## The Fourth Dimension

GA 324a

### Questions and Answers XII

7 March 1920, Stuttgart

*QUESTION: According to Einstein's theory, there is a tremendous amount of energy stored in one kilogram of matter. Is it possible to tap a new source of energy by breaking matter apart—that is, by spiritualising it?*

The [Note 47] issues you raise are not related directly to the part of Einstein's theory that we discussed today. [Note 48] It certainly would be possible to release energy through the fission of matter. The theoretical aspects present no particular difficulties. The only question is whether we have the technology to utilize this energy. Would we be able to put to use the gigantic forces that would be released? We would not, if they destroy the motor they are meant to run. We first would have to develop mechanical systems capable of harnessing this energy. From a purely theoretical perspective, releasing large amounts of radiant energy for use in a mechanical system requires a substance that can resist the energy. Releasing the energy is quite possible and much easier than utilizing it.

*QUESTION.- Would it be possible to eliminate matter altogether, so that only energy or radiation is left?* [Note 49]

In a certain respect, matter is eliminated as in what happens in vacuum tubes. Only a flow of electricity remains. Only speed remains and speed is the determining factor in the mathematical formulas that refer to this phenomena. [Note 50] The question is, Does the formula (E = mc2), in which energy and mass appear at the same time, sufficiently consider the fact that mass as such is different from energy? Or, when I write this formula, am I very abstractly separating two things that are actually one and the same? Is this formula justifiable? [Note 51] It is justifiable only for potential energy, in which case Einstein's formula (E = me2) is simply the old formula for potential energy in a new disguise. [Note 52]

*QUESTION: Can't we take \( p \times x\) as our starting point?* [Note 53]

A difficulty arises here simply because when I relate two members of one system of magnitude to something that belongs to another system—for example, if I relate the time it takes two people to do a certain job to a factor supplied by the Sun's setting—the process in the whole system (because it can truly be applied to all members of the system) very easily assumes the character of something that does not belong to any system but can stand on its own. You must not assume that an abstraction, such as a year, that is derived from the solar system is also valid in another system. For example, if you confirm how much a human heart changes in five years, you can then describe the condition of a person's heart as it was five years ago in comparison to what it is now. But by simply continuing the same arithmetical process, you also can ask what that person's heart was like a hundred and fifty years ago or what it will be like three hundred years from now.

This is what astronomers do when they start from the present state of the Earth. They neatly calculate changes over periods of time that make as little sense with regard to present conditions on Earth as our calculations about the state of a human heart in three hundred years. We always forget that a conclusion that is valid with regard to the immanent time of a process ceases to have meaning when the process comes to an end. Thus I cannot transcend the organism as a currently living total system. The total system allows me to keep my concepts within the system, and I immediately violate the system when I step outside its bounds. The appearance of validity is evoked because we are accustomed to relating to systems of magnitude in the sense of total systems and then make absolutes out of factors that apply only within such systems of magnitude.

Answers to questions raised by Georg Herberg during the lecture cycle

Geisteswissenschaftliche Impulse zur Entwickelung der Physik: Zweiter Naturwissenschaftliche Kurs('Spiritual Scientific Impulses for the Evolution of Physics: Second Scientific Course") (GA 321).The date of this question-and-answer session cannot be ascertained with certainty on the basis of documents in the Rudolf Steiner archives. It is unlikely that the questions date from March 13, 1920—the time ascribed to them by Hans Schmidt in his book

Das Vortragswerk Rudolf Steiners('The Lectures of Rudolf Steiner"), Dornach, 1978, expanded second edition, p. 319—because the theory of relativity was not mentioned in either Steiner's lecture on that date or Eugen Kolisko's lecture on "hypothesis-free chemistry" on the same day. Steiner's approach to the question suggests that it may belong to the previous question-and-answer session (March 7, 1920), which took place after Hermann von Baravalle's lecture on the theory of relativity.The word

rotationin the transcript of the document seems meaningless in this context and has been replaced byradiation.Steiner is referring here to the phenomenon of electrical conductance in rarefied gases and, in particular, to cathode rays—that is, to streams of high-speed electrons emitted from the cathode of a vacuum tube. Steiner's remarks coincide with the standard thinking of physicists on the subject.

The kinetic energy \(1/2mv^2 = eU\) that is imparted to the individual electrons (with the charge \(e\) by an electrical field of voltage \(U\) plays a determining role in all calculations related to cathode rays. Furthermore, the force \(K\) (Lorentz force) with which a charge e is deflected in a magnetic field \(B\) is a function of the speed \(v\).

$$K = evB$$On the subject of cathode rays, see also Steiner's lecture of January 2, 1920 (GA 320).

Einstein's formula \(E = mc^2\) establishes the proportionality of energy and inert matter. It is often called the most important result of the special theory of relativity. As is the case with other basic formulas in physics, there are no real proofs, but at best certain justifications (see below) of the formula \(E = mc^2\). Thus, this formula is seen as a postulate underlying relativistic physics. According to Einstein [1917], §15, where \(c\) is the speed of light, the kinetic energy of a body with a resting mass \(m\) moving at a speed \(v\) is

$$E_{kin} = \frac{mc^2}{\sqrt{i - v^2 / c^2}}$$If we develop the relativistic term \(E_{kin}\) for kinetic energy in a series, the result is

$$E_{kin} = mc^2 + 1/2mv^2 - \frac{3/8 mv^4}{c^2} + ...$$If \(v ˂ ˂ c\) the term remaining in the non-relativistic borderline case \(v/c \rightarrow 0\) is \(mc^2 + 1/2mv^2\). Thus, the resting energy \(mc^2\) must be added to the ordinary kinetic energy \(1/2mv^2\) if non-relativistic mechanics is to result (as the borderline case \(v/c \rightarrow 0\) from relativistic mechanics. This changes nothing in non-relativistic mechanics, because \(mc^2\) is an unchangeable constant that influences only the conventionally determined null point on the energy scale.

This passage in the transcript reads "...mass and energy are only a new disguise for the old formula, p.g. energy." It has not been possible to reconstruct the meaning of this formula, if indeed it was correctly recorded. What is intended here is probably the formula for the potential energy \(U\) of a body of mass \(m\) in the gravitational field.

$$U = mgz$$where \(g\) is the gravitational constant and \(z\) the \(z\)-coordinate. In fact, the thoughts presented in Note 40 show that \(E = mc^2\) plays the role of a potential energy of sorts (resting energy), though it is not directly significant for calculations in non-relativistic mechanics.

If \(p\) is interpreted as force in the sense of

potentia, the formula \(W = p \times s\) represents the work \(W\) of an unchanging force \(p\) over a distance of \(s\).