As part of Ra I realised that I needed a character to become invisible. Since this requirement is coming up quite soon I decided to sit down and work out how this cloak of invisibility would work. I ran into some interesting problems. It turns out that becoming invisible is less than half of the problem.

I haven't written any more of Ra yet, so the cloak might not come into the story in the next chapter, or even at all. Even if it does appear, the cloak might not function as described below, and even if that's the case I probably won't spend a huge amount of time laboriously explaining the full mechanism behind it in the story. So, other than the fact that an invisibility cloak might appear in Ra in the future, this article contains no spoilers.

What you should already know

Here are two things that have already been established in the story. The chapter What You Don't Know covers this in detail.

Firstly, there is a special kind of mana called "chi" (the Greek letter Χ) which is given off whenever magic spells are carried out. Chi mana exists only in very small quantities. The universe is almost completely dark in the chi spectrum. Chi mana is also very weakly interacting. It passes through physical matter (including human bodies) with ease. They are most similar to real neutrinos, except that the universe is flooded with neutrinos whereas chi particles are very rare.

Secondly, there are special magic rings called "oracles". An oracle is enchanted so that when a chi particle passes its mouth, it is transmuted into a photon of visible light moving in the same direction. By holding an oracle up and looking through it, you can essentially "see magic". Augmented reality for mages.

A third fact revealed in other chapters (starting in Sufficiently Advanced Technology) is that there exist full-body magic shields. When using one, the wearer is enclosed by a surface set a few centimetres out from his or her skin, which can absorb physical attacks. Naturally, this closed "bubble" contains only a small amount of air, but this is a secondary problem.

Transparency in the visible spectrum

Invisibility cloak #1

Within the rules already described, it's quite easy to conceive of a magic shield ("cloak") whose surface is enchanted to function like an oracle. This would allow you to see magic in whatever direction you looked.

What is also easy to conceive of is an oracle which works in exactly the opposite fashion to a conventional oracle: it converts photons of visible light into invisible chi particles. Looking through such an oracle, you would see only perfect darkness.

Given these two developments, it's easy to devise a cloak of invisibility: Make a shield which operates like an "opposite oracle" on the way in, and like a conventional oracle on the way out.

Watch what happens when a photon of visible light passes through you while wearing this cloak:

The photon of visible light hits the surface of the cloak from the outside. The photon is converted to a chi particle which passes into the cloak interior. The chi particle hits the surface of your skin from the outside and passes into your body, unchanged. The chi particle hits the surface of your skin from the inside and passes out into the cloak interior, still unchanged. The chi particle hits the surface of the cloak from the inside. The chi particle is converted back into a photon of visible light which passes out into reality.

Thus, all the light falling on the cloak is eventually emitted in the same direction from the far side of the cloak, and what a person standing on the far side of you sees is exactly what they would expect to see if both you and the cloak were not there. The cloak and everything inside it is invisible!

Some additional assumptions have to be made here for this to work:

That the different visible wavelengths (colours) of photons can be put into a correspondence to different wavelengths of chi particles, and that this transformation can be reversed. If the chi particles are not of different "wavelengths", they must at least be able to differ from each other along some kind of usable spectrum (which, for the sake of argument, we shall refer to as "wavelengths" from here on). Otherwise, at point S when we receive a random chi particle, we have no way of knowing what colour of photon to turn it back into.

when we receive a random chi particle, we have no way of knowing what colour of photon to turn it back into. That the transformations at the cloak and at your skin occur instantaneously, or at least very quickly. Any kind of delay in propagation results in a curious "delay" effect whenever the "invisibility" cloak is moving. The background image projected forwards will be out of date, making it possible to tell where the cloak is, although it would admittedly be much more difficult to see than you just standing there.

That chi particles in flight move at the speed of light, or at least very quickly, for the same reason.

I'm going to go ahead and dismiss these issues for now because from a storytelling perspective I can just say "yes, this is all the case" quite easily without it being too implausible given what we already "know". There's one other issue which is much harder to crack.

You're blind while you're wearing the cloak! It's pitch black in there!

Visible light cannot enter the cloak from the outside: it is all converted into chi particles. You're invisible, but you also can't see out of the cloak.

This problem arises in other models of fictional invisibility too: for example, if you have your body chemistry somehow altered so that visible light passes through you, or are somehow "shifted out of phase with the universe".

Human vision works like this: a photon falls on your eyeball, your retina absorbs the photon, and a nerve impulse sends the image to your brain. If you can see, then a person standing behind your retina should at the very least notice a dark patch in mid-air where this absorption is taking place. Conversely, if you are invisible, then photons passing through your eyeball must pass through without being absorbed: thus, you cannot see.

Invisibility cloak #2

The solution to this problem is to modify our cloak so that it lets the light through as well as creating chi particles. Let's see what happens now:

The photon of visible light hits the surface of the cloak from the outside. The photon is left unchanged, but a chi particle is also generated. The photon and the chi particle hit the surface of your body - your retina, let's say. The photon is absorbed (and seen) but the chi passes through. The chi particle emerges unchanged from the back of your head. The chi particle hits the surface of the cloak from the inside and is converted back into a photon.

Great: you can see again. But you're not invisible anymore.

Firstly, when the photon hits your body it may be reflected (or re-emitted) instead of being absorbed. When the re-emitted photon arrives back at the cloak surface, it'll escape without a problem. You're now plainly visible again.

Worse, the cloak is a few centimetres thick. It's quite possible for an incoming photon to pass through the cloak and straight out again without passing through the wearer's body. In this case, see what happens:

The photon of visible light hits the surface of the cloak from the outside. The photon is left unchanged, but a chi particle is also generated. Both the photon of visible light and the chi particle hit the surface of the cloak from the inside. The chi particle is converted back into a photon while the original photon is unchanged. There are now two photons.

Your cloak of invisibility now not only leaves you completely visible but wraps your whole person in a few-centimetres-thick glowing shroud of amplified light!

Invisibility cloak #3

Let's make a second modification to our cloak. Make it so that visible light exiting the cloak is suppressed. Now, light rebounding off your brightly-coloured clothing doesn't escape, so you can't be seen. And let's look at the edge of the cloak:

Photon enters the cloak. Becomes a photon + chi particle. Photon and chi particle both exit the cloak. The photon is absorbed. The chi particle is converted to a photon identical to the original.

Great. We're now totally invisible - which is to say that we are transparent in the visible spectrum - but we can also see perfectly!

There's only one small drawback, which is that torches don't work. In fact, philosophically speaking, torches cannot work if you wish to remain invisible. A torchbeam, by definition, gives away your location! Invisibility means that light emitted by you - regardless of source - must not escape the cloak where it can be seen by hunters. A laser sight would have the same problem. Of course, if it's so dark that you need a torch, it's probably also so dark that a cloak of invisibility is of no particular use. So, this would be a good place to stop in most cases.

Transparency in the chi spectrum

Now let's consider a different problem. With cloak #3, you can't be seen if visible light falls on you. But what if there's a chi source nearby?

Chi particle enters the cloak. It passes through unaltered. Chi particle enters your body unaltered. Chi particle exits your body unaltered. Chi particle exits the cloak. It is converted into some sort of visible photon.

Oh, snap! All a hunter needs to do is put a significant chi source behind you (who are normally invisible) and when you walk in front of it you'll light up in brightly visible purple and orange! We need to reconfigure our shield again. But we can't modify the cloak exit transition, because that'll break our transparency in the visible spectrum. We have to do something to the cloak entry transition.

Invisibility cloak #4

Let's change our cloak entry transition so that it destroys incoming chi particles.

Chi particle enters the cloak. It is absorbed. Darkness. Darkness. Nothing exits the cloak.

What we now have is a cloak which is invisible as usual but whose interior is completely dark in the chi spectrum. If you walk in front of a chi source, you'll absorb all of it. The only way the hunter could see you is if the hunter is watching through an oracle of his or her own. Through the oracle, you would show up as a big dark shadow. At least we've made things harder.

Is this the best we can do? Can we be transparent in the entire visible spectrum and the entire chi spectrum simultaneously?

Invisibility cloak #5

Um, yes. But the solution suddenly becomes much less elegant.

The major problem is this:

The spectrum of visible and magical radiation falling on your cloak must be exactly the same as the spectrum of visible and magical radiation that leaves it. All of the information stored in this spectrum has to be retained in transit somehow.

But when visible light hits your skin, it's absorbed. This destroys some of the information.

That means that the information stored in the visible part of the spectrum has to be stored somewhere else in the spectrum while it's in transit through the cloak (and possibly your body), then restored.

The logical place to put this information is in a dedicated section of the chi spectrum.

But that means that the information previously stored in that dedicated section of the chi spectrum is destroyed instead.

Where do we put it? How can we find room?

There are several approaches available here, of differing levels of complexity. Here's one:

Take the entire original spectrum of both visible and magical radiation. Compress the spectrum horizontally so that the whole thing will fit just in the chi wavelengths. Store this compressed spectrum in the chi wavelengths as you'd expect, BUT also retain all of the original visible light information in the visible part of the spectrum. Notice how the new spectrum has two copies of the original visible light information. The new spectrum hits your body, and much of the visible part of the spectrum is absorbed (i.e. you can see it). No matter: we have a copy of this information encoded into the chi part. When the radiation exits the cloak, reverse this transformation. First, discard all the visible light, whether it's a photon that passed through unaltered, a photon emitted from a torch or simple darkness. Next, take the chi part of the spectrum and expand it to cover both the chi and visible parts of the spectrum as before.

The above solution assumes - dubiously - that there is infinite granularity in the range of possible chi wavelengths (or, if not, that the two transformations don't result in a noticeable loss of fidelity).

Another solution would involve no "compression" in the spectral information, but just moving all the wavelengths "up by one" so that they are no longer visible. This in turn requires that there are infinitely many available chi wavelengths, such that this wavelength shift can be carried out for incoming information of any wavelength.

Both of these alternatives require us to introduce some further assumptions about the nature of magic. As a writer of fiction, I'm able to wave my hands around as much as I like to justify these assumptions, but I'm sure you'd agree that there's a distinct loss of elegance the more I do this.

These solutions can be broadened to accommodate more forms of incoming radiation, with a commensurate increase in technological difficulty because of the extra compression required. For example, it would probably be desirable to be invisible in infrared as well.

Invisibility cloak #6

These solutions become more troublesome if we add more requirements. We've already established that, while wearing the cloak, you want to be able to see in the visible spectrum. What if you want to be able to see in the chi spectrum as well (i.e. by using a conventional oracle under the cloak, in the form of a monocle or similar)? Suddenly you have a requirement to let the chi spectrum through unaltered as well. It would presumably be possible to use a more advanced transformation to let a narrow band of chi mana through unaltered while storing all of the necessary information in side-bands. But if you want to be able to see the whole chi spectrum, you've run out of places to store this information.

Essentially, the problem becomes one of out-of-band signalling. You have a requirement to be able to observe and therefore absorb the entire spectrum of information falling on your cloak. But you also need to store all of that information unmodified somewhere so that it can be rebroadcast on the other side of your cloak. This means that you have to pick some sort of out-of-band signal to use: not chi particles, not visible light. One option might be radio, but now you're in a situation where any passing radio broadcast causes you to shine like a light, just like the chi source did! Another option is conventional electronic circuits. But in that situation you've not only sacrificed your lightweight magical shield for a physical object which you have to carry, you've also basically built real, fully non-magical thermoptic camouflage, making no use of the convenient chi phenomenon at all!

We can do better. The last solution is to add your selective "oracle" capability to the invisibility shield itself. This means that all the information you desire is crammed into the visible spectrum in some form at cloak entry, then safely discarded at cloak exit.

Conclusions

If you already have the literally magical technology that is necessary to become invisible, you are still going to have a hard time getting practical use out of it, because you have to be able to see.

I now have a reasonable idea of the level of skill and intelligence which is necessary for a fictional character to be able to construct each of these cloaks. For example, I know that none of them are completely impossible, which is something of a relief.

I eventually decided not to put any of the mathematics into this article because mathematically the major problem is just working out exactly what mathematical objects to use to represent the various things. I eventually decided that an incoming spectrum would probably be a function f mapping wavelengths λ to intensities, and that the spectrum would undergo some sort of transformation e.g. P , Q , R , S , T upon passing through the cloak in each direction and upon passing into and out of the human body and on being reflected. After that, the rest was actually quite boring, consisting of observations like "For transparency, we must have S ( P ( f )) = f for all f " and "If we want to be able to see, we must have P ( f ) = f " and so on. None of this actually helped me in my work very much.

This is also a classic example of a science fiction invented thing - in my case, magic - which, when taken all the way to its logical conclusion, quickly results in phenomena which are too complicated to be palatably explained to readers or used meaningfully in storytelling. I have the same problem with many other things, usually time travel. The writer has a duty to overthink things.

Once again, I can't guarantee which (if any) of the described magical cloak technologies will appear in future installments of Ra. Still, I hope this has been a vaguely interesting look at how I work.