Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (115 page)

This splitting-up of the concept of energy into two varieties — liquid and frozen — can’t help but remind us of our splitting-up of the concept of mass into two varieties — strange and normal (and we mustn’t forget that this second dichotomy was imposed on us by Einstein’s equation). The analogy is clear; indeed, it cries out to be made. But despite its salience, this analogy leads us to a problem, for already in Einstein’s day, people had known for roughly a century that the two varieties of energy (dynamic and static) are fully interconvertible (otherwise conservation of energy would not hold), whereas we have just been insisting that the two varieties of mass (strange and normal) are
not
interconvertible. If they were, then an iron atom or a pearl or a boulder could just poof out of existence, provided that it left in its wake the proper amount of strange mass — that is, some heat, some sound, some light… But that never happens — or at least this is what any sane person would naturally think. In sum, then, as far as
mass
is concerned, it seems that there has to be a watertight partition between the two varieties, while as far as
energy
is concerned, there is no partition at all between the two varieties. And therefore, our budding mass–energy analogy goes up in smoke. What a shame!

But here is where Einstein’s “instinct for cosmic unity” comes into play. As Banesh Hoffmann put it, to insist on the existence of a watertight partition between strange and normal mass “would be to imagine two types of mass for no good reason when one would suffice. The distinction would be inartistic and logically indefensible.” If we take Hoffmann’s word for it, then, Einstein must have said to himself in 1907, in essence, “My unflagging faith in nature’s uniformity leads me to conclude that it must be possible for an ordinary lump of matter possessing
normal
mass to be converted into a quantity of
strange
mass or vice versa, even though nothing of the sort has ever been seen
anywhere.” This moment of deep inspiration for Einstein, triggered by his esthetic of simplicity, would be analogous to Jan’s epiphany when, faced with the threat of repossession, she broke the invisible financial barrier and imagined the previously unimaginable idea of converting her frozen assets into liquid assets.

But what could have prodded Einstein to break the analogous barrier in the concept of mass, which had seemed so definite and so firm? What metaphorical “repo person” came knocking one fine day and put sufficiently intense mental pressure on him? An esthetics-based longing for cosmic unity alone couldn’t have done it, because as we said above, it was simply
self-evident
that there was no interconvertibility between the two varieties of mass. Clocks, blocks, and rocks
never
evaporate into flashes of light, sound waves, or anything else. They just sit there, inert and immutable. All this was clear as day. What, then, might have led Einstein to see things otherwise?

Recall how Banesh Hoffmann summarized Einstein’s state of mind concerning mass and energy in 1907. If we rephrase that quote using the terminology of this chapter, Einstein would be thinking essentially the following: “Normal mass somehow has to possess energy because it is essentially the same thing as strange mass, and the latter, according to the equation I derived two years ago, possesses energy. Analogy thus forces me to generalize, and so I conclude that
all
types of mass possess energy.” The analogy clearly resides in the words “it is essentially the same thing as”, but once again we have to wonder
why
Einstein would have been confident of such an analogy, given the vast difference between how one conceives of normal mass and strange mass, and given that there was nary a shred of experimental evidence for the idea that locked up inside every single piece of ordinary, innocent-seeming matter were vast hidden reserves — indeed, inconceivably enormous reserves — of energy.

The key hint for Einstein could well have been potential energy, for as we pointed out above, potential energy is reminiscent of normal mass. While other forms of energy involve movement, potential energy is inert. Likewise, while strange mass involves movement, normal mass is inert.

Up to this point, the analogy between potential energy and normal mass is strong, but in Einstein’s mind, it would have been weakened by the fact that
all
forms of energy, including potential energy, are interconvertible, whereas for mass, the notion of interconvertibility applies only to one side of the partition, pointedly excluding normal, “frozen” mass. This is a most disturbing asymmetry — but for that very reason, it is most provocative! Why should there be an impermeable membrane separating strange from normal mass, if the analogous membrane within the concept of energy is perfectly permeable? This is the key question leading to the key breakthrough.

It would clearly be a wild leap in the dark to propose that normal, “frozen” mass also can participate in the fluidlike phenomenon of conservation of total mass. It would lack any justification except a deep esthetic desire for unification, reinforced of course by a suggestive analogy — namely, the fact that potential energy participates in the conservation of total energy. But no matter how suggestive the analogy, to make such a leap would be reckless, because it would oblige one to believe in the wild idea of lumps of mass poofing into and out of existence — an unheard-of kind of event at that time.

Furthermore — and this made the notion even more surrealistic — Einstein was most aware that, because of the enormous multiplicative constant
c
²
in his equation, the metamorphosis of even the most insignificant quantity of normal mass into strange mass would make an inconceivably huge amount of energy materialize seemingly out of nowhere (although it would actually have always been there, just hidden out of sight in innocent-seeming lumps of matter, thus strongly analogous to chemical potential energy lurking silently and invisibly in chemical bonds). This release of gigantic reserves of hidden energy would allow the development of stupendous sources of energy, not to mention stupendous weapons. If one day this kind of metamorphosis could be carried out, the world would be profoundly changed.

In sum, the new interpretation of
E
=
mc
²
amounted to a daring leap into wild science-fiction scenarios. And yet, though it was based on nothing but an intuitive esthetics-based analogy, this is exactly the leap that Einstein made in print in 1907, thereby opening the door to a revolutionary vision according to which a material object having normal mass could be converted into other, intangible forms of mass, thereby freeing up vast amounts of hidden energy that had been locked up inside it as a kind of potential energy. 1907 is thus the year in which the metaphorical new tower of Pisa started to lean, thereby attracting a great deal of attention. From that moment on, the soon-to-be-cliché phrase “Einstein’s relativity theory” became inseparable, in the public’s imagination, from the equation
E
=
mc
²
.

In 1907, however, there didn’t exist the tiniest shred of experimental evidence for Einstein’s extension of the original meaning of his equation. Only many years later — in the year 1928 — thanks to a subtle fusion of relativity and quantum mechanics, was the idea of
antiparticles
(such as the positron, antiparticle of the electron) proposed on theoretical grounds by the English physicist P. A. M. Dirac, and a few years after that, the sudden and total mutual annihilation of two stationary lumps of matter — specifically, an electron and a positron — was experimentally observed in a process that gave rise to just two photons (the elegant and indispensable word “photon” had finally been coined, in 1926, by Gilbert Lewis) zipping away from each other at the speed of light (by definition!), and undulating with exactly the amount of electromagnetic energy that, when divided by
c
²
, equaled the sum of the two late particles’ normal masses. In other words, this experimental discovery showed that ordinary matter having
normal
mass (in this case, the electron and the positron, which could be thought of as mutually annihilating “nano-boulders”, so to speak) could indeed suddenly cease to exist, as long as it was simultaneously supplanted by a burst of radiation energy possessing exactly the same amount of
strange
mass. Thus, after twenty-five years had passed, experimental confirmation finally arrived for Einstein’s risky leap that had been based solely on an analogy grounded in esthetics.

We find it revelatory, as does Banesh Hoffmann, that Einstein’s dramatic conclusion in 1907 (namely, that
mass always contains energy)
was nothing but the flip side of his 1905 discovery (namely, that
energy always possesses mass).
It’s as if, after writing down his equation, he at first read it in only one direction (“
m = E/c
²
”
— that is, “an inconceivably tiny amount of mass is possessed by any standard-size portion of
energy”), and then finally realized, after two years, that it could be read in the other direction as well (“
E = mc
²
”
— that is, “an inconceivably huge amount of energy lurks hidden in any standard-size portion of mass”). This shows that even for the most audacious of spirits, it sometimes takes a great deal of time and intense concentration, not to mention analogy-driven cognitive dissonance, to carry out what might seem, after the fact, to be the most elementary of conceptual reversals.

Below we offer a summary of the many-voiced symphony of ideas about energy and mass in Einstein’s mind that eventually led to his breakthrough in 1907, resulting in a far deeper understanding of the meaning of the equation that he had first written down in his
annus mirabilis
.