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

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This is a mathematical description of all known particles and all known

forces between them, enabling us to explain all of the behaviour of these

particles . . . As far as we know, there is no single physical phenomenon

that cannot be regarded as some consequence of the Standard Model,

and yet its basic formulae are not terribly complicated. We do admit that

the model is not absolutely perfect . . . however, the degree of perfection

reached is quite impressive.

But the Standard Model does not represent a return to triumphalism

of the kind characterized by Kelvin’s possibly apocryphal speech to the

British Association for the Advancement of Science in 1900. Despite the

model’s obvious and unmitigated successes, its deep ﬂ aws have been

painfully apparent since its inception in the late 1970s.

The Standard Model has to accommodate a rather alarming number

of ‘fundamental’ particles. Six quark ﬂ avours multiplied by three possible

colour values gives 18 different types of quark. Add the leptons—the elec-

tron, muon, and tau, and their neutrinos, and we have 24 fermions. Then

there are the anti-particles of all these, making 48, to which we need to

add the ﬁ eld quanta: the photon, the W

, W

−

, and Z

particles and eight

different types of gluon, making 60 in total. All of these particles have

been ‘observed’ so to speak, but we should also add the so far unobserved

Higgs boson, making 61 particles in all. This hardly seems the stuff of a

fundamental theory.

These 61 particles are connected together in a framework that requires

20 parameters that cannot be derived from theory but must be obtained

by measurement. As Lederman put it in 1993:

The idea is that twenty or so numbers must be speciﬁ ed in order to begin

the universe. What are these numbers (or parameters, as they are called in

the physics world)? Well, we need twelve numbers to specify the masses

of the quarks and leptons. We need three numbers to specify the strengths

of the forces . . . We need some numbers to show how one force relates to

another. Then we need a number for how the CP-violation enters, and a

mass for the Higgs particle, and a few other handy items.

The pattern of particle masses is particularly troublesome. For the quarks,

we must distinguish between the mass of a ‘naked’ quark and a quark

‘dressed’ in a covering of gluons whose energy contributes to the quark

the standard model

291

mass. The mass of a naked up quark has been determined to be between

1.5 and 3.3 MeV; the naked down quark mass between 3.5 and 6.0 MeV.

When we compare these ﬁ gures with the measured mass of a proton

(uud) of 939 MeV we get some idea of the scale of the mass contributed

by the binding energy of the gluons.

The charm quark has a ‘running’ mass of 1270 MeV, the strange quark

a mass of 104 MeV.

The top quark has a running mass of 171,200 MeV,

the bottom quark a mass of 4200 MeV. This looks like a pretty random

pattern of values, with no rhyme or reason. The masses of the leptons are

likewise unfathomable.

The mixing angles, which determine how strongly the weak and elec-

tromagnetic forces act on both the quarks and the leptons, must also be

determined by experiment. The masses and mixing angles are the results

of the interactions of the quarks and leptons with the Higgs ﬁ eld. The

inability of theory to predict these values from ﬁ rst principles may there-

fore reﬂ ect the simple fact that the properties of the Higgs ﬁ eld and the

precise nature of the symmetry-breaking mechanism are not properly

accounted for in the Standard Model.

The Standard Model is not a theory in which the strong, weak, and

electromagnetic forces can be said to be properly uniﬁ ed. And, of course,

the model makes no attempt to accommodate the fourth known force

of nature: gravity. This is a force so weak that it is of no consequence

in the interactions between the fundamental particles. But it is always

attractive, proportional to the particle mass, and cumulative. Scale up

the quarks into nucleons, nucleons into atoms, atoms into molecules,

molecules into solid matter, matter into planetary bodies, and the force

of gravity becomes irresistible.

These quark mass data are taken from C. Amsler et al., Physics Letters B, 667, 2008, p. 1.

The ‘running’ mass reﬂ ects the fact that mass values vary when measured at different

energy scales.

Although the neutrinos were thought to be massless, recent observations of the ﬂ ux of

neutrinos from the sun suggest that they oscillate between the types, an electron neutrino turn-

ing into a muon or tau neutrino, etc. This is possible only if the neutrinos possess very small

masses. This can all be accommodated in the Standard Model but at the cost of introducing

further parameters.

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292

The gravitational ﬁ eld implies a quantum ﬁ eld theory of the gravita-

tional force, and a force carrier, called the graviton. To account for the pro-

perties of the gravitational force, the graviton would need to be a spin-2

ﬁ eld boson. Familiar (and by now tried and trusted) approaches to a quan-

tum ﬁ eld theory of gravity lead to a result which is non-renormalizable.

Impasse.

With no disconcerting or inexplicable experimental results to pursue and

no theoretical predictions within reach of experiment, there was now no

guidance on how the Standard Model should be developed. Or, indeed,

no guidance on whether the Standard Model should be abandoned in

favour of an altogether different approach.

Although the mass of the Higgs boson could not be predicted, physi-

cists at CERN and Fermilab were able to place lower and upper bounds

on its value. Approval was given in the late 1980s for the construction of

a new facility, the Superconducting Supercollider (SSC), in Waxahachie,

Texas. This was to be an 87-kilometre circumference ring producing a col-

lision energy of 40 TeV, potentially capable of bringing the Higgs boson

within reach of experimental physics. On giving his approval, US Presi-

dent Ronald Reagan had urged his Cabinet secretaries to ‘Throw deep.’

Construction began in 1991. The project was directed by Roy Schwitters.

Budget estimates mushroomed, from $4.4 billion in 1987 to $12 billion

in 1993. Despite efforts by President Bill Clinton to garner support for the

project, it was cancelled by Congress. Nearly 23 kilometers of tunnel had

been excavated and nearly $2 billion had been spent.

Two years later a more modest project was approved to construct the

Large Hadron Collider (LHC) at CERN, using the 27-kilometre tunnel that

houses the LEP. Rubbia declared that CERN would ‘pave the LEP tunnel

with superconducting magnets.’ The LHC is expected to eventually pro-

duce a collision energy of 14 TeV, less than half the energy that could have

been achieved with the SSC, but nevertheless with a theoretical capabil-

ity of generating one Higgs boson every couple of hours.

On the morning of Tuesday, 16 September 2003 a small but highly dis-

tinguished international group of physicists gathered in CERN’s large

auditorium to celebrate the double anniversary of the discoveries of the

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weak neutral currents (1973) and the W and Z particles (1983). After a

brief welcome by Maiani, then CERN Director General, Weinberg stood

to describe the twists and turns that had led ultimately to the creation of

the Standard Model of particle physics. He concluded as follows:

Well, those were great days. The 1960s and 1970s were a time when experi-

mentalists and theorists were really interested in what each other had to

say, and made great discoveries through their mutual interchange. We have

not seen such great days in elementary particle physics since that time, but

I expect that we will see good times return again in a few years, with the

beginning of a new generation of experiments at this laboratory.

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PART VI

Quantum

Reality

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297

David Bohm was arrested on 4 December 1950 and charged with contempt of court.

He had joined the Communist Party in November 1942 and had been part of a

close-knit group of radical young physicists studying at Berkeley under Oppenheimer.

In March 1943 one among this group—Joseph Weinberg—had been caught betraying

atomic secrets by an illegal FBI bug planted in the home of Steve Nelson, a key ﬁ gure in

the Communist Party apparatus in the Bay Area of San Francisco. This evidence was

inadmissible in court and, in an attempt to expose Weinberg’s betrayal by more legal

means, the House Un-American Activities Committee (HUAC) had called Bohm to

testify in May 1949.

Einstein had advised Bohm to refuse, suggesting that he ‘may have to sit for a while’,

meaning that the penalty for his silence might be a short spell in prison. He had chosen

to testify, but refused to divulge names at the hearing and at a subsequent HUAC hear-

ing in June. Princeton University had expressed support and declared Bohm a ‘thorough

American’.

But events over the next twelve months would conspire to whip anti-Communist sen-

timent in America to fever pitch. Earlier testimony by Whitaker Chambers, a former

Soviet agent and editorial staff member of Time magazine, had revealed the names of

two highly placed Communists in US President Harry Truman’s administration—Alger

Hiss at the State Department and Harry Dexter White at the Treasury. White died of a

heart attack in August 1948. Hiss was convicted on two counts of perjury in January 1950

and sentenced to two concurrent ﬁ ve-year prison sentences. As the ‘red scare’ gathered

Hidden Variables

Princeton, Spring 1951

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298

momentum, in February 1950 Republican Senator Joseph McCarthy saw an opportunity

to launch an anti-Communist crusade. It became a witch-hunt.

HUAC had concluded in September 1949 that Weinberg and Bohm had been mem-

bers of a Communist cell that had passed atomic secrets to the Soviets. After Bohm’s

arrest he was bailed, but now the Princeton University administrators withdrew their

support. Bohm was suspended from his post for the duration of the trial.

Bohm came to trial on 31 May 1951. He was acquitted (as was Weinberg a few years

later). But Princeton University did not renew Bohm’s contract when it expired the follow-

ing month. John Wheeler, who had helped to bring Bohm to Princeton, later summarized

the prevailing sentiment: ‘I found it hard to accept Bohm’s decision to shield those who

adhered to Communist ideology at a time when the Soviet Union was suppressing its

own people and threatening world peace.’ Einstein wanted to offer Bohm a position at the

Institute for Advanced Study but Oppenheimer, fearing for his own position as Director

of the Institute, vetoed the move.

With his life turning upside-down, it was hardly possible for Bohm to concentrate on

his physics. He had just ﬁ nished writing a book, simply titled Quantum Theory, and

was correcting the proofs. But he admitted that it was ‘hard to concern myself with getting

all these [mathematical] formulas correct.’

The book was published in February 1951. It received many favourable reviews. On

the question of interpretation, Bohm had stuck fairly closely to the orthodoxy of the

Copenhagen school, though he was closer in spirit to Pauli than to Bohr. Einstein wel-

comed the book, claiming it was the clearest presentation of the Copenhagen interpretation

he had ever read. But, of course, this didn’t mean that Einstein accepted what Bohm had

written. Einstein asked for an opportunity to explain his objections, and invited Bohm to

visit him.

In 1935 Einstein, Podolsky, and Rosen had asserted that quantum theory is

incomplete. They had left open the question of whether or not the theory

could be somehow ‘completed’, declaring only that this should be pos-

sible in principle. The simplest way to complete the theory and restore

causality and determinism is to invoke hidden variables of some form.

Einstein himself had toyed with just such an approach in May 1927.

This was a modiﬁ cation of quantum theory that combined classical wave

and particle descriptions, with the wavefunction of Schrödinger’s wave

mechanics taking the role of a ‘guiding ﬁ eld’ (Führungsfeld), guiding the

physically real point-particles.

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299

In this scheme, the wavefunction is responsible for all the wave-like

effects, such as diffraction and interference, but the particles maintain

their integrity as local, physically real entities. Instead of waves or particles,

as the Copenhagen interpretation demanded, Einstein’s hidden variables

version of quantum theory was constructed from waves and particles.

But Einstein had lost his enthusiasm for this approach within a mat-

ter of weeks of formulating it. The guiding ﬁ eld was capable of exerting

‘spooky’ non-local inﬂ uences. When de Broglie had stood to present his

‘double solution’ on the second day of the ﬁ fth Solvay conference later

in October that year, Einstein had already rejected this approach. He had

remained silent through de Broglie’s presentation.

This experience probably led Einstein to conclude that his initial

belief—that quantum theory could be ‘completed’ through a more direct

fusion of classical wave and particle concepts—was misguided. He

subsequently expressed the opinion that a complete theory could only

emerge from a much more radical revision of the entire theoretical struc-

ture. One such possibility was an elusive grand uniﬁ ed ﬁ eld theory, the

search for which took up most of Einstein’s intellectual energy in the last

decades of his life.

In his book Quantum Theory, Bohm appeared to have accepted Bohr’s

response to the EPR argument as having settled the matter in favour of

the Copenhagen interpretation. He wrote: ‘EPR’s criticism has, in fact,

been shown to be unjustiﬁ ed, and based on assumptions concerning the

nature of matter which implicitly contradict the quantum theory at the

outset.’ Despite what he had written, this conclusion had left him with a

distinct feeling of dissatisfaction.

In his description of the EPR argument, Bohm had pushed the gedank-

enexperiment into a different domain of applicability. He considered a

molecule consisting of two atoms in a quantum state in which the total

electron spin angular momentum is zero. A simple example would be a

hydrogen molecule, H

, with its two electrons spin-paired in the lowest

(so-called ‘ground’) electronic state.

See Chapter 13, pp. 116–117.

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

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