Baggott J. The Quantum Story: A History in 40 Moments

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PROLOGUE

Stormclouds

London, April 1900

At the beginning of the twentieth century there were plenty of reasons

for believing that the great journey that was physics was close to reach-

ing its ﬁ nal destination.

The structure that was classical physics had been built on foundations

laid by Isaac Newton’s grand synthesis in the seventeenth century. A fur-

ther two hundred years of scientiﬁ c endeavour had created a seemingly

unassailable model of the world. This model explained everything, from

the interplay of force and motion in the dynamics of moving objects,

thermodynamics, optics, electricity, magnetism, and gravitation. Its

scope was vast. It described everything, from the familiar objects of

everyday experience on earth to objects in the furthest reaches of the

visible universe. There seemed little room for doubt about the basic cor-

rectness of classical physics, its essential truth.

But Newton had been obliged to compromise. He needed an abso-

lute space and an absolute time to provide a framework against which

all motion could be measured. Much more worrisome was the force of

gravity. In all of Newton’s mechanics, force is a physical phenomenon

exerted through contact between one object and another. Newton’s grav-

ity was an inﬂ uence felt through a curious, mutual action-at-a-distance

between objects. He was accused of introducing ‘occult agencies’ into his

otherwise rational, physical, and mathematically precise description of

the world. In a General Scholium, added to the 1713 second edition of his

most famous work Philosophiæ Naturalis Principia Mathematica (The Math-

ematical Principles of Natural Philosophy), he wrote:

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Hitherto we have explain’d the phænomena of the heavens and of our

sea, by the power of Gravity, but have not yet assign’d the cause of this

power . . . I have not been able to discover the cause of those properties of

gravity from phænomena, and I frame no hypotheses.

Gravity was a force that was somehow exerted instantaneously, with no

intervening medium other than a hypothetical, all-pervading, tenuous

form of matter called the ether that was thought to ﬁ ll the void.

Newton had also extended the scope of his mechanics to describe light,

concluding that light consists of tiny particles, or corpuscles. Two of his

contemporaries, English natural philosopher Robert Hooke and Dutch

physicist Christiaan Huygens, had argued that light consists instead of

waves. Such was Newton’s standing and authority that the corpuscular

theory held sway for a hundred years.

In a series of papers read to the Royal Society in London between 1801

and 1803, nearly eighty years after Newton’s death, English physicist

Thomas Young revived the wave theory as the only possible explanation

of light diffraction and interference phenomena. In one experiment, com-

monly attributed to Young, it was shown that when passed through two

narrow, closely spaced holes or slits, light produces a pattern of bright

and dark fringes. These are readily explained in terms of a wave theory of

light in which the peaks and troughs of the light waves from the two slits

start out ‘in step’ (or in phase). Where a peak of one wave is coincident

with a peak of another, the two waves add and reinforce. This is called

constructive interference, and gives rise to a bright fringe. Where a peak

of one wave is coincident with a trough of another, the two waves cancel.

This is called destructive interference, and gives a dark fringe.

Despite the apparently inescapable logic of his explanation, Young’s

views were roundly rejected by the physics community at the time, with

some condemning his explanation as ‘destitute of every species of merit’.

The wave theory of light was to prove ultimately irresistible, however.

In the 1860s Scottish physicist James Clerk Maxwell fused electricity

and magnetism into a single theory of electromagnetism. The intimate

connection between electricity and magnetism had been established for

some years, most notably through the extraordinary experimental work

of Michael Faraday at London’s Royal Institution. Drawing on analogies

with ﬂ uid mechanics, Maxwell proposed the existence of electromag-

prologue stormclods

netic ﬁ elds whose properties are described by a set of complex differen-

tial equations.

Maxwell had made no assumptions about how these ﬁ elds were sup-

posed to move through space. Nevertheless, when the equations are cast

in a way that makes explicit the interdependence of the electric and mag-

netic ﬁ elds as they move through free space, they point unambiguously

to a wave-like motion. And, as Maxwell himself discovered, the speed of

these electromagnetic waves is precisely the speed of light.

But waves are disturbances in something. Waves rippling on the sur-

face of a pond are disturbances in water. The noise of a tree falling in a

forest is derived from sound waves propagating through the air. All wave

motion requires a medium to support it, so precisely what medium was

meant to support light waves? The ether was once again called to duty.

Faraday had rejected the notion of the ether, but Maxwell leaned heavily

on the concept in developing his theory.

It seemed that neither gravity nor electromagnetism could be

explained without the ether. But if the ether existed, then certain physical

The historical development of Maxwell’s equations is described in detail in Crease, A Brief

Guide to the Great Equations.

light

source

Wavefront

fig 1 Thomas Young discovered that passing light through two narrow, closely-spaced

holes or slits would produce a pattern of alternating light and dark fringes. These could

only be explained, Young, believed, in terms of a wave theory of light in which overlap-

ping wavefronts interfere constructively (bright fringe) and destructively (dark fringe).

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consequences could be anticipated. The earth’s motion through space

could be expected to drag the ether along with it. And, just as a sound

wave will appear to be travelling faster if a strong wind moves the air that

carries it, so a light wave is expected to appear to travel faster if caught in

an ‘ether wind’. This meant that there should be measurable differences in

the speed of light depending on the direction it is travelling relative to the

earth’s motion through space. This proposal was put to its most stringent

test by American physicists Albert Michelsen and Edward Morley in 1887.

They could ﬁ nd no evidence for a drag effect and hence no evidence for

relative motion between the earth and the ether.

As the century turned, Newton’s grand mechanical design remained

largely unassailable. Physicists were either willing to forgive gravitational

action-at-a-distance or quietly forget that this was a problem, because the

structure worked so wonderfully well and it was so obviously right. Newton

had been shown to be fallible on the question of light, but it was now clear

how a wave theory of light ﬁ tted into the equally wonderful structure created

by Maxwell, despite some hesitancy on the question of the wave medium.

We could, perhaps, forgive physicists of the late nineteenth century their

sense of triumph. In 1900, the great British physicist Lord Kelvin (William

Thomson) famously declared to the British Association for the Advance-

ment of Science that: ‘There is nothing new to be discovered in physics

now. All that remains is more and more precise measurement.’

It is a famous declaration, one that characterizes the mood of the

time, although, it seems, one that may well be apocryphal.

The simple

truth is that in the last decades of the nineteenth century the mechanical

structure of classical physics was beginning to creak under the strain of

accumulating contrary evidence. In April 1900, Kelvin delivered a lecture

to the Royal Institution concerned with what he perceived to be nineteenth

century ‘clouds’ over the dynamical theory of heat and light.

Not triumphalist, but prescient.

The stormclouds were gathering. But nobody could tell precisely where

the storm would break.

In his 2007 biography of Einstein, Walter Isaacson explained that he could ﬁ nd no direct

evidence that Kelvin had made this pronouncement.

See Kragh, Quantum Generations, p. 9.

PART I

Quantum

of Action

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Max Planck had once been counselled against a career in theoretical physics. His profes-

sor at the University of Munich had advised him that, with the discovery of the principles

of thermodynamics, physics as a subject had been largely completed. There was, quite

simply, nothing more to be discovered.

But, as the turn of the nineteenth century approached, there was nevertheless conﬂ ict

between rival theories of physics. The principles of thermodynamics reinforced a vision of

nature as one of harmonious ﬂ ow. Energy, which could be neither created nor destroyed,

ﬂ owed continuously between radiation and material substance, in themselves unbroken

continua. Ranged against this view were the atomists, who offered a rather different per-

spective. Matter was not continuous, they argued, it was composed of discrete atoms or

molecules. The thermodynamic properties of material substances could be calculated

from the mechanical motions of the atoms or molecules from which they were composed,

using statistics.

Planck was a master of classical thermodynamics. There were aspects of the atomists’

statistical-mechanical models which served to undermine his world view, and his life’s

work. Although he accepted that the atomic conception of matter had scored some notable

successes, he regarded it as a ‘dangerous enemy of progress’ which would ultimately ‘have to

be abandoned in favour of the assumption of continuous matter.’

In 1897 Planck had chosen the theory of cavity radiation, or so-called ‘black-body’

radiation, as the ground on which to engage his atomist rivals; as a place where he could

ﬁ nally reconcile mechanics with thermodynamics. But what he would discover just three

The Most Strenuous

Work of My Life

Berlin, December 1900

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years later would complete his slow conversion to the atomist doctrine. And, almost as a

by-product, he would quietly sow the seeds for the most profound revolution in our scien-

tiﬁ c understanding of the world; a revolution whose repercussions can still be widely felt,

more than a century later.

Planck’s problem with the atomist doctrine was relatively simply stated.

By reducing the calculation of thermodynamic quantities to the statis-

tics of atomic or molecular motions, the atomists had opened the door

to some discomforting consequences. What thermodynamics argued to

be unquestionably irreversible and a matter of irresistible natural law,

statistics argued was only the most probable of many different possible

alternatives.

The conﬂ ict was most stark in the interpretation of the second law of

thermodynamics. This was the subject of Planck’s 1879 doctoral thesis,

and it was a subject on which Planck prided himself as one of the world’s

leading experts. The second law claimed that for a substance—such as a

gas—contained in a closed system, prevented from exchanging energy

with the outside world, the thermodynamic quantity known as entropy

would increase spontaneously and inexorably to a maximum as the gas

reached equilibrium with its surroundings.

Entropy is a somewhat abstract quantity that we tend to interpret as

the amount of ‘disorder’ in a system.

In 1895, with Planck’s approval, his

research assistant Ernst Zermelo took the argument directly to the atom-

ists in the pages of the German scientiﬁ c journal Annalen der Physik.

If, to take an example, we were to release two gases of different

temperature in a closed container, the second law would predict that

the gases would mix and the temperature would equilibrate, with the

entropy of the mixture increasing to a maximum. However, according to

the atomists, the behaviour of the gases is a consequence of the underly-

ing mechanical motions of the atoms or molecules of each gas, and the

equilibrium state of the mixture is simply its most probable state. This

implies, argued Zermelo, that there is nothing in principle to rule out

For example, as a block of ice melts, it transforms into a more disordered, liquid form. As

liquid water is heated to steam, it transforms into an even more disordered, gaseous form. The

measured entropy of water increases as water transforms from solid to liquid to gas.

the most strenuous work of my life

a sequence of events in which the motions of the atoms or molecules

are all reversed. If this were to happen, the gases would surely separate,

returning to their initial temperatures and spontaneously reducing the

entropy of the mixture, in complete contradiction to the second law.

The atomists’ leading spokesman, Austrian physicist Ludwig Boltzmann,

responded. Entropy does not always increase, he argued, in contradiction

to the most commonly accepted interpretation of the second law. It just

almost always increases. Statistically speaking, there are many, many more

states of higher entropy than there are of lower entropy, with the result

that the system spends much more time in higher entropy states. In effect,

Boltzmann was saying that if we wait long enough,

we might eventually

catch the system undergoing a spontaneous reduction in entropy.

This is as miraculous an event as a smashed cocktail glass spontane-

ously reassembling itself, to the astonishment of party guests.

To Planck, this stretched the interpretation of the second law to breaking

point. In seeking to ﬁ nd a compelling refutation of Boltzmann’s statistical

argument, Planck chose as a battleground the physics of cavity radiation.

This seemed a perfectly safe choice. The theoretical physics of cav-

ity radiation appeared to have no connection with atoms or molecules.

It was a problem of continuous waves of electromagnetic radiation, as

described by Maxwell’s theory, and of thermodynamics, whose second

law would drive the radiation to equilibrium. Planck had reasoned that if

he could show how equilibrium was established without recourse to the

statistical-mechanical models of the atomists, he could undermine the

very basis of the mechanical description.

The behaviour of cavity radiation was by now well understood. Heat

any object to a high temperature and it will gain energy and emit light.

We say that the object is ‘red hot’ or ‘white hot’. Increasing the tempera-

ture of the object increases the intensity of the light emitted and shifts it

to a higher range of frequencies (shorter wavelengths). As it gets hotter,

the object glows ﬁ rst red, then orange-yellow, then bright yellow, then

brilliant white.

Admittedly, we would have to wait for a time much longer than the present age of the

universe.