Translation:The Bad Nauheim Debate

by Albert Einstein, Philipp Lenard, Hermann Weyl and Ernst Gehrcke

General Discussion on the Theory of Relativity

Lenard: I was very pleased to have heard, that someone has spoken about the aether today. Yet I have to say, that the simple mind of a natural scientist is in conflict with a theory, in which the theory of gravitation is extended from mass-proportional forces to other forces. I refer to the example of the decelerating train. To fulfill the relativity principle, gravitational fields are imagined when non-mass-proportional forces are in use. I also like to say, that one can use two images for physical thought, that I denoted as images of first and second kind. For example, Mr. Weyl spoke in terms of images of the first kind, as he expressed all processes by equations. By images of the second kind, the equations can be interpreted as processes in space. I would like to prefer the images of second kind, while Mr. Einstein remains still at images of first kind. Concerning images of the second kind the aether is indispensable. It was always one of the most important auxiliaries for progress in natural science, and its rejection means the rejection of the thinking of all natural scientists by images of the second kind. At first I would like to pose the question: How does it happens, that it shall be indistinguishable according to the theory of relativity, whether (in the case of the decelerating train) the train is decelerating or whether the world around is decelerating?

Einstein: It is for sure, that we observe effects in relation to the train, and if we want we can interpret them as inertial effects. The theory of relativity can interpret them as effects of a gravitational field as well. Now, where does this field come from? You think, that it is the invention of Mr. Relativity-Theoretician. But it is not a free invention, as it fulfills the same differential laws as those fields, which we are accustomed to interpret as the effects of masses. It is true, that something from this solution remains arbitrary, when one looks upon a limited part of the world. The gravitational field that dominates relative to the decelerating train, corresponds to an induction effect that is caused by the distant masses. So I would like to summarize in short: The field is not arbitrarily invented, because it fulfills the general differential equations and because it can reduced to the effect of all distant masses.

Lenard: Mr. Einstein's explanations have told me nothing new; they also have not bridged the gap between the images of first kind and the illustrative images of the second kind. I'm of the opinion, that the imagined gravitational fields must correspond to processes, but those processes were not noticed by experience.

Einstein: I would like to say, that what humans consider as illustrative or not, has changed. The view about illustrativeness is so to speak a function of time. I'm of the opinion, that physics is conceptual, not illustrative. As an example for the changing view about illustrativeness, I remind you of the view on illustrativeness of Galilean mechanics in different periods.

Lenard: I have expressed my opinion in the paper "On the Principle of Relativity, Aether, Gravitation", that the aether has failed in certain relations because it was not treated in the right way. The principle of relativity works with a non-euclidean space, that assumes different properties from place to place and in successive times; so there might be something in space whose conditions are the cause of those different properties, and this something is exactly the aether. I understand the usefulness of the relativity principle, as long as it is applied only to gravitational forces. For forces that are not proportional to the mass, I consider it as invalid.

Einstein: It lies in the nature of things, that one can only speak of the validity of the relativity principle, when it is valid for all laws of nature.

Lenard: Only if one imagines suitable fields. I think the relativity principle can only make new statements on gravitation^{[WS 1]}, since the gravitational fields that were included in the case of non-mass-proportional forces don't add any new point at all, except the one that gives the principle an apparent validation. Also the equality of all references systems creates difficulties for the principle.

Einstein: There is no coordinate system that is principally preferred by its simplicity; thus there is no method to distinguish between "real" and "non-real" gravitational fields.

Lenard:^{[WS 2]} My second question is: What says the relativity principle about the prohibited thought experiment, in which the earth is for example stationary, and the rest of the world rotates around the earth's axis, in which case superluminal velocities occur?

The first statement is not a claim, but a new definition of the term "aether".^{[WS 3]}

Einstein:^{[WS 4]} A thought experiment is an experiment, that is principally executable (although not factically). It serves to vividly summarize experiences, form which theoretical consequences can be drawn. A thought experiment is only prohibited, when a realization is principally impossible.

Lenard: I think it can be summarized: 1. That it's better if one refuses to proclaim the "rejection of the aether". 2. That I still consider it necessary to restrict the relativity principle to a gravitational principle, and 3., that superluminal velocities are apparently still problematic for the relativity principle; because they occur in the relation^{[WS 5]} of any arbitrary body, as soon as one wants to ascribe it not to the body, but to the entire world, which is equally permitted according to the relativity principle in its most simple form that was used until now.

Rudolph: That the general theory of relativity is brilliantly confirmed, does not constitute a prove against the aether. The Einsteinian theory is correct, only its view on the aether is not correct. In addition, it will be only acceptable together with Weyl's supplementation. But in this case, Einstein's theory even emerges from the aether hypothesis, when the gaps (that occur between the aether walls when they are moving) are forced to remain empty by the centrifugal force due to direction changes.

Palagyi: The discussion between Einstein and Lenard has made a deep impression upon me. One encounters here again the old historic opposition between experimental and mathematical physics, as it already existed between, for example, Faraday and Maxwell. Mr. Einstein says that there is no preferred coordinate system. But there is one. Let me think biologically, then any man carries his coordinate system within himself. In the course of this thought, a refutation of the theory of relativity is contained.

Einstein alludes to the fact, that no opposition between theory and experiment exists.

Born: The theory of relativity even prefers images of the second kind. I consider the example of the earth and the sun. If the attraction wouldn't exist, the earth would flee in a straight line etc.

Mie: I never understood, that the view in which the aether was essentially the same as seizable matter, should have been only discovered by the theory of relativity. This was already done long before by Lorentz in his book "electrical and optical phenomena in moving bodies". Also Abraham in his textbook, in the time when he was still in opposition to the theory of relativity, said: "The aether is empty space". I'm of the opinion, that even by approving Einstein's gravitational theory, one has to distinguish between mere fictitious gravitational fields, that one introduces into the world by the choice of coordinate system, and the real gravitational fields that are given by objective facts. I have recently shown a way, how one arrives at a "preferred" coordinate system, in which all fields that are only fictitious are excluded from the outset.

Einstein: I cannot see, why such an preferred coordinate system should exist. At most one could think to prefer such coordinate systems, in relation to which the Minkowskian expression for ds² is approximately true. But neglecting the fact, that such systems do not exist for extended spaces, such coordinate system are surely not exact, but can only be defined approximately.

Kraus alludes to the epistemological difference between the images of first and second kind, by arguing that the images of first kind are of higher value than the images of second kind.

Lenard: The principle of the center of gravity was introduced now; yet I think that this can be of no influence on principal questions.

The Discussion concerning the theory of relativity

at the Meeting of Natural Scientists.

By Prof. Dr. H. Weyl (Zürich)

At the Meeting of Natural Scientists in Bad Nauheim a session of the united mathematical and physical section (September 23) was dedicated to the theory of relativity. Lectures by Weyl, Mie, von Laue and Grebe bear witness of the current scientific work in the field of relativity theory. Besides the debate over these lectures, however, also a general discussion concerning the principles took place, the became nearly exclusively a confrontation between Einstein and Lenard. One simply must conclude, that Lenard doesn't grasp the meaning of Einstein's theory; therefore the opponents didn't find each other at all, the confrontation remained a sham fight and without result.

The theory of relativity is based on two fundamental principles, that normally have nothing to do with each other; these are 1. the relativity of simultaneity, 2. the relativity of motion. The first forces the fusion of space and time to a unified four-dimensional continuum, that is denoted by Minkowski as the "world". A world-point is a "here-now", marked for example by a starting signal, a flashing and instantly dimming spark or some other event of minute spatial and temporal extension. My body is in any instant of my life at a certain world-(= space-time-)location; thus it traverses a one-dimensional succession of world points, a world line, as well as any other body. Who once saw a graphical driving plan, knows how to graphically illustrate such a world line (the world lines of trains that are driving on a path). According to the old understanding, the spoken word "now" intersects not only the course of my inner life into past and future, but it brings this cut by a single stroke into the entire world: it intersects the world in a similar way into two parts, that are without space between each other: the past and the future, like a horizontal plane bisects the space into a lower and upper part. According to the relativity principle, however, the bisection of past-future is of a different kind when it is seen from world point O, and it corresponds to the one that in three-dimensional space is caused by a complete circular cone (it is sketched in the vertical projection in the figure; the curved line is the world line of my body, that is of course bisected through O into two parts, the past part and the future part of my life). In the front cone all those world points are located that have an influence on my actions in O, out of it are all the events, that lie finished behind, where "nothing can be changed": the mantle of the front cone separates my active future from my active past. The border is formed by the fastest possible propagation of action at all: that of light. However, all those events are located in the back cone, for which I have either lively experiences or by which I was informed somehow; only these events maybe have influenced me until now. In the exterior of it, however, all of that lies which I will experience or would experience, if my live lasts infinitely or my view might penetrate everything; the mantle of the back-cone separates my passive past from my passive future. Between active future and passive past an empty world-area lies, with which I'm neither actively nor passively connected in the instant O. — The stage of reality is not a stationary three-dimensional space in which things are engaged in temporal progression, but a four-dimensional world in which time and space are inseparably connected to each other. This objective world does not happen, but it exists; a four-dimensional continuum, but neither space nor time. Only in the view of the consciousness that crawls upon within the world-lines of the bodies, a section of this world "lives up" and passes by as an image that undergoes spatial and temporal changes.

The fusion of space and time that is taught by the theory of relativity, was not attacked at the Nauheim discussion. Only the second point was concerned, the relativity of motion. It lies in the essence of the expression "motion", that one can only speak about motion in relation to a solid reference body (such a role is played by the "lasting and well-founded earth" in ordinary live). By itself, none of the possible states of motion of a body is preferred over other ones, i.e. so preferred that it would deserve the name "stationary". This evident principle is seemingly contradicted in a clear way by experience. Experience shows, that centrifugal forces arise at a "rotating" flywheel which stresses the flywheel - maybe until breaking; but in the "stationary" case nothing can be experienced. In an immediately stopped train everything falls apart; why, asks Lenard, is the church steeple not falling into pieces as well, as it experiences an equally strong motion pressure relative to the train, as the train relative to the church steeple. The old solution of the dilemma as defended by Lenard in Nauheim is as follows: If we attribute to space, independent of all matter by which it is filled, a certain geometrical structure by which (in particular) straight lines can be distinguished form curved ones, then the same is true for the world. The Galilean principle of inertia says, that a body that is not influenced from outside, executes a motion with a straight line as its world line. While according to Einstein: It can not be denied of course, and it comes clearly from the Galilean principle of Inertia, that there must exist some sort of "guidance" in the world which forces a very certain "natural" motion upon the body, when one brings it into motion with a certain direction and a certain velocity. But this "guidance" is a physical force-field, exactly like the electrical field from which electrical forces do arise. Together with inertial forces, something comes into light which was until now be interpreted as the "geometrical structure": the "guidance field", as something real, as an acting power of shaking force in some cases. Therefore it impossibly can be a formal or given condition of the world independent of matter and its states; on the contrary, the guidance field must interact with matter and must change when the state of matter is changing. In the development of this thought it became clear - and in this lies the success of Einstein's theory - that what was known as gravitation until now, is only a partial phenomenon of the guidance field. The planetary motion follows the path that is given by the guidance; while in the old mechanics the motion doesn't comply with the Galilean principle, but is diverted from its path by a special force that was ad-hoc invented by Newton, the "force of gravity". However, according to Einstein, inertia and gravitation constitute a inseparable unity; therefore inertial and gravitational masses must necessarily be the same; earlier it was impossible to understand the meaning of this connection.

To Einstein's principles of relativity of simultaneity and relativity of motion, the principle of relativity of magnitude was added by me. It makes it possible to derive the electromagnetic phenomena (besides gravitation), without introducing a specific electric or magnetic force whose laws have to be taken from experience. I think, only by this extension the theory of relativity has found its natural completion; but at the moment it is disputed by an even higher extent than Einstein's theory.

Response by Prof. Dr. E. Gehrcke.

The report that was given by Weyl (Umschau, October 23, 1920; p. 610) on the relativity session in Nauheim requires an extension in various ways.

A not completely unimportant point that arose in the Nauheim meeting with remarkable clarity, has to be supplemented to Mr. Weyl's report: In the discussion Einstein has in fact unequivocally expressed his disapproval of Weyl's theory and has given an explanation, that a theory that is based on the pure mathematical demands of symmetry, like that of Weyl, has to be rejected. — When Mr. Weyl tries to bring his considerations more closer to the public, then such an interesting point like the statement of Einstein concerning Weyl's theory should not remain unmentioned by him, so that in the public from the outset no false opinion can occur, how the creator of the theory of relativity stands to the specific relativism of Weyl.

Mr. Weyl thinks that he is allowed to conclude, that Lenard hasn't grasped the meaning of the theory of relativity. That is only a rebuttal to a statement of Lenard in the meeting in Nauheim, that the relativists had not shown any understanding for the requirements of reality search in physics, and that they undertake no attempt to bridge this "gap". Weyl should consider, that even when someone possesses as a mathematician a virtuous skill in using mathematical symbols, he might show a lack of understanding for other abstractions than the quantitative relations of mathematics, of which more universally gifted natures are free. By using Weyl's papers it might be easy to create a list of epistemological errors and conceptual confusions; in this connection it shall be alluded to the recently published paper by Rikpe-Kühn: Kant contra Einstein.

The point that was more closely examined by Mr. Weyl concerning the discussion between Einstein and Lenard, namely the example of the decelerated train, lacks an essential objection that was more closely explained by Lenard, that for the creation of a gravitational field according to our current knowledge, some masses must be present that generate the gravitational field. In the case of the train accident, where according to the relativists not the train, but the entire surrounding should have been decelerated, no formation of masses or nothing that might produce the gravitational field that decelerates the surrounding can be seen. The relativist was therefore forced in Nauheim to explicitly assume gravitational fields without gravitating masses that generate them. Yet besides other things it remained unanswered, where this energy of this gravitational field is coming from. From all of those things nothing was mentioned by Weyl.

Finally the discussion in Nauheim has brought Einstein to the explanation, that according to the general theory of relativity, bodies can have any arbitrary velocity faster than that of light. Also this case, with its conclusions that will not treated further at this place, was not mentioned by Weyl. So the debate in Nauheim was in no way "without result".

Response to Prof. Dr. Gehrcke

by Prof. Dr. H. Weyl.

I cannot leave unchallenged the remarks by Mr. Gehrcke concerning my "Umschau"-article on the theory of relativity. It do not care of the first purely demagogic part of his statements, in which he brings the authority of Einstein's name against me into this field (of all people Mr. Gehrcke, according to whom this authority is only based on advertising and suggestion!) and who presented me to the public as an "Only-Virtuoso" of the mathematical technique and (with reference to Ripke-Kühn) as a philosophical scatterbrain. I only want to conclude, that Einstein and I are indeed not of the same opinion concerning my extension of the theory of relativity, and regarding the relations to philosophy, I wish to allude the reader of "Umschau" to the paper "Zur Einsteinschen Relativitätstheorie" by E. Cassirer, the member of Neo-Kantianism who is most competent for this confrontation.

It followed from my article (which was the result of the invitation of the editor of Umschau) that I didn't wanted to give a report of the Nauheim discussion, but following this discussion to highlight the two points of relativity theory, which I consider as decisive. But also, if I had that other intention, I wouldn't been able to report on the "results" that were mentioned by Mr. Gehrcke. It cannot be spoken about, that Einstein's theory would be forced to assume gravitational fields without masses that generate them. The "fictitious gravitational fields" that were alway mentioned by Lenard as well, are only necessary when the law by which the masses generate the guidance field, is misinterpreted so as if everything happens the same way in any reference system as in Newton's "absolute space". Such a formulation is impossible, when one really has understood the unity of inertia and gravitation that was called by me the "guidance field". Also inertia, the "Galilean guidance field" that brings a body to fly in a straight line with constant velocity, and which according to Newton-Lenard exists once and for all time without material cause, has according to Einstein its cause in the generating masses. Namely, this neutral basis of gravitation is caused by the collective action of all masses in the universe; analogous to, for example, the charges on the plates of a capacitor that cause the homogeneous electrical field between the plates, from which the field in the immediate surrounding of the excited electrons are lifted out as small steep conical mountains from a plane. Here as well as there it is of course impossible to separate in a strict manner the homogeneous field that is caused by the collective action of all particles (the "Galilean guidance field"), from the conical mountains the belong to any single particle ("gravitation"). In Nauheim also Einstein alluded to this solution, which I can only sketch at this place, and which removes the great cosmological difficulties with which Newton's theory of gravitation has to struggle.

Also the second "result" that was constructed by Mr. Gehrcke, is only a repetition of old misunderstandings; I take on any guarantee, that in Nauheim no "relativist" has admitted the possibility of body motions by superluminal velocity. Lenard, as his closing words in the discussion show, heard something like that in the words of Einstein; but completely erroneously.

Zürich.

On the Theory of Relativity.

by Prof. Dr. E. Gehrcke

I want to express at this place that Einstein, at the Nauheim meeting of natural scientists, has admitted the possibility of superluminal velocities from the standpoint of his general theory of relativity. When Mr. Weyl thinks that he can deny that, then only another contradiction between him and Einstein - at least at the time of the Nauheim meeting - is to be stated. The explanation of Einstein concerning superluminal velocities, as unsatisfactory as it may by, has actually been given, and it would have been better for Mr. Weyl to verify the evidence before assuming an error of Lenard.

The 86. Meeting of the German Natural Scientists

By K. Körner

The debate didn't deviate from the objective and factual stream, into which it was directed by the readers and the vigorous chairman. At first a dialog between Lenard and Einstein evolved, the first lively presenting his objections, the second responding calmly and with extraordinary clarity.

While Lenard accepts the special theory of relativity, he rejects the general theory. He denies, that the aether was abolished by the theory of relativity; it cannot vanish at all, as it is the only thing that makes it possible for us to understand optical and electrical phenomena in an illustrative way. Other reasons for contention were for him the fictitious gravitational fields introduced by Einstein, and the termination of the "common sense" which was necessary for both the physicists and the (in the scientific sense) naive man. When e.g. in an immediately stopped train everything is falling around, then by the common sense one can decide, whether the change of the train's motion or that of the earth is the cause for it. If one additionally thinks, that one cannot say whether we are in rotational motion, or the environment - then one only has to assume the latter, to see that one has to admit superluminal velocities. That was a result, to which the theory of relativity leads by itself, and which contradicts its own assumption, that the speed of light cannot be superseded. The theory of relativity kills itself!

On the other hand, Einstein stresses that illustrativeness is a changing concept. The Galilean mechanics is for us the highest point of illustrativeness, while it was very non-illustrative for Galileo's contemporaries. And in the present we find electricians, for whom nothing is more illustrative than the electric field, and for whom the electrical phenomena even become images for mechanical ones. Thus one cannot use such a changing concept for or against the theory. To the example of the decelerating train he remarks, that this is without any doubt an interaction between masses, and for the success it is irrelevant, which mass is moved against the other. To let decide the "common sense" in this question, is no less problematic as it was before in respect to illustrativeness. To the example of the rotational motion it has to be said, that the role of the speed of light in the general theory of relativity is completely different as in the special theory, and that the first requires no constant speed of light at all. — Nearly all other speakers in the debate agreed with Einstein in the essential points - for example von Laue, Mie (who responded to Lenard that the aether was abolished not only by the theory of relativity, but already three decades earlier by H. A. Lorentz) and particularly inspired by Born, who feels attracted to Einstein's theory just because of its illustrativeness.

The Theory of Relativity at the Meeting of Natural Scientists in Bad Nauheim

By H. Weyl in Zürich.

On occasion of the German Mathematical Society, at the meeting of natural scientists in Bad Nauheim last year in a combined session of the mathematical and physical section, the theory of relativity was the center of a series of lectures and a general discussion; about that a report should be given at this place - after a considerable long time which, however, is maybe beneficial for clarification and calm judgment of the facts.

The first part of the session was constituted by four lectures in the field of the theory of relativity: 1. H. Weyl, Elektrizität und Gravitation; 2. G. Mie, Das elektrische Feld eines um ein Gravitationszentrum rotierenden geladenen Partikelchens; 3. M. v. Laue, Theoretisches über neuere optische Beobachtungen zur Relativitätstheorie; 4. L. Grebe, Über die Gravitationsverschiebungen der Fraunhoferschen Linien. The four lectures were followed by "special" discussions that were related to the content of the lecture. The last and most dramatic part, the general discussion concerning the theory of relativity, was essentially a duel between Einstein and Lenard. Planck fulfilled his duty as chairman with great skill, strength and impartiality; it was mostly thanks to him, that this "Nauheim Relativity Discussion", in which opposing epistemological fundamental-views of science were confronted with each other, has taken a worthy development.

...^{[WS 6]}

The two last points that were discussed before were also mentioned in the general discussion (that was mostly used by Lenard) between Lenard and Einstein. For clarities sake it may be allowed, to separate two additional controversies from this dialog, that are of minor importance in respect to the main difference which will be discussed at the end.

At first it's about the existence of the aether. Lenard thinks that Einstein in the course of formulating the special theory of relativity, was much to rush to proclaim the rejection of the aether. Indeed he can refer to the fact, that Einstein again speaks of an aether in the general theory of relativity.^[1] However, one shall not be deceived by the equal terminology about the factual difference! The old aether of the light theory was a substantial medium, a three-dimensional continuum, from which any place P in any time t is located at a certain space point p (or at a specific world location); the recognizability of the same aether location at different times is essentially for it. By this aether the four-dimensional world disintegrates into a three times infinite continuum of one-dimensional world lines; consequently it allows to absolutely distinguish between at rest and in motion. Only in this sense (something different was never claimed by Einstein) the aether was rejected by the theory of special relativity; it was replaced by the affine geometric structure of the world, that doesn't determine the difference between "at rest" and "in motion", but separates uniform motion from all other motions. The substantial aether was considered by its inventors as something real, that is comparable to ponderable bodies. In Lorentzian electrodynamics it was transformed into a pure geometrical, i.e. a forever solid structure that won't be influenced by matter. In Einstein's special theory of relativity another one took its place, the affine geometric structure. In the general theory of relativity eventually the latter was, as an "affine connection" or "guidance field", transformed back into a state-field of physical reality, that is in effective connection with matter. And therefore Einstein considered it convenient, to reintroduce the old word aether for the completely changed concept; whether this was useful or not, is less a physical than a philological question.

Second: the superluminal velocity. Lenard thinks, that the general theory of relativity reintroduces superluminal velocities, since it allows e.g. the rotating earth as reference frame; so that superluminal velocities occur in sufficiently great distances. This is an obvious misunderstanding. If $x_{1}x_{2}x_{3}$ are the space coordinates that are measured in respect to the rotating earth, $x_{0}$ is the corresponding "time" (its precise definition isn't relevant now), then the coordinate lines $x_{0}$ upon which at constant $x_{1}x_{2}x_{3}$ only $x_{0}$ varies, won't all have a time-like direction, i.e. in those coordinates there isn't everywhere $g_{00}>0$. Einstein claims indeed, that such a coordinate system is valid; also in those coordinate systems his general invariant gravitational laws are valid. However, he insists that the world line of a material body always has a time-like direction, so that concerning a material body (and its "signal velocity") no superluminal velocity can occur. A coordinate system of the kind mentioned before, cannot be represented in its entire extension by a "reference mollusk", i.e. one cannot think about a material medium, whose single elements follow the coordinate lines $x_{0}$ of that coordinate system as world lines. —

But it's time now, that I come to speak about the decisive difference between Lenard and Einstein. Lenard claims, that Einstein's theory operates with fictitious gravitational fields, to which no generating mass can be found and which was only introduced for the sake of the relativity principle. The illustrative example by Lenard, i.e. the train that is immediately stopped by an oncoming train, should serve as the basis of the discussion. Why, asks Lenard, falls the train into pieces but not the church steeple next to the train, although according to Einstein it can be said of the church steeple with the same justification as of the train, that it became decelerated? It seems to me that the answer to this is simple. In Einstein's theory like in the older interpretation there is a guidance field that is followed by a body according to the Galilean principle, as long as no forces act on it. The catastrophe happens at the train and not at the church steeple, since the first is thrown out of its path by the molecular forces of the oncoming train, but the church steeple is not. This answer is also completely in agreement with "commons sense", which whole-heartedly agrees that the inertial-tendency of the guidance field (that opposes to the forces) can be seen as a physical reality. But the question is now: is the guidance field a single unity, or can the two components "inertia" and "gravitation" principally be separated, so that only the first exists once and forever as the affine linear structure of the four-dimensional world, and only the second is produced by matter? Here, concerning the equality of all types of motion, the state of affairs is quite analogues as for the equality of all directions in space. According to Democrit, there exists an absolute "above-below" per se; the real falling direction of a body is composed of its absolute direction and the deviation from it that stems from a physical cause. For example, Democrit could argue against Newton (who sees the fall direction as an unity) in the same way as Lenard against Einstein: If another direction as the true one is installed as the normal direction, then one has to introduce in addition to it and the real deviation, a third fictitious deviation that is everywhere the same and is not connected with matter; and this is only to satisfy the principle of the equality of all directions in space. As soon as one admits an absolute direction above-below, one can distinguish between real and fictitious deviations; as soon as one admits a preferred, "rational" coordinate system, then one has (with Mie and Lenard) to distinguish between real and fictitious gravitational fields. However, from the relativity standpoint such a separation is impossible. But when we, with Newton and against Democrit, claim the indecomposability of the real falling direction into an absolute above-below and a deviation from it, then we must provide a physical cause not only for the deviation, but also for the falling direction as a whole; in the same way also Einstein has the duty to show, how and by which law the guidance field as a whole is produced by matter. This was required by Lenard with full justification from him, and that is the deepest and essentially decisive point of his objections. It must openly be admitted, that there still exist serious difficulties for the theory of relativity in its current formulation. To answer, Einstein alludes to his cosmology of the spatial closed world; and he responds to Lenard: The field is not arbitrarily invented, since it fulfills the general differential equations and because it can be reduced to the effect of all distant masses. As long as one adheres to the difference of matter and field at all (only then the requirement, that matter generates the field, is meaningful and valid), then Einstein's cosmology means, that besides the inner seams of the field upon which the single matter particles act so that they dominate the field, no other infinitely distant seam (that act as an agent that determines the field in the infinite) is added; the entirety of distant masses took its place. The co-rotation of the plane of Foucault's pendulum with the fixed stars makes that very clear. However, the difficulty is not solved yet. At first it is to say, that by Einstein only the laws are given, that bind the inner differential connection of the field, but there is no clear formulation of the laws, by which matter determines the field (by the way, that is not essentially different in the case of the electromagnetic field). But second and especially it is completely excluded that matter can uniquely determine the field, if one considers mass, charge, and state of motion as the characteristics of matter. Because one can introduce such an coordinate system into the world, that by the following projection of the world on a four-dimensional Cartesian image space, not only the world channel of one particle, but of all particles assume a simultaneously given form, e.g. that all those channels become vertical straight lines. Compared to Mach, whose reference body is always a rigid body, Einstein's coordinate system became so "softened", that it can simultaneously cling to the motion of all bodies, so that one can transform all particles to rest at the same time; thus it has no meaning anymore, to even speak about the relative state of motion of different bodies against each other. This problem was recently highlighted by Reichenbächer more clearly.^[2] The principle, that matter generates the field, can afterwards only be upheld, when within the concept of motion a dynamical factor is integrated; so the analysis of the concept of motion is not about the contrast between absolute or relative, but between kinematics or dynamics. —

In the second meeting at the other day, F. P. Liesegang (Düsseldorf) showed some excellent graphs for the illustration of the space-time relations in special relativity, and H. Dingler (Munich) read, as it appeared only as a formal protest against the relativity theory and without noticing the public, his critical remarks concerning the fundamentals of the theory; it is strange, that in Dingler the Poincaré-oriented conventionalism is connected with a dogmatical stubbornness of the born aprioristic philosopher. That the tragedy is not missing a the end of the satyr play, Mr. Rudolph developed a fantastic aether theory with "gaps" between streaming aether walls, star lines, etc. and with their aid he (out of nothing) determined the mass of the sun up to an arbitrary number of decimals...

I have tried in a free way to allude to the questions, that came to speak at the Nauheim discussion, but not to give an objective report about the development of the session; for a shortened, but equivalent reproduction of the lectures and the discussion, the reader is referred to the issue of December 1920 of the Physikalische Zeitschrift.

---

1. See especially the Leiden inauguration speech of Einstein concerning Ether and the Theory of Relativity, Springer 1920
2. Schwere und Trägheit, Physik. Zeitschr. 22 (1921), p. 234-243

Notes by Wikisource

1. "gravitation" presumably means in this context "mass-proportional" gravitational fields generated by real masses, as opposed to the "non-mass proportional" forces that follow after the comma.
2. The name of Lenard is not present in the original version at this place, but it seems to be clear that the following question was posed by him.
3. It's unclear to whom this line belongs. However, the "new definition of the term aether" evidently refers to Einstein's new definition in his Leyden speech, as it was discussed by Weyl below.
4. The name of Einstein is not present in the original version at this location, but as this is the answer to the question above, it seems to belong to Einstein.
5. The word "Relation" presumably means "relative motion" in this context. See also the discussion on superluminal velocity given by Weyl below.
6. p. 51-58 are omitted in this translation, as they contain the discussion of the lectures by Weyl, von Laue, Grebe, and Mie. It follows Weyl's description of the "general discussion" between Lenard and Einstein, in which two critical points presented by Mie (preferred reference frame, relativity of acceleration) are concludingly discussed as well.