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Would throwing a fireball leave a trail of frost in its wake? Would transmuting too much lead into gold cause a small meltdown? Would collecting enough power to cast a really big spell like causing an earthquake incinerate the caster if they don't take proper precautions?

To clarify the total amount of energy doesn't change, but it doesn't have to follow physics on how the magic sucks in the energy or expels it out. That would be why the fireball leaves a trail of frost, to keep itself energized and 'burning' it is sucking in the heat from it's path leaving behind a cold zone. Major battles could have an interesting affect on the local weather...

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    $\begingroup$ I believe there is a much needed followup question about the second law of thermodynamics or entropy balances. For example, your fireball leaving a trail of frost could satisfy the conservation of energy, but you'd definitely be destroying entropy at the same time, which is certainly non-physical. I will ask later if someone else hasn't by that time. $\endgroup$ – NauticalMile Sep 25 '14 at 3:09
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    $\begingroup$ In some places, Terry Pratchett has the magic of Discworld follow conservation laws. One example allows a wizard to levitate by exchanging energy/momentum with a falling weight. $\endgroup$ – Neil Slater Sep 25 '14 at 11:24
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    $\begingroup$ @NauticalMile That would be interesting. I wonder if we constrained magic to follow all physical laws what would still be possible. For instance telekenisis would still be possible, but angular momentum would greatly reduce the range of it. $\endgroup$ – Godric Seer Sep 25 '14 at 12:08
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    $\begingroup$ If you read the Eragon series (Paolini), he creates restrictions on the caster by setting up a system where the magic used takes up as much energy from the caster as it would have to do it manually. To the point where you can kill yourself by trying to do something that it beyond your power. It doesnt get into the Physics necessarily but an interesting concept none-the-less. The primary explanation of it comes about halfway into book #2 if you want to read it. $\endgroup$ – James Sep 25 '14 at 15:58
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    $\begingroup$ @Cragor I'll make a slight clarification to my first comment to answer your question; making fireballs is definitely possible, it just can't be done effortlessly in the manner in which bowlturner or yourself are implying. They cannot just take energy from one place in a uniform temperature environment and move it to another without harnessing some other potential energy to begin with (some of it could be recovered at the end). I will definitely tackle this concept in a future post (or series of posts), so stay tuned :). $\endgroup$ – NauticalMile Sep 25 '14 at 18:16
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If magic had to follow conservation of energy, the magical part would be where that energy came from. In most cases in the real world, if you want to put energy into something, then you have fairly constrained ways to do so. If you want to put in thermal energy, you need to touch it with something hotter. If you want to put in kinetic energy you need to apply a force to it.

Magic, even if it was constrained by conservation of energy, could avoid some of these shortcomings. You could for heat something up without having something hotter. You could move something without applying a force directly (which would break conservation of linear momentum). You could transfer energy from whatever source the case has access to, to another object with 100% efficiency (breaking the second law of thermodynamics). The exact effects would depend on what other physical laws you force it to obey and what source of energy the caster is allowed.

Limiting magic to conserve energy would be an interesting mechanic. Depending on where casters are allowed to draw energy from for their spells, you could impose many different types of constraints on the magnitude of spells that could be cast. Forcing them to pull from their own physical stores would be a much tighter limit than simply allowing them to move energy around at will (much like your fireball example).

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    $\begingroup$ The Kingkiller Chronicles has a magic system much like this; other books enforce this idea more or less strongly. $\endgroup$ – PipperChip Sep 25 '14 at 18:42
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    $\begingroup$ What if magic was control over entropy? Usable energy comes out of nowhere because it separates from where it always was but unusable to do work. If based on near omnicient intelligent control of atoms, Maxwell's Demon is an example. Read up on the resolution to that paradox for interesting ideas. Itnis a natural hook for linking knowledge with powers. $\endgroup$ – JDługosz Dec 13 '14 at 2:40
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    $\begingroup$ Hmmmm. I could get a lot of energy by consuming a little dirt. $\endgroup$ – Joshua Feb 22 '15 at 2:38
  • $\begingroup$ The magic in Full Metal Alchemist respects conservation of energy but not necessarily laws of entropy (depending on which series you look at). $\endgroup$ – Shufflepants Mar 29 '17 at 15:09
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In several magical system, energy is pulled from other resources. Common resources are fire, live force, a magical power source, the energy of your body, or energy from the surrounding world. In these cases a magician can easily sling a fireball with out any obvious power source.

It really depends on how you design your magical system. The main limiting factor on a magicians strength and how over powered your mages are, depends on where they draw their power. There is no need for any of the things you listed to happen. Giving us more information on your magic could help us nail things down, but currently lighting a fire doesn't leave a frost trail and there is no requirement that magic do so. You could have a system whereby magicians can transfer heat, and concentrate heat into a single area. That would leave a large frosty area, and a fireball in the center, but nothing about the conservation of energy says a hypothetical magician couldn't get the energy from the fire in another way.

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  • $\begingroup$ Lighting a fire is using fuel to burn, throwing a fireball is basically plasma, keeping it burning requires energy, where is it getting the continuous source? $\endgroup$ – bowlturner Sep 25 '14 at 12:08
  • $\begingroup$ @bowlturner - Where does your magic power come from? In D&D it comes from an alternate plane of existance. It is brought into the prime material plane(or what ever plane you are on) and then manipulated. $\endgroup$ – Chad Sep 26 '14 at 17:48
  • $\begingroup$ Yes many magical systems do something similar, often magic uses some 'other' force or energy. The idea behind the question was what if the energy had to come from the same plane? All normal energy like we know it, just a 'magical' way of manipulating it. $\endgroup$ – bowlturner Sep 26 '14 at 18:11
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Historically, many things that were considered magical were actually electricity and magnetism. These two forces act as invisible energy transfer mechanisms that allow otherwise isolated systems to interact. Because this was not understood at the time, it was often mistaken for magic, which is mysterious, by definition.

To have your magic obey all thermodynamic laws as well as conservation of momentum, you need only introduce a mysterious kinetic mechanism to your universe. You see, any process that has a negative Gibb's Free Energy will be thermodynamically favorable and would ideally move forward to equilibrium. But in reality, all processes and reactions take time and some reactions take an infinite amount of time. This is the concept of reaction kinetics. The vast majority of favorable reactions in our universe are held back by kinetics. The most obvious kinetic barrier is separation by large distances (relative to the reactive system). For example, a highly exothermic acid-base neutralization reaction is clearly favorable, but it won't even begin if the two substances are not mixed.

So what you really want is an ability for magicians to mysteriously connect distant systems. With a wave of his hand the heat of his volcano lair is transferred to his enemies. Maybe he sends his foes flying, while back at home one of his giant pendulums slows to a standstill. This places definite limits on your mage's powers: he can only heat something to some fraction of the temperature of his forge, and can only spin something at some portion of the speed of the flywheel system in his basement. But if he is able to access the differential motions of the stars and planets, then there is no practical limit to the forces he can exert. Thus a mage's reach determines his power.

For your magic system, nobody should know exactly how these distant systems come to interact, or else it ceases to be mysterious and thus ceases to be magic. You don't need to explain it, and furthermore, you had better not.

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  • $\begingroup$ Some overexcited magician could end up dropping planets to their suns... Let's hope the 'stellar' mages are sensible enough to take energy from the motion of planets from star systems ELSEWHERE, not their own. (I'm thinking on spells like building a castle of gold out of nothing, which may take enough energy from e=mc^2 to slow down some celestial bodies) $\endgroup$ – Oxy Jun 13 '16 at 8:56
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In a system I implemented for an RPG world, using magic used up some of the area's background magical energy, which, if enough was used, would make it harder to use magic the next time. Some forms of magic were inherently more draining on the magical auras than others.

The magic auras would regenerate slowly, but this effectively limited the ability of magicians to throw magic around without having to consider the consequences.

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  • $\begingroup$ In essence, Dark Sun $\endgroup$ – user3082 Sep 23 '15 at 6:13
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In Charles Stross's story The Concrete Jungle available online

"Even though we don't really know how the medusa effect works, other than that it relies on some kind of weird observationally mediated quantum-tunneling effect, collapse of the wave function, yadda yadda, that makes about 1 percent of the carbon nuclei in the target body automagically turn into silicon with no apparent net energy input. That right?"

"Have a cigar, Sherlock."

"Sorry, I only smoke when you plug me into the national grid. Shit. Okay, so it hasn't occurred to anyone that the mass-energy of those silicon nuclei has to come from somewhere, somewhere else, somewhere in the Dungeon Dimensions . . . damn. But that's not the point, is it?"

When his truck was hit, the tires became incindiary. The nuclear change took energy from another universe, but the new state was then chemically unstable and rather than turning to a neat statue, the medusa's victum burns up.

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Magic certainly seems to violate conservation of energy. When something seems to violate a conservation law, there are two main alternatives. One, the conservation law might not hold. Or two, our understanding of reality is incomplete and the seeming imbalance is balanced outside our previous consideration.

The question when comes: How likely are we to have missed something that could balance out the seeming violation? With hypotheticals like magic, time travel, and macroscopic teleportation with corrected momentum the answer to that is that they require something beyond our current consideration already. As such there is never real logical reason to think they'd violate conservation laws.

The consequence of this is that there is no reason to think magic would have to change from what we expect to preserve conservation laws. Giving some appearance of having considered the issue will make the system more believable to many people, but that is just an emotional response. No logical reason requires it, unless your goal is to really explain magic exhaustively, that is, to uncover the hidden mechanics of it. Which unless you can demonstrate magic in the real world is probably better left undone.

A sidenote to those with very good memories, the logic is essentially the same as in my time travel vs conservation of energy answer, but this time I am actually trying to explain it in a way that is possible to understand.

PS: This answer probably seems like I am going around the question with vague platitudes. But sadly enough physicists currently label vast majority of the known universe as dark "something". As such, having the effect something hypothetical has on baryonic matter seem to violate conservation laws really is meaningless. All it really tells us is that physicists would be willing to spend ridiculous amounts of money for a way to experiment with it.

ADDENDUM Zero ups on answer and bowlturners comments made clear he did not understand my meaning. I think it is safe to say I need to give a better explanation. I think some examples how the idea works would be easiest. Probably long and boring, but... The basic issue seems to come up relatively often, so it might be worth the effort.

I'll start with the trivial example: forward time travel. Time traveller pops into time machine at time A, pops out at time B, and there is no sign of him in between or any form of energy bleed. It seems clear conservation of energy has been violated. After all there is one traveler worth of energy missing between times A and B.

Except there really is not. For time travel from time A to B to be possible the times A and B must be connected. There must be a path that allows the passage of a human intact between the two times. That path can contain the missing energy and if the energy contained by the path equals the missing energy everything is fine. Given that we know the path contains the energy of the time traveller passing thru it and that we were missing one traveller of energy and that the path covers exactly the same time where energy was missing, we actually know this is true. Conservation of energy preserved!

Backward time travel is less trivial or to be more exact, if it existed the implications would be non-trivial. Lets say our intrepid time traveller pops in at time B and comes out at time A. Now outside A-to-B everything is fine, but A-to-B there seems to be one traveller of excess energy. It is probably easy to see the next step: If you seem to be missing energy between A-to-B and you have path going from B-to-A with the exact correct magnitude of energy with direction of time reversed and switching the sign on energy... The numbers match up again...

At this point I really need explain how this is related to magic and conservation of energy, you know, the actual question. It comes down to a very simple question: "Why did most people not consider the path used for time travel when considering conservation of energy?" The answer is equally simple: "Because we know we do not need to consider such things." More than that we actually know that a claim that "Conservation laws are preserved you just can't see it!" is a sure sign of really bad physics and almost certainly false. In other words, we know how conservation of energy is supposed to work and we know that that understanding is solid enough that anything contradicting it is almost certainly false.

Problem is that this knowledge has some big built-in assumptions in it that even people who understand the physics far better than I do usually forget. Specifically, it is assumed that hypothetical effects that have never been observed despite being easy to spot due to appearing like flagrant violations of the conservation laws can be ignored when considering how conservation laws work. For example, you can and should ignore the idea of a wormhole between times balancing the energy, since in practice considering such has never been necessary. Which means they must be rare enough that ignoring the possibility is the correct default. Or the existence of a "mana field" that acts as a sink or source to balance out spells. I mean that would be really obvious, so claiming something like that exists and solves your conservation law issue is an obvious case of hand-waving and needs to be rejected. We know that is not how conservation laws work!

Except, if you engage in speculation. Then you must adjust your assumptions to be consistent with your premise. If you assume time travel works, whether for a setting or a thought-experiment, you must also take worm holes into account when considering conservation of energy. The fact that you do not need to when time travel and worm holes are unknown is no excuse. If you assume a world where magic exists and creates spectacular effects thru manipulation of all pervading magical energy, then you must take the existence of that energy field into account when considering conservation laws. You can't first say "magic exists" and then continue by assuming that conservation of energy must work the same way it does without magic.

This might seem like quibbling but it is actually a very serious and fundamental question. The conservation laws are based on the symmetries and invariants existing in the reality. If an aspect of reality interacts very weakly with what we are interested in, it can be ignored. For example, it is not really necessary to consider "dark matter" when doing chemistry. But if we are specifically considering something like time travel or magic that is fundamentally based on interaction between "mundane" and "speculative" and try to ignore the "speculative" part when considering conservation laws... It cannot work. Considered separately, the parts will not have symmetry. It may look like conservation laws are being violated, but in reality they simply do not apply to asymmetric fragments, they apply to the whole interacting system.

In summary, you cannot assume magic exists and then assume that existence of magic does not affect how energy is conserved. It is not even possible. Only way "magic" can be ignored when considering conservation laws of "magical effects" is if "magic" does not interact significantly with "magical effects". Apart from being silly this would imply that "magic" is not relevant for existence of "magical effects" and they would be just as likely to exist in our no-known-magic world as in a high-magic fantasy world. Pointless.

Hope somebody will read this. Hope it is somehow useful to someone. But TBH I mostly wrote this to clarify my own thinking on the subject. There have now been two questions where this, the nature of conservation laws with hypothetical effects assumed, has come up and both times I pretty much totally failed to communicate my thinking. Next time I will be ready!

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  • $\begingroup$ Stories with magic have 'rules' the magic follows to put constraints on what can be done with it. This question was asking what might be expected if this rule was applied. $\endgroup$ – bowlturner Dec 13 '14 at 13:08
  • $\begingroup$ @bowlturner And my answer was "nothing". Obeying conservation laws puts no extra constraint on hypotheticals like magic or practical time travel that already require extensions to physics to exist. You can ALWAYS safely assume that the seeming violation is balanced within the extended area of new physics. Which is invisible by default. Conservation laws are only an issue if you actually give a detailed explanation of how they work (the extended physics) and things still do not balance. $\endgroup$ – Ville Niemi Dec 13 '14 at 14:30
  • $\begingroup$ So your really saying that because magic is involved, nothing matters, it's just more hand waving when things don't seem to make sense? Sorry but in my opinion you completely missed the point of the question. $\endgroup$ – bowlturner Dec 13 '14 at 15:04
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    $\begingroup$ @bowlturner No. I am saying that reasoning relying on otherwise reasonable assumption, we specifically assume not to hold is invalid. We can't first assume that magic or something else requiring a significant extension of known physics exists, and then follow with reasoning that has the implicit assumption of no significant extension of known physics. I am sorry that I am so bad at explaining things that pointing out basic rules of logic looks like "hand waving", but I still do not think assuming extended physics both exists and can be ignored in the same statement makes sense. $\endgroup$ – Ville Niemi Dec 13 '14 at 15:33
  • $\begingroup$ @bowlturner So, no, I don't think that because magic is involved, nothing matters. But if we assume magic (or practical time travel or FTL or..) exists, the rest of our reasoning must be consistent with a world where that is possible. Not with our real world where it is safe to assume such things do not exist. $\endgroup$ – Ville Niemi Dec 13 '14 at 15:43
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I'm going to try to keep to the original question, and only impose a single constraint on magic use: Energy has to be conserved.

Distance Constraints

Conservation of energy doesn't force smooth flow of energy. So without further constraints, the energy needed could "teleport" from anywhere. It could all be drawn from distant stars, and wouldn't really change anything. So we could also assume that energy has to flow continuously, or at least cannot travel more than a short distance without significant loss.

Is the User a Conduit?

Basically, does the energy she uses have to go through her, or can she just manipulate it from a distance? In the first case, she is basically an energy transformer, changing energy from one type to another as it passes through her body. In this case, the fireballs energy would all be given to it from her, and probably at the start, so that the energy might come from the air around her, other sources she had stored up, etc.

If not, then she can manipulate energy instead. This is more like the example of a fireball with a trail of frost. But depending on how much control the magic user has, it could be more extreme. For example, by manipulating the light energy instead, the fireball could be surrounded by its own blackout where it absorbed all the light to stay fueled.

What Counts as Energy?

If all types of energy can be used, this opens up a huge world of potential. Nuclear from the force that holds atoms together, chemical energy from most compounds, residual heat energy found in everything. Taking the energy from something would be as devastating as delivering more energy, just imagine reducing any object to absolute 0: It would shatter immediately.

You could also limit the magic user to only controlling some types of energy, heat and kinetic probably being the most typical and intuitive.

Conjuration

Keep in mind that if energy is conserved, mass must be conserved too. Thus, to make any matter out of nothing, a large amount of energy would be needed.

Storage

Does magic add new ways to store energy? Special crystals, life force, etc? Or does the energy used have to be drawn from normal methods in the immediate surroundings?

Energy transfer

Consider the difference between launching a fireball, and simple increasing the heat in an area to be a burning temperature. One requires aim, time, energy loss as the fireball travels, etc. The other is basically an instant flash-burn.

My opinion

In order to keep magic from being more or less invincible and kind of silly, I could keep these restraints:

  • Continuity Energy must flow continuously. This way only local sources are available, you can't cast spells through some materials, etc.

  • Range Keep range of effect within a few feet. If a magic user wants to bombard a distance castle, she can't just pull all the energy from the walls, she either has to get really close, or create something to deliver the energy there, i.e. a storm or giant fireball or shock-wave in the earth.

  • Rate Limit the rate of energy transfer too. A small fireball might be more or less instantaneous. Melting diamond would take time and continued applied energy.

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    $\begingroup$ Diamonds evaporate when heated. $\endgroup$ – user3082 Sep 23 '15 at 6:20
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If magic has immutable laws then it is science and can be studied as such. The equivalent of Isaac Newton would come along and start to sort it all out. If you doubt this then note that Newton was an advocate of alchemy.

Isaac Newton was a dedicated alchemist, a fact usually obscured as unsuited to his stature as a leader of the scientific revolution. Author Philip Ashley ... concludes that the two major aspects of Newton’s research—conventional science and alchemy—were actually inseparable...

Alchemy was an ancient tradition of speculative philosophy that promised miraculous powers, such as the ability to change base metals into gold and the possibility of a universal solvent or elixir of life.

Isaac Newton and the Transmutation of Alchemy: An Alternative View of the Scientific Revolution Paperback – July 7, 2009 by Philip Ashley Fanning

Newton is not generally famous for that because it turned out to be a dead end. However had it had been factual he would have discovered the basic rules.

We would now have university course on all aspects of magic except that it would simply be called science.

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To answer that question, you'd have to posit a theory about how magic works.

In the real world, I can certainly start a fire without creating frost around it. But that doesn't mean that the energy to create the fire came out of nowhere. The energy came from chemical reactions in the wood and air: we are converting energy from chemical bonds into heat.

So if a sorcerer creates a fireball, where does the energy come from? If the answer is "from nowhere, it just happens", that's pretty much the definition of magic, things happen without regard to the laws of physics. If we suppose that magic is bound by such laws, you'd have to propose a source for the energy and a mechanism for its conversion from one form to another.

Sure, you could say that there's some mechanism that sucks heat out of the air to produce the fireball, and so flinging a fireball leaves a trail of frost or snow behind it.

You could suppose that the energy comes from the sorcerer's body, so that he is weaker by an amount of energy equal to that of the fireball. Hmm, if we assume that the sorcerer eats 2000 calories worth of food before throwing the fireball, then he could create a fireball with 2000 calories of energy. Let's see, I think that's enough heat to boil 25 kilograms of water, or about 6 1/2 gallons, assuming it started at room temperature. I don't know how much heat it takes to kill someone, though I guess that would be enough. It's surely enough eat to set a grass hut on fire, but not enough to blow up a stone building. Of course before he could throw another fireball he would have to eat another 2000 calories.

You could postulate that there is some great pool of energy available to magic users, not accessible or even visible to people without their special skills or inborn abilities or whatever. I think Larry Niven once wrote a story called "When the Magic Goes Away" or something like that, where he postulated this form of energy called "mana" that magic-users drew on, and that was a non-renewable energy source. So as magicians of ancient times did their tricks, the mana was all used up, and today there is none left, and that's why there are no sorcerers or wizards any more.

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  • $\begingroup$ That's assuming that magic uses chemical energy like the body does. If it used nuclear energy you could get a lot of energy that way. $\endgroup$ – Oldcat Aug 3 '15 at 21:44
  • $\begingroup$ @Oldcat Sure. I guess you could suppose that when he throws a fireball, he picks up a rock and throws the rock, and somehow converts some of the nuclear energy in the matter in the rock to kinetic energy and heat. I'd have lots of questions about just how that would work, but then I'd have questions about how he'd convert body energy into a fireball. $\endgroup$ – Jay Aug 4 '15 at 4:05

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