What's the smallest change to physics required to allow magic?

Question

Yesterday my 7-year-old daughter asked me:

Why can't I do magic for real?

I answered: because of the law of conservation of energy! And I briefly explained this law.

Thus she grumbled, "a single law stole so much from us!"

This made me wonder about an alternate universe where magic is allowed by physics. What's the minimum set of changes that our local laws of physics would require?

edit:

By "magic", my daughter means any way to obtain a result without any effort. For example, she would like to cook an egg by magic, or clean up the room by magic, or transform a stone into a car by magic, and so on.

This is why the conservation of energy looked like the most obvious answer: if you find a way to violate that principle in a controlled manner, you can create energy out of nothing and destroy it in a closed system. Then it's just a matter of imagination, and you can create techniques and tools to do anything without any effort (except imagination, but imagination is not a form of physical energy).

Answer 1

Tl/Dr: the smallest change isn't one to the laws of physics. It's a small change to the definition of magic.

This is a favorite topic for me. I could talk for hours about it. Not kidding. Find me in chat if you want. There's more magic in the world than we often think!

Let's start off slow, with the straight forward physics part of the question.

Why I cannot do magic for real?

I answered: because of law of conservation of energy! And I briefly explained this law.

Thus she grumbled "a single law stole us so much!"

Let's take this one apart. Few people know this, but conservation of energy is actually dug far deeper into the fundamentals of science than it appears. Emmy Noether, in 1915, proved what is now called Noether's Theorem. This theorem is so profound that not only is it considered the single greatest addition to mathematical physics by a woman, but may consider it to be the greatest addition to mathematical physics period. Her theorem focused on Lagrangian mechanics, which are systems that are path invariant. For example, it doesn't matter if I roll a rock up a hill, or if I simply lift it up and put it there: the potential energy in the rock is identical in each case. Virtually all of modern physics is developed under this assumption. She proved that, if there is a symmetry in the system, there must be a corresponding conserved value, because that conservation law will fall right out of the equations. Thus:

• If you have time invariance (the laws of physics do not change over time), you must have a conservation of energy law.
• If you have a translational invariance (the laws of physics are the same everywhere), you must have a conservation of momentum law.
• If you have a rotational invariance (the laws of physics are the same no matter which way you face), you must have a conservation of angular momentum law.

So, by this rule, not only would you have to remove the conservation of energy, but you would have to remove the time invariance of the laws of physics. To have "magic" violate the conservation of energy, we need the rules of physics to change every time we cast a spell. Woof!

Or do we? Noether's theorem works for Lagrangian systems. It doesn't work for other systems, such as those where the path you take matters. What if the path we take does matter? What if the road less traveled really does make all the difference? Suddenly we find ourselves in a different environment, where we didn't even need to change the laws of physics to permit magic, just our preconceptions.

The challenge with "magic" is that much of what we read in fantasy is so, well, fantastical that we develop a definition of magic that is roughly translated as: "magic is the ability to do things you can't do in real life." This is my least favorite definition, and I love encouraging people to shift to another one. This one is a dead end. It always leads to thoughts that start out with "If only I could... but I can't."

I prefer the definitions which push at the possible. In this technological world, it's impossible to provide an answer to this question without quoting Arthur C. Clarke's "Any sufficiently advanced technology is indistinguishable from magic." It's such an over-used trope that we often wave our hand and say "yadda yadda, we've heard this before." However, I'd like to draw attention to one little word in that sentence: "indistinguishable." Okay, fine, it's a big word. Six syllables. His definition of magic doesn't include anything about what the magician is doing. It's about what the audience observes. He points out that, while we often like to separate things into nice easy piles using the law of the excluded middle, such as "magic" and "not magic," it turns out that for some things, it is frustratingly hard to categorize things this way. You really end up needing a third category: "magic," "not magic," and "hmm... maybe magic."

I find this third category to be the key to a belief in magic. Let's take the case of Penn and Teller. You've almost certainly heard their names, as two of the most respected illusionists in the magic industry. They've been at it for 45 years, and have seen it all. In fact, they've seen too much. For a few seasons, they hosted a show "Penn and Teller: Fool Us," with the basic premise of inviting lesser known magicians up onto their stage to do magic for them. The goal is for the magician to "fool" Penn and Teller so that they can't tell how it was done.

What's fascinating about this is the monologue they give to the audience before the show (and by "they" I mean Penn, of course). He explains that, after 45 years of magic, they've seen it all. They know how all the tricks work. And somewhere, along the way, the magic went away for them, and all that was left was the tricks. So while, obviously, the goal of such a show is to make money, like any show, the private goal for them is to come across just one act which fools them so thoroughly that they, for a moment, get to feel the same mirthful feeling of wonder, bubbling up from their gut, that they got from seeing magic when they were five years old. (And, every now and then, they actually got their wish. Warning for you and your 7 year old, video does contain curse words, but watching Penn's face just might be worth it).

As you start exploring these things which are indistinguishable from magic, you realize that they show up all over in the our culture. There's something magical about watching the sun rise. It doesn't seem to quite matter that I know it's caused by a $(7.2921150 \pm 0.0000001) ×10^{−5} \text{(rad/s)}$ rotation of the earth with respect to the inertial frame, and Rayleigh and Mie scattering of photons off of the atmosphere. There's something there which isn't quite captured in the scientific jargon, and is different every day, and yet the same. We see it in live music. We see it in the poet's fascination with love.

I have a young daughter myself. I was there when she was born. I know the biochemistry. I can explain exactly what happens for the first three divisions of the egg after conception (which is the first point where the male DNA is fully expressed. Some scientists consider that to be the moment where it becomes another human being). I can explain exactly which hormones the baby had to emit into my wife's bloodstream to convince her Uterus to let it stick around just a little while longer. I know of that, between stage 28 and 31 of the embryo's eye, it begins a "testing pattern" of sorts, a pattern we literally only see once in our life and never see again, which is responsible for helping sort out the mapping from the optic nerve to the visual cortex. I can tell you that she, as newborn, had roughly 26 billion cells, expelled from my wife's body under the influence of some of the most powerful drugs our body has ever developed.

And you know what? Despite all of that, I'll be damned if I'm to distinguish those 26 billion cells from anything but a miracle. Damned I say. When I watch her stare in marvel at a Gestalt pattern, trying to make sense of what she sees, she's not the only one staring in marvel. I watch her eye darting back and forth, and truly have to question "How could this ever be treated as nothing more than a squishy bag of cells?"

To me, that's the state where magic occurs. Not when you know something is impossible, but when you're not entirely sure. Is the old lady with a Tarot deck simply reading my biophysical tells and telling me what I want to hear in exchange for my money, or does she really know something that I don't?

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By "magic" my daughter means any way to obtain a result without any effort. For example, she would like to cook an egg by magic, or clean up the room by magic, or transform a stone into a car by magic and so on.

"Without any effort" is a hard definition of magic. Many fantasy novels have spells which take a great deal of effort. At the very least, you have to say some words or wave a wand. What does "effort" mean? It takes 10.8 calories per hour to run the human brain, and its hard to say if it burns any more doing heavy thinking. A child at play burns about 400 calories per hour. Ask your daughter which takes more effort: playing on the playground, or math homework.

Some things take very little effort at all, because what we wanted was almost already there. We just had to coax it into being. If there is already an egg, suspended on a string over a pot of boiling water, cooking an egg with a magic wand could take as little effort as waving the wand in a manner which breaks the string, and lets the egg settle into the boiling water. In fact, if she can do this messily enough, there's a good chance a parent will rescue her (and the kitchen), and finish cooking the egg for her! How's that for little effort?

The key to such a sense of magic is sensitivity. Sensitivity to everything in the environment around you. If you'll notice, magicians in the fairy tale books often wont cast a spell unless the time is right for it. I certainly wont be casting my egg-cooking spell unless I notice someone has already decided to suspend the egg over a pot. I'm not going to do a "pull a quarter out from behind your ear" trick unless I'm confident I can palm the quarter there in the first place.

Is it magic? Well, I know the trick, so it's just an illusion to me. However, if I do that to my daughter, and she smiles, that's magical to me! So if I can do an illusion that she thinks is magic, and she can distort her face into a smile, and I think its magic, how badly do we want to draw the lines between the events. Can we just say "Me producing a quarter from her ear causing her to smile" is actually magic? Am I really forced to put a line between those two parts, and make the magic go away?

Where does this all lead? Anywhere you want, really, but I do think one of the most amazing places it leads is into exploring what your body can actually do. It is so much more capable than we think, and its full of magic. For example, you eat food. You can look around with your eyes, process the scene, identify something which contains calories and nutrition, break it up mechanically with your mouth and chemically with your stomach, and extract value with your intestines. Everything I just mentioned is in the upper torso. As far your legs are concerned, the fact that they get calories and nutrients in the blood stream is, well, magical.

Now let's put your legs in a position to be magical. Jump (from a reasonably high height) and land on the ground. One of the first real warnings you get that you hit the ground is a strain in the patellar tendon from being stretched by the lower leg reacting to the ground while the upper leg and rest of body continue downward. Sensory nerve signals travel at 80-120mph. That's about a 80ms round trip from the leg, to the brain, and back, ignoring processing time. If you had to take effort to resolve this situation, you wouldn't have time to innervate your leg muscles fast enough to catch yourself. In reality, with processing time, the numbers look closer to 200 or 300ms.

Instead, the signal takes two paths. One path notifies your brain that something's amiss. The other path goes up your leg, to a ganglia at the bottom of your spinal column. There' it has a monosynaptic link to quadriceps. A monosynaptic link is one where a sensory neuron connects directly to a motor neuron, without any interneurons between to do processing. It's the single fastest link possible in the human nervous system. That link innervates your quadriceps as fast as they possibly can, to catch you. In fact, they are contracting before you are even aware that you hit the ground:

This is known as the Patellar Reflex, and its what the doctor tests when they bump your knee and your leg twitches:

This reflex is a reflex of proprioception which helps maintain posture and balance, allowing to keep one's balance with little effort or conscious thought.

Without even thinking about it, your legs catch you, three to four times faster than you could catch yourself if you expended "effort." Without them "thinking" about it, they are provided with the nutrients and energy needed to make that trick possible. By the way, while the patellar reflex is the best known of these, many other tendons exhibit a similar reflex, such as the ankle and elbow. Every one of these does something you couldn't do with effort if you tried.

Do I really have to say that's not "magic?"

Answer 2

The problem is mostly one of semantics. You can't "do magic for real", because all of the things that you can do for real you consider to not be magic.

You can have a conversation with a person on the other side of the world, and if you drop enough money on it you can have dinner with them tomorrow. But those things don't count as "magic", despite being utterly impossible 100 years ago, because we can now do them for real.

Magic needn't always violate conservation of energy. So far as the laws of physics are concerned, the energy required to read someone's mind (either for general-purpose telepathy or to work out what card they picked) could be very small indeed, well below what the human metabolism can provide. Producing a rabbit "from nowhere" would require an immense amount of energy, but producing a rabbit from somewhere is a problem of transportation.

So in some sense, the minimum change to the currently-understood laws of physics to allow magic is absolutely any change, or even none at all. Whenever we discover something new, or even just invent a new way of arranging ideas we already knew, then something that formerly was as far as we knew "magic" is now "for real".

And that's without even getting into the beliefs of those who genuinely think that current scientific theories are fundamentally overlooking certain phenomena that reasonably can be called "magic", or that the definition of "magic" should include things that current science acknowledges do happen for real.

Most magic, though, is "things we wish were possible but believe are not". If by "do magic" you mean the power to do anything you wish, as opposed to just doing a few new things, then nothing we'd recognise as similar to the laws of physics will allow that. The reason is that laws of physics describe what must happen in a given situation (or at any rate what will very probably happen), and one can always wish that what actually happens is different from what the laws predict will happen.

Answer 3

I'd say it entirely depends on what magic means to you.

Something that follows no discernible rules

Example: magic granted by supernatural/godly/other-dimensional beings, who might grant a wish or not, in the way you imagined or not. The beings can't be studied or reasoned with; they act entirely randomly.

Well, if you can't study magic in a scientific way because it is unpredictable due to its inherent features, then you might just as well throw all science out of the window. If you know what something behaves like without magic, but cannot tell when magic is influencing it and in which way it influences it, then you might just as well know nothing about it. If magic only happens very rarely, you can stick to all your normal science and just chalk up any deviations to magic.

Why can't you do magic for real in this case? Well, you've got no way of knowing where such godly/otherwoldly beings are, and how to convince them to do magic for you. You might just need to try harder and have more luck than winning the lottery 10 times in a row.

Reproduceable magic whose effects violate current laws of physics

If you can measure magic and its influence scientifically, and the results go against what your non-magic science predicts -- well then it's pretty much time to add something to your non-magic science.

• some kind of elementary force joining your 4 forces (electricity, gravity, weak and strong nuclear force). Once you learn the rules of this new force, add it into current theory, everything becomes predictable again because you won't be violating the new laws anymore
• set up a new theory for an n-dimensional space instead of our regular 3D+time space. Properties of those invisible dimensions might result in things that might seem like magic to us, but are entirely explainable. Example: imagine not knowing that the earth is round. You think the earth is a flat plane, and you want to discover where this plane ends. You walk in a straight line for ages, sail the seas in a straight line, walk some more -- just to realize that by some inexplicable magic you eventually arrived again where you started out. You must have encountered a fearful daemon to have your way deviated back to your beginning, indeed!
• It might even require trying to quantify something like 'soul', 'will', 'determination', etc.

Whichever it is -- you will need to add something to current physics to get to a once again comprehensive physical world model. (this one interpretation of the famous Arthur C.Clarke quote of "Sufficiently advanced technology might seem like magic")

Why you can't do magic for real in this case? Well, do you know what it is you are supposed to be doing, i.e. what the magic looks like? And, would it still be magic if it's just a strange part of science we haven't discovered yet?

New applications for current physical laws

The primary interpretation of Arthur C.Clarke's quote "Sufficiently advanced technology is magic". Imagine Thomas Edison, who invented the light bulb. Yes, he knew what electricity was, what a phone was, and I'm pretty sure he also knew about wireless transmission. Would he think the abilities of an old-fashioned mobile phone magical? Perhaps. A smartphone? I sure bet he would. And that's only what we've done with science in the last 150 years.

All in all, you must never forget -- science is not set in stone. First comes the theory to explain observations (all apples I have ever seen fall downward). Eventually, if the theory has been sufficiently verified (not only I have seen apples fall downward, but my family too and my neighbors and my professors and people on the other side of the globe), it becomes a law (all apples fall down and not up). And only then can it be used to predict things that haven't happened yet (when I let go of the apple in my hand, it will fall downward).

However, the first time an apple floats upward, it requires a really hard look at current laws and the circumstances under which the apple fell upwards (I was hanging upside-down from a tree -- in my perspective, the apple went from my toes to my head instead of the other way round).

So, there is plenty of ways of finding 'magic' even within our current physical laws :). And of course, you can do 'magic' by studying science and trying to come up with new, revolutionary ways of using it!

Answer 4

You might point out to her that she already does magic.

Tell her to turn on a light. Can she explain how she did that? Have her turn on the TV, and explain to you how she can bring up images of people (even dead people, if she likes reruns) who talk to her. Get a copy of Dragon speech recognition software and install it on your computer, then ask her how something can respond to her voice. At seven, she's probably too young to have experience firing a gun

but she's surely familiar with the idea. Ask her how pulling a trigger is different from throwing a lightning bolt.

The answer, of course, is that she's used to doing everyday things, and doesn't think about them, but the things she can't do are magic. It's like with artificial intelligence: "If we know how to make a computer do it, it's not AI." As Paul Simon put it, "These are the days of miracle and wonder".

Magic, in general, has effects without physical causes. Depending on what stories you read, it is either accomplished by calling on supernatural beings or simply by the exercise of will, just as we move our fingers simply by wanting to. Wishing makes it so. Trying to tell a seven-year-old that this just doesn't seem to work outside of stories is a pretty hard sell - children fundamentally believe in magic.

As for your literal question, the answer is that no set of changes in physics will allow magic to work. Conservation laws simply don't count, since you can simply assert that any unaccounted-for energy required is provided by magical transmutation, including fusion. (Because it's magical, there are no radiation side effects.)

The big problem with making magic scientifically usable is that it destroys science. That is, no experiment can be trusted: its outcome may be altered by magical means. With no experiments which can be trusted, the cornerstone of scientific endeavor, Poppert's falsifiability, becomes impossible.

Answer 5

None

Magic is possible, as soon as we find a way to tab into a source of unlimited energy.

The point is that just because we didn't discover that source yet, does not mean it does not exist.

But, after you found it, this will happen:

Any sufficiently analyzed magic is indistinguishable from science.

(Agatha Heterodyne)

Of course, to get the "make a wish -> see it happen" kind of magic to work, you "just" have to make cause and effect stop working at the place you are at and wait for the random chaos to be in the shape you want it to.

Answer 6

Everything, or nothing.

You've noted the law of conservation of energy. Well, this isn't the only reason. Suppose you want to conjure up matter as your magic trick. The law of conservation of mass applies, obviously, unless you're taking it from somewhere else, which would violate the universal speed limit.

But there's more to it. Something has to happen to the air that used to be in the space your conjured object now occupies. Conservation of mass applies, after all. This has to happen before the new object can occupy this space. Why would it? You'll need to make alterations to fluid dynamics.

The short of it is, if you're going to change physics, you have to change it all because it's all so related. Maybe I've decided I want kinetic energy to be $K = mv$ instead of $K = \frac{1}{2}mv^2$. Well, $W = \int F \cdot dx = m \int a \cdot dx$. Now we're talking about the basic $F = ma$ formula that physics is built on. If you're gonna change that, the whole universe is now entirely different.

But on the other hand, maybe there's a way you can make all this stuff work without actually changing any laws of physics. Though if so, stop talking about it on worldbuilding.se and go patent the ever-loving crap out of it.

Answer 7

This made me wonder of an alternative universe where magic is allowed by physics. What's the minimum set of changes that our local physics laws would require?

The laws of physics require that if magic exists then they don't. The minimum change to physics that would allow real magic is the nonexistence of physics. All science depends on the expectation that the universe operates by regular cause and effect. If the laws of physics are no longer laws, just guidelines, then the ground is cut from under the feet of the whole idea of physics.

That is not to say that our understanding of the laws is necessarily complete. Perhaps someone could cause things to happen by willing them in some manner that is functionally equivalent to magic but actually is within the wider laws of physics, if we but knew them.

That is not to say that the physical constants such as the speed of light, or rules like the conservation of mass-energy, that we think of as applying everywhere necessarily do. That is not to say that what we think of as "the universe" actually is all of the universe.

That is not to say that there cannot be a God who created the physical universe and its laws, or intervenes therein.

That said, if anyone can think of some nifty physics workarounds to explain apparently magical doings, don't be shy, because it would really help with the story I'm stuck on.

Answer 8

Well, technically speaking, there's nothing wrong with our world. Magic and miracles are just manifestations of power which humans aren't able to do.
But in itself, magic isn't opposed to science. It's just too difficult for us humans (well, some kinds of magic are illogical, but that's not the point here).

The changes required are for us to be more powerful. As for how much more, it all depends on what you want to do. For exemple, invisibility would be possible if we naturally did these kinds of things which already aren't fiction anymore. (tell me if you have a better link)

So it is more about us than about the world we live in.

Answer 9

Since most magic as described violates various conservation laws, or the laws of thermodynamics, it is by definition impossible.

However, since we want to go from impossible to at least improbable the best thing to do is look at quantum mechanics and see how to change probability.

We "know" that Space-Time is a seething flux of energies and matter, with particle-antiparticle virtual pairs appearing and disappearing all the time at the Planck scale(no one has actually "seen" this, but we can infer this from effects in the visible universe, and it allows us to make mathematical calculations to describe what is happening). While we really don't understand this very well (the supposed energy in a volume the size of a coffee cup could theoretically boil the oceans of Earth, yet there are no visible effects due to gravitational lensing on the scale of the Universe), gaining the ability to tap into this source of energy, or dump energy back into this as some sort of heat sink would allow you to do serious magical activity without violating thermodynamic laws (you are simply transferring energy and matter to and from a vastly larger pool, and using different timescales to manifest the effects).

Quantum mechanics also postulates that things and effects are due to the "collapse" of wave functions due to the activities of an observer. The Schrödinger's cat thought experiment is a good example of how this effect is supposed to work

Getting a rabbit out of a hat then becomes a matter of arranging for an observer to collapse a wave function where a rabbit is already in the hat. Since the probability of a particular rabbit being in a particular hat at a particular time is a known function (or at least calculable in principle), then a sufficiently trained observer should theoretically be able to "find" the probability of a rabbit being in the hat, reach in and grab the rabbit out of the infinite possibilities of rabbits/not rabbits/ alligators/ other things being or not being in the hat. Obviously this will require a lot of care and attention.....

Of course the less "probable" the effect you want (walking through a wall, for example) the more difficult it will be to do. This degree of difficulty, coupled with the amount of computational power and focus needed to "find" and "observe" the magical effect desired explains why magic traditionally has been in the realm of the gods and a very select body of wizards. (Read Lord of the Rings or Le Mort d'Arthur very carefully to see just how little actual "magic" Gandalf or Merlyn do. Remember in LOTR, Gandalf is actually the equivalent of an angelic being to keep it in context).

I find blowing smoke rings far easier and more relaxing....

Answer 10

The smallest change to the expression of the laws of physics that allows magic would be something along the lines of "The laws of physics are <real laws of physics>, except that, when I say 'abracadabra' whatever I say next will happen."

Answer 11

imagination is not a form of physical energy

I believe the answer is predicated on dispelling this false assumption. Imagination is a function of the human brain, which uses electrical and chemical signals to produce conscious thought as well as control involuntary processes.

It is well established that the brain uses more energy than any other human organ, accounting for up to 20 percent of the body's total haul. http://www.scientificamerican.com/article/why-does-the-brain-need-s/

So, while it may not be a 1:1 correlation (thinking hard has been found to cause only a minor increase in calories burned as per http://www.scientificamerican.com/article/thinking-hard-calories/ which alludes to the fact that perhaps the most complicated tasks our brains do have nothing to do with conscience thought at all), imagination DOES indeed require energy.

There is nothing that says that physics and magic have to be mutually exclusive, and, in basically all popular fantasy novels and games, magic is something that doesn't just happen and also seems to follow some predefined laws. Fantasy games generally use the concept of some arbitrary energy unit that is consumed when a spell is cast (otherwise the player would simply cast the most devastating spell over and over until the game was over). In LOTR, why didn't Gandalf just transform the opposing army into firewood or rutabagas using a word? In my opinion it would have made a VERY uninteresting book. It seems that even imaginary universes can't exist without laws, because without laws no one would care about them and they would cease to be (being imaginary and all).

Considering the possibility of alternate universes with different physical laws where a being COULD simply make something happen with no expediture of energy, that universe probably ceased to exist because one of these beings thought it should cease to exist (bad case of the "Mondays"). In a universe like ours, that scenario is prevented by the fact that too much energy would be required to convert all the remaining matter in the universe into energy.

If we impart some rules on magic, suddenly it doesn't look so daunting. What is lacking is OUR human ability. We don't need to change laws. We need to evolve. If we could evolve a way to generate an ultra-powerful magnetic field (why not? eels can generate electricity) or lasers (advanced bioluminescense), then why couldn't we channel that ability to convert photons into matter (http://www3.imperial.ac.uk/newsandeventspggrp/imperialcollege/newssummary/news_16-5-2014-15-32-44)? With enough ability, why couldn't we arrange that matter in any way we want? After all, "stuff" is just a bunch of atoms arranged in particular ways. With enough metabolism to back the activity, why couldn't we arrange freely available sunlight into a pizza? That sounds a lot like magic AND science to me. Now, since it wouldn't be a lossless conversion, you couldn't infinitely make pizzas from sunlight and energy gained by eating the pizzas, so you would need an external energy input, but I am pretty sure that the wizards in games and books have external energy sources too (potions, food). It all works out.

And that being said, go back to the electric eel for a second. I believe it meets the definition of magic (produces electricity capable of killing a human via cell vibrations simply by "thinking" about it). We've explained how it works, making it science, but as soon as we explain exactly how ANY magic works, THAT will become science too. Being a magician might be just like being a computer programmer... a skill you learn using your mind and body. The programmer arranges code and types it with his fingers. The magician architects matter structures and arranges them with his hand, or wand, or staff, or whatever.

So, tell your daughter the truth... magic is absolutely possible AND it is real, but has some rules (because without these rules, it wouldn't have the opportunity to exist). The magic we see in movies isn't "real" magic because movies and books have a REALLY bad habit of NOT considering rules (ever watch the cops in most cop shows? They'd all be in jail...). Then head off to the aquarium or science museum and see some in action. Eels turn food into energy into motion back into energy. We turn food and light into electrical and chemical impulses which we interpret as thought, which we then turn into a painting, converting that thought into a physical thing with brush that looks a lot like that instance of light we originally saw reflecting off the object we painted.

We might not be able to turn a rock into a new bicycle (well, we can, but it is a long process involving first extracting the iron and so on), but neither could Gandalf turn Orcs to rutabagas. Therein lies another lesson for a child... even the most powerful and amazing forces follow rules.

Answer 12

Providing that something is "magic" depending on personal background (in example a country-side may look "magic"), if few humans were able to manipulate mind and cause allucinations to someone else, than the person subject to allucinations may as well live a whole life believing to see real magic, so in a certain sense he will "have magic" without even the need to change a physical law.

However, you are asking specifically for a change of a physical law. The fact that we are in practice out of control on nature is basically the "lack of magic". To have magic we need to have control on nature, the simplest thing came to my mind is Entropy, Entropy can only increase:

• If we have a box with air particles randomly travelling inside the box in practice it never happens that the particles will be ALL on the same side of the box.

If people can be in someway able to control phenomenas that actually look random, we can start getting amazing things! (so give the ability to reduce Entropy.. in some way)

In example, air particles could randomly hit a body only from one side, effectively helping making the body levitate in thin air. Of course we are still respecting energy conservation (after a particle hit the body and the body moves, the particle lose energy and get cooler).

We are currently 4 dimensional beings (at least) because we move forward in time and we have a volume, being able to choose a immediate near future where to live (in example the future where all air particles hit a body from below at same time) may make us 4.1 dimensional beings and could explain the ability to influence our surroundings.

In such world the magic would still be limited by other natural laws, and understanding we have of other natural laws gives us more control (we know better immediate futures where we can walk).

A strong mage may know that items have thermal energy, so he can levitate objects that are in void (with the constraint that those objects will become cooler). Freezing someone would be indeed a possible magic in such world.

Of course there will not be any counter magic, every mage simply wins (from his personal point of view), because every mage go in his immediate future. I'm still not sure how that will affect a civilization. There will be a explosion of divergin futures (right now I don't believe our universe would be much "divergin")

Answer 13

I think you need to define 'magic' first.
What would seem magical to a child of 7 might not seem so to a physics professor or an engineer.
If you'd told an educated 17th-century European that he could see someone on the other side of the world this morning, talk to him, hear him, as if he were in the same room - that might indeed seem magical to him. Then to clinch it, tell him he and this other man could have breakfast together in the same room, at the same table, passing food back and forth to each other. That would seem beyond magical. But to your daughter? Ho hum.
So what would she call magical? Probably the ability to be in more than one place at the same time would be the most impressive. Then the ability to know the future in precise detail. Those two are about as magical as you can get.
For the first, you'd need to be able to violate the conservation of matter and energy. For the second, you'd also have to violate the laws of entropy.
When you violate these, you've trampled over the law of cause and effect, and then nothing at all remains of physics.
Which goes to show that if you abandon the smallest part of physics, you lose all of it. I am not saying that we know or understand all of physics, but we have reached a stage where we can say that what we have may be incomplete, but it's an integrated, unified structure with no spare parts to jettison.
So you and your daughter have to accept - it's physics or magic, but not both, and you'd better both hope it's physics.

Answer 14

Let's take the most well-known alternative universe which involves magic: Harry Potter.

What do people in Harry Potter do that we, as Muggles, can't do in the real world?

• We can't channel energy as spells through wands from our bodies
• We can't make potions as described in the universe(but some of them we could, if science advances enough)
• We can't teleport(Apparate) or use Floo Networks or Portkeys.
• We can't make other objects move telekinetically or change their physical characteristics directly(we can through irradiation, but let's leave that out).
• We can't make things out of nothing
• We don't have things that have different sizes from the inside and outside.
• We can't predict the future
• We can't talk to ghosts
• We can't transform into animals
• We can't animate otherwise lifeless objects(such as statues or Inferi).
• We don't have animals that breathe fire or anything similar

Some of these things can be changed by manipulating Nature, some can't. Let's analyse them one by one.

We can't channel energy as spells through wands from our bodies

This can simply be achieved by violating the law of conservation of energy, as you suggest. Then we'll be able to yield infinite energy without any being taken away from the body. We could also make it any form we wanted, leading to different kind of spells(not all, though).

We can't make potions as described in the universe(but some of them we could, if science advances enough)

Well, in our world, medicines are a kind of potion. In that sense, we can make potions, but not most of them, like the Polyjuice Potion. I'm doubtful if some could be made at all, like the potion which makes pictures move, 'cause that's not how pictures work.

We can't teleport(Apparate) or use Floo Networks or Portkeys.

This'll also require the violation of the law of conservation of mass-energy, or the attempted teleportation of a single person will destroy all life on earth, as the only way to really "teleport" is to convert oneself purely to energy and back into being at the destination. We can use some types of Floo networks(faxes and the Internet come to mind), but they're no match for really being able to send people though. Wormholes, if made possible, would also be a type of apparition, as the feeling described in the books could be similar to the one of travelling through a wormhole.

We can't make other objects move telekinetically or change their physical characteristics directly

Here I'm talking about the chess set and Transfiguration. Transfiguration will also require conversion to pure energy and back, or somehow being able to split any element to hydrogen and recombine to needed element. I'm not sure how you'd breathe life into the 'raised' object though.

We can't make things out of nothing

I'm not really sure how this one works, but your theory of the law of conservation of energy should come here too I suppose.

We don't have things that have different sizes from the inside and outside

We'll have to change the law of conservation of space - effectively allowing fitting a 787 Dreamliner jet inside a courier carton.

We can't predict the future

This'd require time travel. Perhaps someday we'll evolve into 4D or 5D beings or something and then this one will come in, but until then, no future predictions for you(reliable ones, at least).

We can't talk to ghosts

A ghost is just a lone soul, without a body. Can't blame Nature here. The concept of a soul is not natural; life is just the effect of thousands of chemical processes happening in sync inside living things - they stop, the soul's gone. So we could make a crude comparison to a radio that's on as alive and one that's off as lifeless. Basically nothing physics can really do here, it's not involved.

We can't transform into animals

This one's similar to the fourth or fifth one. Undefined behavior on recombination.

We can't animate otherwise lifeless objects

We do have a variant of this one already - robots. But they are 'alive' for a reason similar to the seventh one - a series of processes that make it possible. I'm not really sure, but my best guess here would be 'everything about the way living things work will need to change'.

We don't have animals that breathe fire or anything similar

This is similar to the first - we'll need to break the law of conservation of mass-energy. Any animals alive in the world simply can't absorb energy from their surroundings fast enough to project it out at that rate. And living things are carbon-based, which means breathing fire will burn them up from the inside. So I guess life will have to exist as non-carbon based - iron as a candidate, anyone?

So I'll second what some others have said: depends on your definition of magic - but I don't think any single law will be enough - our world is too different and too complicated.

Answer 15

Laws of physic are just an old habit

There are already quite inspiring answers here. I just want to point out something not outlined so far.

We are used to see the laws of physic as stable and everlasting, they have ever been, they will ever be, they will never change. We only believe that. We have no evidence.

When where these laws born? Have they already been before the universe was born? Are they a fixed part of our universe and could never have been different from what they are now? That is implausible.

A least, we already know that our universe is not mechanic, but has an unforseeable base of events in the smallest known parts of matter, not following the used thoughts of cause->impact.

Think of this possibility: As the universe was born in a big bang, there have been no laws of physic. Matter and energy was something completly new, and nothing and no one told them how they should behave. But they happened to be. And they interacted with each other and got used to behave in new ways that never have been defined. As time goes by, this used-to-behave become a habit, this habit established over some X*1.000.000.000 years. These habits are what we see as stable laws with obviously (?) no exception. (Compare this book: Rupert Sheldrake: Morphic Resonance - The Nature of Formative Causation)

You know, habits have their own power, and it is difficult to diverge from them after getting older than xy years. What about the universe? It is quite old, yeah.

You don't need to change the laws of physic. It is enough to persuade the universe to deviate from its habits a bit. Nothing needs to break. It is always possible that something quite improbable happens.

The magician knows how to summon the universe to do something really crazy. Little daughters do crazy things, too, not foreseen by adults.

Answer 16

A magic wand is simply a Star Trek transporter combined with a replicator and miniaturized. Of course, voice activation/recognition is simple for a race this advanced. When not speaking the wand uses telepathy to communicate with the wizard - of course most wizards need to sync their brain waves with the wand, which is why Harry Potter and the rest had so much trouble using it. It took years of practice and schooling.

The wand does not violate any sort of physical rules, as it absorbs matter from the air, ground, or whatever is handy and converts it to energy and back again. You probably couldn't re-animate anyone, but even today using CPR we can revive someone who has been dead a few minutes.

By replicating nano-bots you could form a swarm of them into any shape and have them move around and do stuff. They could even seem like ghosts, by simply changing their color,arrangement, and density.

Using a proper containment field, it could even store energy/matter in a micro blackhole inside the wand.

Answer 17

By "magic" my daughter means any way to obtain a result without any effort. For example, she would like to cook an egg by magic, or clean up the room by magic, or transform a stone into a car by magic and so on.

The first two are easy. They've been available for millennia. You tell a servant to do it.

Transforming a stone into a car is more difficult. (I suspect the OP added that themselves ;-)

A rich person could order a car and get someone to wait round the corner with it. They then tell the child to close their eyes. Hide the stone and the car appears.

This is why the conservation of energy looked like the most obvious answer: if you find a way to violate that principle in a controlled way, you are able to create energy out of nothing and destroy it in a closed system.

Who says it's a closed system? The planet Earth isn't a closed system. We continually get energy from the sun. Maybe the sun outputs mana, we just haven't detected it yet.

In the far future who knows what's possible? You simply can't specify a local closed system as a counter-argument to magic.

Answer 18

As others have said, it partly depends on what one means by 'magic'. Here's my two cents:

Magic is the capacity for people to make things happen in the world immediately through acts of speech (or gestures, which can be construed as a means of speech ['sign language']). I.e 'wishing makes it so'.

This used to be impossible given known physics, but not anymore - or haven't you heard of Siri? More generally, our continuing expansion of the things we can do with computers and programming (e.g 'the Internet of Things') can - and in my opinion maybe should - be construed as laying the infrastructure for a future in which practical magic actually exists.

Answer 19

Magic is real. The only reason your daughter - or most other people for that matter - can't do it is because some well financed evil wizard and his army of rainbow vampires is draining all the mana from the mabric. Getting only a pixel of the mana that's left takes a lot of meditation, fingerpainting, hugging, a healthy diet, singing and other rituals. Patience and will are both fruit and fuel in this endeavor. It's basically a matter of opening the eye.

Also trippin'...'

Answer 20

The Standard Model of particle physics has different composite theories, such as electrodyamics and chromodynamics (EM and strong nuclear forces, respectively). I recently went to a physics talk where the presenter proposed another composite theory based on combinations of different particles and their interactions. A composite theory could add another "force" depending on how it dictates interactions. A new boson, such as is suggested by the LHC, could provide support for a new, artificial force.

In short, a new force, artificial or otherwise, may be your answer.

Answer 21

Cort Ammon wrote:

If you have time invariance (the laws of physics do not change over time), you must have a conservation of energy law.

OK, posit then that time invariance gets broken -- the laws of physics did change -- the Old Gods woke up, and they're not (for instance) great believers in all that bookkeeping nonsense in Thermodynamics; it cramps their style. And those big, sudden entropy/enthalpy changes look (to the survivors) indistinguishable from magic.

Answer 22

Our laws of physics are just as good as any other, or just as bad as any other for magic

(this answer is unfortunately a response to the many other answers here) There is one simple reason we can't do magic, because if we could do it, it would not be magic. If we lived in a world without the conservation of energy, we would be just as bored as we are now. What makes magic fun in fiction is that the characters do mundane things like say words, and get special effect. In any world used to that set of rules it would not be fun, it would be boring work.

If fact we do not live in a world that conserves energy any more or less than a common magical world. Most magical worlds have power sources, and ours is no different. Our most common power source is the sun. It constantly provides us with new energy external to our system, no different than channeling spirits, or drawing mana is in any magic setting.

We can also imagine people living in a world without electromagnetism thinking about how magical we are to be able to move objects at a distance with magnets, and make lightbulbs glow.

As for doing something without any effort, that is also a logical flaw. No one in fiction uses zero effort. There is always a wave of the hand, a magic word or at least a thought. Are voice operated systems magic? We always need a way to explain intent otherwise the events would just be random and not magical at all. What about magic that does things before you ask? Is Google telling you about traffic without you even asking magic?

So magic and supernatural can only exist in fiction because that is what the words mean.

If we don't have an energy issue any more than any other magic world, and we can give commands to things our world is just as fit as any other for magic. We simply need to push our tech level to achieve the ease of use for whatever your definition of magic is

Answer 23

Without overthinking this the answer is derived simply by definitions of the problem

Reading answers pretty carefully I haven't seen anyone directly go into the definitions of physics or magic for their responses. And so this answer grabs a dictionary and answers the question objectively.

Physics is a science first; science is a philosophy.

Physics is an accepted philosophy about what effects occur with a given cause. I'll refer to Oxford's definition which lumps the sciences (philosophies) into mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.

Diving deeper:

Science here refers only to the natural sciences. While many people including scientists bow down to natural sciences as a surrogate for God and grant it omnipotent power over all things known and knowable, science itself just shrugs and reminds us that it is indeed a box with walls, and some things are very much outside of its box. I.e., (Natural) Science is not just magic with a funny spelling as every science fiction story will tell you.

The box of stuff that natural science can work with is exactly defined. Anything you can observe or have observed that doesn't fit inside this definition, can't even be looked at by anyone practicing the natural sciences. It's outside of the box that science drew for itself. This definition, has been elusive, but has some fundamental commonalities.

WILLIAM T. RICHARDS, PRINCETON UNIVERSITY, NEW JERSEY, 1928

“Almost every man of science since the time of Aristotle has tried his hand at defining his profession, and a continuation Of this practice must without the least hope of originality…. Science is the systematic description of phenomena.”

“Phenomena," with its implication of reproducibility and of common experience, separates the physical sciences alike from the arts, and from some aspects of the psychical. Again, the word "description" patently suggests the necessity of a language for the expression of scientific generalizations; the language employed is conditioned by the nature and degree of development of each branch of science, mathematical statement being, of the common medium of the physical sciences. Finally, the qualifying adjective "systematic" serves to distinguish scientific statement from merely casual, if empirically substantiated, expression of experience.

Therefore, when your question asks to change physics, you are asking for a world where phenomena cannot be systematically described. That is all that is needed to allow observations which would qualify as magic, or, more literally, "supernatural" which exactly means "situated or placed above natural." A supernatural phenomena is, therefore, a phenomena which defies any of the qualifiers of a natural phenomena.

The philosophy that suggest all known and unknown observations do and forever will obey natural laws is a dogmatic religion called scientism. It is irrational. It's premises do not vest in reason or fact, are purely axiomatic assumption about unknowns, and are antithetical to scientific progress. But it has a purpose.

When we approach a phenomenon with the scientific philosophy, there can be no assumption except that the phenomenon can be "systematically described." It is absolutely imperative to observe that this is an ASSUMPTION, and without that assumption, you simply cannot put your observed phenomenon into the natural science box. If you even consider that your observed phenomenon was, for example, the product of a druidic curse; then none of your scientific tools will do you any good. Your problems will manifest everywhere at once, but specifically; you will NEVER be able to reproduce the curse, and therefore you will never be able to use the word "systematically" to describe it. The phenomenon certainly can still be studied, but never with that supernatural assumption. Your assumption MUST be that the phenomenon, no matter how bizarre, is a reproducible, common experience, that can be described mathematically.

The following assumption is untrue about natural science:

if we could do it, it would not be magic

Because of the box William T. Richard and many others have drawn around science, "reproducible" is not the one and only part of the definition. But now that we have a good definition of science, phenomena, and physics, let us explore breaking it by going into definitions of supernatural phenomena, which are all currently allowed by physics.

Miracles

A miracle is very simply any phenomena that can not be reproduced. It is a one-off event that nature can't ever do again under any circumstances.

Physics allows miracles as it currently exists. Miracles are outside of the box of things physics can even look at, because they CAN NOT be reproduced; therefore they CAN NOT be studied. An example of such a phenomenon is the apparition at Fatima, Portugal on October 13, 1917. This event was witnessed by thousands of people, including children, and was extensively documented through photographs, eyewitness accounts, and official church investigations.

The apparition at Fatima is a phenomenon (check), with common experience (check), however it cannot be reproduced, and it can not be systematically described. Therefore, neither physics nor science in general can deny the apparition at Fatima, the phenomenon was also not provable as a natural event. Thus, physics currently does allow apparitions such as those documented around the world by photographs and accounts. Physics will never (and can never) describe this miracle, or any other, because miracles are not in the box. Other miracles that work fine with modern physics include walking on water, parting seas, raising dead, multiplying food, healing blindness or cancer or heart disease, and crumbling city walls with a song. Physics will certainly say that it can't happen again, but it can never declare that a well documented and commonly observed phenomenon didn't happen since it can't reproduce the effect.

Spells

Spells are a very tricky thing to escape the physical box because they claim to be reproducible. That reproducibility puts the phenomenon of a spell they produce squarely inside the box of stuff science can look at. In order to allow spell with the current definition of science, you either have to deny common observation (as we see with the observer effect in quantum mechanics), or you have to deny a systematic description of it (as we see with the spontaneous event called radioactive decay). There is no possible way to describe the phenomenon of an atom of Carbon 14, for example, decaying into a Nitrogen-14 and an electron. We will never have a mathematical description of when that event will happen, because it has no cause. It is by definition, a spontaneous event. Another such spontaneous event is wavefunction collapse of a quantum entangled particle.

So those real-world examples form the basis for allowing a spell: reproducible magic. Physics currently allows such things because we know about the quantum weirdness and radioactive decay, but we can describe them mathematically, so they are still inside the box of science.

In order to take a spell outside the box of science, and put it into the supernatural, you have to remove the mathematical description. In other words, the effect your spell creates has to be reproducible, but not have any mathematical description. This is not terribly hard to do since math relies unequivocally on the equality sign. You can not describe anything with math when the right side and the left side are not equivalent. This is the foundation of all laws of conservation. An example:

Since the question asks for the "minimum change," I will use an atomic-sized violation. Let's assume that when you snap your fingers (and you alone, no one else can do it), that then next time a Carbon-14 atom decays under your microscope, an electron flies off, but the Carbon-14 is still Carbon-14, and not Nitrogen-14. Here you have created a spell which very simply masks the aging of something, so that science will plainly see the beta emissions and count them, and they will THINK that the sample is X years old; but in fact, the carbon is not actually diminishing. You have created electrons from nothing. This little spell would effectively be a fun wizard college prank or cantrip, bacause you are creating something (an electron) from nothing, violating the law of conservation of matter and energy. What this trick could do is hide a stash of barley in an old jar, then ask your friends to enjoy some homebrew beer using your "fresh" barley 1,000 years later (you're a wizard, remember), and tell them with a shocked look on your face when the dusty ancient crumbs pour out that you "just packed that barley last week! What possibly happened? We must get this to the lab!" They will find week-old barley dust, and great fun will ensue in the journals and universities across the globe.

Elixir of Life

Again by breaking the equality sign, you can reverse the processes of entropy operating on your DNA as each cell undergoes mitosis. It requires only a tiny fraction of energy to override the energies which find their way into your DNA while it is unwinding and recombining. This DNA protection scheme is outside the box of physics despite being a repeatable and commonly observable phenomenon, because again it creates a small amount of energy from nothing, defying a mathematical definition. Every cell in your body repeats it so long as the potion is in your bloodstream, but the source of the repairs defy math. Modern science would fail to classify this as "natural" despite its repeatability.

The Elixir of Life does not need any changes in physics to exist, it is already defined outside of science, and so can live harmoniously with the laws of physics as they are. And so long as the elixir itself can not be manufactured, there can be no argument saying "physics is broken." They can't repeat the Elixir; therefore physics is just fine. Physicists will be loosing many nights of sleep, but physics itself has no problem with an inability to put it into the box. It just ignores those things.

The smallest change to physics needed to allow magic

is any arbitrary amount of inequality measured in any commonly observed and repeatable phenomenon. Either something from nothing, or nothing from something.

Answer 24

All the laws of the physics (or, the last of the nature) are eternal: they work always as expected.

However, there are also laws which work only once. That is magic.