Conservation Laws: Limits to Cheating

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This is a STUB ONLY at this time to provide the link structure on another page. Please don't edit until I can get a first draft up here -- Rocketguy

Conservation Laws

The conservation laws (conservation of momentum, conservation of energy, and the second law of thermodynamics (Entropy doesn't decrease), are fundamental to our understanding of the physical universe. If working in the real world, one may dislike them, but obedience is strictly enforced by the Universe.

In a work of fiction, of course, one can do anything; however, discarding these fundamentals is not to be done lightly or carelessly and doing so is one of the surest ways to make your work of science fiction not be 'hard' or 'tough' and to quickly cross the line in to fantasy. Fantasy of course is a genre of its own with its own conventions and literature and if that's what one intends to write, so be it. But if you want a work which is 'realistic' in the physical sense, there is usually some way, as an author, to get what you want without discarding the conservation laws.

The conservation of energy -- the realization that energy may change from one form to another, but not be created or destroyed -- is in some ways the birth of all physics. The concept has proven so useful that with every new discovery, rather than treating it as a violation of the conservation law, we have instead found ways to add new forms of energy to the account. Objects in motion in the real world slow down -- but the energy shows up as frictional heat. Burning fuel appears to create energy -- but we now know it was there in the molecular bonds in the material in the first place. Even nuclear energy, which was quite mysterious when first discovered, we now consider an example of the same thing, in that we now (thanks to Einstein) appreciate that mass is just another kind of energy, and if one converts a tiny amount of mass in to energy, a large amount of energy is the result. If tomorrow, some new phenomenon were found that appeared to violate this law, we would almost certainly find a way to book-keep it as a new form of energy, rather than junking such a useful concept as conservation of energy.

Momentum is much the same. If you push on a heavy object, you feel it pushing back on your hand. If you eject mass to the left, you are pushed to the right. If you push on the air to move forward, you create a wind going aft. People have theorized (but not yet achieved an accepted experimental validation) various drives which might 'push on nothing' -- so called 'reactionless' drives. For story purposes (and who knows, perhaps in reality), these can be re-cast as a drive which 'pushes on something big' -- the large-scale structure of space-time, for example -- without throwing away the conservation of momentum. And in any case, space is not empty; perfectly conventional real-world propulsion systems have been proposed which push on the thin plasma between the planets or between the stars, or which interact with the magnetic fields found between the stars. One might envision improving the performance of such systems to whatever degree desired for story purposes without throwing all of physics out the window. However, even if such a drive were to exist, if momentum and energy are still conserved, its usefulness would be limited -- pushing even on a large reaction mass still follows the same mechanics as propellers -- the power required scales with the product of thrust and velocity, which means any such drive, even if it existed, would be useful at low velocities rather than high.

Thanks to the Nobel-winning work of Emmy Noether[1] we now understand that every symmetry of the universe carries with it a corresponding conservation law. It can be shown that symmetry to time coordinate carries with it the conservation of energy, and symmetry with the space coordinate carries with it the conservation of momentum. In other words, violating these conservation laws means that if you do something tomorrow it doesn't necessarily produce the same result as today, and if you do something a meter to the left, it might turn out differently than it does a meter to the right. If the universe is not predictable, you don't need conservation laws -- but then it's hard to stay in the realm of 'science' fiction.

The non-decrease of entropy is a bit more subtle, but everyday examples abound. If you put a bit of dye in a glass of water, you expect to see it spread through the water -- the reverse process, where the water spits out the drop of dye, doesn't take place. If you drop an ice cube in the glass of water you expect to end up with cool water; you'd be very surprised indeed to start with a glass of water and see that it had divided itself in to a bit of water and a bit of ice unless you move energy around (like putting the glass in to a freezer). This property of a system we call 'entropy'. You can think of it as a measure of how randomly arranged or ordered the system is. There's generally only a few ways for the atoms to be arranged that we think of as 'ordered', and many many ways we can think of them as 'disordered', and those can be treated with more rigor and math. For simple systems where all the atoms are mixed up together, we can describe that as "temperature" -- and one way to summarize the Second Law of Thermodynamics is "heat flows from high temperature to low temperature". This has major consequences for spacecraft propulsion, because we want to move a lot of energy about. In doing so, the energy flows from a high-temperature (low entropy) source to a lower-temperature sink. In some cases, that 'sink' can be the propellant being expelled -- well and good. In many cases, it can't be, and it has to go somewhere else. Space is short on good heat sinks -- vacuum, in spite of endless poetry about 'the cold of space' is an outstanding thermal insulator (as in a vacuum flask, Dewar flask, or Thermos bottle), and nearly the only way to get waste heat out through it is to radiate it. ((See 'Radiators' -- Page not created yet))

Cheating If one wishes to 'appear' to violate these conservation laws, there are some tiny chinks in the structure of physics one can look to; but remember that centuries of experimentation on these laws will still be 'right' and there must be some very good reason why any 'cheating' is restricted to very special circumstances.

In highly curved spacetime, space and time really aren't quite the same from place to place or time to time. Therefore, defining just what is meant by 'energy' and 'momentum' can get a bit tricky. This is, however, much more likely to be a question of doing the bookkeeping properly than 'violating' the conservation laws.

It is much easier to invent (and in the real world, to seek) new forms of energy, or to find new things to push on. That can produce much the same effect for story purposes without loosing magic in the world.

The Second Law is a bit fuzzier. It applies to a closed system without energy flow in or out of the system. Those energy flows are not always obvious. There have been very small microscopic systems in which it appears that room-temperature energy flowing in to the system is producing useful work without a low-temperature reservoir (so far, only at tiny levels). The 'randomness' character also means that when looking at small fluctuations, what this might mean at all is somewhat debatable. Still, handle with care; unless you think through all the implications, ignoring the Second Law can lead you in to pure fantasy very quickly without intending to do so. Ignoring the implications of this law -- in particular, neglecting radiators on your ships where they really should be there -- is one of the current hallmarks of how 'hard' your science fiction is meant to be.