DOC.

16

FUNDAMENTAL DIFFICULTY IN

PHYSICS

339

Doc.

16

Comment

on a

Fundamental

Difficulty

in Theoretical

Physics

Zurich,

2

January 1911

Our

present

physical

world

picture

rests

on

the fundamental

equations

of

point

mechanics

and

on

Maxwell's

equations

for the

electromagnetic

field in

a vacuum.

It becomes

more

and

more

apparent

that

all

those

consequences

of

this

foundation that refer

to

slow,

i.e.,

not

rapid periodical

processes,

are

in excellent

agreement

with

experience.

We

have

[1]

succeeded

in

arriving

at

a general

formulation

of

the limits

of

validity

of

thermodynamics

with

the

help

of

point mechanics,

and

in

deriving

from the latter the fundamental

laws

of

thermodynamics.

We

have

succeeded

in

entirely

different

ways

in

determining

the

absolute

sizes

of

atoms

and molecules

with

undreamed-of

accuracy.

We

have also

been

able to derive

the

law

of thermal radiation for

long wavelengths

and

high

temperatures

from

statistical mechanics

and

electrodynamics.

But

the foundations of

the

theory

leave

[2]

us

in

the

lurch

when

it

comes

to all

those

phenomena

that

involve

the transformation of

energy

of

rapid

periodical

processes.

We

know

of

no

flawless

derivation of the

law

of

radiant heat for short

wavelengths

and

low

temperatures.

We

do not know

the

reason

[3]

why high

molecular

temperatures

are

needed

for

the

generation

of

short-wave

radiation,

and

why

the

absorption

of

the

latter

can produce elementary

processes

of

relatively

great

energy.

We

do not know

why

the

specific

heat

at low

temperatures is

smaller than

predicted

by

the

Dulong-Petit

law. We know

just

as

little

about

why

those

mechanical

degrees

of freedom of

matter

that

must

be

postulated

in

order

to

comprehend

the

optical

properties

of

transparent

bodies

make

no

contribution

to

the

specific

heats of these

bodies.

[4]

But

one

thing

has

been done.

M. Planck has shown

that

one

arrives at

a

radiation

formula that

is in

agreement

with

experience

if

one

modifies

the formulas

resulting

from

our

theoretical foundations

as though

the

energy

of

oscillations

of

frequency v

could

only

occur

in

integral

multiples

of the

quantity

hv.

This modification also leads to

a

[5]

modification

of the

consequences

of

mechanics

that

has

thus far

proved

useful if

rapid

oscillations

are

involved.

A

proper theory

has not

yet come

into

being,

but

it

can

be said

[6]

with

certainty:

point

mechanics

is

not valid

for

rapid periodic processes,

and the

customary conception

of the distribution of radiant

energy

in

space can

also not

be

maintained.

[7]

A.

Einstein