String Theory For Dummies. Andrew Zimmerman Jones
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4-1: The circle has symmetry, but the trapezoid doesn’t.
The most fundamental form of symmetry in physics is the idea of translational symmetry, which is where you take an object and move it from one location in space to another. If we move from one location to another, the laws of physics should be the same in both places. This principle is how scientists use laws discovered on Earth to study the distant universe. Another familiar symmetry is rotational symmetry: if we make some experiment on a bench facing south or east, we generally do not expect to see a difference.
In physics, though, symmetry means way more than just taking an object and flipping, spinning, or sliding it through space.
The most detailed studies of energy in the universe indicate that, no matter which direction you look, space is basically the same in all directions. The universe itself seems to have been symmetric from the very beginning, at least to a good approximation.
This does not mean that the outcome of the experiment will be necessarily the same! For instance, while the laws of gravity are, as far as we believe, the same now as they were in the distant past, we know that the universe looked very different back then, compared to now.
Symmetries like rotation, translations, and translations through time are seen as central to the study of science, and in fact, many physicists have stated that symmetry is the single most important concept for physics to grasp.
Indeed, symmetry is so important in physics that we can use it even when it’s no longer there. Take a small drop of water, which is a perfect sphere. If we cool it enough, it will become an ice crystal, and as we all know from playing with snowflakes, they are not spherically symmetric. Yet, they do have a beautiful residual symmetry, in many ways richer and more interesting than the original droplet. This is an example of spontaneous symmetry breaking.
Another example is the fact that the equations describing the universe are invariant under time-translations (redefining our clocks), while the universe itself is not: We actually believe that it had a beginning with the Big Bang.
In a much more sophisticated way, the study of how the fundamental symmetries of nature are broken is one of the keys to understanding modern physics. An important example that’s a bit beyond the scope of our discussion is the famous Higgs boson, which is a cornerstone of particle physics and is intimately related to breaking a symmetry — specifically, the symmetry of the electroweak force mentioned in the previous section.
Another type of symmetry which plays a big role in string theory, and has been getting a lot of attention from theoretical physicists, is called supersymmetry. On top of having a catchy name, it is a required ingredient to make sense of string theory. Supersymmetry makes some very strong predictions on the elementary particles that should exist in the universe, and because of that we know that it is not exactly realized in the universe: It can only be one of the spontaneously broken symmetries. We will tell you all about this in Chapter 10.
Chapter 5
What You Must Know about Classical Physics
IN THIS CHAPTER
No matter how complex modern physics concepts get, they have their roots in classical ideas. To understand the revolutions leading up to string theory, you need to first understand these basic ideas. You’ll then be able to understand how string theory recovers and generalizes them.
In this chapter, we present some physics concepts that you need to be familiar with to understand string theory. First, we discuss three fundamental concepts in physics: matter, energy, and how they interact. Next, we explain waves and vibrations, which are crucial to understanding stringy behavior. Gravity is also key, so Sir Isaac Newton’s important discoveries come next. Finally, we give a brief overview of electromagnetic radiation, an important aspect of physics that led directly into the discovery of both relativity and quantum physics — the two theories that together gave birth to modern string theory!
This Crazy Little Thing Called Physics
Physics is the study of matter and its interactions. Physics tries to understand the behavior of physical systems from the most fundamental laws that we can achieve. String theory could provide these most fundamental laws and explain all of the universe in an elegant way.
One other key principle of physics is the idea that many of the laws that work in one location also work in another location — a principle known as symmetry (we cover this in more detail later in this section and also in Chapter 4). The connection between physics in different locations is just one sort of symmetry, allowing physics concepts to be related to each other. Science has progressed by taking diverse concepts and unifying them into cohesive physical laws.
That’s a very broad definition of physics, but then physics is the broadest science. Because everything you see, hear, smell, touch, taste, or in any way interact with is made of matter and interacts according to some sort of rules, that means physics is literally the study of anything that happens. In a way, chemistry and all the other sciences are approximations of the fundamental laws of physics.
No laughing matter: What we’re made of
One of the traits of matter (the “stuff” that everything is made of) is that it requires force to do something. (There are some exceptions to this, but as a rule, a force is any influence that produces a change, or prevents a change, in a physical quantity.) Mass is the property that allows matter to resist a change in motion (in other words, the ability to resist force). Another key trait of matter is that it’s conserved, meaning it can’t be created or destroyed but can only change forms. (Einstein’s theory of relativity showed this wasn’t entirely true, as you see in Chapter 6.)
Without matter, the universe would be a pretty boring place. Matter is all around you. The book you’re reading, as you lean back comfortably in your matter-laden chair, is made of matter. You yourself are made of matter. But what, exactly, is this stuff called matter?
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