After putting the data into Einstein’s model, it turns out that one chocolate biscuit should satisfy the daily energy requirements of 200 million people. So what’s the problem?
Physicists are excellent at juggling energy: they add it, take it away, multiply and divide it; convert it from one form to another. However, if you ask them a simple question, such as how much energy does one biscuit really have, the trouble begins.
A cosmic relay
The packaging says that one biscuit from the pack weighs 13.5 grams and contains 67 kcal, i.e. 280 kJ (joules and calories are simply two different units for measuring energy, in the same way kilometres and miles are two different units for measuring distance). After eating the biscuit, that amount of energy is added to my body’s ‘energy pool’, which allows me, for example, to click away on my keyboard for half an hour in a seated position, or spend five minutes sprinting. And here we have a textbook example of the conversion of energy: from chemical energy, in the fats and sugars of biscuits, to kinetic energy, i.e. movement. If we were to examine the cells of my muscles under a microscope when they receive the order “Contract!”, we would observe that the adjacent molecules of actin and myosin move relative to each other in response to this order. The change in shape of these molecules is precisely that fundamental moment when chemical energy is changed into movement. Each time the actin molecules bend, this is accompanied by the breaking down of sugar molecules, one after the other, ultimately into carbon dioxide molecules, which are then exhaled into the atmosphere in my breath.
What happens next with my movement? In the case of running, the kinetic energy of the body will eventually end up almost completely as heat and, therefore also, in essence, as movement, just disordered and uncontrolled; the movement or vibration of particular atoms and molecules to the same degree in every direction. The air molecules around me accelerate and spin, the tarmac under my feet heats up slightly from the friction of my shoe soles, and the constant shifting of actin and myosin in my muscles, as well as faster blood flow, heats my whole body from within. In the case of what physicists call ‘useful work’, this produces some more orderly transformation. Let’s assume that when I munch on a biscuit, I am energetically turning the crank-handle of a modern dynamo bulb; in this case, the movement of my hand leads to the charging of a lithium-ion battery. The energy stored in it can be used later, which allows us to define it easily as potential energy.
But the work of those 67 kcal can also be traced in the opposite direction. What wizardry put this energy into the biscuit? In order to answer this question, we have to take a look at a wheat field or a cocoa plantation where the plants beaver away at sticking together the molecules of carbon dioxide sucked from the air, creating, among other things, a huge variety of carbohydrates, including starch and sugar, which ensures the cohesion and sweetness of my biscuit. Every bond like this between carbon atoms is like a coiled spring, and releasing the energy contained in it is precisely that chemical ‘kick’ which drives muscle movement and everything else. At this moment, only one step separates us from the sun; the energy necessary to compress the chemical spring actually comes from the sun. Added to this, the energy of the photons travelling through the solar system ultimately comes from the thermonuclear oven at the heart of our star. So, here is the energy relay in all its glory – from nuclear energy, through light, then chemical, to kinetic, heat and potential energy.
And what of this energy?
At this point we could ask a few fundamental questions: What is this energy? Where did it come from? And will it eternally circulate around the universe?
The first question is more than problematic. Although energy is one of the most important concepts in physics – and maybe because of this – it doesn’t have one single definition. Richard Feynman, in his famous physics lectures, claimed that it was not so much that he did not know what energy was, as he was not convinced that something called energy existed. When we talk about specific types of energy, everything is fine; we can measure inflow and outflow, and also calculate it. We also know that, no matter what, the total amount of energy cannot change. But the meaning of the word ‘energy’ itself is, at the very least, rather murky.
Other scientists have tried to juxtapose different forms of energy, wondering what they have in common. What precisely is passed on during the relay described above? It usually turned out, in the course of such reasoning, that the occurrence of energy is always associated with some kind of change – whether it is actually happening, or merely sets up the potential to cause change. In other words, energy is something akin to the ‘cause of change’. The majority of physicists are not bothered by problems with definitions, in the same way that the majority of economists don’t need a sharp, clear definition of money. After all, why bother with definitions when we have more interesting problems to deal with?
The second question takes us straight to the secrets of the Big Bang: for in as much as one can describe the transformation of one form of energy into another with no great difficulty, its appearance out of nothing seems to conflict with the first law of science: the principle of the conservation of energy. The particles that emerged from the hot beginning were already ‘pre-filled’ with energy, whose origin basically cannot be described in the usual language of natural sciences.
Interestingly, it’s possible we know the answer to the second question. For, as it turns out, during each energy conversion a certain amount of heat is generated (with a tiny exception: it is possible to describe elementary quantum events in which no ‘leak’ occurs). The sun does not convert nuclear energy directly into light; along the way, it heats itself up to thousands and millions of degrees. Chlorophyll isn’t an ideal machine and, as it absorbs each photon, a slight vibration passes through the molecule. The losses from the Polish energy network are estimated at 12%; for each 100 kWh of energy sent from the power station to my house, 12 get lost somewhere along the way. And what? You thought that buzzing from the transformer comes from nowhere?
The best way to think about these losses is as a special type of tax – a cosmic tax on activity. In contrast to a real tax, however, this one, squeezed from each energy transaction, doesn’t go to some cosmic money box, but dissipates throughout the universe, never to be recovered. It’s a bit like if, after paying with a 100 złoty note in a shop, 80 złoty made it to the cashier’s hand and the rest simply evaporated. Alternatively, we can imagine that there is a special denomination – let’s say a one grosz [the smallest Polish coin denomination – ed. note] piece – that cannot be spent, nor exchanged for any higher denomination, but for every purchase we get part of the change in single grosz coins. They would amass in our pockets, cupboards and, in time, in our dustbins, and we wouldn’t be able to put them to any good use. This is a depiction of our universe, gradually transforming all of its spare energy into ‘warm noise’.
What’s worse, unlike money, energy cannot be printed. Therefore, every completed conversion in the world brings us inexorably closer to the complete squandering of our energy assets and achieving the moment that cosmologists rather poetically call the ‘thermal death of the universe’.
How much energy is there in a biscuit?
But let’s return to our biscuit. I mentioned earlier that its energy content is 67 kcal or 280 kJ. This is very precise information. But what does ‘a biscuit contains this or that amount of energy’ actually mean in practice? How do we calculate how much energy ‘sits’ in a given portion of matter? For many of us at this moment, a thought may be running through our minds that physics seems to have a precise method of establishing this. So let’s convert, say, 13.5 grams of biscuit according to Einstein’s famous theorem, E = mc². A moment for calculation and… we get a result that is a ‘tiny bit’ higher than 280 kJ: 1.2 quadrillion joules, more or less the amount that all of the nuclear power stations of the world produce in half an hour. This is the amount of energy released by an explosion of 300,000 tonnes of TNT; it would blow a crater with a diameter of one kilometre in the Earth’s surface. After converting it into kilocalories, we get the impressive result of 290 billion kcal. Hmm… Can one biscuit really contain so many calories that it could meet the daily energy needs of 200 million people? It appears this matter requires some deeper analysis.
In order to understand why the ‘energy content’ of a chocolate biscuit can simultaneously contain 27 and 290 billion kcal, and that both of these values are in some sense ‘true’, we must return to the fundamental concept of energy conversion. When the biscuit reaches our digestive systems, 67 kcal is the amount of energy that will be absorbed by my body; but it doesn’t necessarily have to be the entire amount of energy contained in the biscuit. Have you ever wondered why some foods have ‘more calories’ and others less? Why do 100 grams of peeled banana contain nearly 100 kcal, but 100 grams of spinach only 20? Let’s go further: the nutritional value of 100 grams of wood is 0 kcal. Why? Because after 100 grams of wood passes through my digestive system, not a single molecule of any sort of the molecular ‘batteries’ that supply my cells with energy would be produced. However, if exactly the same piece of wood went through the digestive tract of a termite, it would be able to break it down chemically, thanks to the presence of an enzyme called cellulase in its intestines, which can break down molecules of cellulose. (Interestingly, termites themselves do not produce cellulase, but in the end portions of their intestines live single-celled protozoa from the metamonad family that feed off tiny bits of wood. These do not produce cellulase themselves either, but they harbour colonies of bacteria in the posterior parts of their single-celled bodies, and it is only these bacteria that can breakdown the cellulose molecular chains.)
Spinach contains easily absorbable sugars that we can skilfully strip of their energy, but also long chain carbohydrates and cellulose that pass through our digestive tracts virtually unchanged, as so-called roughage. A ‘professional’ herbivore, like a cow, who grows a nice cocktail of bacteria in its rumen just for such occasions, would be able to extract much more energy from 100 grams of spinach than our miserable 20 kcal. And there are organisms that are able, speaking delicately, to have a nice feast even on the remains of this digestive process. In short, the energy ‘content’ of a given portion of matter is the amount of energy that one can release from it during the defined conditions of a concrete process, but, in practice, one can never get to the ‘energy floor’ – the state of matter where all the energy contained within it has been completely exhausted.
Remember the second part of Back to the Future? In front of an amazed Marty, “Doc” Brown chucks banana skins into the fuel tank of his futuristic DeLorean car and then pours in his beer dregs, lastly adding the beer can itself. The observant viewer will note that the engine has the inscription ‘Mr Fusion’. The calculation of how much energy can be produced by the nuclear fusion of a given material depends, according to the maxim above, upon the choice of particular reaction and the conditions. If we focus only on the energy in the banana skin and beer (let’s say there was 50 millilitres), and assuming at the same time that the DeLorean uses the same nuclear fusion technology that is found in the thermonuclear furnaces of the stars, we get a result of 6.3 billion joules, i.e. 1.7 GWh. That’s a lot of fuel. On the other hand, the DeLorean not only flies, but also has a time machine on board, which, as we discover in the film, requires ‘1.21 jiggowatts’ of energy in order to break the space-time continuum and transport its passengers through time…
Therefore, one can think about any portion of matter like an onion that releases successive layers of energy. Here on Earth, only moderate meddling within the most external, thinnest layers of this skin occurs, and almost all the activity of the biosphere and human civilization can be boiled down to breaking chemical bonds and the transfer of electrons to slightly higher or lower energy levels. Atomic nuclei, whose energy charge we use in nuclear power plants, are left completely intact by these activities. The travels of biological matter between plants, animals, bacteria and soil are really the passing around of powerful batteries, containing unimaginable amounts of energy, which future generations of organisms will either extract a minute percentage of energy from, or will add about the same to.
The most decisive step in stripping atoms of their energy is in getting to the ‘energy of mass’; i.e. to that dose of energy which has to be supplied to the universe in order to generate a portion of matter rather than, for example, light or a magnetic field. If we were to release the energy contained in the material bonds of a biscuit, in spinach, and in a can of beer – or in every lonely proton rushing through the cosmic void – and were to convert these particles of matter into light, we would recover these portions of energy. And it was Einstein who gave us the formula for the size of these portions.
Bottomless
Can we go even further? After using the energy from chemical bonds and nuclear power and then the energy of mass, would there be any deeper layers left? Physicists are cautious about this. They only ever talk about relative energy levels – how much energy can be released in a given case, or how much energy it requires. There is no absolute ‘level zero’. Today, we already know that even the lowest describable energy state – meaning simply a vacuum – is also not a sterile nothingness, the ‘metaphysical zero energy state’. This vacuum pulsates with various forms of activity and, in the right conditions, can even ‘spit out’ particles.
Therefore, is it possible that, from the very fact of existing in space-time, we are simply floating in a bottomless ocean of energy, and that we don’t even need a single particle to create an inexhaustible power plant. Maybe all we need is the right key, a lockpick that allows us to drop a vacuum into a deeper, yet unknown energy state, and take away the rest in the desired form: light, heat, matter – whatever we want, however we want it?
Translated from the Polish by Annie Jaroszewicz
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