einstein

was better suited to theorizing. Fortunately, Paul Habicht was a good machinist, and by August 1907 he had a prototype of the Maschinchen, or
little machine, ready to be unveiled. “I am astounded at the lightning speed with which you built the Maschinchen,” Einstein wrote. “I’ll show up on
Sunday.” Unfortunately, it didn’t work. “I am driven by murderous curiosity as to what you’re up to,” Einstein wrote a month later as they tried to fix
things.
Throughout 1908, letters flew back and forth between Einstein and the Habichts, filled with complex diagrams and a torrent of ideas for how to
make the device work. Einstein published a description in a journal, which produced, for a while, a potential sponsor. Paul Habicht was able to
build a better version by October, but it had trouble keeping a charge. He brought the machine to Bern, where Einstein commandeered a lab in one
of the schools and dragooned a local mechanic. By November the machine seemed to be working. It took another year or so to get a patent and
begin to make some versions for sale. But even then, it never truly caught hold or found a market, and Einstein eventually lost interest. 13
These practical exploits may have been fun, but Einstein’s glorious isolation from the priesthood of academic physicists was starting to have
more drawbacks than advantages. In a paper he wrote in the spring of 1907, he began by exuding a joyful self-assurance about having neither the
library nor the inclination to know what other theorists had written on the topic. “Other authors might have already clarified part of what I am going to
say,” he wrote. “I felt I could dispense with doing a literature search (which would have been very troublesome for me), especially since there is
good reason to hope that others will fill this gap.” However, when he was commissioned to write a major year-book piece on relativity later that year,
there was slightly less cockiness in his warning to the editor that he might not be aware of all the literature. “Unfortunately I am not in a position to
acquaint myself about everything that has been published on this subject,” he wrote, “because the library is closed in my free time.” 14
That year he applied for a position at the University of Bern as a privatdozent, a starter rung on the academic ladder, which involved giving
lectures and collecting a small fee from anyone who felt like showing up. To become a professor at most European universities, it helped to serve
such an apprenticeship. With his application Einstein enclosed seventeen papers he had published, including the ones on relativity and light
quanta. He was also expected to include an unpublished paper known as a habilitation thesis, but he decided not to bother writing one, as this
requirement was sometimes waived for those who had “other outstanding achievements.”
Only one professor on the faculty committee supported hiring him without requiring him to write a new thesis, “in view of the important scientific
achievements of Herr Einstein.” The others disagreed, and the requirement was not waived. Not surprisingly, Einstein considered the matter
“amusing.” He did not write the special habilitation or get the post. 15
The Equivalence of Gravity and Acceleration
Einstein’s road to the general theory of relativity began in November 1907, when he was struggling against a deadline to finish an article for a
science yearbook explaining his special theory of relativity. Two limitations of that theory still bothered him: it applied only to uniform constantvelocity
motion (things felt and behaved differently if your speed or direction was changing), and it did not incorporate Newton’s theory of gravity.
“I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me,” he recalled. “If a person falls freely, he will not
feel his own weight.”That realization, which “startled” him, launched him on an arduous eight-year effort to generalize his special theory of relativity
and “impelled me toward a theory of gravitation.” 16 Later, he would grandly call it “the happiest* thought in my life.” 17
The tale of the falling man has become an iconic one, and in some accounts it actually involves a painter who fell from the roof of an apartment
building near the patent office. 18 In fact, probably like other great tales of gravitational discovery—Galileo dropping objects from the Tower of Pisa
and the apple falling on Newton’s head 19 —it was embellished in popular lore and was more of a thought experiment than a real occurrence.
Despite Einstein’s propensity to focus on science rather than the merely personal, even he was not likely to watch a real human plunging off a roof
and think of gravitational theory, much less call it the happiest thought in his life.
Einstein refined his thought experiment so that the falling man was in an enclosed chamber, such as an elevator in free fall above the earth. In this
falling chamber (at least until it crashed), the man would feel weightless. Any objects he emptied from his pocket and let loose would float alongside
him.
Looking at it another way, Einstein imagined a man in an enclosed chamber floating in deep space “far removed from stars and other
appreciable masses.” He would experience the same perceptions of weightlessness. “Gravitation naturally does not exist for this observer. He
must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling.”
Then Einstein imagined that a rope was hooked onto the roof of the chamber and pulled up with a constant force. “The chamber together with the
observer then begin to move ‘upwards’ with a uniformly accelerated motion.”The man inside will feel himself pressed to the floor. “He is then
standing in the chest in exactly the same way as anyone stands in a room of a house on our earth.” If he pulls something from his pocket and lets
go, it will fall to the floor “with an accelerated relative motion” that is the same no matter the weight of the object—just as Galileo discovered to be
the case for gravity. “The man in the chamber will thus come to the conclusion that he and the chest are in a gravitational field. Of course he will be
puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of
the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chamber is suspended at rest in the
gravitational field.”
“Ought we to smile at the man and say that he errs in his conclusion?” Einstein asked. Just as with special relativity, there was no right or wrong
perception. “We must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws.” 20
A related way that Einstein addressed this same issue was typical of his ingenuity: he examined a phenomenon that was so very well-known that
scientists rarely puzzled about it. Every object has a “gravitational mass,” which determines its weight on the earth’s surface or, more generally, the
tug between it and any other object. It also has an “inertial mass,” which determines how much force must be applied to it in order to make it
accelerate. As Newton noted, the inertial mass of an object is always the same as its gravitational mass, even though they are defined differently.
This was obviously more than a mere coincidence, but no one had fully explained why.
Uncomfortable with two explanations for what seemed to be one phenomenon, Einstein probed the equivalence of inertial mass and gravitational
mass using his thought experiment. If we imagine that the enclosed elevator is being accelerated upward in a region of outer space where there is
no gravity, then the downward force felt by the man inside (or the force that tugs downward on an object hanging from the ceiling by a string) is due
to inertial mass. If we imagine that the enclosed elevator is at rest in a gravitational field, then the downward force felt by the man inside (or the
force that tugs downward on an object hanging from the ceiling by a string) is due to gravitational mass. But inertial mass always equals
gravitational mass. “From this correspondence,” said Einstein, “it follows that it is impossible to discover by experiment whether a given system of
coordinates is accelerated, or whether . . . the observed effects are due to a gravitational field.” 21
Einstein called this “the equivalence principle.” 22 The local effects of gravity and of acceleration are equivalent. This became a foundation for his