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The quantum theory was based on the idea that particles like electrons could be described not as pointlike particles but as a wave of
some sort, described by Schrôdinger's celebrated wave equation. (The
wave represents the probability of finding the particle at that point.)
But Dirac realized that there was a defect with Schrôdinger's equation. It described only electrons moving at low velocities. At higher velocities, the equation failed because it did not obey the laws of objects
moving at high velocities, that is, the laws of relativity found by Albert
Einstein.
To the young Dirac, the challenge was to reformulate the Schrôdinger equation to accommodate the theory of relativity. In 1928 Dirac
proposed a radical modification of the Schrôdinger equation that fully
obeyed Einstein's relativity theory. The world of physics was stunned.
Dirac found his famous relativistic equation for the electron purely by
manipulating higher mathematical objects, called spinors. A mathematical curiosity was suddenly becoming a centerpiece for the entire
universe. (Unlike many physicists before him, who insisted that great
breakthroughs in physics be firmly grounded in experimental data,
Dirac took the opposite strategy. To him pure mathematics, if it was
beautiful enough, was the sure guide to great breakthroughs. He
wrote, "It is more important to have beauty in one's equations than to
have them fit experiments ... It seems that if one is working from the
point of view of getting beauty in one's equations, and if one has a
really sound insight, one is on a sure line of progress.")
In developing his new equation for the electron, Dirac realized that
Einstein's celebrated equation, E = mc
2 , was not quite right. Although
it is splattered over Madison Avenue ads, children's T-shirts, cartoons,
and even the costumes of superheroes, Einstein's equation is only partially correct. The correct equation is actually E = ± mc
2 . (This minus
sign arises because we have to take the square root of a certain quantity. Taking the square root of a quantity always introduces a plus or
minus ambiguity.)
But physicists abhor negative energy. There is an axiom of physics
that states that objects always tend to the state of lowest energy (this is
the reason that water always seeks the lowest level, sea level). Since
-
The quantum theory was based on the idea that particles like electrons could be described not as pointlike particles but as a wave of
some sort, described by Schrôdinger's celebrated wave equation. (The
wave represents the probability of finding the particle at that point.)
But Dirac realized that there was a defect with Schrôdinger's equation. It described only electrons moving at low velocities. At higher velocities, the equation failed because it did not obey the laws of objects
moving at high velocities, that is, the laws of relativity found by Albert
Einstein.
To the young Dirac, the challenge was to reformulate the Schrôdinger equation to accommodate the theory of relativity. In 1928 Dirac
proposed a radical modification of the Schrôdinger equation that fully
obeyed Einstein's relativity theory. The world of physics was stunned.
Dirac found his famous relativistic equation for the electron purely by
manipulating higher mathematical objects, called spinors. A mathematical curiosity was suddenly becoming a centerpiece for the entire
universe. (Unlike many physicists before him, who insisted that great
breakthroughs in physics be firmly grounded in experimental data,
Dirac took the opposite strategy. To him pure mathematics, if it was
beautiful enough, was the sure guide to great breakthroughs. He
wrote, "It is more important to have beauty in one's equations than to
have them fit experiments ... It seems that if one is working from the
point of view of getting beauty in one's equations, and if one has a
really sound insight, one is on a sure line of progress.")
In developing his new equation for the electron, Dirac realized that
Einstein's celebrated equation, E = mc
2 , was not quite right. Although
it is splattered over Madison Avenue ads, children's T-shirts, cartoons,
and even the costumes of superheroes, Einstein's equation is only partially correct. The correct equation is actually E = ± mc
2 . (This minus
sign arises because we have to take the square root of a certain quantity. Taking the square root of a quantity always introduces a plus or
minus ambiguity.)
But physicists abhor negative energy. There is an axiom of physics
that states that objects always tend to the state of lowest energy (this is
the reason that water always seeks the lowest level, sea level). Since