Why Does E=mc2?: (And Why Should We Care?) by Brian Cox (PDF)

Description

The international bestseller: an introduction to the theory of relativity by the eminent physicists Brian Cox and Jeff Forshaw What does E=mc2 actually mean? Dr. Brian Cox and Professor Jeff Forshaw go on a journey to the frontier of twenty-first century science to unpack Einstein’s famous equation. Explaining and simplifying notions of energy, mass, and light-while exploding commonly held misconceptions-they demonstrate how the structure of nature itself is contained within this equation. Along the way, we visit the site of one of the largest scientific experiments ever conducted: the now-famous Large Hadron Collider, a gigantic particle accelerator capable of re-creating conditions that existed fractions of a second after the Big Bang. A collaboration between one of the youngest professors in the United Kingdom and a distinguished popular physicist, Why Does E=mc2? is one of the most exciting and accessible explanations of the theory of relativity.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book tries to introduce the special theory of relativity, and a formula that can be derived thereof; E = mc^2. First, it does so on a phenomenological level. We learn why the speed of light is constant, in that it was actually not Einstein that came up with this notion, but Faraday and Maxwell. Maxwell’s equations show that the electric and magnetic fields are moving as waves at the speed of light. And this speed is given due to physical properties of the wave and physical constraints. Like the speed of sound, the wave of moving air that propagates to give us sound can only move so fast. If you fly faster, you will break the wall of sound and drag the soundwaves behind you. And thus, like sound waves, the waves of the electric and magnetic fields simply cannot move faster. Einstein’s genius was then to explain that, if an observer of a train and a passenger on the train that moves with 90% of the speed of light both see the speed of light on the train as constant, then the passenger must experience time much slower.The book continues easily enough. The authors derive the time dilation effect using only Pythagoras formula and even explain once that “1 / 2” means “1 divided by 2”. But then, already in the next chapter, they derive that in the four-dimensional spacetime, everybody must experience the same distances. Yes, the pure spatial distances get shorted when traveling close to lightspeed, but the time gets elongated. So, the “time-distance” in spacetime is experienced by all the same; it is invariant. And they want to derive the formula here as well, again Pythagoras a^2 + b^2 = c^2, but now, without explaining anything, just out of the blue, it actually has to be c^2 = a^2 – b^2. Why we have to subtract the one term nobody knows; it is not explained. It just happens to lead then to the correct results, but why would we subtract one term?The book then goes on to derive the formula E = mc^2. In order to do that, the authors explain that not only energy is conserved, due to the law of conservation of energy, but also momentums. When a billiard ball hits a standing billiard ball, the moving one will transfer its momentum to the standing one and itself stand still. In three dimensions, the momentum will be described by the formula p = mv, thus the mass times the velocity. Checking the momentum in four-dimensional spacetime, we get a bring mc. The part which points off in the time direction is γmc, if speeds are small compared to c, γ becomes 1 and γmv become mv, the three-dimensional formula. But calculating a bit on with γmc, we can calculate it with c and say, γmc^2 is conserved, as c is constant. For small speeds, γ is 1+ ½(v^2/c^2). Multiplying it with γmc^2, we get mc^2 + ½mv^2. For small speeds, this term is thus conserved. ½mv^2 is the kinetic energy, so what we have found is that the energy is conserved and mass is conserved, multiplying it with c does not make a difference. But what we have also found is that energy and mass are convertible, and this with the formula E = mc^2.In a chapter listing examples why the formula E = mc^2 is important, also outside stars and nuclear reactors, the authors list the burning of wood or coal among others, without really explain why. They list that weighing up all products from the fire, charcoal and the gases, we get a little bit less mass than the wood or coal and oxygen had before. But in school, I learned in chemistry that there is energy released here because it is an oxygenation. Oxygenations always release energy. The authors should have pointed out the fact that because the products lose a little bit of energy, oxygenations release energy. Nuclear fission or fusion processes are introduced, that are generally a million times more energy releasing than chemical process, where molecular bonds are broken and rearranged.The next chapter then introduces the standard model for elementary particles and explain it via gauge symmetry, where the interactions of elementary particles can be drawn using Feynman diagrams. This part was absolutely incomprehensible for me, a negative aspect of putting a complicated formula at the beginning, and then trying to explain its meaning throughout the text entirely without any mathematics. Just in the last one or two pages, it is revealed why the standard model was discussed to such lengths in this book: Looking only at the first two lines of the master equation, the elementary particles would have no mass. Therefore, the Higgs fields that affects different particles differently was introduced. Mass is thus is a result of the Higgs field. In these last pages, bosons are then mentioned as well, without having ever been explained before.In the last chapter, the authors discuss how Einstein thought about Galileo’s equivalence principle, that two object with different weights take exactly the same time to fall, if other influences, such as air resistance, are excluded, which led him to conclude the equivalence of gravity and acceleration that underlines his theory of general relativity. He thus realized that all that gravity actually does is bending spacetime. Consequently, the earth around the sun actually follows a straight line, just that the line happens to bend around the sun in spacetime in almost a circle due to the sun’s mass. Light that passes close to the sun also appears to come from someplace else, due to the directly line having been bend by the sun. In this manner, general relativity was also proven in 1919.In an appendix, the authors state that they often get the question why in the formula c^2 = a^2 – b^2, one term has to be subtracted and try to explain it better. In my opinion, not successfully. All in all, I kept wondering for whom this book was written. It starts by explaining that “1 / 2” means 1 divided by 2, but then quickly reaches a level which only educated physicists can understand. These different levels were just mindbogglingly inconsistent for me. Moreover, outside physics, I could find some very stupid mistakes, such as the statement that Muslim scientists used experiments to prove axioms as early as in the 2nd century (Location 542). As far as I know, Muhammed lived in the 7th century. There could not have Muslims before.As teenager I have read once a book where the special and general theory of relativity were outlined. I do not remember which book it was, but for me these theories were much easier to understand thirty years ago with that book than with this one now. Therefore, I’m left to conclude that to somebody who wants to read an introduction into Einstein’s theories, I would not recommend this book. There are better ones out there.

⭐This book is wonderful because by way of working through the famous mass/energy equivalence it explains the profound wonder of Einstein’s “spacetime” universe in layperson’s terms. I have been casually acquainted with the theories of relativity for decades, having read books on general and special relativity (and being a bit of a scifi buff), and knew the basics such that mass and energy are interchangeable and that time slows down for objects approaching light speed. But here are some things no one had ever explained before:1. Einstein and his colleagues deduced the nature of the universe by using simple mathematic formulas. For example, the elemental Pythagorean Theorem of geometry is used to calculate the slowing down of time as objects approach light speed. The authors point out that the most complex phenomena in the universe, from subatomic particle interactions to cosmic forces of time and space, follow the elegant rules of mathematics. Nobody knows why the seemingly infinite universe should follow these wonderfully simply rules, but it does!2. That space and time are components of an integrated whole called spacetime. I had heard the cliché that “time is the fourth dimension” but did not understand it intellectually. This book explains how space and time are integral parts of each other. All matter moves at exactly the same speed through spacetime. If the velocity of an object through space increases, its velocity through time decreases such that the combined movement through space and time is always constant.3. The nature of “C” has been somewhat obscured by calling it the “speed of light.” “C” is the maximum attainable speed of EVERYTHING through the SPATIAL DIMENSION OF SPACETIME. A photon travelling at “C” is going at maximum velocity through space and at zero velocity through time. An object at rest travels at zero velocity through space and maximum velocity through TIME. That is why times passes fastest for objects at rest and slowest for those at light speed.4. “C” is THE constant of the universe. Everything else is malleable. Time and space and matter and energy must shrink or expand in changing circumstances, but “C” never does. If one were to approach the speed of light the distance between the stars would shrink such that one could travel to the end of the universe in one lifetime. Fifteen billion years would have passed to people standing relatively still on earth, but for the astronaut travelling near light-speed perhaps only 20 years have passed (the 20 years is allowing time to accelerate and decelerate from rest to lightspeed and back). In a relativistic universe space shrinks into nothingness when “C” is reached. This explains why nothing can exceed the speed the light. A photon travels a dimensionless universe in a timeless instant. This also explains why travel BACKWARD through time is not possible.5. Toward the end of the book the authors give the equation that explains every subatomic particle and every force in the known universe. It’s a difficult equation comprehensible only to physicists, but still, knowing that you can express the entire nature of the universe in a few lines of mathematics is mind-bending!If a layperson wants to comprehend the nature of the universe by reading one book, this is it!

⭐Like many people I suspect, I dived into Stephen Hawking’s ‘A brief history of time’ with gusto, only to find myself completely lost after the initial chapters had so compellingly grabbed my attention, lulling me into a false sense of security as the complexity of the science and theories ramped up to a level far beyond the comprehension of mere mortals such as I. This book achieved something of the same effect, but in reverse.It may be that this is as clear and simple a review of the steps leading to einstein’s world-changing and brain-bending theories as is feasible without dumbing down the content, however this short book nevertheless seems more intent on provoking wonder at the beauty and insight of science than on conveying the ideas with the clarity of expression required for a true layman. Personally I found quite a lot of the material hard to follow, as it jumped around between complex equations, bizarre yet entertaining thought experiments, and straight-up history of science. Nonetheless the latter part of the book does a far better job of walking through general relativity than the previous sections on special relativity and quantum mechanics. Elsewhere, in their eagerness not to abandon the maths, and in their enthusiasm for the subject, for me the authors lost something of their purpose: I felt a little lost at many points. When they focused purely on the content of the theories, they were much easier to understand.Yet some of the images used, such as the topographical representation of a journey through the landscape of spacetime, and the elevator thought experiment to explain gravity, were brilliant and generated the oft-quoted ‘Ionian enchantment’ (you’ll have to trust me on that!) and it was definitely an engaging and stimulating read, with a nice conversational style, plenty of geeky humour and colourful cultural references. There is enough content to have materially shifted my understanding of the subject and I enjoyed the read, so I am recommending this and giving it 4/5.I respect the authors for wanting to take the reader, as far as possible, through the journey of the underlying science. Paradoxically, I have found Brian Cox’s more recent TV series far more ‘dumbed down’ and incoherent. I can’t help feel there should be a midpoint in between the two and if anyone can do it, professor Cox is the man!

⭐Professor Cox’s book seemed to be the perfect choice to help me understand the esoteric implications of Einstein’s special theory of relativity and the subsequent development of quantum mechanics. And it did indeed contain much fascinating material and many brain-twisting analogous experiments. However, the inevitable complexity of this subject required fairly deep concentration and frequent reference to earlier chapters. The logic of some of the equations was difficult to follow as a non-mathematician, and a couple of times I found I need a few days break before continuing. Consequently, for anyone not reasonably well versed in the subject, this book may benefit with a second (or a third!) reading.However, the excellent explanation of spacetime towards the end of the book was very well illuminated with excellent diagrams and analogies. These and Professor Cox’s other explanations of the content and implications of the theories make the concentration worthwhile, all the more so because of his enthusiastic humour for a subject very clearly close to his heart.This cannot have been an easy project for Professor Cox, and credit to him for his worthy attempt. However, I strongly recommend Brian Greene’s “The Fabric of the Cosmos: Space, Time and the Fabric of Reality” for a really superb, much clearer explanation of Einstein’s theories. Professor Greene makes it all so easy and so much more enjoyable.

⭐I have struggled over the years to understand Einstein’s theories. I did get my head around relativity but not the others.I made the it one of my goals to properly understand his theories when I retired 3years ago reading his own book aimed at laymen with “university maths” (I fall slightly below that) .His book helped but reading this REALLY helped me to understand. Einstein’s theories developed from earlier work by others Maxwell etc and assumed certain things remained unchanged or were preserved : speed of light, Momentum, energy etc.This Book helped me understand that and the steps and concepts of his theories. I had to reread some parts to either understand, believe, or remember!I feel a great sense of achievement but still need to work through gravity but I am more confident of succeeding thanks to this book!

⭐I’m a layman in the world of physics, but I enjoy it no end. So seeing this title and author I jumped at it. It came highly recommended by a friend.Firstly it starts of fairly easy going, but then it gets quite hard ( for me) to get what’s going on. I had to go on YouTube to further expand my understanding of some of the terms e.g. Gauge symmetry. Also I have the Kindle version and its frustrating at times, when formula and figures are referenced and you can just flick the page as easily. It would be nice if I could have expanded the formula on every page.I’m not going to act like I suddenly get general and special relativity but Brian and Jeff have definitely helped with my understanding. It’s probably a book I Will read again or certain tricky chapters.

⭐This is an extremely interesting book I would say as a novice you need to do a little bit of research before you read it it but if you’re prepared to stick at it and go with the flow so this is probably one of the most interesting reads you will ever have when it comes to physics. The explanations are very reminiscent of professor Cox you can hear him in your head when you’re reading the book. It seems to flow well l&d explanations are quite simple even though the concepts are are astronomical. I would recommend this book you can dip in and out of it it you can reference it you can reread it.

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