Nuts And Bolts: Taking Apart Special Relativity

By Jim Spinosa

"Nuts and Bolts:Taking Apart Special Relativity" is an attempt to disprove Einstein's theory of special relativity. Written to appeal to a wide audience, "Nuts and Bolts" explains the formidable equations of special relativity in unprecedented detail. When Einstein's equations and thought experiments are subjected to exacting scrutiny,
the incoherence of the former and the contradictions in the latter become apparent. Einstein's formicary is overturned, and the formerly ensorcelled experience no formic side effects. It’s difficult to believe that Einstein’s theories are wrong. It’s even more difficult to believe that any errors in his theories were not detected decades ago by the plethora of physicists and philosophers who have studied his theories. It’s difficult to believe that in the theory of special relativity there is at least one instance in which the common denominator for two algebraic fractions is incorrectly determined. With general relativity, the case is different. The errors appear to be in the tensor calculus itself that Einstein uses and not in the calculations that he makes using the tensor calculus. It seems that if we are going to say that general relativity is wrong we are also going to have to say that the Riemann-Christoffel curvature tensor is incorrect. Also, we will have to question the validity of the tensor calculus operations known as contraction and covariant differentiation. Here the issues become more complex. Do we want to deny the mathematicians the right to use entities such as “special” tensors of rank two? When two “special” tensors of rank two are multiplied the result is the number one (a scalar of rank zero) instead of the tensor of rank four that is required by the laws of tensor multiplication. Other errors are more subtle; for instance, in the justification of covariant differentiation the second derivatives of the coefficients of “ordinary” tensors are shown not to be always equal to zero, yet later in process it seems to be implied that the second derivatives of “ordinary” tensors are always equal zero.
Perhaps, that was Einstein’s genius choosing an obscure mathematics—tensor calculus—that physicists would be unfamiliar with. Then he would somehow have had to work his way backward from the result he wanted—Newton’s law of planetary motion with one extra term that could be used to explain the precession of Mercury and the other planets. Next, by choosing the appropriate coefficients for his particular version of the Pythagorean Theorem—his version of a formula for measuring distance in his particular space—he could make the flawed tensor calculus produce the results he wanted. The physicists who questioned his work might have thought “It is difficult to believe that tensor calculus is flawed. If there were any flaws in it they already would have been spotted by mathematicians.”
What part do philosophers play in all this particularly the philosopher of science Karl Popper? It’s as though Karl Popper employed a simple, yet effective deception. He seems to be an honest, hardworking, straightforward philosopher of science searching for clarity in science. Yet, strangely he does not seem to condemn some unscientific theories and the unscientific theories he does condemn seem completely unaffected by his condemnation.

• Language: English
• Publisher: Jim Spinosa
• Release date: Oct 6, 2010
• ISBN: 9781458020260

Jim Spinosa

Born in 1955,Jim Spinosa remembers,as a youngster,being entranced by the science fiction novels heperused in a small,corner bookstore in Denville,NJ. The cramped confines of that store had claimedto contain the largest selection of books in Northern New Jersey. His penchant for science fiction engendered an interest in physics. Often daunted by the difficulty of physics textbooks,hequestioned whether physics could be presented as clearly and concisely as science fiction,without sustaining any loss in depth Nuts and Bolts:TakingApart Special Relativity is an attempt to answer that question.

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Nuts & Bolts: Taking Apart Special Relativity

By Jim Spinosa

Published by Jim Spinosa at Smashwords

Copyright© 2010 Jim Spinosa

Smashwords Edition, License Notes: This e-book is licensed for your personal enjoyment only. This e-book may not be re-sold or given away to other people. If you would like to share this book with another person, please purchase an additional copy for each person. If you're reading this book and did not purchase it, or it was not purchased for your use only, then please return to Smashwords.com and purchase your own copy. Thank you for respecting the hard work of this author.

Ironic Dedication: To the unsung workhorses of Mathematics and Science—the subscript and the superscript.*

*Except for the overly complicated subscripts and superscripts, such as the letter T appended with both the superscript abc and the subscript def, which are the sine qua non of optometrists, not to mention the sub-subscripts, such as the letter T appended with both the superscript abc and the subscript def each of which is further appended by its own subscript, such as superscript a appended by the number one etc. **

**At this juncture, it seems appropriate to mention that Smashwords does not accurately reproduce complicated subscripts or superscripts especially if they are floating images. Smashwords does reproduce endnote numbers, but these superscripts are lowered to midscripts.

Mene, mene, tekel, upharsin

CONTENTS

Introduction

1. The Definition of Simultaneity

Step 1: An Error Found or an Error Manufactured?

Step 2: The Michelson-Morley Experiment Is Flawed

Step 3: Inspired Insight or Inspired Ambiguity?

Step 4: The Method of Synchronizing the Clocks Is Missing

Step 5: The Relativity of Simultaneity

Step 6: Another Interpretation

Step 7: Einstein’s Dilemma

2. The Twisted Path to the Transformation Equations and Beyond

Step 1: Metal Rods Turned into Cartesian Coordinates

Step 2: The Misapplication of Mathematical Rules

Step 3: A Change of Direction

Step 4: Return of the Misapplication of Mathematical Rules

Step 5: More Strange Equations

Step 6: The Transformation Equations

Step 7: Not So Simple Calculation

Step 8: Another Version of the Not So Simple Calculation

Step 9: Another Metal Rod Coordinate System

3. Components of a Radius and Confusing Clocks

4. The Limits of Special Cases and Running On a Train

5. Scalars or Vectors or Neither?

6. Conclusion: Sorting Through a Bag of Broken Parts

Note on Equations (3.18) and (3.19)

Endnotes for the Introduction and Chapters 1, 2, 3, 4, 5, 6 and the Note on Equations (3.18) and (3.19)

About the Author and Contact Information

Introduction

Zur Electrodynamik bewegter Körper (On the Electrodynamics of Moving Bodies) was published in Vol. 17 of the Annalen der Physik in 1905. Two other papers by Albert Einstein appeared in Vol. 17: On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular–Kinetic Theory of Heat and On a Heuristic Point of View Concerning the Production and Transformation of Light. Arthur I. Miller writes, in his book Albert Einstein’s Special Theory of Relativity, "As far as we know the editorial policy of the Annalen was that an author’s initial contributions were scrutinized by either the editor or a member of the Curatorium; subsequent papers may have been published with no refereeing. Einstein’s having appeared in print in the Annalen five times by 1905, his relativity paper was probably accepted on receipt."¹

Arthur I. Miller also includes this incident in his description of the initial reception of Albert Einstein’s paper, "In the fall of 1907 the relativity paper was rejected by the University of Bern as his Habilitationsschrift. One experimentalist wrote, ‘I cannot at all understand what you have written.’"² As A. I. Miller notes, in the endnote that accompanies the previous quotation, this assessment was by a professor of experimental physics Aimé Forster.

One of the obstacles that may have hindered Aimé Forster’s appreciation of the relativity paper is addressed by A. I. Miller, the first part of the special relativity paper is, in fact, nothing less than an epistemological analysis of the nature of space and time.³ Epistemology is the branch of philosophy that concerns itself with theories about the nature, sources and limits of knowledge. With this in mind, it seems reasonable to try to gain a clear understanding of Einstein’s philosophy of science.

It is difficult to address the significance of Einstein’s many comments on the general principles that govern the field of knowledge known as physics. He certainly did not dismiss the notion that the empirical testability of a theory was a crucial criterion for judging a theory’s validity. However, it was also crucial to Einstein that the premises of a theory have a naturalness and logical simplicity. This is what Miller refers to as Einstein’s idea of the inner perfection⁴ of a theory. In the endnotes that accompany the Introduction to his book, Miller cites a well-known statement by Einstein, which Einstein wrote forty-five years after his completion of the special relativity paper, Miller writes, "in Reply to Criticisms (1949) he [Einstein] described, ‘concepts and theories as free inventions of the human spirit (not logically derivable from what is empirically given).’⁵ Statements such as the one above, which seem to refer to the inner perfection of a theory are balanced by statements such as, The first point is obvious: the theory must not contradict empirical facts. However evident this demand may in the first place appear, its application turns out to be quite delicate."⁶ Miller’s conclusion is that the essence of Einstein’s scientific method was inarticulable.

If we turn our attention to Einstein’s book Relativity: The Special and the General Theory, we can examine Einstein’s inarticulable scientific method in operation. In chapter eight, which is entitled On the Idea of Time in Physics, he gives us a definition for determining the simultaneity of distant events. Einstein’s definition is written in the form of a dialogue between himself and the reader. In this dialogue, Einstein is investigating a meteorological phenomenon that — according to weather lore, familiar to us all — should be restricted to works of fiction and thought experiments. Namely, he is investigating lightning flashes that strike points A and B, repeatedly. Incidentally, the weather lore that lightning never strikes the same place twice is considered discredited by the multiple lightning strikes received by skyscrapers such as the Empire State Building. Einstein is not interested in exploring the conjunction of the atmospheric conditions and topographic features that conspire to produce such results. Instead, he is interested in determining whether these distant lightning flashes occur simultaneously. It should be further noted that a railroad line runs through points A and B.

"After thinking the matter over for some time you then offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line AB should be measured up and an observer placed at the mid-point M of the distance AB. This observer should be supplied with an arrangement (e.g., two mirrors inclined at 90 degrees) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous. I am very pleased with this suggestion, but for all that I cannot regard the matter as quite settled, because I feel constrained to raise the following objection: ‘Your definition would certainly be right, if only I knew that the light by means of which the observer at M perceives the lightning flashes travels along the length A => M with the same velocity as along the length B => M. But an examination of this supposition would only be possible if we already had at our disposal the means of measuring time. It would thus appear as though we were moving here in a logical circle.’"⁷

A minor error in terminology occurs when Einstein expresses his desire to be certain that the velocity of light along the length A => M is the same as the velocity of light along the length B => M. The velocity of light is a vector. A vector has both magnitude and direction. The light beams are traveling in opposite directions so they cannot have the same velocity. However, the light beams can have the same magnitude. If the light-beam vectors have the same magnitude, it would mean their speeds are equivalent, which is the point Einstein is trying to make.

There is another error that is more serious. The definition does not take into consideration that the earth is in motion and further that the motions of the light beams are independent of the earth’s motion. In other words, the light beams are not carried along by the earth’s motion. All the earthbound objects we commonly observe in motion such cars, planes and trains are carried along by the earth’s motion. Also, all the objects we commonly observe as being at rest such as buildings, bridges and telephone poles are carried along by the earth’s motion. Thus, the observer standing still at the midpoint M of the length AB is being carried along by the earth’s motion. Since the endpoints of the length AB are also being carried along by the earth’s motion, the observer at the midpoint M is at rest relative to the endpoints of the length AB. Thus, the observer at the midpoint M maintains a constant distance from the endpoints. This is not the case with the light beams that originate from either endpoint. The observer at the midpoint M is rushing toward one light beam and away from the other light beam, although he seems to be standing still. This is because the earth is in motion and the motions of the light beams are independent of the earth’s motion. Of course, both light beams are traveling toward the observer at the midpoint M at the speed of light.

Einstein’s definition of a test to determine the simultaneity of distant events provides an example of the naturalness and the logical simplicity that he believed should characterize the premises of a theory. The naturalness of his definition resides in the fact that it agrees with our observations of the everyday world. For example, let an observer stand at the midpoint of a smooth and level stretch of two-lane highway 60 miles in length. Also, station an automobile at each end of this 60-mile length of highway, and let the automobiles start traveling at a given time with a constant speed of 30 mph. If the two automobiles pass by the observer standing at the midpoint at the same instant, the two automobiles began their journey at the same instant. This is precisely the same claim that Einstein makes for the flashes of lightning occurring at points A and B. If the observer standing at the midpoint between points A and B sees the flashes of lightning at the same time, they were both produced at exactly the same instant.

The logical simplicity of his definition resides in minimal number of measurements required to assess the simultaneity of distant events and the straightforwardness of the observations required.

We can now return to Einstein’s dialogue with the reader—picking up where we left off.

"After further consideration you cast a somewhat disdainful glance at me—and rightly so—and you declare: ‘I maintain my previous definition nevertheless, because in reality it assumes nothing about light. There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled. That my definition satisfies this demand is indisputable. That light requires the same time to traverse the path A => M as for the path B => M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own free will in order to arrive at a definition of simultaneity.’"⁸

Einstein overreaches with his statement, "There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled." The following example shows that the one demand Einstein makes on the definition of a test to determine simultaneity is not enough to obtain an accurate definition of a test to determine simultaneity. A definition of a test to determine simultaneity that everyone will agree is incorrect can still yield in every real case an empirical decision as to whether or not two distant events occur at the same instant. For example, if instead of stationing the observer at the midpoint M between points A and B, let’s say we station the observer at a point that is closer to point A than it is to point B. Let’s say the observer in our experiment is stationed one-third of the way from A to B. This observer can provide us with an empirical decision in every real case as to whether or not the two distant events occurred at the same instant. Yet, no one would conclude that this definition of distant simultaneous events fulfills the demands required of an accurate definition. If the flashes of lightning at points A and B occurred at the same instant, our observer stationed one-third of the way from point A to point B would observe that the flash of lightning at point A occurred before the flash of lightning at point B because he is closer to point A than he is to point B. To reiterate,