{'fraction_non_alphanumeric': 0.029393753827311696, 'fraction_numerical': 0.004082465809348847, 'mean_word_length': 5.079404466501241, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Reply to the "Certain Conceptual Anomalies in Einstein's Theory of Relativity" and Related Questions

Since its inception, Progress in Physics, has maintained the importance of freedom of expression in science [1]. As a result, the journal has sometimes published works even though the editorial staff differred either with the premise or with the conclusions of a paper. The editorial board maintains that it is best to disseminate works, rather than to unknowlingly suppress seminal ideas. The validity of all scientific arguments will eventually be discovered. For this reason, the journal strongly upholds the rights of individual scientists relative to publication. At the same time, many questions focusing on fundamental aspects of Einstein’s theory of relativity have been submitted to the journal. Most of these letters were not published as they were concieved by authors who did not properly grasp the concepts outlined within the classic textbooks on this subject, such as The Classical Theory of Fields by Landau and Lifshitz [2] and others [3]. Recently, the editorial board made the decision to publish a work by Stephen J. Crothers [4] even though some questions remained relative to its basic premise. We chose to move to publication for two reasons. First, Crothers is a capable scientist who has already demonstrated substantial insight into General Relativity [5]. Indeed, the editorial board has written in support of these ideas [6]. Second, the journal has received substantial correspondance from both amateurs and established scientists. These letters have focused on perceived problems with Einstein’s theory of relativity. The editors therefore feels compelled to address these concerns, both relative to Crothers [4] and to other serious scientists who had previously worked, with success, on numerous applications of the theory of relativity. In general, the correspondance we have received has expressed doubt concerning the validity of some key points in Einstein’s theory. We found that these questions originated in the fact that the scientists asking the questions were educated as physicists, while the base of Einstein’s theory is Riemannian geometry. It is therefore not suprising that some confusion might arise. The meaning of Einstein’s theory is the geometrization of physics, the expression of all physics through the geometrical properties of the four-dimensional pseudoRiemannian space (the basic space-time of the theory of relativity) or its extensions. Many physicists came to the theory of relativity from the other fields of physics; they learned Einstein’s theory through brief courses which gave the theory in its historical sense, often with artifically introduced principles and postulates. When the meaning of Einstein’s theory, the geometrization of physics, was finally understood through the joint intellectual powers of Albert Einstein and Marcel Grossmann, all the physical principles came out from the consideration; they all became covered by the particular properties of the geometry within four-dimensional pseudoRiemannian space. Such a “historical” approach, which is very common in most brief courses on the theory of relativity for physicists, often carries a student away with speculations on the principles and postulates, instead of studying Riemannian geometry itself. As a result, serious physicists erred relative to simple questions which remained open after their brief education. Only a small minority of physicists, who devoted their life to understanding the theory of relativity, were lucky enough to be able to study the special (more advanced) courses on this subject. Here we collected twelve of the most common questions on the basics of Einstein’s theory, asked by the readers and some of our colleagues. We hope the answers will remove most key problems with a real, solid understanding of the theory. First. Naturally, each term in Einstein’s equations in emptiness (i.e. with zero right-hand-side) vanishes. This is due to that fact that, in such a case, the scalar curvature is zero R= 0, so Einstein’s equations become the vanishing condition for Ricci’s tensor: R = 0. In the same time, Ricci’s tensor R isn’t a number, but a 2nd-rank tensor whose components are 16 (only 10 of whom are independent). The formula R = 0, i.e. Einstein’s equations in emptiness, means 10 different differential equations with zero elements on the right-hand-side. These are differential equations with respect to the components of the fundamental metric tensor g : each of 10 equations R = 0 is expressed in the terms containing the components of g and their derivatives according to the definition of Ricci’s tensor R . Nothing more. (With nonzero elements on the right-hand-side, these would be Einstein’s equations in a space filled with distributed matter, e.g. electromagnetic field, dust, liquid, etc. In such a case these