MODERN PHYSICS

The study of Modern Physics is the study of the enormous revolution in our view of the physical universe that began just prior to 1900. At that time, most physicists believed that everything in physics was completely understood. Normal intuition and all experiments fit into the context of two basic theories:

1. Newtonian Mechanics for massive bodies;
2. Maxwell’s Theory for light (electromagnetic radiation).

Consistency of the two required that there be a propagating medium (and, therefore, a preferred reference frame) for light. However, even a little thought made it clear that there was trouble on the horizon. And then came many new experimental results that made it clear that the then-existing theoretical framework was woefully inadequate to describe nature.

In a relatively short period of time, physicists were compelled to adopt:

1. The theory of special relativity based on the idea that there was no propagating medium for light (so that light traveled with the same speed regardless of the “frame” from which the light was viewed);
2. The theory of quantum mechanics, according to which the precise position and precise momentum of a particle cannot both be determined simultaneously. In fact, one must think of particles not as particles, but as waves, much like light.
3. At the same time, experiments made it clear that light comes in little quantum particle-like packets called photons.
4. In short, both particles and light have both a particle-like and wave-like nature.

It is useful to focus first on the inconsistencies of the “ether” picture and of the above-outlined naive picture of space and time. This will lead us to the theory of special relativity. Thinking carefully about Galilean transformations between coordinate systems that underpinned the pre-relativity view of space and time reveals the latter inconsistencies.

Before proceeding, let me just emphasize that in this course we will be embarking on an exploration that has been repeated in a certain sense several times now. Indeed, the business of looking for inconsistencies in existing theories now has a long history of success, beginning with the development of special relativity, general relativity, and quantum mechanics. We have learned not to be arrogant, but rather to expect that the best theories of a given moment are imperfect and to look for difficulties (perhaps subtle ones) or extensions that are suggested by thought experiments that push the theories into a new domain.

As an example, the development of the Standard Model of fundamental interactions (that you may have heard of) began with the realization that the theory that was developed to explain the weak interactions would violate the laws of probability conservation when extended to high energies. In fact, nowadays, we have many arguments that suggest that the Standard Model is itself little more than an “effective” theory valid at the energy scales that we have so far been able to probe. It has undesirable features when we try to extend it to higher energies (e.g. from the scale of the masses of the new W and Z bosons to the Planck mass scale that is some 16 orders of magnitude larger).

The ether picture for light propagation:

• At the end of the 19th century, light waves were an accepted fact, but all physicists were “certain” that there had to be a medium in which the light propagated (analogous to water waves, waves on a string, etc.).
• However, the “ether” in which light propagated had to be quite unusual. The speed of light was known to be very large (the precise value we now know is c = 3.00 × 10⁸ m/s). A medium that supported this high speed had to be essentially incompressible (i.e. something vastly more incompressible than water, and even more vastly incompressible than air).
• And yet, it was clear that light traveled over great distances from the stars, implying that this ether extended throughout a large section of the universe.

This means that the planets, stars, galaxies, . . . , were traveling through this ether according to Newton’s laws without feeling any frictional, viscosity, . . . , type of effects.

• Well, for anyone thinking about this nowadays, this is obviously ridiculous. But, at the end of the 1900’s it was impossible for physicists to accept the fact that there was no ether medium in which light traveled and it was bizarre to imagine that light could travel through “vacuum”, despite the fact that Maxwell’s equations were most easily understood in this context.
• We will shortly turn to the Michelson-Morley (MM) experiment performed in 1887 in which MM set out to demonstrate the existence of the ether.

We will learn that they failed. To show how entrenched thinking can become, it should be noted that Michelson (who was quite a brilliant guy) never believed the result of his experiment and spent the next 20

years trying to prove his original result was wrong. He failed, but provided ever-increasing accuracy for the precise speed of light.

• It would be natural to presume that Einstein’s theory of special relativity was a response to this experiment.

But, in fact, he stated that when he developed his theory he was completely unaware of the MM result. He simply was thinking of Maxwell’s theory of light as a medium independent theory and asking about its consequences. This is not totally implausible given the fact that the MM experiment was performed in the “back-woods”, frontier town of Cleveland Ohio (some would say that the MM experiment is still the most important thing, other than some baseball greats, to come out of Cleveland). And communications were not so hot back in those days. To understand the ideas behind the MM experiment and to set the stage for how we discuss space and time in an “inertial” frame, we must consider how to relate one frame to another one moving with constant velocity with respect to the first frame. The 1900’s view of this relationship is encoded in “Galilean transformations”.