Energy Conservation: It's Not Just a Good Idea, It's the Law

Michael Eades latest blog points us to a review of Gary Taubes' Good Calories, Bad Calories by Dr. George Bray. Gary Taubes was given the opportunity to respond, and as usual, pretty much brings the wood, from the standpoint of logical clarity and consistency. I haven't read Bray's review in detail, but skimming over it I have to wonder how carefully he read the book. Indeed, he seems to essentially agree with Taubes that fat storage is driven by hormonal factors as part of overall metabolic regulation, and gives some examples where obesity results from failures in these regulatory mechanisms (which we'll also explore in subsequent posts in the Energy Regulation series). Despite this apparent agreement, Bray spends about 13 pages simultaneously trying to disagree with Taubes. Smells like cognitive dissonance, at least from my cursory reading. Taubes reply does a nice job at cutting through the fog.

Bray (like many others) seems to interpret Taubes work as somehow implying a violation or misunderstanding of the First Law of Thermodynamics, which is sort of humorous considering Taubes has a degree in physics from Harvard. Physics students pretty much get these sort of fundamental laws beaten into them from day one. In addition to Bray's review, there was a lot of noise about the First Law of Thermodynamics in response to the recently reported study about low-carbohydrate vs. low-fat diets. Being a physicist, I find misapplication of the First Law thoroughly annoying, so let's dig into this topic a bit and hopefully raise the level of understanding.

Use of the term "First Law of Thermodynamics" is a bit of historical accident. Bray actually uses the term I prefer, "Law of Conservation of Mass and Energy". Actually, "Mass" is redundant, since mass is just another word for energy, so let's shorten that to the "Law of the Conservation of Energy". The statement of energy conservation is simple: in a closed system, the total quantity of energy does not change. Energy may change "forms", e.g. the stored electrical chemical energy of battery can be converted to a light. But the total amount remains unchanged. The field of thermodynamics was largely developed in the 19th century, before we knew about atoms and such. We now understand that energy conservation in "thermodynamic systems" (consisting of very large numbers of atoms) simply follows from the more general law of energy conservation for all physical systems.

Why is energy conservation a "law"? There are many "conservation laws" in physics, and they all arise because of symmetries. Mathematically, physicists model the world via equations of motion, which basically tell how the state of the system under study changes as a function of changes in time and space coordinates. A "coordinate" is just a numerical label for a point in space (or spacetime). Suppose we're doing an experiment inside of a cubical box, 1 meter on each side. We might pick a point in the box, say the bottom left front corner, to be the "origin", labeled as (0,0,0). The top right back corner is then (1, 1, 1) in meters.

But this choice is arbitrary. I could just as easily pick any other point as the origin, say the front left corner of the parking lot, and update all of my other coordinate values accordingly. This is called a "transformation". Similarly, I could move my experiment box from it's original location. In neither case would I expect the experiment to have a different outcome. That's a symmetry: I changed one thing (coordinate origin, location of box), but it did not change the physics occurring inside the box. In this case, we would say the laws of physics are symmetric with respect to position.

A given symmetry in the equations of motion implies that some physical quantity is conserved, i.e. cannot change in a closed system. Symmetry with respect to position implies the conservation of linear momentum. Suppose I turn the box and observe the same outcome. This rotational symmetry implies conservation of angular momentum. Now let's do the experiment today, come back tomorrow, and repeat. If we get the same result, we have a time translation symmetry, which implies the conservation of energy. So basically, the "Law of Energy Conservation" arises from the observed fact that all of the fundamental equations of motion in physics are invariant under time shifts. It doesn't matter whether you look now or later, the laws governing how systems evolve in space and time are unchanged. Note that this is not the same as saying that the state of the system doesn't change, just that the laws which predict how the system goes from one state to another are not affected by the passage of time (this doesn't have to be true, it is just observed to be so in all cases so far).

Now, the above discussion is a bit watered down. The mathematically rigorous version is "Noether's Theorem", and involves differential calculus and continuous transformations. One of the best physics books I've read is Lagrangian Interaction, by Noel Doughty. Very technical, but a highly illuminating read on the power of symmetry in understanding the universe. There are many other fascinating and powerful applications of symmetry as well, one of my favorites being in Probability Theory. But we'll visit that another time.

So, to review: The First Law of Thermodynamics is just another statement of the more general Law of Energy Conservation. Energy conservation in a closed system arises because the laws of physics do not change with time. If you were to ever observe an apparent violation of energy conservation, it must be either that you are not observing a closed system (haven't taken everything into account), or you've discovered new laws of physics. The former is far more likely than the latter. For example, suppose you put some water in a cup, stuck in a thermometer, and put the whole she-bang into the freezer. The temperature would drop as time passed, indicating that the average energy of the water is decreasing. But this does not imply violation of energy conservation. Were you to also measure the net heat output from the freezer, you'd find the missing energy.

Back to our original story. Bray makes the point "Over the period of about 100 years from 1787 to 1896, the Laws of Conservation of Matter and Energy were shown to apply to human beings, just as they do to animals." That's a no-brainer given what we've learned above, since humans and animals are physical systems, ultimately governed by the same physical laws as the subatomic particles which comprise these systems. They didn't know about atoms and Noether's Theorem in the 19th century, so the explicit study of energy conservation in living organisms is understandable. But now it's not even a point of discussion, so I don't know why Bray (and so many others) keep lecturing about it. As far as anyone can tell, energy conservation is built-in to the fabric of the universe. The core issue isn't violation of this law, it's whether your metabolic theory or experiment has done a complete accounting of all energy inputs and outputs.

Energy enters the body in the form of food. In healthy people, the only way it can leave the body is through physical exertion or heat. Energy may be used in the body to fuel other biological processes ("base metabolic rate"), or it can be stored in various chemical forms. Misinterpretations seem to arise because there is an assumption that base metabolic rate and heat output are independent of caloric intake, and further independent of macronutrient composition. If you assume that intake is independent of storage and output, you can draw some strange conclusions. The body has ways of regulating total input, storage, and output in an attempt to maintain energy balance in a healthy range. As such, the output side must be related to the input side, otherwise energy regulation would be doomed to failure.

Consider a simpler example: drinking water. When we're thirsty, we drink water. The signal for thirst is generated in the brain as a function of the detected water content in the body. Too low, you get thirsty. But when you drink some water, it takes time for the water to get absorbed into the blood and signal the brain. So we tend to drink more water than we actually need; that's probably also a good evolutionary strategy, sort of "better safe than sorry". The body then has mechanisms to get rid of the excess, mostly as urine. The amount of urine we produce is clearly correlated to the amount of water we drink. If water output were independent of water input, we'd be in constant danger of either dehydration or water poisoning, depending on availability of water. Like food in Western society (and increasingly elsewhere), water is abundantly available, yet people aren't dropping dead from over-hydration because the input, usage, and output are regulated by the body. Why should we expect any different for energy regulation?

Like I said earlier, if it appears that energy conservation is violated in an experiment, such as the recent low-carb vs. low-fat diet study, the most likely explanation is that the experimenters did not measure all of the energy output. They did estimate physical activity, but it's more difficult to measure heat output. Similarly, Taubes is not saying "calories don't count", but rather that you must consider all methods of energy output when discussing energy balance. Further, you must consider the physiological mechanisms that control energy input, storage, and output, because that tells you relationships amongst them. When you do this, you find not only that output correlated with input, but also that the macronutrient composition potentially affects input, storage, and output as well. Macronutrients not only affect energy balance but other physiologically important quantities. Blood sugar, for example, is tightly regulated. If it goes too high or too low, the body has problems. So we would expect a different biological response if we eat the same calories as sugar or as fat, and of course this is exactly what is observed. It should not be surprising that high-carbohydrate or high-fat diets have very different effects on metabolism. Violation of energy conservation is not required to explain the results, just that the system has different responses to different inputs, and that the caloric content of food is only one aspect that is detected and monitored by the body.

Bray actually seems to agree with this point: "The concept of energy imbalance as the basis for understanding obesity at one level does not preclude any of the influences that affect or modify food intake or energy expenditure, including the quantity and quality of food, toxins, genes, viruses, sleeping time, breast feeding, medications, etc. They are just the processes that modify
one or other component of the energy-balance system." I think the fundamental disagreement may be whether fat storage depends sensitively on the precise balance between energy intake and output, i.e. that storage is driven by eating even a little too much. But that implies a pronounced lack of robustness in the regulatory system, one which is not observed, any more than it is in regulating water balance.

Anyway, the next time someone tells you that low-carb diets can't work because they violate the First Law of Thermodynamics, you can reply with "Low-carbohydrate diets exhibit continuous symmetry under time translation transformations, hence do not violate conservation of energy." That ought to shut 'em up.