The Science Book

235

See also: Albert Einstein 214–21 ■ Erwin Schrödinger 226–33 ■
Paul Dirac 246–47 ■ Richard Feynman 272–73 ■ Hugh Everett III 284–85

A PARADIGM SHIFT

precision. For example, the
more accurately one measures
a particle’s position, the less
accurately one can determine
its momentum, and vice versa.
Heisenberg found that for these
two properties in particular, the
relationship could be written as:
횫x횫p ≥ /2
where 횫x is the uncertainty of
position, 횫p the uncertainty of
momentum, and h is a modified
version of Planck’s constant (p.202).

An uncertain universe
The uncertainty principle is often
described as a consequence of
quantum-scale measurements—for
example, it is sometimes said that
determining a subatomic particle’s
position involves the application of
a force of some sort that means its
kinetic energy and momentum are
less well defined. This explanation,
put forward at first by Heisenberg
himself, led various scientists
including Einstein to spend time
devising thought experiments that
might obtain a simultaneous and
accurate measurement of position
and momentum by some form of
“trickery.” However, the truth is

far stranger—it turns out that

uncertainty is an inherent feature

of quantum systems.

A helpful way of thinking

about the issue is to consider the

matter waves associated with

the particles: in this situation, the

particle’s momentum affects its

overall energy and therefore its

wavelength—but the more tightly

we pin down the particle’s position,

the less information we have about

its wave function, and therefore

about its wavelength. Conversely,

accurately measuring the

wavelength requires us to consider

a broader region of space, and

therefore sacrifices information

about the particle’s precise

location. Such ideas might seem

strangely at odds with those we

experience in the large-scale world,

but they have nevertheless been

proved real by many experiments,

and form an important foundation

of modern physics. The uncertainty

principle explains seemingly

strange real-life phenomena such

as quantum tunneling, in which

a particle can “tunnel” through a

barrier even if its energy suggests

that it should not be able to. ■

Werner Heisenberg

Born in the southern German

town of Würzburg in 1901,

Werner Heisenberg studied

mathematics and physics at

the universities of Munich and

Göttingen, where he studied

under Max Born and met his

future collaborator Niels Bohr

for the first time.

He is best known for his

work on the Copenhagen

interpretation and the

uncertainty principle, but

Heisenberg also made

important contributions to

quantum field theory and

developed his own theory

of antimatter. Awarded the

Nobel Prize in Physics in

1932, he became one of its

youngest recipients, and his

stature enabled him to speak

out against the Nazis after

they seized power the

following year. However,

he chose to stay in Germany

and led the country’s nuclear

energy program during

World War II.

Key works

1927 Quantum Theoretical

Re-interpretation of Kinematic

and Mechanical Relations

1930 The Physical Principles

of the Quantum Theory

1958 Physics and Philosophy

This uncertainty is a

property inherent

to the universe.

Subatomic particles have

wavelike qualities.

This means that you cannot

accurately measure both

a particle’s position and

its momentum.

Uncertainty is

inevitable.

h⎯