Preface

In the development of Einstein’s relativity theories, as well as in the book that follows, thought experiments play a vital, indispensable role. Thought experiments have been extolled as a golden means for achieving insights and formulating new theories. Galileo and Newton used them extensively in their work on astronomy and physics long before Einstein. But there is a dark side to thought experiments, which is dangerous. It is therefore necessary to examine the nature of thought experiments, as well as their application, to understand how they can be useful—and how they can hurt and lead to terrible errors of judgment, as well as absurd results.

We can categorize thought experiments into three basic classes:

(1) Those that are credible and similar to real experiments that we can do in the field or in the laboratory;

(2) Those that are incredible, involve a contradiction, or require substances or apparatus that simply don’t exist; and

(3) Those that require such a stretch of our imagination and belief that we have the right to be wary and skeptical. All three types are involved in Einstein’s work.

The first, credible type is easy to recognize. It is usually an experiment that cannot be achieved because of limitations in cost, time, or technological resources. If, for example, it involves distances that cannot be achieved here on earth, or conditions, such as the absence of gravity, that can only be approximated in distant outer space—or if we want a train to move at half the speed of light—we need thought experiments.

The second, incredible type is also easy to recognize. If we want to impose conditions such as an observer being in two places at the same time, or a beam of light making a right turn, or experiencing a crash before it happens, we had better leave science and pursue a career in politics or art.

Thought experiments of type 2 have no place in physics (even if they sometimes creep into the literature).

Then there are the imaginative thought experiments of type 3. For example, we may want to speed up a marble until it weighs as much as a two-ton truck, or speed up a train until it shrinks in half, or create matter out of nothing. Or we may send one of two twin brothers into space and have him return younger than the twin he left behind. These are not thought experiments that we would begin with—but they may be thought experiments we end with, as the implication of a theory in which we have come to believe.

Type 1 thought experiments cannot easily be defined in terms of rules and regulations—we must fall back on experience, common sense, or intuition. But we can usually find the fallacies or contradictions in a type 2 thought experiment fairly easily.

There is yet, however, another type of thought experiment, type 4, that does not belong to any of the above three types.

It is one that is so unclearly formulated, or involves ambiguous concepts, that it leads into a morass. We need to dissect it, perform an autopsy, and let it go. If it is important, we need to reformulate it and see what results it then yields. That is what we have to do with some of Einstein’s thought experiments. It is a tedious task involving logic, linguistics, and common sense.

But to return to the positive aspects: I have found that the image of a speeding train in relation to the embankment over which it moves provides at least three distinct thought experiments that yield important results. One such experiment leads to demonstrating the contradiction between Einstein’s two basic principles of Special Relativity Theory (SRT). Another shows that the speed of light is not constant when the source is in motion with respect to the observer. A third, and most surprising, one leads to a new way of looking at the Doppler effect, and shows that, contrary to popular belief, the Doppler effect is symmetric (until quite recently I could not find a convincing demonstration of this).

The Doppler effect is the same whether the source of light or the receiver is in motion. That will come as a surprise to the scientific community.

Let me review the organization of this book.

Chapter 1 is the introduction.

Chapter 2 establishes the importance of the principle of relativity and the importance of embracing the symmetry that is embodied in Einstein’s first principle—that all motion is relative. In point of fact, this principle is in essence Newton’s first principle of inertia, but without the assumption of absolute rest—because we no longer believe that the sun is the absolute center of the universe, as did Einstein and Newton.
(Einstein was well aware that this principle is in contradiction to the absolute constancy of the speed of light, his second principle. That is to say, there is a contradiction if we accept the immutability of space and time, as Newton does.

Einstein therefore needs to demonstrate that, contrary to Newtonian thinking, time is deformable, that is, relative. This is a case where a type 4 thought experiment comes in.)

In Chapters 3 and 4, I examine Einstein’s defense of SRT. He uses ambiguous concepts of synchronization and simultaneity in his works of 1905 and 1917, respectively. (The definitions and logic are a problem when it comes to synchronization. The ambiguities of concepts lead to type 4 thought experiments when it comes to simultaneity.)

Chapter 5 discusses the Michelson–Morley experiment, which triggered the Lorentz Transformation discussed in Chapter 6. It is the basis for Einstein’s derivation of SRT. The problems in that derivation are due, in part, to the fact that “relative time” is false (as shown in Chapter 3). In part, the problem is that the Lorentz Transformation is only valid for a “round trip” of light (an inappropriate choice of a type 1 thought experiment).

In Chapter 7, we must derive the correct formula for the Doppler effect, as a prelude to dealing with the age of the universe in Chapter 8.
Chapter 9 consists of a counterexample for General Relativity. It is not a follow-on to the above development but shows that Einstein’s reasoning here was faulty as well. The counterexample shows the problem or drawing a false inference from what is otherwise a good example of a type 1 thought experiment.

We could end the story there, but I wanted to indulge in some speculations based on recent data and current beliefs in cosmology. This resulted in Appendices I and II. The third appendix is not relevant to the discussion but shows that E = mc2 leads into logical difficulties—which I don't know how to resolve.

Conclusions, Truths and Consequences, and the Epilogue are short chapters for those readers who want things “in a nut shell.” They also offer a taste of the author’s attitude towards science, philosophy, epistemology, and metaphysics.

Addendum:

Email received 5-2-01 from Colleen.Wunsch@Physik.Uni-Augsburg.de

On behalf of Professor Eckern, Editor in Chief, Annalen der Physik, I acknowledge receipt of your fax … relating to your paper “Einstein’s Fuzzy Logic”.
… there is no hope of getting this material published in Annalen der Physik, particularly as the editors recently unanimously decided not
to publish, or to even discuss contributions which claim to have obtained counter-examples to Einstein’s Theory of Special Relativity … (Note: Annalen is the journal where Einstein published in 1905)

edition steinherz