, rather than just poofing out of existence when it left the flashlight,
mutated
from one form to another. Before the two flashes were produced, the strange mass resided in the chemical bonds inside the flashlight’s battery, whereas after the flashes’ release, it resided in the vibrations of the electromagnetic waves making them up (and thus, if one were to weigh a mirror-lined box in which the rays had been captured and were bouncing back and forth, one would find that the box weighed ever so slightly more than it had before the rays were captured in it).

This fluidity of strange mass — the fact that strange mass can glide back and forth between different forms — could not have failed to remind Einstein of the fluidity of energy (for energy, likewise, is constantly gliding from one form to another), and such a connection would have come to his mind all the more easily given that his equation had revealed an unexpected link between mass and energy. But even if a given type of strange mass could easily mutate into other types of strange mass, it still seemed totally self-evident that
normal
mass could
not
mutate. As we stated above, one never sees boulders or other solid objects (or liquids or gases, for that matter) simply vanishing into flashes of light, or springing magically out of them. Material things are made of tangible
stuff
, and as such they seem to belong to a different class of things from intangible energy and its “strange mass”. This sharp distinction makes for a rigid, uncrossable barrier inside the concept of mass, as described earlier, dividing it into two subspecies that are not interconvertible.

Like all physicists of the time, Einstein was intimately familiar with the principle of conservation of energy — the solidly confirmed fact that energy can change form but without ever increasing or decreasing. Countless experiments had shown that heat (thermal energy) could be converted into movement (kinetic energy) of macroscopic objects (for example, of a piston in a cylinder) and vice versa (rubbing something warms it up), and that chemical energy in a battery can be converted into electromagnetic energy, and so on. The technology of the day relied on this fundamental principle.

Einstein had an unswayable faith in the law of conservation of energy; now, all of a sudden, he found himself face to face with a similar new conservation law — namely, the conservation of strange mass. That is to say, strange mass, much like energy, could apparently glide from one form to another without increasing or decreasing. For example, if a crystal absorbed some radiation, a bit of
electromagnetic
strange mass (that is, a ray of light) would suddenly go out of existence and at the same moment a bit of
thermal
strange mass would instantly come into existence; likewise, in an act of radiation, the reverse transformation could take place. We can therefore imagine that in Einstein’s mind, thanks to the analogy between the laws of conservation of energy and conservation of strange mass, there was starting to exist a tight analogical link between the concepts of
energy
and
strange mass
.

So far, we have completely neglected to mention an extremely important type of energy — namely,
potential energy
, suggested in 1799 by the French physicist Pierre
Simon de Laplace. This is perhaps the most peculiar and unintuitive form of energy, since it depends solely on the positions of objects relative to each other, but peculiar or not, it plays a crucial role in the conservation of energy. For example, a ball rolling down a hill gains kinetic energy while losing potential energy (which is proportional to its altitude), and vice versa: if it rolls uphill, then it loses speed (and therefore kinetic energy) and all the while it gains potential energy. Another example of how potential energy plays a key role in the conservation of energy is furnished by a spring. In its neutral state (neither stretched or compressed), a spring has no potential energy, but the act of compressing or stretching it gives it some. As long as one holds the spring tight, preventing it from snapping back to its neutral state, its energy remains potential, but at the moment of release, this positional energy is converted into kinetic energy, with the
total
energy remaining perfectly constant at every instant of the process.

Thus energy, like mass, seems to come in two very different varieties: on the one hand, there are all the
dynamic
forms of energy that have to do with movement — heat (jiggling of molecules), waves, rotation, movement through space, etc. — and on the other hand, there is
static
or
potential
energy, which seems very different, because it has nothing to do with movement, just with position. Recalling our financial allegory, we might be inclined to dub the first variety
liquid
energy, since it always involves something that flows, whereas the second variety, potential energy, exists in the absence of any kind of motion, which could encourage us to dub it
frozen
energy.