Special Relativity: A Concise Guide for Beginners

By Paul G. Bennett

As a boy, Einstein had imagined riding a beam of light and wondered if he would be able to see his reflection whilst holding a mirror. According to Newton, he would be moving so fast that light from his face, would not be able catch up with the mirror to become reflected back into his eyes. Travelling along at the speed of light, the wave front would appear frozen, however Maxwell had shown that light is an oscillating electromagnetic field and therefore such a stationary wave was impossible. Einstein resolved this conflict by realising that space and time are relative.
This book is based upon a PowerPoint presentation that I gave, to convey the nature of this remarkable theory. Most of the explanation is given in terms of diagrams and simple descriptions, without much recourse to mathematics. It also acts as a prequel to my following book which deals with General Relativity. This and other physics titles (together with electronic downloads), are available from Lulu

• Language: English
• Publisher: Lulu.com
• Release date: Oct 2, 2011
• ISBN: 9781470924812

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Special Relativity: A Concise Guide for Beginners

Special Relativity: A Concise Guide for Beginners

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This book has been adapted from PowerPoint slides that were used for a series of lectures on relativity. Some of the graphics and colours have been removed from the original, in order to make it amenable for print and to reduce the cost of the book. This has also resulted in the addition of extra text, so as to clarify and expand upon some of the contents of the original slides. There is also a large Appendix for those who desire more mathematical detail.

As a boy Einstein imagined riding along on a beam of light, whose waveform would therefore appear stationary. However, according to Maxwell’s theory no such ‘frozen’ wave can exist, since he had shown that light is an oscillating electromagnetic field. The young Einstein also imagined what he would see, if he looked in a mirror which was travelling with him at the speed of light. Would he see his own reflection, or would he see nothing due to the fact that light from his face, would never be able to catch up with the mirror and not therefore be reflected to his eyes? This was Einstein’s earliest realisation that the speed of light must be constant for all observers and the need to elevate this fact (which is more rigorously demonstrated by Maxwell’s equations), to a physical law, resulted in the discovery of the relative nature of space, time and mass. In particular, time slows down for a moving observer and there is also a contraction in their length! Even today more than a 100 years after the birth of relativity, some people still believe that they have found a flaw in the theory. They send in papers that claim that they have proved that the theory is wrong. The simple fact is however, that special relativity is logically self consistent and once we accept the experimental and theoretically derived fact that light can only be observed to travel at a fixed speed, the conclusions follows almost inevitably.

"If I pursued a beam of light with velocity c I should observe such a beam as a spatially oscillating electromagnetic field at rest. However there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations"   

(EINSTEIN)

Light is an oscillating self sustaining electromagnetic field, as depicted below (the electric field is in blue, the magnetic field is red). If you could catch up with a beam of light, its wave would appear ‘frozen’, which contradicts Maxwell’s equations of electrodynamics. [An oscillating magnetic field is required to produce an oscillating electric field, which in turn generates an oscillating magnetic field etc. etc, thus sustaining the propagation of the light wave]

So, Special Relativity (SR) resulted from the study of Maxwell’s Laws of Electromagnetism (EM), while the need to extend this theory for non uniform motion (acceleration) and also to make it valid in gravitational fields, led to General Relativity. [SR is thus only a limited case of GR.] Special Relativity explains the constancy of the speed of light in empty space far away from any matter, while GR explains the local constancy in a gravitational field. SR is mandatory when dealing with very high velocities comparable to the speed of light, while the incredible accuracy of GR becomes evident when dealing with large gravitational fields. In this book we will be concentrating upon SR, which is then developed into Einstein’s theory of GR in a sequel publication. It is worth emphasising that there is only one theory of relativity and that is GR. However for ease of teaching and historical reasons, it is often split into these two categories, even though SR is only a special and simplified case of GR. [It is also true to say that the ‘Holy Grail’ of physics is to produce a quantum theory of gravity, which would replace GR, although all such laws of physics would still need to conform with SR.]

The conflict between Newton’s particle mechanics (as exemplified by the success of statistical thermodynamics) and Wave theory (as exemplified by Maxwell’s laws of electromagnetism), becomes evident when we study Black Body Radiation and its resolution resulted in the birth of Quantum Theory! Another such conflict is ‘brought to light’ when we consider the propagation of EM radiation (light) and the Newtonian view of space and time, one that can only be resolved with Special Relativity. In his theory of SR, Einstein demolished the concept of the luminiferous Aether, which was believed to be the medium by which light waves propagate (cf. page 29). Some people such as the physicist Sir Oliver Lodge, believed that the aether was where the spirit resided after death. Sir Oliver was one of the first persons to transmit and receive a radio wave (later patented by Marconi, who sent Morse code messages and later speech.) In 19th Century, physicists such as Lord Kelvin posited a vortex theory of atoms, which believed that atoms were like knots in the aether.  

PART  I   The fundamentals of Special Relativity

Let us first make a brief overview on these momentous developments in physics, before taking a majestic ride through Einstein’s legacy. What relativity tells us, is that space contracts for an object that is in motion relative to us and also time slows down for that object (its mass is also observed to increase.) At the very least the reader has to just accept this as an experimentally verifiable truth about the universe, irrespective of any theoretical reasoning. It is only counter intuitive to our everyday experience, because we are never subjected to speeds that are remotely close to that of light. It is not that SR is hard to understand (the mathematics is mainly school level algebra), but rather it is hard to believe. In his development of the theory, Einstein was probably influenced by Immanuel Kant’s view, that space and time were products of our perception. Specifically, Kant believed that what we know of the world, conforms to certain a priori categories, which although we recognise by experience do not arise from experience. These categories (e.g. space and time) are like filters laid-down by the mind, which turn sense data into objects of knowledge. In other words, it is the prior condition of the mind (the way that our brains are ‘wired’), that allows us to perceive space and time.

The coordinate transformations that replaced those of Galileo and even the famous relationship E = mc², had already been discovered by Lorentz and Poincare respectively (both came from studies of