Sceptic: “Generally, anything that we have accelerated to near the speed of light was externally accelerated using external magnetic force. A space craft would be accelerated by either firing mass out opposite the he directing for travel or by some use of internal force. What I have not seen demonstrated is the fact that the increased mass is relative. If theoretically, you have enough fuel to accelerate to the speed of light, the matter that you are carrying would be increasing at the same rate as the craft. The pilot would see no difference and would simply keep running the ion engine or firing fuel out the back and keep accelerating. Externally, the shipping would be flattening to nothing and becoming increasingly massive. At the speed of light when the object becomes impossibly nonexistent, the mass would be impossibly infinite, but to the pilot, nothing has changed. I am sure someone can explain why this is impossible and how suddenly having more ship to push and more fuel to push it is a problem. Please do.”

Me: “You don't end up with more of any particular matter - the mass of any given quantity simply becomes greater (so you have no more fuel than you left with). The energy required to accelerate the ions from the thrust drive increases as the velocity of the craft approaches the speed of light, because the mass of those ions is also increasing exponentially due to relativistic effects. While you could argue that the increased mass of these ions propelled from the thruster at some significant fraction of the speed of light (c) gives the craft greater thrust, the energy required to accelerate these ions from rest in the first place will also increase. This will usually require either an increase in potential difference (voltage) - in the case of a Hall effect thruster, or electric and magnetic field strength in the case of pulsed inductive thruster or similar. However these fields are generated, and however your electricity produced, you will never have an increasing amount of fuel with which to do this.

Either way, the supply of useful energy on the spacecraft will only decrease as work is done, but the mass of the spacecraft will increase. A pilot would notice only the acceleration at any given thrust level decreasing exponentially as the speed of the spacecraft approached a larger fraction of c. As relativistic effects start to bite, the mass of the craft becomes so great that the available acceleration diminishes asymptotically to an infinitesimally small figure (think a newly hatched guppy fish trying to tow a supertanker in an ocean of molasses). It doesn't matter how hard you push or how much fuel you take - you will never get to a significant fraction of light speed!

Confusion is exactly the problem. People get confused with what the rest mass is and what the relativistic mass is defined to be, partly because they never understood what mass is even in Newtonian mechanics and maybe also because people are sloppy in calling either just "mass". As long as you are clear about both you can talk about either or both, but still "The energy goes into increasing the mass" is wrong. The energy is not being converted into mass, the relativistic mass is defined to be the kinematic response of the object. It's up to you whether you want to talk about relativistic mass or not, but I would not recommend using it because it's far better (as I see it) to just talk about rest mass and not regard the mass as fundamental but rather keep the spacetime parameters as fundamental to the theory.

For those of you who want to go for it on their own, this is the book to go for. I always accepted the fact that parts of the syllabus would be boring. I liken it to competitive sport. You have to put in hours of quite repetitive, difficult practice to get the fundamentals right. But the rewards of doing that are expertise in the most general of sciences. That means an education that can take you just about anywhere. Along with the other 2 books (“The Theoretical Minimum: What You Need to Know to Start Doing Physics (Theoretical Minimum #1)”, and "Quantum Mechanics: The Theoretical Minimum (Theoretical Minimum #2)"), this one is also an excellent example of how one doesn't need to become a world-class physicist to benefit massively from physics books, unlike some would have you believe. ( )

With the third installment of The Theoretical Minimum, it seems that Leonard Susskind and Art Friedman have found their respective stride. This book covers Special Relativity and Classical Field Theory as the title suggests, and as the context of the series suggests it covers the subjects in an engaging manner meant for the common man. Of course, Susskind does suggest that you should have a small backing in Calculus and Linear Algebra to make it go more smoothly but the book is still entertaining nonetheless.

Since this is the third book in the series, Susskind suggests that you go and take a peek at the section on Hamiltonians and Lagrangians from the first book and brush up on that. Once you have done that, Professor Susskind explains the idea of relativistic motion in a way that most should be able to understand. For example, if you go into space and apply a constant amount of force to your body, you should be able to accelerate to a velocity faster than that of light! To that incredibly wrong statement, Professor Susskind has an answer. Generally, if you accelerate to a velocity that is an appreciable fraction of c, you will also accumulate mass and be forced to use more force.

In any case, the book contains 11 chapters which are called Lectures in this case. We get to build Lagrangians and apply them to fields and do all sorts of interesting things with advanced mathematics. The book is also funny in the opening portions of the chapters. So with all that, I give this book a 5 out of 5.

PS, I also liked the Groucho reference. ( )

"Physics is always harder without the mathematics." People who agree with that startling little remark tucked away on p 279 (in the context of Maxwell's equations for electromagnetism) are the ones who will like the Theoretical Minimum books, of which this is the third volume. They will be looking for topic treatments that are one or two notches more challenging than "popular" ones, and, provided that they already have a good grasp of calculus, they will not only find them but find them ensconced in typical Susskindian wit.