Here I explain some of the errors in the book “Why does e=mc²? (and why we should care)” by Brian Cox and Jeff Forshaw. The book makes little attempt to actually explain any physics, mostly relying on meaningless drivel and vague generalisations; so the scope for error is highly limited, but here are some of the worst howlers I could find:

Preface xiii: “Mass is a measure of how much stuff an object contains. A cricket ball is more massive than a table-tennis ball, but less massive than a planet.”

What does the expression “how much stuff an object contains” mean? Surely in scientific terms it can only mean how many protons, neutrons and electrons an object is composed of. But Einstein’s famous 1905 paper in which he supposedly derived the equation e=mc², was given the title “Does the inertia of a body depend on its energy content?”. Einstein’s verdict was yes, the inertial mass does depend on the energy content; Cox apparently disagrees and thinks it just depends on the amount of stuff it contains. So who is right?

If we take a spring and compress it, we have added energy to it; yet it still contains the same number of particles. But its gravitational and inertial mass will have increased because of the added energy, the energy being stored by squeezing electrons (which repel each other) together in uncomfortable positions. Of course the mass of the extra energy added to a spring by compressing it, is far too small to be measured with a weighing machine; but at the end of his famous paper, Einstein surmised “It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.”.

Einstein words did turn out to be prophetic, but in 1905 the structure of the atom was yet to be discovered, so Einstein had no idea how the energy in a Uranium atom was stored. In fact it comes from 92 protons in the nucleus being jammed together in close proximity. Protons repel protons, so the source of the energy is intrinsically the same as with a spring. It is just that the protons are much closer together, and in a big bunch, so the energy stored is much greater than by the electrons in the spring. As you can see the energy of nuclear fission, where the nucleus of an element like uranium splits in two, results from the repulsion between protons; it is not the result of Einstein’s relativity, as so often stated (I am not sure whether or not Cox claims it is). But Einstein may well have been the first to predict that the mass loss of a radio-active sample could be tested experimentally.

Since the very essence of the equation e=mc² is that energy has mass, one has to question whether the author really has understood what he is trying to write about. Perhaps he just remembered being taught that “ Mass is a measure of how much stuff an object contains” at school as part of Newtonian physics, and has never quite got to grips with the fact that Newtonian physics is just a very good approximation.

Page 18: “Faraday discovered that if you push a magnet through a coil of wire, an electric current flows in the wire while the magnet is moving. He also observed that if you send a pulse of electric current along a wire, a nearby compass needle is deflected in time with the pulse. A compass is nothing more than a magnet detector; when no electricity is pulsing through the wire, it will line up with the direction of the earth’s magnetic field and point toward the North Pole. The pulse of electricity must therefore be creating a magnetic field like the earth’s, although more powerful since the compass needle is wrenched away from magnetic north for a brief instant as the pulse moves by.”

The first sentence is correct, a current only flows in the coil whilst the magnet is moving. The rest of the paragraph about the compass is wrong, you can see the experiment performed at 7.30 mins. The point is that a steady electric current produces a steady magnetic field. A compass needle is a bar magnet with a north pole at one end and a south pole at the other; and if it it placed near a straight wire carrying a large direct (one-way) current, it will point across the wire for as long as the current continues to flow. So why does Cox talk about a “pulse” and a “brief instant”?

Clearly he is getting confused with the idea of electromagnetic induction, an example of which he described in the first sentence, which requires a changing magnetic field. Electromagnetic induction can also be performed using electric currents. If two separate coils are placed close to each other, then when a current is switched on in one coil, it induces a brief surge of current in the other; then nothing happens in the second coil until the current in the first coil is switched off, then there is a surge of current in the opposite direction as to when the current was turned on. That is why transformers only work with alternating current.

A little learning is a dangerous thing. Perhaps Cox should have tried to understand the basics of Maxwell’s equations himself before trying to teach others.

Page 27: “In the case of Maxwell’s waves, the speed is predicted to be equal to the ratio of the strengths of the electric and magnetic fields, and this ratio can be measured very easily. The strength of the magnetic field can be determined by measuring the force between two magnets.”

The book is full of statements of the completely obvious, which require no understanding on the part of the author, and impart no information to the reader; and at first sight “The strength of the magnetic field can be determined by measuring the force between two magnets” might look like a classic example of this, but it is actually wrong.

The magnetic force is defined as the force per metre between two infinitely long straight wires carrying direct currents. This is because we can gain a meaningful measure of how many electrons are moving at what speed and how far apart they are. Permanent magnets are the result of electrons orbiting atomic nuclei, and so are useless in this regard.

Essentially if a squillion electrons in each wire are moving at a squillionth of the speed of light, then the magnetic force between the two wires would be equal in magnitude to the electric force between two electrons. So arguably the magnetic force between two electrons both moving at the speed of light, would be equal in magnitude to the electric force between two electrons, always assuming equal distances apart. That is where the speed of light ratio comes in, but obviously it cannot be deduced from permanent magnets.

Okay, so this is not really schoolboy physics, but I think it is basic first-year university physics. I thought that maybe Cox missed out on the first-year because he was busy performing “things can only get better”. But according to Wikipedia he actually got a first class BSc in physics from Manchester University, so how could this fact have eluded him?

Page 29: “Everything that moves in the universe must make its way through the ether, which must offer little or no resistance to the motion of solid objects, including things as large as planets.”

Things as large as planets are not solid; they are made up of protons, neutrons and electrons held together by electromagnetic forces. Wrong physics, so a bad argument.

In a moment of weakness Isaac Newton did actually make the same argument in an attempt to defend his particle theory of light against the wave theory of his rival Huygens. But Newton could perhaps be partly excused on the grounds that he did not understand the structure of matter, as it had not been discovered in his day. But one would think that in this day and age, Cox really ought to have gathered that objects are made up of protons, neutrons and electrons held together by electromagnetic forces.

Page 40 “The second part, checking the consequences against nature, was not much used by the ancient Greeks. If it had been, then the world might well be a very different place today. This seemingly simple step was introduced to the world by Muslim scientists as early as the second century and took hold in Europe much later, in the sixteenth and seventeenth centuries.”

An attempt by Cox to show how devoutly he worships the god of Equality, by attributing scientific achievement to Muslims. The only problem is that Muhammad was born around 570 AD. Surely getting Muhammad’s birth date wrong by hundreds of years warrants a Fatwa. I think this error was corrected in later editions of the book, but Cox is not a Christian, so he is not entitled to repent and be forgiven. Equality-believers believe that an act of blasphemy is indelible, so bring on his punishment, “as ye sow, so shall ye reap.”

42: “Now, imagine putting the light clock on a train that is whizzing along past someone standing on a station platform. The million-dollar question is: How fast does the clock on the train tick according to the person on the platform? Until Einstein, everybody assumed that it ticks at the same rate—one tick every x Nanoseconds.”

The idea that a light clock runs at different rates depending to its speed through space, was extensively discussed by physicists prior to Einstein.

61: “So what happens to the angular momentum the earth loses by tidal friction? The answer is that it is transferred to the moon, which speeds up in its orbit around the earth to compensate for the slowing down of the earth’s rotation. This causes it to drift slightly farther away from the earth.”

Actually as the moon moves further from the earth, its orbital speed reduces, it slows down rather than speeding up.

At the end of the sixteenth century, Kepler carefully analysed astronomical data, and concluded that the planets were orbiting the sun in ellipses, which were nearly circular, and that the orbital speed of a planet depended on the square root of its distance from the sun; that is a planet 9 times as far from the sun would orbit at a third of the speed; and the same law applies to the moon’s orbit of the earth. So why does the author claim that moon speeds up in its orbit as its distance from the earth increases?

If you read the quote carefully, I think you can hear the creaking of the gears in the author’s brain. The angular momentum of the moon is by definition its orbital velocity times its distance from the earth. So he is thinking; if the moon is gaining angular momentum, then that suggests it must be going faster; on the other hand if it was to reduce its orbital speed then its angular momentum ought to reduce.

Unfortunately to resolve this paradox, I need to employ some mathematics. So if your mathematical skills are on a par with Cox’s, you might want to skip the next bit and just take my word for it that the maths does work out.

If the distance of the moon from the earth were to quadruple (that means be multiplied by 4), then its orbital speed would halve according to Kepler’s law, because the square root of 4 is 2 (you might want to check this with your calculator). So if the moon’s distance quadruples, its angular momentum will be 4 (its distance from the earth) times ½ (its orbital speed). 4 times ½ equals 2 (again you might want to check this with your calculator), so the angular momentum will have doubled, despite the fact that the orbital speed of the moon has reduced.

I am sorry to have had to employ such complex mathematics, but do not worry if you did not understand it, not everybody can be a mathematical genius like myself. I also should apologise for not explaining what a square root is; but if you want to find out about that, then it is one of the gems of information in Cox’s wonderful book (on page 48). To many of Cox’s fans this explanation alone may well be worth the price of the book; which is probably a good thing, because there is not much other useful information in the book.

62: “The strong nuclear force sticks the atomic nucleus together at the heart of the atom, and the weak nuclear force allows stars to shine.”

The energy for stars to shine comes from nuclear fusion, which involves protons and neutrons sticking together in the nucleus. So it is the strong nuclear force that allows stars to shine. The weak nuclear force is the reason a neutron can split into a proton and an electron; it does produce energy, but is not what powers stars.

Around this point I stopped reading, because the book appeared to be degenerating into merely discussing the religious niceties of the literal interpretation of Einstein’s special relativity. But an discussion alerted me to an even grosser error later in the book:

148: “The force of repulsion between the protons gets larger and larger as the protons get closer and closer together. In fact, it doubles in strength for every halving of the distance.”

The first thing about particle physics is surely that electrons and protons attract each other, but like charges repel. The second thing is perhaps that the force between charges is inverse square, that is it quadruples in strength for every halving of the distance.

So is it possible that Cox does not know the second thing about particle physics? Unlikely, this is most probably just a careless mistake. I guess he realises that most purchasers of popular physics are so ignorant and gullible that you can put any old nonsense in a book, and they will still buy it and believe it must all be true because the author is famous.

But is the author really famous? Did Cox really write any of the book? I saw a review by a woman who purchased an audio version of the book, and was disappointed to find that Cox’s dulcet tones were completely absent. So apparently Cox did not read the book out loud. But has he actually read it at all? If so, how could he have missed such blatant errors? But then again if he merely employed a ghost writer, why would he employ somebody so incompetent? Yet Forshaw is a professor at Manchester University, so should he not understand basic physics? It is almost as mysterious as special relativity itself.

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