Einstein's delayed 1923 acceptance speech for his hideously delayed Nobel prize--finally offered to him in 1921 for his "work on the photoelectric effect" of 1905--is generated here into a piece of Found Word Art, fashioned by the language-generator residing in the WORDLE site. As in the other cases of word art generated by Wordle, the work is the product of the vocabulary-digester at Wordle, which in this case consumed the entire text of the speech and displayed it according to the appearance of the most popularly-used words. The results of these jaunts into Wordle have been fascinating to me, as I hope they are to you.

The full text of the Einstein speech (which is tricky to find in full text versions) is below. I'm sorry to say that I've messed up the equations, trying to fit them into typepad.

Also you can click on the Wordle display to make it not only larger but **clearer.**

*The Einstein "Acceptance Lecture" for the Nobel Prize, 1923*

Fundamental ideas and problems of the theory of relativity

by Albert Einstein

Lecture delivered to the Nordic Assembly of Naturalists at Gothenburg*

July 11, 1923

Page 1

THEORY OF RELATIVITY

If we consider that part of the theory of relativity which may nowadays in

a sense be regarded as bona fide scientific knowledge, we note two aspects

which have a major bearing on this theory. The whole development of the

theory turns on the question of whether there are physically preferred states

of motion in Nature (physical relativity problem). Also, concepts and dis-

tinctions are only admissible to the extent that observable facts can be as-

signed to them without ambiguity (stipulation that concepts and distinctions

should have meaning). This postulate, pertaining to epistemology, proves to

be of fundamental importance.

These two aspects become clear when applied to a special case, e.g. to clas-

sical mechanics. Firstly we see that at any point filled with matter there exists

a preferred state of motion, namely that of the substance at the point con-

sidered. Our problem starts however with the question whether physically

preferred states of motion exist in reference to extensive regions. From the

viewpoint of classical mechanics the answer is in the affirmative; the physic-

ally preferred states of motion from the viewpoint of mechanics are those of

the inertial frames.

This assertion, in common with the basis of the whole of mechanics as it

generally used to be described before the relativity theory, far from meets

the above "stipulation of meaning". Motion can only be conceived as the

relative motion of bodies. In mechanics, motion relative to the system of

coordinates is implied when merely motion is referred to. Nevertheless this

interpretation does not comply with the "stipulation of meaning" if the co-

ordinate system is considered as something purely imaginary. If we turn our

attention to experimental physics we see that there the coordinate system is

invariably represented by a "practically rigid" body. Furthermore it is as-

sumed that such rigid bodies can be positioned in rest relative to one another

Page 2

THEORY OF RELATIVITY

in common with the bodies of Euclidian geometry. Insofar as we may think

of the rigid measuring body as existing as an object which can be experienced,

the "system of coordinates" concept as well as the concept of the motion of

matter relative thereto can be accepted in the sense of the "stipulation of

meaning". At the same time Euclidian geometry, by this conception, has been

adapted to the requirements of the physics of the "stipulation of meaning".

The question whether Euclidian geometry is valid becomes physically signif-

icant; its validity is assumed in classical physics and also later in the special

theory of relativity.

In classical mechanics the inertial frame and time are best defined together

by a suitable formulation of the law of inertia: It is possible to fix the time

and assign a state of motion to the system of coordinates (inertial frame) such

that, with reference to the latter, force-free material points undergo no ac-

celeration; furthermore it is assumed that this time can be measured without

disagreement by identical clocks (systems which run down periodically) in

any arbitrary state of motion. There are then an infinite number of inertial

frames which are in uniform translational motion relative to each other, and

hence there is also an infinite number of mutually equivalent, physically pre-

ferred states of motion. Time is absolute, i.e.independent of the choice of

the particular inertial frame; it is defined by more characteristics than log-

ically necessary, although - as implied by mechanics - this should not lead

to contradictions with experience. Note in passing that the logical weakness

of this exposition from the point of view of the stipulation of meaning is

the lack of an experimental criterion for whether a material point is force-

free or not; therefore the concept of the inertial frame remains rather prob-

lematical. This deficiency leads to the general theory of relativity. We shall

not consider it for the moment.

The concept of the rigid body (and that of the clock) has a key bearing

on the foregoing consideration of the fundamentals of mechanics, a bearing

which there is some justification for challenging. The rigid body is only ap-

proximately achieved in Nature, not even with desired approximation; this

concept does not therefore strictly satisfy the "stipulation of meaning". It is

also logically unjustifiable to base all physical consideration on the rigid or

solid body and then finally reconstruct that body atomically by means of

elementary physical laws which in turn have been determined by means of

the rigid measuring body. I am mentioning these deficiencies of method

because in the same sense they are also a feature of the relativity theory in

the schematic exposition which I am advocating here. Certainly it would be

Page 3

logically more correct to begin with the whole of the laws and to apply the

"stipulation of meaning" to this whole first, i.e. to put the unambiguous rela-

tion to the world of experience last instead of already fulfilling it in an im-

perfect form for an artificially isolated part, namely the space-time metric.

We are not, however, sufficiently advanced in our knowledge of Nature’s

elementary laws to adopt this more perfect method without going out of our

depth. At the close of our considerations we shall see that in the most recent

studies there is an attempt, based on ideas by Levi-Civita, Weyl, and Edding-

ton, to implement that logically purer method.

It more clearly follows from the above what is implied by "preferred states

of motion". They are preferred as regards the laws of Nature. States of mo-

tion are preferred when, relative to the formulation of the laws of Nature,

coordinate systems within them are distinguished in that with respect to them

those laws assume a form preferred by simplicity. According to classical me-

chanics the states of motion of the inertial frames in this sense are physically

preferred. Classical mechanics permits a distinction to be made between (ab-

solutely) unaccelerated and accelerated motions; it also claims that velocities

have only a relative existence (dependent on the selection of the inertial

frame), while accelerations and rotations have an absolute existence (in-

dependent of the selection of the inertial frame). This state of affairs can be

expressed thus: According to classical mechanics "velocity relativity" exists,

but not "acceleration relativity". After these preliminary considerations we

can pass to the actual topic of our contemplations, the relativity theory, by

characterizing its development so far in terms of principles.

The special theory of relativity is an adaptation of physical principles to

Maxwell-Lorentz electrodynamics. From earlier physics it takes the assump-

tion that Euclidian geometry is valid for the laws governing the position of

rigid bodies, the inertial frame and the law of inertia. The postulate of equiv-

alence of inertial frames for the formulation of the laws of Nature is assumed

to be valid for the whole of physics (special relativity principle). From Max-

well-Lorentz electrodynamics it takes the postulate of invariance of the ve-

locity of light in a vacuum (light principle).

To harmonize the relativity principle with the light principle, the assump-

tion that an absolute time (agreeing for all inertial frames) exists, had to

be abandoned. Thus the hypothesis is abandoned that arbitrarily moved and

suitably set identical clocks function in such a way that the times shown by

two of them, which meet, agree. A specific time is assigned to each inertial

frame; the state of motion and the time of the inertial frame are defined, in

Page 4

THEORY OF RELATIVITY

accordance with the stipulation of meaning, by the requirement that the

light principle should apply to it. The existence of the inertial frame thus

defined and the validity of the law of inertia with respect to it are assumed.

The time for each inertial frame is measured by identical clocks that are sta-

tionary relative to the frame.

The laws of transformation for space coordinates and time for the transi-

tion from one inertial frame to another, the Lorentz transformations as they

are termed, are unequivocally established by these definitions and the hypo-

theses concealed in the assumption that they are free from contradiction. Their

immediate physical significance lies in the effect of the motion relative to the

used inertial frame on the form of rigid bodies (Lorentz contraction) and on

the rate of the clocks. According to the special relativity principle the laws of

Nature must be covariant relative to Lorentz transformations; the theory

thus provides a criterion for general laws of Nature. It leads in particular to

a modification of the Newtonian point motion law in which the velocity of

light in a vacuum is considered the limiting velocity, and it also leads to the

realization that energy and inertial mass are of like nature.

The special relativity theory resulted in appreciable advances. It reconciled

mechanics and electrodynamics. It reduced the number of logically inde-

pendent hypotheses regarding the latter. It enforced the need for a clarifica-

tion of the fundamental concepts in epistemological terms. It united the mo-

mentum and energy principle, and demonstrated the like nature of mass and

energy. Yet it was not entirely satisfactory - quite apart from the quantum

problems, which all theory so far has been incapable of really solving. In

common with classical mechanics the special relativity theory favours certain

states of motion - namely those of the inertial frames - to all other states of

motion. This was actually more difficult to tolerate than the preference for

a single state of motion as in the case of the theory of light with a stationary

ether, for this imagined a real reason for the preference, i.e. the light ether.

A theory which from the outset prefers no state of motion should appear more

satisfactory. Moreover the previously mentioned vagueness in the definition

of the inertial frame or in the formulation of the law of inertia raises doubts

which obtain their decisive importance, owing to the empirical principle for

the equality of the inertial and heavy mass, in the light of the following con-

sideration.

Let K be an inertial frame without a gravitational field, K’ a system of co-

ordinates accelerated uniformly relative to K. The behaviour of material

points relative to K’ is the the same as if K’ were an inertial frame in respect

Page 5

of which a homogeneous gravitational field exists. On the basis of the em-

pirically known properties of the gravitational field, the definition of the

inertial frame thus proves to be weak. The conclusion is obvious that any

arbitrarily moved frame of reference is equivalent to any other for the for-

mulation of the laws of Nature, that there are thus no physically preferred

states of motion at all in respect of regions of finite extension (general rel-

ativity principle).

The implementation of this concept necessitates an even more profound

modification of the geometric-kinematical principles than the special rel-

ativity theory. The Lorentz contraction, which is derived from the latter,

leads to the conclusion that with regard to a system K’ arbitrarily moved rel-

ative to a (gravity field free) inertial frame K, the laws of Euclidian geometry

governing the position of rigid (at rest relative to K’) bodies do not apply.

Consequently the Cartesian system of coordinates also loses its significance

in terms of the stipulation of meaning. Analogous reasoning applies to time;

with reference to K’ the time can no longer meaningfully be defined by the

indication on identical clocks at rest relative to K’, nor by the law governing

the propagation of light. Generalizing, we arrive at the conclusion that grav-

itational field and metric are only different manifestations of the same physical

field.

We arrive at the formal description of this field by the following consid-

eration. For each infinitesimal point-environment in an arbitrary gravita-

tional field a local frame of coordinates can be given for such a state of mo-

tion that relative to this local frame no gravitational field exists (local inertial

frame). In terms of this inertial frame we may regard the results of the special

relativity theory as correct to a first approximation for this infinitesimally

small region. There are an infinite number of such local inertial frames at

any space-time point; they are associated by Lorentz transformations. These

latter are characterised in that they leave invariant the "distance" ds of two

infinitely adjacent point events - defined by the equation:

&z = C2&Z - dxz _ d

Y

2 _ dZ2

which distance can be measured by means of scales and clocks. For, x, y, z, t

represent coordinates and time measured with reference to a local inertial

frame.

To describe space-time regions of finite extent arbitrary point coordinates

in four dimensions are required which serve no other purpose than to pro-

Page 6

THEORY OF RELATIVITY

vide an unambiguous designation of the space-time points by four numbers

each, x

1

, x

2

, x

3

and x

4

, which takes account of the continuity of this four-

dimensional manifold (Gaussian coordinates). The mathematical expression

of the general relativity principle is then, that the systems of equations expres-

sing the general laws of Nature are equal for all such systems of coordinates.

Since the coordinate differentials of the local inertial frame are expressed

linearly by the differentials dx

v

of a Gaussian system of coordinates, when

the latter is used, for the distance ds of two events an expression of the form

ds2 = %w d-y+,

kpv = gv,)

is obtained. The g

uv

which arc continuous functions of x

v

, determine the

metric in the four-dimensional manifold where ds is defined as an (absolute)

parameter measurable by means of rigid scales and clocks. These same para-

meters g

uv

however also describe with reference to the Gaussian system of

coordinates the gravitational field which we have previously found to be

identical with the physical cause of the metric. The case as to the validity of

the special relativity theory for finite regions is characterised in that when

the system of coordinates is suitably chosen, the values of g

uv

for finite regions

are independent of x

v

.

In accordance with the general theory of relativity the law of point mo-

tion in the pure gravitational field is expressed by the equation for the ge-

odetic line. Actually the geodetic line is the simplest mathematically which

in the special case of constant g

uv

becomes rectilinear. Here therefore we

are confronted with the transfer of Galileo’s law of inertia to the general

theory of relativity.

In mathematical terms the search for the field equations amounts to ascer-

taining the simplest generally covariant differential equations to which the

gravitational potentials g

uv

can be subjected. By definition these equations

should not contain higher derivatives of g

uv

with respect to x

v

than the sec-

ond, and these only linearly, which condition reveals these equations to be a

logical transfer of the Poisson field equation of the Newtonian theory of grav-

ity to the general theory of relativity.

The considerations mentioned led to the theory of gravity which yields

the Newtonian theory as a first approximation and furthermore it yields the

motion of the perihelion of Mercury, the deflection of light by the sun, and

the red shift of spectral lines in agreement with experience.*

Page 7

To complete the basis of the general theory of relativity, the electro-

magnetic field must still be introduced into it which, according to our pres-

ent conviction, is also the material from which we must build up the el-

ementary structures of matter. The Maxwellian field equations can readily

be adopted into the general theory of relativity. This is a completely un-

ambiguous adoption provided it is assumed that the equations contain no

differential quotients of g

uv

higher than the first, and that in the customary

Maxwellian form they apply in the local inertial frame. It is also easily pos-

sible to supplement the gravitational field equations by electromagnetic

terms in a manner specified by the Maxwellian equations so that they con-

tain the gravitational effect of the electromagnetic field.

These field equations have not provided a theory of matter. To incor-

porate the field generating effect of ponderable masses in the theory, matter

had therefore (as in classical physics) to be introduced into the theory in an

approximate, phenomenological representation.

And that exhausts the direct consequences of the relativity principle. I shall

turn to those problems which are related to the development which I have

traced. Already Newton recognized that the law of inertia is unsatisfactory

in a context so far unmentioned in this exposition, namely that it gives no

real cause for the special physical position of the states of motion of the in-

ertial frames relative to all other states of motion. It makes the observable

material bodies responsible for the gravitational behaviour of a material

point, yet indicates no material cause for the inertial behaviour of the mate-

rial point but devises the cause for it (absolute space or inertial ether). This

is not logically inadmissible although it is unsatisfactory. For this reason

E. Mach demanded a modification of the law of inertia in the sense that the

inertia should be interpreted as an acceleration resistance of the bodies against

one another and not against "space". This interpretation governs the expecta-

tion that accelerated bodies have concordant accelerating action in the same

sense on other bodies (acceleration induction).

This interpretation is even more plausible according to general relativity

which eliminates the distinction between inertial and gravitational effects.

It amounts to stipulating that, apart from the arbitrariness governed by the

free choice of coordinates, the g

uv

-field shall be completely determined by

the matter. Mach’s stipulation is favoured in general relativity by the circum-

stance that acceleration induction in accordance with the gravitational field

equations really exists, although of such slight intensity that direct detection

by mechanical experiments is out of the question.

Page 8

THEORY OF RELATIVITY

Mach’s stipulation can be accounted for in the general theory of relativity

by regarding the world in spatial terms as finite and self-contained. This hy-

pothesis also makes it possible to assume the mean density of matter in the

world as finite, whereas in a spatially infinite( quasi-Euclidian) world it should

disappear. It cannot, however, be concealed that to satisfy Mach’s postulate

in the manner referred to a term with no experimental basis whatsoever

must be introduced into the field equations, which term logically is in no

way determined by the other terms in the equations. For this reason this

solution of the "cosmological problem" will not be completely satisfactory

for the time being.

A second problem which at present is the subject of lively interest is the

identity between the gravitational field and the electromagnetic field. The

mind striving after unification of the theory cannot be satisfied that two

fields should exist which, by their nature, are quite independent. A math-

ematically unified field theory is sought in which the gravitational field and

the electromagnetic field are interpreted only as different components or

manifestations of the same uniform field, the field equations where possible

no longer consisting of logically mutually independent summands.

The gravitational theory, considered in terms of mathematical formalism,

i.e.Riemannian geometry, should be generalized so that it includes the laws

of the electromagnetic field. Unfortunately we are unable here to base our-

selves on empirical facts as when deriving the gravitational theory (equality

of the inertial and heavy mass), but we are restricted to the criterion of math-

ematical simplicity which is not free from arbitrariness. The attempt which

at present appears the most successful is that, based on the ideas of Levi-

Civita, Weyl and Eddington, to replace Riemannian metric geometry by

the more general theory of affine correlation.

The characteristic assumption of Riemannian geometry is the attribution

to two infinitely adjacent points of a "distance" ds, the square of which is a

homogeneous second order function of the coordinate differentials. It fol-

lows from this that (apart from certain conditions of reality) Euclidian ge-

ometry is valid in any infinitely small region. Hence to every line element

(or vector) at a point P is assigned a parallel and equal line element (or vec-

tor) through any given infinitesimally adjacent point P’ (affine correlation).

Riemannian metric determines an affine correlation. Conversely, however,

when an affine correlation( law of infinitesimal parallel displacement) is math-

ematically given, generally no Riemannian metric determination exists from

which it can be derived.

Page 9

The most important concept of Riemannian geometry, "space curvature",

on which the gravitational equations are also based, is based exclusively on

the "affine correlation". If one is given in a continuum, without first pro-

ceeding from a metric, it constitutes a generalization of Riemannian geom-

etry but which still retains the most important derived parameters. By

seeking the simplest differential equations which can be obeyed by an affine

correlation there is reason to hope that a generalization of the gravitation

equations will be found which includes the laws of the electromagnetic field.

This hope has in fact been fulfilled although I do not know whether the for-

mal connection so derived can really be regarded as an enrichment of physics

as long as it does not yield any new physical connections. In particular a field

theory can, to my mind, only be satisfactory when it permits the elementary

electrical bodies to be represented as solutions free from singularities.

Moreover it should not be forgotten that a theory relating to the elemen-

tary electrical structures is inseparable from the quantum theory problems.

So far also relativity theory has proved ineffectual in relation to this most

profound physical problem of the present time. Should the form of the gen-

eral equations some day, by the solution of the quantum problem, undergo

a change however profound, even if there is a complete change in the param-

eters by means of which we represent the elementary process, the relativity

principle will not be relinquished and the laws previously derived therefrom

will at least retain their significance as limiting laws.

John, you do such a fine job in creating these pieces of Wordle art, I am wondering whether you might take a request. I'd love to see one that captures your favorite Einstein quotes in English. I think that would be extremely cool. Let me know if I can help you with that.

Probably my favorite Einstein quote: "If, at first, the idea is not absurd, then there is no hope for it." It explains a great deal about me! :>)

BTW, I am a friend of Patti. Tell her I said hi!

Posted by: Jeff De Cagna | 09 September 2008 at 05:46 AM

Thanks, Jeff, for the comment and the idea. I've just responded to it with a new post for 9 September. Thanks!

Posted by: john ptak | 09 September 2008 at 11:00 AM