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# 1.1: Patterns and Phenomena

You likely use the term "energy" in a reasonably accurate sense -- that is, a physicist would likely not cringe when hearing the way the word is used in daily contexts. Phrases such as "I burned the energy in the ice cream by jogging", or "the car is out of energy" are motivated largely by the origins of the word in physics. However, the story of energy in science is, like most things, long and complicated.

Early philosophers supposed that there was "something" which was never lost in the universe. However, that "something" was poorly defined, or simply misguided, such as "earth, wind, water, and fire". Even Newton and his colleagues often either dismissed energy or were confused about the concept (Newton himself thought there was little distinction between energy and momentum, since they were both defined by objects being in motion). It would take up until the 19th century to iron this out properly into the working picture of energy we have today.

The discoveries of the 19th and 20th centuries on the role of energy (and momentum) in physics are the primary reasons this course is taught in this order! In other words, the idea that follows is a really big deal, and has been called by many the most beautiful and important aspect of physics. The idea in question is a proof by a female mathematician, named Emmy Noether, published in 1918, which more or less states:

"For every observed symmetry in the universe, there is an associated conserved quantity"

To understand this a little more deeply, you can watch this excellent video on this very topic.

## The "Most Beautiful Theorem in Physics" - Noether's Theorem

This is such a widely renowned idea because it seems to place energy (and momentum) at the most fundamental level -- as fundamental as the symmetries in our universe. The math behind the proof is complicated and general, but the idea can be expressed simply. In the context of physics, we recognize the following symmetries in the world around us:

1. Translational Symmetry: When placed in deep space, an object "here" is indistinguishable from an object "there". More specifically, it seems that any experiment performed in a lab at UC Davis will have the same results as if it were performed in Australia.
2. Rotational Symmetry: When rotated about an axis, an object seems to behave much the same as it did before. When performing an experiment in a North facing lab and a West facing lab, one should get the same results (unless of course the experiment specifically depends on directions in some way).
3. Symmetry Through Time: The universe seems to behave identically whether observed last week or this morning.

These symmetries guarantee three conserved quantities in the universe. We call these quantities:

1. Linear Momentum ⇔ Translational Symmetry
2. Angular Momentum ⇔ Rotational Symmetry
3. Energy ⇔ Symmetry Through Time

The focus of the next chapters will be on exploring the consequences of energy conservation. You will learn more about linear and angular momentum later on.

# Now we know that energy must exist. What is it?

The principle of conservation of energy and the Energy-Interaction Model that allows us to make effective use of this principle, applies to literally every kind of interaction. Once it was realized that “heat-energy” (now called thermal energy) was not some kind of special substance, but just one of the many ways energy increased or decreased in interactions of matter, scientists began to appreciate the universality of whatever it is that we give the label “energy” to.

It isn’t easy to define energy. During an interaction or process energy decreases in some “ways” and increases in “other ways.” In this course we use the phrase “energy system” to label a “way” a physical system can “have” energy in the Energy-Interaction Model. During an interaction between one physical system and another physical system what scientists have always found, is that the energy in some energy system(s) decreases and in other(s) it increases, but the net result is that the total amount of energy in all systems remains constant.

Sometimes it was an apparent discrepancy in the energies “adding up” properly that led to the discovery of new energy systems. That is, there were ways that physical systems could have energy that were not previously known.

In a way, the idea of energy and its use as a conservation law as we and others have presented it, really does seem to be the way our universe actually works. That is, the model seems to be exactly how the universe works. And it works this way in all circumstances. It works this way for all interactions. There appear to be no exceptions. So if it works so well, why doesn’t it just answer all of our questions?

It is true that the idea of energy conservation applies to every kind of interaction imaginable. So that is not the problem. The problem comes with the kinds of questions it can address and the kinds of answers it can be used to develop.

# Kinds of Questions

The Energy-Interaction Model, like all conservation principles, allows us to make very definite statements, predictions of all kinds of numerical parameters, and to answer all kinds of questions regarding what the possibilities are when an interaction occurs. What this kind of an approach cannot do is tell us much about the details of what happens during an interaction or process.

For example, an energy conservation approach can tell us precisely how much energy it takes to break apart some complicated molecule in order to rearrange its constituents into some desired product. But it can’t tell us how to cause the rearrangement to happen. It can’t help us with the details of knowing what kinds of catalysts we should try, for example to speed-up the process.

What scientists have been able to do, however, is to create a systematic approach to getting answers without having to know the messy details of how a process proceeds. This approach is extended in the last chapter of Part 1, which treats the models of thermodynamics. Thermodynamics can be thought of as the art of getting answers to the questions you are interested in without knowing “what you ought to know” to be able to do it. It sometimes almost seems like magic.

One way to think about the way the Energy-Interaction Model is used is that it is a “before and after” approach. We know some things before an interaction occurs and we use the model to answer questions and predict numerical values certain parameters will have after the interaction or process occurs. That is, we can know the before and we can know the after, but we cannot know much about what goes on during the process.

One way to get around this limitation is to redefine the interaction or process so that the before and the after get closer together. This often works to a large degree. And thermodynamics has all kinds of other tricks to get by the limitations of “not knowing the details.”

But if this kind of approach has limitations as we have been describing, why don’t we just develop theories and models that give us the details we want? There are several kinds of reasons. First, detailed models work only for a small range of phenomena, so you have to develop lots of different models, or at least variations of models, for each new question. Second, models that address the fine details get harder and harder to understand and use. High-speed numerical computers are helping us out a lot here. For example, there are plenty of questions that we really need precise and detailed answers to. Such as when will the next big earthquake hit Northern California? Details matter! Experts in getting really detailed information form models that make use of the tremendous computational power that is becoming ever more available are giving us some answers, and for those of us who live in Northern California, the answers are not so pleasant.

So the Energy-Interaction Model can’t do all our work for us, but it can answer “before and after” kinds of questions for essentially every interaction of matter we will encounter. This is why it is worth investing some mental energy in getting really comfortable with using this model with many types of phenomena.

Some common energy units and conversions to SI:

• 1 kWh = 3.6 MJ
• 1 erg = 10-7 J
• 1 cal = 4.184 J
• 1 food Calorie (big “C” calorie) = 1 kcal = 4.184 kJ
• 1 ft•lb = 1.36 J
• 1 eV = 1.602 x 10-19 J
• 1 BTU = 778 ft•lb = 252 cal = 1.054 kJ