When Words Fail

by Frank Wilczek

Nobel Laureate in Physics 2004

Herman Feshbach professor of physics at MIT

http://frankwilczek.com/Wilczek_Easy_Pieces/306_When_Words_Fail.pdf

Scientists have to struggle

with words that don't fit reality

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Language is a social creation. 

It encodes the common experience 

of many people, past and present, 

and has been sculpted mainly 

to communicate our everyday needs. 

Ordinary language 

is most certainly not a product 

of the critical investigation of concepts. 

Yet scientists 

learn, think and communicate in it 

during much of their lives. 

Ordinary language is therefore

an unavoidable scientific tool 

— rich and powerful, 

but also quite imperfect.

One scientific imperfection of language,

perhaps the most obvious, is its incompleteness.

For example, there are no 

common words for several 

of the most central concepts

of quantum theory, 

such as the linearity of state-space 

and the use of tensor products 

to describe composite systems. 

To be sure, we’ve developed 

some applicable jargon 

— ‘superposition’ and ‘entanglement’, 

respectively, are the words we use — 

but the words are unusual ones, 

not likely to convey much to outsiders,

and their literal meaning is misleading to boot.

Although it creates cultural barriers 

and contributes to the balkanization of knowledge,

such enrichment and slight abuse of language 

is not conceptually problematic.

Much more insidious, 

and more fundamentally interesting, 

is the opposite case: 

when ordinary language is too complete. 

When something has a name, 

and is commonly employed in discourse, 

it is seductive to assume 

that it refers to a coherent concept,

and an element of reality. 

But it need not.

And the more pervasive the word, 

the more difficult it can be to evade its spell.

Few words are more pervasive than ‘now’.

According to his own account, 

the greatest difficulty Einstein 

encountered in reaching

the special theory of relativity 

was the necessity to break free 

from the idea that there is 

an objective, universal ‘now’: 

“[A]ll attempts to clarify 

this paradox satisfactorily 

were condemned to failure 

as long as the axiom 

of the absolute character of times, 

viz., of simultaneity, unrecognizedly 

was anchored in the unconscious. 

Clearly to recognize this axiom

and its arbitrary character really implies

already the solution of the problem.”

[Einstein, A. “Autobiographical notes” in Albert Einstein,

Philosopher-Scientist (ed. Schilpp, P.) (Library of Living

Philosophers, 1949).]

Einstein’s original 1905 paper 

begins with a lengthy discussion, 

practically free of equations,

of the physical operations involved 

in synchronizing clocks at distant points. 

He then shows that these same operations,

implemented by a moving system of observers, 

leads to differing determinations

of which events occur “at the same time”.

As relativity undermines ‘now’, 

quantum theory undermines ‘here’. 

Heisenberg had Einstein’s analysis 

specifically in mind when,

in the opening of his seminal paper 

on the new quantum mechanics in 1925, 

he advocated the formulation of physical laws 

using observable quantities only. 

But while classical theory 

has a naïve conception 

of a particle’s position, 

described by a single coordinate 

(a triple of numbers, 

for three-dimensional space), 

quantum theory requires 

this to be replaced 

by a much more abstract quantity.

One aspect of the situation is that 

if you don’t measure the position, 

you must not assume

that it has a definite value. 

Many successful calculations 

of physical processes 

using quantum mechanics 

are based on performing

a precise form of averaging 

over many different positions 

where a particle ‘might be found’. 

These calculations would be ruined 

if you assumed that the particle 

was always at some definite place. 

You can choose to measure its position, 

but performing such a measurement

involves disturbing the particle. 

It changes both the question and the answer.

Einstein himself 

was never reconciled 

to the loss of ‘here’. 

In his greatest achievement,

the general theory of relativity, 

Einstein relied heavily 

on the primitive notions of events 

in space–time and (proper) distance 

between nearby events. 

These notions rely on unambiguous

association of times and places 

— ‘nows’ and ‘heres’ — 

to individual objects of reality 

(though not, of course, 

on the existence of a universal ‘now’). 

Understandably impressed 

by the success of his theory,

Einstein was loath to sacrifice its premises. 

He resisted modern quantum theory, 

and did not participate in its sweeping success 

in elucidating problem after great problem.

Ironically, the sacrifice he feared 

has not (yet) proved necessary. 

On the contrary, 

in the modern Theory of Matter, 

we retain ‘nows’ and ‘heres’ 

for the fundamental objects of reality. 

These primitives 

are no less important 

in the formulation 

of the subatomic laws 

of quantum theory 

than in general relativity. 

The new feature is that 

the fundamental objects of reality 

are one step removed 

from the directly observed: 

they are quantum fields, 

rather than physical events.

It is possible 

to avoid ordinary language

and its snares. 

Within specific domains of mathematics, 

this is accomplished by constructing

exact definitions and axioms. 

Purity of language is also forced on us 

when we interact with modern digital computers,

since they do not tolerate ambiguity.

But the purity of artificial languages 

comes at a great cost in scope, 

suppleness and flexibility.

Perhaps computers 

will become truly intelligent 

when they learn to be tolerant 

of ordinary, sloppy language 

— and then to use it themselves! 

In any case, for us humans 

the practical and wise course 

will be to continue 

to use ordinary language,

even for abstract scientific investigations, 

but to be very suspicious of it. 

Along these lines, 

Heisenberg’s considered formulation, 

put forward in The Physical Principles 

of Quantum Theory in 1930, was: 

“[I]t is found advisable to introduce

a great wealth of concepts 

into a physical theory, 

without attempting 

to justify them rigorously, 

and then to allow experiment to decide 

at what points a revision is necessary.”

Looking to the future, 

after ‘now’ and ‘here’,

what basic intuition 

will next require reformation?

As the nature of mind 

comes into scientific focus, 

might it be ‘I’? 

Perhaps the following remarks 

of Hermann Weyl, stimulated 

by deep reflection on the aspects 

of modern physics discussed here 

and stated in his Philosophy of Mathematics 

and Natural Science (1949), point in that direction: 

“The objective world 

simply is, it does not happen. 

Only to the gaze of my consciousness, 

crawling upward along the life line of my body, 

does a section of this world come to life 

as a fleeting image in space 

which continuously changes in time.” 

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Frank Wilczek is in the Massachusetts Institute of

Technology, Cambridge, Massachusetts 20139, USA.