footlong and fancy-free: why size doesn't matter

Joule's apparatus for measuring the mechanical equivalent of heat energy. A descending weight attached to a string causes a paddle immersed in water to rotate. Caption by Wikipedia, 6 May 2014Joule's apparatus for measuring the mechanical equivalent of heat energy. A descending weight attached to a string causes a paddle immersed in water to rotate. Caption by Wikipedia, 6 May 2014.
No energy? No matter!

Zero, zip, nada, none: that's how much is left after you turn matter into energy, via a bomb or a power station. But what kind of power station is best? It's actually impossible to say.

I’ve heard that coal-fired power stations are dirty, wind-farms are ugly, and nuclear power stations are dangerous (but much more efficient at producing energy).

Do you agree? I don’t, and I’ll provide the supporting logic in a minute. But first let’s unpack the conventional wisdom and hold it up to the light until it withers and dies!

Power stations are designed to transform matter into energy, or one form of energy into another. If you’ve got nothing better to do, you can use Einstein’s equation, E=MC2, to work out the energy equivalent of the mass1 of any given chunk of matter. The equation says that energy (E) equals mass (M) multiplied by the speed of light (C) squared.

I’ve heard that the reason why you get so much energy via nuclear processes2 is that the speed of light (squared) is such a big number. Really?

Light travels at roughly 186,000 miles per second. Squaring 186,000 yields 34,596,000,000, which is a big number, (or so they say, and yet in billions it's really only just over 34, a mere two digits.)

But let’s see what happens when we choose different units. In kilometres per second, the speed of light squared is roughly 90,000,000,000 – even bigger than 34,596,000,000. But in parsecs -- a unit of distance beloved by astronomers and cosmologists – light travels way less than 1 measly parsec per second.

So light travels further and faster on 1 tank of kilometres than it travels on 1 tank of miles or 1 tank of parsecs, unleaded or leaded. And 1 is a small number; in fact it's the smallest (positive integer) there is.

Ignore the previous paragraph. It’s not even wrong. Light travels exactly the same distance at the same speed in miles per second as in kilometres per hour, parsecs per week or any other units or combinations thereof.

Table of Surveying, from the 1728 'Cyclopaedia', Volume 2. 
Cyclopædia: or, An Universal Dictionary of Arts and Sciences (two volumes in folio) was an encyclopedia published by Ephraim Chambers in London in 1728, and reprinted in numerous editions in the eighteenth century. The Cyclopaedia was one of the first general encyclopedias to be produced in English. Caption by Wikipedia, 11 January 2017.Table of Surveying, from the 1728 'Cyclopaedia', Volume 2. Cyclopædia: or, An Universal Dictionary of Arts and Sciences (two volumes in folio) was an encyclopedia published by Ephraim Chambers in London in 1728, and reprinted in numerous editions in the eighteenth century. The Cyclopaedia was one of the first general encyclopedias to be produced in English. Caption by Wikipedia, 11 January 2017.

The same applies to anything that can be measured: distance, mass, gravity, acceleration, volume, density, momentum, rotation, energy etc. What you measure is not affected by the units you use. How you calibrate your measuring instrument does not dictate the outcome of your measurement. A 12-inch hotdog is just as long as a foot-long!

Now light may be fast, but it may not be the fastest thing in the universe. (Alternatively: Light may be fast now, but may not always have been or will be as fast). Physicists think there may be sub-atomic particles that travel faster than light (e.g. the particle known as the tachyon). But even if it's true that light is the fastest thing in the universe, it may not be the fastest thing there is. And likewise, the shortest plank may be shorter elsewhere and elsewhen. Such as in other universes, other times, other dimensions.

According to the eggheads, it's not impossible there are universes other than the one in which we live and love. They say it's not impossible for the speed of light to be faster or slower in another universe than it is in this one. So the numerical value of a so-called constant may not in fact be constant, but rather variable! And terms such as “fast” and “fastest” (not to mention “constant”) are not meaningful unless the relative context is absolutely tightly defined.

If there are shorter planks than the shortest plank, and faster speeds than the fastest speed, then there’s no such thing as shortest or fastest. Nothing is absolutely fast or slow or long or short or dense or diffuse or hot or cold or large or small. Size doesn't matter: it's how you measure it that counts. The only absolute is Everything (cap E, one word), and every thing else is relative, including the size of numbers such as 90 billion, which is

  • larger than the number of days in the week

  • but smaller than the number of stars in the Milky Way galaxy (estimated at 400 billion) and

  • dwarfed by the estimated 5,000,000,000,000,000 ants (5 quadrillion, short scale) on Earth alive at any one time.

IMHO, absolute comparisons between different methods of producing energy can never be meaningful because they’re not engauged (physics joke: an oxymoron if ever there was one). It's difficult if not impossible to find common ground on which to base the comparison. For example, say you wanted to compare the energy you can get from a coal-fired power plant with the energy you can get from a nuclear power plant. Would you base the comparison on

  • mass (e.g. 1 kg of coal vs 1 kg of uranium), or

  • volume (e.g. 1 cubic metre of coal vs 1 cubic metre of uranium), or

  • density (e.g. the number of coal molecules in one cubic metre vs the number of uranium molecules in one cubic metre), or

  • number (e.g. 100 truckloads of coal vs 100 truckloads of uranium, or even 100 molecules of coal vs 100 molecules of uranium), or

  • financial costs (startup) (of building a coal-fired power plant vs the cost of building a nuclear power plant), or

  • financial costs (ongoing, of running the plant, including repairs and maintenance), or

  • ”externalities” (e.g. impact on the environment, the community, social/political institutions), or

  • various different combinations (please specify) of the above, or

  • all of the above, or

  • none of the above, but rather something else entirely (please specify)?

I don't know whether you would get more or less energy from burning coal in a coal-fired power plant than you would get from applying nuclear processes to the same amount of coal. I don't know if it's even currently technically possible, in theory let alone practice, to get energy by splitting or joining the nuclei of atoms in the coal molecule.

But whether it’s in the form of coal, gas, oil, water, uranium, plutonium, einsteinium, californium, damp carpet or camel dung, matter is a key ingredient in many recipes for cooking up energy3. In energy matters, matter matters. Maybe that's because matter IS energy IS matter.

And you can of course get usable energy without matter. Hydroelectric power installations, for example, convert the potential energy of dammed water into electrical energy. (Only dammed water can be used to produce energy; holy water is too placid.) On a personal level, the energy you expend on formulating a plan to get even can help transform the white-hot energy of rage into the icy-cold energy of revenge! But it’s impossible to make a valid comparison between the rage you feel at reading boring blogposts, such as this one, versus the rage you feel about footnotes in blogposts, such as this one. Bore-rage and foot-rage are completely different types of rage. To compare them would be nothing at all like comparing cilantro with coriander, and nobody wants to go there!


FOOTNOTES

1. Mass is a tricky term to define. It doesn't necessarily mean weight, though in most sublunary circumstances it does.
2. In this post "nuclear processes" refers to cutting up or joining together the nuclei of atoms (fission or fusion, respectively).
3.Exceptions I can think of include electromagnetic induction, in which electricity is produced by a varying magnetic field, the strong force, the weak force (or the electroweak, if you prefer). Solar power is derived from the matter burnt in the furnace we call the Sun. Wind power relies on molecules of matter comprising Earth’s atmosphere.

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