Donate books to help fund our work. Learn more→

The Rudolf Steiner Archive

a project of Steiner Online Library, a public charity

The Fourth Dimension
GA 324a

Questions and Answers XI

7 March 1920, Stuttgart

FIRST QUESTION: Is the law of the absolute propagation of light correct?

SECOND QUESTION: Is there any reality to the relativity of time assumed by Einstein?

I assume that your first question deals with whether light in absolute space travels at a constant speed. [Note 35] As you know, we cannot really talk about the propagation of light in absolute space because absolute space does not exist. What basis do we actually have for talking about absolute space? You said, and rightly so, that you assume the propagation of light is infinitely great and that light derives its actual propagation from the resistance of the medium. Now I ask you, in your view is it altogether possible to speak of the speed of light in the same sense that we speak of the speed at which any other body travels?


If we do not hypothetically equate light with any other body, we cannot measure its speed in the same way as that of any other body. Let's assume that an ordinary body, a material object, is flying through space at a certain speed. This object is at a specific place at a specific moment in time, and our entire method of measuring speed depends on considering the difference in the object's location from its point of departure at two different times. This method of measurement remains possible only if the moving material body completely leaves the points on the line in which it is moving. Let's assume that it does not leave these points but leaves traces behind. Applying this method of measurement immediately becomes impossible if the object moving through a given space does not leave that space but continues to occupy the line of movement, not because we cannot measure the differences but because the propelling speed constantly modifies the propelled object. I cannot apply my ordinary method of measurement when, instead of dealing with matter that leaves the space empty behind it, I am dealing with an entity that does not completely vacate the space but leaves traces behind. Thus, we cannot speak of a constant speed of light in the same sense that we speak of the speed of a material object, because we cannot formulate an equation based on differences in location, which, of course, provide a basis for calculating speed.

Thus, when we are dealing with the propagation of light, we find ourselves compelled to speak only about the speed of the outer propagation of light. But if we speak about the speed of the propagation of light, we would be obliged to go back constantly to the source of the spreading light in order to measure its speed. In the case of the Sun, for example, we would be obliged to go back to the origin of the spreading light. We would have to begin measuring where the spread of light began, and we would have to assume hypothetically that the light continues to replicate indefinitely. This assumption is not justified, however, because the frontal plane in which the light is spreading, instead of always simply growing larger, becomes subject to a certain law of elasticity and reverses direction when it achieves a certain size. At that point we are no longer dealing simply with spreading light but with returning light, with light retracing the same path in reverse. On an ongoing basis, therefore, I am not dealing with a single location that I assume to exist in light-filled space—that is, with something that is spreading from one point to another—but with an encounter between two entities, one of which is coming from the center and the other from the periphery. Thus, I cannot avoid asking the fundamental question, are we really dealing with speeds in the ordinary sense when we consider the transmission of light?

I don't know whether or not I have made myself understood. I am not dealing with speed of propagation in the ordinary sense, and when I take the step from ordinary speeds to speeds of light, I must find formulas based on formulas for elasticity. If I may use the image of material movement, such formulas must reflect how elastically related portions of space behave in a closed elastic system with a fixed sphere as its boundary. [Note 36] Therefore, I cannot use an ordinary formula when I shift to describing the behavior of light. For this reason I see a fundamental error in Einstein's work, namely, that he applies ordinary mechanical formulas—for that is what they are—to the spreading of light and assumes hypothetically that light can be measured in the same way as any material body flying through space. [Note 37] He does not take into account that spreading light does not consist of material cosmic particles speeding away. Light is an event in space that leaves a radiant trace behind, so that when I measure it (reference to drawing that has not been preserved), I cannot simply measure as if the object comes this far and leaves nothing behind. When light is transmitted, however, there is always a trace here, and I cannot say that it is transmitted at a specific speed. Only the frontal plane is transmitted. That is the main point. I am dealing with a specific entity in space that has been subsumed by the spreading element.

And then I see a second error that has to do with the first, namely, that Einstein applies principles to the whole cosmos that actually apply to mechanical systems of points that approach each other, thus disregarding the fact that the cosmos as a whole system cannot be merely a summation of mechanical processes. For example, if the cosmos were an organism, we could not assume that its processes are mechanical. When a mechanical process takes place in my hand, it is not essentially determined merely by the closed, mechanical system because my entire body begins to react. Is it is acceptable to apply a formula for other movements to the movement of light, or is the reaction of the entire cosmos involved? A universe without light is even more difficult to imagine without the reaction of the entire universe, and this reaction works very differently from speeds in a closed, mechanical system. [Note 38]

It seems to me that these are Einstein's two principal errors. I have studied his theory only briefly, and we all know that mathematical derivations can indeed coincide with empirical results. The fact that starlight that has passed the Sun, for example, coincides with theoretical predictions does not verify Einstein's theory once and for all. [Note 39]

These two principal underlying factors are why Einstein's way of thinking is always so paradoxical and abstract. The situation here is somewhat similar to the example from Wilhelm Busch that you used earlier, where an arm is raised forcefully and you almost have the feeling that you are going to be slapped on the face. It's a bit like that when Einstein draws conclusions from what would happen if a clock sped away at the speed of light and then returned. [Note 40] I ask you, is there any reality to this notion? I absolutely cannot complete the thought, because I am forced to wonder what happens to the clock. If you are accustomed to restricting your thoughts to reality, you cannot carry thoughts such as this through to completion. [Note 41] The passages where Einstein presents such thoughts show that his conclusions are based on fundamental errors such as the one I just mentioned. That was my first comment. On the subject of time, we would need to begin basing our thoughts on elastic formulas rather than ordinary mechanical formulas. We would need to borrow from the theory of elasticity. By extension, any distribution or spreading that forms a frontal plane cannot be imagined as an entity that continues to spread out to infinity. It always reaches a certain sphere where it turns back in on itself. If we want to address the reality of the situation, we cannot say that the Sun radiates light that vanishes into infinity. That is never the case. There is always a boundary where the spreading force of elasticity is exhausted and turns back in on itself. There is no such thing as an infinite system that meets the criteria of spreading out and disappearing into nothingness. Any spreading entity reaches a boundary where it turns around, somewhat as if it were obeying the law that governs elastic bodies. When we speak of light, we are never dealing with something that continues to spread indefinitely in all directions. Instead, we always find a situation comparable to standing waves. That is where we must look for the formulas, not in ordinary mechanics. [Note 42]

Then there is still the question of time itself. In fact, time does not go through all these transformations, does it? Here in the realm of mechanics time as such is not a reality. Take the very simplest formula, \(s = e \times t\). According to the ordinary law of multiplication, s must be essentially identical to \(c\),—otherwise the space \(s\) would be identical to the time, which is impossible. In this formula, I can think of space only as somehow mathematically identical to \(c\).

We cannot multiply apples and pears, can we? We have to put one in terms of the other. In mathematical formulas, time can only be a number, which, however, does not mean that the reality of time is a number. We can write the formula like this only when we assume that we are dealing with an unnamed number. [Note 43]

The formula \(c = s/t\) is a different matter. Here we have a space \(s\) of a certain size as it relates to the size of the number \(t\). The result is the speed c. This is the reality of the situation regardless of whether I imagine atoms, molecules, or matter that occupies a specific, perceivable amount of space. I must imagine that any thing I confront empirically has a specific speed. Any further conclusions are just abstractions. Time is something that I derive from the divisor and the distance traveled is something I derive from the dividend, but these are abstractions. The reality—and this applies only to mechanical systems—is the immanent speed of each body. For example, when physicists accept atomic theory for other reasons, they must not assume that atoms exist without immanent speed. Speed is a true reality. [Note 44] Thus we must say that we abstract time as such from events and processes. It is actually an abstraction from events. Only the speeds of what we encounter can be seen as realities.

When we understand this completely, we can no longer avoid concluding that what I call time appears as a result of phenomena. It plays a collaborative role in phenomena, and we must not disregard it as a relative. [Note 45] The collaboration of this abstracted factor yields a specific real and fundamental concept of an organism's life span, for example. The life span of an organism cannot be measured externally,—its course is immanent. Any given organism has a specific, inherent life span that is integrated into and results from all the processes taking place in the organism. The same is true of an organism's size. It is intrinsic to the organism and is not to be measured in relationship to anything else. The fitting conclusion is that such concepts of life span and size are not valid in the same way that we ordinarily assume.

Human beings are a specific size. Now let me hypothetically assume that very small human beings exist in our ordinary universe. For all other purposes, the size of human beings relative to other objects is not important. Their typical size is important to human beings, however, because this size is intrinsic. This point is important. Imagining that human beings can be arbitrarily larger or smaller is an offense against the entire universe. For example, certain scientific thinkers wonder what life would be like in a solar system that is infinitely large or small compared with ours. This question is nonsense. Both the sizes and the life spans of the real entities we encounter are matters of inner necessity.

At this point I must state that any entity that can be considered a totality essentially carries its own time within it. I can look at a piece of an inorganic object independent of anything else, but I cannot do the same with a leaf because its continued existence depends on the tree. Thus, I must consider whether or not the entity I am observing is a totality, a whole, self-contained system. Any totality that I observe, however, incorporates time as an immanent factor. Consequently, I do not think much of the idea of an abstract time that exists outside objects and in addition to the time that is inherent in each object or event. Looking at time that is supposed to run from beginning to end is a bit like developing the abstract concept horse on the basis of individual horses. Individual horses exist in the external reality of space, but the concept requires something more. The same is true of time. Whether time is inherently changeable or not is essentially an empty question because each total system in its own immanent existence has its own time and its own speed. The speed of any inorganic or vital process points back to this immanent time.

For this reason, instead of a theory of relativity that always assumes we can relate one axial coordinate system to another, I would prefer to establish a theory of absolutes to discover where total systems exist that can be addressed in the same way we address an organism as a totality. We cannot talk about the totality of the Silurian period in the Earth's evolution, for example, because the Silurian period must be united with other evolutionary periods to form a system that is a totality. It is equally impossible to speak about the human head as a totality, because the rest of the body belongs with it.

We describe geologic periods independently of each other, as if that were the reality of the situation. It is not. One period is a reality only in connection with the entire evolution of the Earth, just as a living organism is a reality from which nothing can be removed. Instead of relating our processes to coordinate systems, it would be much more pertinent to relate them to their own inherent reality, so that we could see the whole systems, or totalities. At that point, we would have to return to a certain type of monadism. We would overcome the theory of relativity and arrive at a theory of absolutes.

We would then truly see that Einstein's theory is the last expression of the striving for abstraction. Einstein functions in abstractions that sometimes become intolerable when his assumptions are applied to very elementary matters. For example, how does sound work when I myself am moving at the speed of sound? If I do that, of course I never hear real sounds, because the sound is traveling with me. To anyone who thinks in real terms, in terms of totalities, such a concept cannot be implemented, because any being that can hear would fall apart if it moved at the speed of sound. Such concepts are not rooted in observations of the real world. [Note 46]

The same is true when I ask whether time is inherently changeable. Of course, it is impossible to confirm any changes in abstract or absolute time, which must be imagined a priori. When we talk about changes in time, however, we must grasp the reality of time, which we cannot do without considering how temporal processes are intrinsically linked to total systems that exist in the world.

  1. Questions and answers during the lecture cycle Geisteswissenschaftliche Impulse zur Entwickelung der Physik: Zweiter Naturwissenschaftlicher Kurs (GA 321). These questions were asked by Hermann von Baravalle (1898-1973), mathematics and physics teacher at the first Waldorf School in Stuttgart), after a lecture he gave on the theory of relativity (Stuttgart, March 7, 1920). To date, no transcript of Baravalle's lecture has been discovered.

  2. The theory of elasticity was one of the theoretical aids used by nineteenth century physicists in formulating their various theories of optics, which all assumed the existence of a physical ether. Later, the electromagnetic theory of light, James Clark Maxwell (1831-1879), in conjunction with the negative outcome of the ether drift experiment (188iff) conducted by Albert Michelson (1852-1931) and Edward Morley (1838-1923), superseded the idea of a quasi-material ether but failed to eliminate it totally from the field of physics. (On the evolution of ether theories and their status in the late nineteenth and early twentieth centuries, see Whittaker [1951-1953]).

    In volume II of his lectures on theoretical physics [1944], §15, Arnold Sommerfeld (1868-1951) discusses an ether model based on a quasi-elastic body. This model originated in the investigations of James MacCullagh (1809-1847), for more information, see Klein [1926]. Sommerfeld shows that the equations for the movement of this body take the form of Maxwells electrodynamic equations for empty space.

    Friedrich Dustmann [1991] shows that this ether model meets many of the requirements for a theory of light that Steiner presents here and elsewhere. In addition, the basis of this quasi-elastic ether model is a specific anti-symmetrical tensor, which from the geometric perspective represents a linear complex, thus forming a bridge to the theory of hypercomplex numbers, which Steiner mentions in his response to a question by Strakosch on March 11,1920. (For more on this subject, see Gschwind [1991], especially section 8.5, and [1986], pp. 158-161).

    It is no longer possible to reconstruct whether Steiner was referring indirectly here to papers on the mechanical and elastic theory of light and was thinking of a suitable extension of or supplement to such theories from his own time. In any case, we must keep in mind that Steiner's suggestions for transforming or reformulating an ether theory for mathematics and physics must not be imagined solely in the context of a purely material and energetic phenomenology of light; see Steiner's responses to questions on March 31, 1920 (Blümel), and January 15, 1921, and the accompanying notes. From this perspective, Steiner's remarks here and in the passages that follow are not to be construed as criticizing the scientific foundations of Einstein's special theory of relativity but rather as calling for an appropriate expansion of the perspectives of physics through the methods and concepts of anthroposophical spiritual science (see also his lecture of January 6, 1923, in GA 326).

    Similar-sounding remarks of Steiner's on the elastic oscillation/return of light are to be found in his lecture of December 6, 1919 (GA 194),—in the teacher's" conference of September 25, 1919 (GA 300a),—and in the lecture of February 16, 1924 (GA 235). Similar statements on the behavior of energy are found in the questions and answers of November 12, 1917 (GA 73).

  3. Albert Einstein (1879-1955), physicist in Zurich, Berlin, and Princeton,—the founder of the special theory of relativity and the general theory of gravitation.

    The only passage in Steiner's written works that addresses the special theory of relativity is in The Riddles of Philosophy (GA 18), pp. 590-593. This passage is fundamentally important for assessing all of Steiner's comments on the theory of relativity in lectures and question-and-answer sessions. To clarify Steiner's primary view on the theory of relativity, this passage will be quoted here in its entirety:

    A new direction in thinking has been stimulated by Einstein's attempt to transform fundamental concepts of physics. Until now, physics accounted for the phenomena accessible to it by imagining them arranged in empty three-dimensional space and taking place in one-dimensional time. Thus space and time were assumed to exist outside and independent of objects and events, in fixed quantities. With regard to objects, we measured distances in space,—with regard to events, we measured durations in time. Distance and duration, according to this view of space and time, do not belong to the objects and events. This view now has been countered by the theory of relativity introduced by Einstein. From this perspective, the distance between two objects belongs to the objects themselves. A specific distance from another object is an attribute, a property just like any other property an object may possess. Interrelationships are inherent in objects, and outside these interrelationships there is no such thing as space. Assuming the independent existence of space makes it possible to conceive of a geometry for that space, a geometry that can be applied to the world of objects. This geometry arises in the world of pure thoughts, and objects must submit to it. We can say that relationships in the world must obey laws that were laid down in thought before actual objects were observed. The theory of relativity dethrones this geometry. Only objects exist, objects whose relationships can be described by means of geometry. Geometry becomes a part of physics. In that case, however, we can no longer say that the laws of geometry can be laid down before the objects are observed. No object has a location in space but only distances relative to other objects.

    A similar assumption is made about time. No event exists at a specific point in time,—it happens at a temporal distance from another event. Thus, spatial and temporal distances between interrelated objects are similar and flow together. Time becomes a fourth dimension that is similar to the three dimensions of space. An event happening to an object can be described only as taking place at a temporal and spatial distance from other events. An objects movement can be conceived of only as happening in relationship to other objects. This view alone is expected to supply faultless explanations of certain processes in physics, but assuming the existence of independent space and independent time leads to contradictory thoughts about these processes.

    When we consider that many thinkers have accepted only those aspects of the natural sciences that can be presented in mathematical terms, the theory of relativity contains nothing less than the nullification of any real science of nature, because the scientific aspect of mathematics was seen as lying in its ability to ascertain the laws of space and time independent of observations of nature. Now, in contrast, natural objects and natural processes are said to determine spatial and temporal relationships,—these objects and events are to provide the mathematics. The only certain factor is surrendered to uncertainty. According to this view, every thought of an essential reality that manifests its nature in existence is precluded. Everything is only in relation to something else.

    To the extent that we human beings look at ourselves in the context of natural objects and processes, we will not be able to escape the conclusions of this theory of relativity. If, however, our experience of ourselves as beings prevents us from losing ourselves in mere relativities as if in a state of soul paralysis, we will no longer be permitted to seek intrinsic beingness in the domain of nature but only above and beyond nature, in the kingdom of spirit. We will not escape the theory of relativity with regard to the physical world, but it will drive us into knowledge of the spirit. The significance of the theory of relativity lies in pointing out the need for spirit knowledge that is sought by spiritual means and independently of our observations of nature. That the theory of relativity forces us to think in this way establishes its value in the evolution of our worldview.

    For further discussion of the specific problems with regard to the theory of relativity addressed by this question-and-answer session, see Unger [1967], chapter VIII, and Gschwind [1986] and the literature they list. See also the additions to this note in Beiträge zur Rudolf Steiner Gesamtausgabe, no. 114/115, Dornach, 1995.

    Rudolf Steiner spoke repeatedly about the theory of relativity and apparently did not distinguish clearly between the special theory of relativity and the general theory of gravitation, which Einstein also called the general theory of relativity. The following lectures and question-and-answer sessions (Q&A) discuss or mention the theory of relativity (RT). The list does not claim to be exhaustive.

    November 27 1913, GA 324a
    1914, GA 18
    August 20 1915, GA 164
    April 15 1916, GA 65
    August 21 1916, GA 170
    August 7 1917, GA 176
    August 29 1919, GA 294
    September 25 1919, GA 300a
    March 1 1920, GA 321
    March 3 1920, GA 321
    March 7 1920, GA 324a
    March 7 1920, GA 324a
    March 24 1920, GA 73a
    March 27 1920, GA 73a
    March 31 1920, GA 324a
    April 18 1920, GA 201
    April 24 1920, GA 201
    May 1 1920, GA 201
    May 15 1920, GA 201
    September 22 1920, GA 300a
    October 15 1920, GA 324a
    January 15 1921, GA 324a
    April 7 1921, GA 76/324a
    April 12 1921, GA 313
    June 27 1921, GA 250f.
    June 28 1921, GA 205
    July 8 1921, GA 205
    August 7 1921, GA 206
    October 14 1921, GA 339
    October 15 1921, GA 207
    November 4 1921, GA 208
    December 31 1921, GA 209
    March 15 1922, GA 300b
    April 12 1922, GA 82/324a
    December 27 1922, GA 326
    January 2 1923, GA 326
    July 28 1923, GA 228
    July 29 1923, GA 228
    July 29 1923, GA 291
    September 15 1923, GA 291
    November 16 1923, GA 319
    January 2 1924, GA 316
    February 20 1924, GA 352
    February 27 1924, GA 352
    March 1 1924, GA 235
    April 16 1924, GA 309
    April 30 1924, GA 300c
    May 17 1924, GA 353
    July 20 1924, GA 310
    July 22 1924, GA 310
    August 19 1924, GA 311

    Rudolf Steiner spoke repeatedly about the theory of relativity and apparently did not distinguish clearly between the special theory of relativity and the general theory of gravitation, which Einstein also called the general theory of relativity. The following lectures and question-and-answer sessions (Q&A) discuss or mention the theory of relativity (RT).

  4. This passage makes it clear that Rudolf Steiners criticism of Einstein's thoughts does not have to do with their scientific foundation but rather with the fact that they have been applied to contexts and domains of life that are no longer solely attributable to physics as an inorganic science.

  5. The British astronomer and astrophysicist Arthur Eddington (1882-1944) undertook an experimental test of Einstein's prediction that light rays are influenced by gravitational fields (gravitational aberration). The test was to measure the change in apparent location of fixed stars close to the Sun during a solar eclipse. Two British expeditions (one to the western coast of Africa, the other to northern Brazil) were assigned to photograph the environs of the Sun during the solar eclipse of May 29, 1919, and compare them to the known locations of the stars. The result was published on November 6, 1919, and proclaimed as a triumph for Einsteins theory. The deviation at the edge of the Sun, as Einsteins theory predicted, was approximately 1.75 seconds of an arc. Questions immediately arose as to whether the accuracy of the results was sufficient to confirm Einstein's theory. Steiner's objection, however, may have less to do with the inaccuracy of his contemporaries' measuring techniques, which were later superseded as this experiment and others were repeated, than with a question of principle, namely, whether even very precise quantitative experimental confirmations of a theoretical mathematical model constitute an adequate guarantee that the model is true or corresponds to reality.

    In his commentary on Goethe's natural scientific works Geschichte der Farbenlehre, Enter Teil, Sechste Abteilung): Newtons Persönlichkeit, Steiner writes about this problem: "Mathematical judgments, like any others, are the results of certain presuppositions that must be assumed to be true. But in order to apply these presuppositions correctly to experience, the experience must correspond to the conclusions that result. We cannot draw the opposite conclusion, however. An empirical fact may correspond very well to mathematical conclusions that we have arrived at, and yet in reality the presuppositions that apply may not be those of mathematical scientific research. For example, the fact that the phenomena of interference and light refraction coincide with the conclusions of the wave theory of light does not mean that the latter must be true. It is completely wrong to assume that a hypothesis must be correct if empirical facts can be explained by it. The same effects may be due to different causes, and the justification for the presuppositions we accept must be proved directly, not in a roundabout way by using consequences to confirm them." (Goethean Science, edited by Rudolf Steiner, volume 4, GAld.)

  6. See Einstein, The Principle of Relativity [1911]:

    The situation is most comical when we imagine causing this clock to fly off at a constant high speed (almost equal to c) and in a constant direction. After it has covered a great distance, we then give it an impulse in the opposite direction, so that it returns to the point where it was originally thrown out into space. We then discover that the hands have scarcely moved at all during its entire trip, whereas the hands of an identical clock, which remained motionless at the starting point for the entire time, have moved considerably. We must add that what is true of this clock, which we have introduced as a simple representative of all events in physics, also applies to any other self-contained physical system. For example, a living organism that we place in a box and subject to the same motion as the clock would be relatively unchanged on returning to its starting point after the flight, while a similar organism that remained in the same place would have made way for new generations a long time ago. For an organism moving at approximately the speed of light, the long traveling time would amount to only a moment. This is an irrefutable consequence of the underlying principles that experience imposes on us...

    The theory of relativity has several important conclusions for physics that must be mentioned here. We saw that according to the theory of relativity, a moving clock runs slower than an identical clock that is not moving. We will probably never be able to use a pocket watch to verify this statement, because the speeds that can be imparted to a watch are minuscule in comparison to the speed of light. Nature, however, does provide objects that are clock-like in character and that can be made to move extremely rapidly, namely, atoms that give off spectral lines. Through the use of an electrical field, these atoms can achieve speeds of several thousand kilometers (channel rays). According to the theory, it is to be expected that the influence of these atoms' movement on their frequency of oscillation is similar to what we deduced with regard to the moving clock.

    Clearly, Einstein does not hesitate to extend his theories, which are based purely on considerations belonging to the field of physics, to objects not belonging to that field alone. Thus he claims implicitly that the theory of relativity does not encompass simply systems belonging to the field of physics in the narrower sense but that the entire cosmos underlies his theory. This relatively indiscriminate view is the primary reason for Steiner's harsh objections to what he calls the abstractness and lack of reality of Einstein's thinking.

    That Einstein really chose not to recognize any significant difference between the different domains of reality is evident from a contemporary report by Rudolf Lämmel (1879-1971), a physicist and ardent popularizer of Einstein's theory of relativity. In his book Die Grundlagen der Relativitätstheorie [1921], Lämmel says:

    The strangest consequence of these new ideas of the theory of relativity is this: distances are shorter for observers at rest than for those who travel them. Similarly, elapsed time seems longer for an observer "at rest" than for one who is traveling with the clock ... Thus, if we send an expedition out into space today, traveling at half the speed of light, when the travelers return at the same speed after an 11 1/2 year absence, they will ascertain that they spent exactly ten years en route.... Thus the questions "How long is this distance?" and "How long is this duration" no longer can be answered in absolute terms but only with regard to specific observers, that is, relatively. This insight is no mere philosophical remark, but a mathematically confirmed relationship.

    In his Zurich lectures to the Physicalischen Gesellschaft (Society for Physics) and the Naturforschenden Gesellschaft (Society for Scientific Research), Einstein took up the above example of the duration of a space trip and concluded that under certain circumstances, the explorers might find on their return that their former contemporaries had aged considerably, while they themselves had been traveling for only a few years. This author objected to Einstein's claim and stated that the conclusion applied to units of measurement and to clocks, but not to living beings. Einstein, however, replied that ultimately all processes taking place in our blood, nerves, and so on, are periodic oscillations and therefore movements. Since the principle of relativity applies to all movements, the conclusion about unequal aging is admissible! ... (p. 84 f).

    For more on the debate about the theory of relativity during the first few decades of the twentieth century, see Hentschel's thorough study [1990],

  7. "The issue here later became known as the "paradox of the clocks" or "paradox of the twins." See the comparable passage in the questions and answers of October 15, 1920.

  8. See Note 36 on ether theory.

  9. See Steiners thorough explanation in his lecture of August 20, 1915 (GA 164). If the formula \(s = e \times t\) is interpreted as an equation of quantities: it is unavoidable to conclude that \(t\) is of a different dimension from \(s\) and \(c\). In any case, \(f\) is certainly not without dimension and that is not what Steiner meant, because the result would be meaningless in the dimensional calculus of physics. Steiner's intent is not to correct the dimensional calculus but rather to point out the problem of the reality of the quantities and calculations that appear in physics. In this sense, no reality can be attributed to the quantity \(t\), though in formulas it must appear to have a specific dimensionality. "Time" \(t\) is not a dimensionless factor but a factor with no reality—that is, a pure number with no reality.

  10. See the following comparable passages on speed as a reality: questions and answers of November 27, 1913,—lectures of August 20, 1915 (GA 164), December 6, 1919, December 27, 1919,and January 2, 1920 (GA 320),—questions and answers of October 15, 1920,—and the lecture of January 6, 1923 (GA 326).

  11. On this point, see Rudolf Steiner's Einleitungen zu Goethes Naturwissenschaftlichen Schriften ("Introductions to Goethe's Natural Scientific Writings") (GA 1), chapter XVI.2, "Das Urphänomen" ('The Archetypal Phenomenon").

  12. Steiner is referring here to unprotected movement through the air, not to travel in airplanes or similar vehicles. See the comparable passages in his lectures of August 7, 1917 (GA 176),—September 25, 1919 (GA 300a), June 27, 1921 (GA 250f); June 28, 1921 (GA 205),—April 30, 1924 (GA 300c),—and July 20, 1924 (GA 310).