To kick off that activity, I started with two popular physics books that may be a little outdated, but should still have plenty of relevant, intriguing material on what has happened in the field post-Einstein. Both books are by prominent string theorists.

*The Elegant Universe*was written in 1999 by Brian Greene, a professor of physics and mathematics at Columbia University. Hyperspace was written five years earlier in 1994 by Michio Kaku, a professor in theoretical physics at The City University of New York.

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#### The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

From what I've read, there's a huge debate going on in theoretical physics right now about whether or not string theory is the future of how we will understand the universe, or if it's a dead end that will never produce meaningful predictions about how the universe works. I'm certainly not qualified to make any judgements about this debate, but I still believe that the investigations of string theory have merit because the exploration of ideas has value in and of itself. String theory has also made significant contributions to both mathematics and physics by developing new mathematical constructs and bringing various far-flung ideas between the two subjects together under one framework.

That, however, is not the point of this book. The point is to give the reader a basic understanding of what string theory is about and how it affects our idea of how space-time works. Brian Greene is an excellent writer, and he does a great job of conveying his ideas in a way that non-theoretical physicists can understand. He starts out with a detailed description of Einstein's theories of Special and General Relativity and how they change our concept of the flow of time and the structure of space. Then he leaves the expanse of space to describe the main features of the very small particles of quantum mechanics. He wraps up this introductory material by explaining how these two sides of the universe—the very large and the very small—are incompatible when viewed within the confines of relativity and quantum mechanics. The two fields even come in direct conflict when trying to calculate what happens inside black holes or during the Big Bang.

This conflict is what string theory attempts to resolve. The rest of the book describes what sting theory is, how it can combine relativity and quantum mechanics into one overarching Theory of Everything, and goes into a number of issues that the theory must address before it can be considered valid. Towards the end of the book, Greene gets caught up in generalities and doesn’t do as good of a job relating the physics he's describing to everyday reality. He talks about strings wrapping around curled up dimensions and branes covering tears in the fabric of space. It's very hard to visualize what he's talking about and what implications it has for the behavior of space-time, but maybe the vagueness betrays the fact that no one really understands what's going on here, yet.

His other explanations are quite good, and reading the book generated tons of questions in my mind about how the concepts he was describing could be extended. For example, when he was describing how it's known that gravity travels at the speed of light, he goes through a thought experiment about what would happen to the planets if the sun suddenly exploded. The gist of the explanation is that the planets would not immediately leave their orbits because it would take time for the change in gravity to reach each planet.

As I was reading, I wondered what would happen if instead of exploding, the sun disappeared entirely, just winking out of existence (never mind how that might physically happen). Would it still take time for the change in gravity to reach the planets? At first I struggled with this idea because it seemed to me that in the first case of the sun exploding, the change in gravity would move along with the remnants of the sun, so the fact that gravity would be limited to the speed of light wasn't surprising. The matter that was traveling outward from the blast would be limited by the speed of light, and the force of gravity would change based on what happened to the matter as it sped outward. What was surprising was that, according to Einstein, even if the sun just disappeared, the planets would still take time to notice the absence of the sun's gravity because the sun was warping the space around it and the planets were following the curve of space in their orbits. The speed at which space would flatten out in the absence of the sun would happen at the speed of light.

Another great part of the book was the discussion of how to visualize higher dimensions. The concept of extra dimensions beyond three is especially hard to grasp because we experience the world in three dimensions, and we have no reference for what a fourth dimension (let alone a tenth dimension) would be like. One way to think about this—the way the book describes—is to imagine how a being in a one dimensional world would see a two dimensional object, and then work your way up to higher dimensions. Another way, that the book doesn't go into, is to think about how we already see our three dimensional world as a two dimensional projection. Our eyes actually see in 2D, and we build 3D models of objects in our minds. Similarly, we can project 4D objects into 3D spaces with computer simulations to try to get a better idea of what they are. One common example is the tesseract, or four dimensional cube. Here is a video showing what it looks like to rotate and unwrap a tesseract:

Even after watching the video, it's still really hard to visualize what's going on, but every way of trying to imagine higher dimensions adds a bit more to our understanding.

Understanding higher dimensions is a big part of string theory because in higher dimensions there is more room to unite all of the forces and fundamental particles into one theory. Greene does a great job describing the issues and implications with string theory, as well as much of the physics history that has led up to it. It was a great read that gave me a much better understanding of what string theory is all about, and I'm looking forward to reading more of his books.

#### Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension

*Hyperspace*is another book about string theory, although the focus here is much more on higher dimensions than the details of vibrating strings and how they interact. Michio Kaku also spends a lot of time on the history of physics, and the older I get the more I appreciate the context that history provides. It will also be interesting to see how his ideas change in later books because of the impact of new technologies that have come into play since this book was written. He talks a fair amount about the possibility of the universe ending in the Big Crunch, but since the Hubble Telescope has been in service and our measurements of the cosmic microwave background (CMB) radiation have gotten better, we have pretty much ruled that out as a possibility. The LHC has also added many new discoveries to physics research and our understanding of quantum mechanics that would impact string theory as well.

Despite its age, this book was a fascinating read. Kaku explores so many interesting topics, including time travel, the tenth dimension, worm holes, and the future of our civilization. Like Greene, he attempts to describe how to visualize higher dimensions, and the additional perspective is helpful. He has an easy conversational style that clearly conveys his ideas, and I especially enjoyed his discussion of how civilizations are predicted to develop:

A Type I civilization is one that controls the energy resources of an entire planet. This civilization can control the weather, prevent earthquakes, mine deep in the earth’s crust, and harvest the oceans. This civilization has already completed the exploration of its solar system. A Type II civilization is one that controls the power of the sun itself. This does not mean passively harnessing solar energy; this civilization mines the sun. The energy needs of this civilization are so large that it directly consumes the power of the sun to drive its machines. This civilization will begin the colonization of local star systems. A Type III civilization is one that controls the power of an entire galaxy. For a power source, it harnesses the power of billions of star systems. It has probably mastered Einstein’s equations and can manipulate space-time at will.We are currently a Type 0 civilization, and when put in this context, it's pretty clear that the most important advances we can make right now are in energy production. Making progress in new computing devices, robotics, and transportation are still important, of course, but we're not going to get anywhere until we dramatically increase the amount of energy available to us.

I also wonder if the process of advancement to a Type I civilization would go faster if more resources were allocated to it. We chronically underfund space exploration and basic research. However, Kaku makes an interesting argument that technological advancement should not outpace social development or else we'll be in critical danger of self-annihilation. We still need to figure out how to function productively as one world-wide civilization instead of a collection of nation-states in constant conflict. We will continue to be on the edge of destruction until we solve the political, social, and environmental problems that we're dealing with. Technology that's too advanced for our social structures will only make things worse.

Putting our sociopolitical issues aside and turning back to string theory, Kaku goes beyond the normal assertions that it has the potential to unify our separate models of the universe, from the Standard Model to the four fundamental forces. He thinks it also has the potential to unify much of the separate fields of mathematics:

One consequence of this formulation is that a physical principle that unites many smaller physical theories must automatically unite many seemingly unrelated branches of mathematics. This is precisely what string theory accomplishes. In fact, of all physical theories, string theory unites by far the largest number of branches of mathematics into a single coherent picture. Perhaps one of the by-products of the physicists’ quest for unification will be the unification of mathematics as well.This seems like a pivotal accomplishment for our civilization, when and if it occurs. The book is packed with high-flying ideas like this that make you think and wonder about what is possible in our future. Kaku strikes a good balance between explaining the history of physics and its future potential. Like

*The Elegant Universe*, I thoroughly enjoyed reading this book, and I look forward to more of Michio Kaku's books.

#### Wish I Would Have Read These Sooner

It would have been very useful to have read books like these in college while taking difficult math and physics courses. It would have helped give context to the things I was learning, and motivated me to pursue a deeper understanding of things I struggled with. I remember having a really difficult time conceptualizing things like black body radiation and the SchrÃ¶dinger equation at the time, and Kaku's example of students not understanding the implications of an exam problem with an intriguing application sounded eerily familiar to me:In the autumn of 1985, on the final exam in a course on general relativity given at Caltech, Thorne gave the worm-hole solution to the students without telling them what it was, and they were asked to deduce its physical properties. (Most students gave detailed mathematical analyses of the solution, but they failed to grasp that they were looking at a solution that permitted time travel.)If I had read books like these in college, I would have had a much better grasp of the general concepts of physics, and some of the things that flew over my head may have found a better place to stick instead. I'm sure I would have been much more motivated to understand the complex equations involved if I would have known that books like these existed (and read them). I'm definitely motivated now. Every aspiring physics major, and even hobbyists, should take a look at these books to see what wonders and paradoxes the universe holds.