In the popular press, diagrams showing the evolution of the universe begin with a great jump in size labeled "inflation." Can we explain the basic ideas behind inflation to our students who have taken our introductory physics course? Probably not. In our standard introductory physics courses, even those with special relativity, something…

This is the fourth paper in a series of four. The first paper in the series, "Vacuum Energy and Inflation: 1. A Liter of Vacuum Energy" [EJ1024183] discusses an example of vacuum energy. Vacuum energy is explained as an energy with a negative pressure whose energy density remains constant in an expanding space. Paper 2, "Vacuum…

In most of our undergraduate physics courses, we study what can happen in space, but space itself plays a passive role. In basic cosmology, the opposite is true. It is the behavior of space that plays the major role. In this, paper #2, we first discuss the nature of a simple expanding space, and then look at the consequence of applying…

This is paper #3 in a series of four papers on "vacuum energy" and inflation. In paper #1 [see EJ1024183] we discussed an example of what we have been calling vacuum energy. It is an energy with negative pressure whose energy density remains constant in an expanding space. We showed that an energy density with these properties exists…

In 1968, Robert Brehme wrote a carefully crafted paper on "The Advantage of Teaching Relativity with Four-Vectors." In his abstract he points out that "the emphasis on relativistic mass is both undeserved and misleading." Our approach is to find the best way to teach introductory physics in a way that includes modern physics. We have found that by…

The behavior of smoke rings, tornados, and quantized vortex rings in superfluid helium has many features in common. These features can be described by the same mathematics we use when introducing Ampere's law in an introductory physics course. We discuss these common features. (Contains 7 figures.)

In our initial article on teaching special relativity in the first week of an introductory physics course, we used the principle of relativity and Maxwell's theory of light to derive Einstein's second postulate (that the speed of light is the same to all observers). In this paper we study thought experiments involving a light pulse clock moving…

This is the third of four articles on teaching special relativity in the first week of an introductory physics course. With Einstein's second postulate that the speed of light is the same to all observers, we could use the light pulse clock to introduce time dilation. But we had difficulty introducing the Lorentz contraction until we saw the movie…

This is our final article on teaching special relativity in the first week of an introductory physics course. One of the profound changes in our view of the world was Einstein's discovery of the lack of simultaneity. He illustrated this result with a thought experiment in which we observe a railroad car passing by us. We see the two ends of the…

We like to begin an introductory physics course with a law of physics that applies to everything, has no known exceptions, and whose consequences are already familiar to students. That law is the principle of relativity. By focusing on the principle of relativity itself, and a careful selection of the thought experiments, we can comfortably…

Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…

Jay Orear, in his introductory physics text, defined the weight of a person as the reading one gets when standing on a (properly calibrated) bathroom scale. Here we will use Jay's definition of weight in a thought experiment to measure the weight of a photon. The thought experiment uses the results of the Pound-Rebka-Snider experiments, Compton…

While the emphasis on SI units in introductory physics textbooks has mercifully eliminated the use of English units, the exclusion of other systems of units is not necessary. For years physicists have simplified calculations by doing things like setting [h-bar] = c = 1. We could not imagine putting 4[pi][epsilon][subscript 0] into the formulas for…

The paper on "Magnetism and Simultaneity" by Adler provides an excellent new thought experiment involving the lack of simultaneity in Einstein's special relativity. Adler uses the lack of simultaneity rather than the Lorentz contraction to derive the formula for the magnetic force on a moving charged particle. Advantages of his derivation are that…

During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…