# QM and consciousness (short)

There are several common misconceptions about the relationship (if any) between QM and consciousness. Some overstate the weirdness, while others understate it. This piece attempts to rectify some of the confusion for a lay audience, but at a level above the usual pop sci treatment.

At a high level:
- Schrodinger's Cat does not have a definite fate before information from the experiment reaches you. Afterward, it does. Therefore, _you_ are the first point at which it has a fate.
- It is hard to see what "you" can possibly mean here other than *your consciousness*.

We'll also see why the two slit experiment has nothing to do with consciousness.

Some caveats:

- While there are numerous competing interpretations of QM, this piece does not depend on any particular interpretation being true. (It does, however, assume -- like most physicists do -- that closely-related theories like Bohmian Mechanics or objective collapse theories are not true.)
- I am not a physicist, but I did publish [some papers](https://www.researchgate.net/profile/Aditya-Prasad/research) related to quantum information science when I was young.

## Superpositions, interference, and entanglement

Recall the Schrodinger's Cat thought experiment. At first, there is an atom in a superposition of decayed and not-decayed. This causes a vial to release poison (or not), which kills a cat (or does not). At every stage, there are two possibilities in superposition. Yet, when you _see_ the cat, you only ever see one result. When does this one result come into being?

The short answer is that the laws of QM never allow the two branches to become one, but they still require you to treat it _as though_ there is just one after you have seen it. What this means is that right up until the point you "see" the cat, you can theoretically prove that there is still a superposition, but once you see it, there is a definite result.

**Fact 1**: Any time there exists a superposition, there exists something called an *interference experiment* which can demonstrate that the state is indeed in a superposition (versus a _classical_ state, where there exists a definite-albeit-possibly-unknown result).

Next, a poison vial acts as a "detector" for the atom, releasing poison if and only if the atom is decayed. The key thing to understand here is that now the atom and vial are in a *joint superposition*, and as such require a more elaborate interference experiment to prove their superposition.

**Fact 2**: To demonstrate superposition, an interference experiment must involve *all* objects in that superposition. If it includes only _part_ of the system (e.g., just the atom or just the vial), then that part will appear to be *classical*.

In the two slit experiment, the detector at the slits behaves exactly like the vial does here: it "measures" the particle[^entanglement], thereby entering into joint superposition with it. This means that if you perform an interference experiment on only the particle (as the screen does), it will *not* show interference. This brings us to our first misconception.

[^entanglement]: When a particle is in superposition, and different "branches" of that superposition cause another particle to behave differently, the particles are said to be *entangled*. This is all a measurement device *is*: indeed, if it did *not* respond differently to different inputs, it would be a poor "measuring device" indeed.

**Misconception 1**:

> *The electron decided to act differently, as though it was **aware** that it was being watched!!* -- New Age movie [What The Bleep](https://youtu.be/DfPeprQ7oGc?t=4m25s)

This counterintuitive result of the two-slit experiment has nothing to do with consciousness. *Any* physical system that interacts with the particle will produce this result, for reasons that are perfectly well understood today[^interference]. The detector did not actually collapse the wave function -- it just changed it into one where there are two distinct branches, and where the particle _alone_ will not show interference.

Now back to the cat. The poison does (or does not) kill the cat. Just like the vial, the cat has now joined the superposition. It therefore does not have a definite fate. And yet, when you *see* the cat, it will surely be *either* alive or dead. So the question is: when, precisely, does the cat *attain* this definite fate? This is called the so-called *measurement problem.*

## Collapse

One (out of fashion) idea is to say that the superposition must "collapse" somewhere along the way. There are two problems with this explanation. The first is theoretical: such a "collapse" would lose information and go against everything we know about physics[^Susskind]. The second is experimental. As our technology grows to do ever-larger interference experiments, we've seen no signs of any upper bound[^macroscopic].

[^Susskind]: Leonard Susskind, father of string theory, puts it well [here](https://youtu.be/iNgIl-qIklU?t=3m3s):

> The most basic principle of physics is that distinctions never disappear.

This principle is called [unitarity](https://en.wikipedia.org/wiki/Unitarity_(physics)).

[^macroscopic]: We've been testing this at ever-increasing scales. For example, already in [2010](http://physicsworld.com/cws/article/news/2010/mar/18/quantum-effect-spotted-in-a-visible-object), they were able to put *trillions* of particles into superposition. There is no evidence of an upper bound beyond which the superposition "collapses."

## Decoherence

A more modern approach is to invoke something called *decoherence*. Recall that to *demonstrate* a superposition, we need to involve every single particle that has been affected by the experiment -- which in this case will include trillions of air molecules, photons (zipping away at the speed of light), etc. It's effectively impossible to wrangle all of th em.

The upshot is that while there still *exists* an enormous superposition, we have no hope of *demonstrating* or *exploiting* it. Thus, for the purposes of calculation, we are free to treat the cat *as though* it has a definite (even if unknown) state. This fact is called **decoherence**. This brings us to our second myth, this one sometimes promulgated by physicists:

**Misconception 2**:

> *If you simply stick a cat in a box and link its fate to the outcome of some quantum event, you’re not likely to put it in a superposition of alive and dead, because decoherence will almost instantly force it into one state or the other*. -- A physics Ph.D. writing for [Quanta magazine](https://www.quantamagazine.org/real-life-schrodingers-cats-probe-the-boundary-of-the-quantum-world-20180625)

Decoherence absolutely does *not* say that it "forces" the cat into one state or the other. It may look that way for all *practical* purposes, but the theory is very clear that the overall superposition does not simply go away[^decoherence-myth].

[^decoherence-myth]: [The decoherence myth](https://plato.stanford.edu/entries/qm-decoherence/#SolMeaPro):

> Unfortunately, naive claims of the kind that decoherence gives a complete answer to the measurement problem are still somewhat part of the ‘folklore’ of decoherence, and deservedly attract the wrath of physicists (e.g. Pearle 1997) and philosophers (e.g. Bub 1997, Chap. 8) alike.

See also [this answer](https://physics.stackexchange.com/a/374212/118804).

## Many worlds

Another common explanation is to say that actually, if we take QM to its logical conclusion, then when you see the cat, you also join the superposition -- just like any other physical device would. It is as though there exist two "worlds," each with one copy of you seeing one result! This may well be true from the perspective of someone *outside* yourself. But the crucial point here is that you are *not* someone outside yourself! This point is subtle and bears careful explanation.

Once you see the cat, QM compels you to treat it as having a definite fate. Yet *before* such an interaction, everything we know strongly suggests that it *does not have one*. This fact has experimental consequences: beforehand, QM predicts that you can theoretically do an interference experiment to prove that it's in superposition (even though decoherence makes this _practically_ impossible). Afterward, the cat's fate is sealed -- not just for you, but for _everyone_ in your world.

In other words, the cat attains a fate in your world when you, specifically, see it. Sometimes people try to make this seem less strange by pointing out that this would be true for any other physical detector as well: from _its_ point of view, _it_ is where the buck stops. But while this is true, _you_ only ever live in _your_ world -- and in _that_ one, you are indeed "special.""

It seems that Eugene Wigner was correct all those decades ago:

> *This [reduction of the quantum state] takes place whenever the result of an observation enters the consciousness of the observer -- or, to be even more painfully precise, my own consciousness, since I am the only observer, all other people being only subjects of my observations.*
> -- (Nobel laureate) Eugene Wigner, 1967[^Wigner]

[^Wigner]: Note that this differs from his earlier "consciousness causes collapse" interpretation. It's not *consciousness in general*, but *yours in particular*, that seems to cause it -- as far as you can ever know.

This is not quantum woo. This is the result of following the physics -- both theoretical and experimental -- as precisely as possible.

Note, however, that this still leaves some key questions unanswered. In particular, when exactly can we say that you have "seen" the result? If some photons from the cat interact with the unconscious parts of your brain, why shouldn't you be free to treat those parts as "external" detectors?

The truth is there's no good explanation yet. All we know is that when you *experience* a dead cat, you are certainly free to say that it is dead. And it is hard to see what "experience" can mean here other than to be _conscious_ of. There are still all sorts of gotchas: for example, what if you clearly see the cat but are too distracted to _register_ that fact? Surely the experiment is over, even though you wouldn't claim to be "conscious" of it.

At the end of the day, we just don't have a good answer here. But be _very_ skeptical of anyone who claims that consciousness (and in particular, _yours_) has nothing to do with QM. As of yet, we have not been able to separate the two.

> *I think consciousness will remain a mystery. Yes, that's what I tend to believe. I tend to think that the workings of the conscious brain will be elucidated to a large extent. Biologists and perhaps physicists will understand much better how the brain works. But why something that we call consciousness goes with those workings, I think that will remain mysterious. I have a much easier time imagining how we understand the Big Bang than I have imagining how we can understand consciousness.*
> ...
> *I’m not going to attempt to define consciousness, in a way that’s connected with the fact that I don’t believe it will become part of physics. And that has to do, I think, with the mysteries that bother a lot of people about quantum mechanics and its applications to the universe.*
> ...
> *Quantum mechanics kind of has an all-embracing property, that to completely make sense it has to be applied to everything in sight, including ultimately, the observer. But trying to apply quantum mechanics to ourselves makes us extremely uncomfortable. Especially because of our consciousness, which seems to clash with that idea. So we’re left with a disquiet concerning quantum mechanics, and its applications to the universe. And I do not believe that disquiet will go away. If anything, I suspect that it will acquire new dimensions.*
>
> -- Edward Witten, a physicist so overpoweringly brilliant that his fellow string theorists casually throw around terms like ["smarter than anyone else"](http://www.nytimes.com/1987/10/18/magazine/a-theory-of-everything.html?pagewanted=all) and "head and shoulders above the rest."

[^interference]: This note is for readers who have had a first course in quantum information science.

Suppose we start with a spin state $|\psi\rangle = \frac{\sqrt{2}}{2}(|x_+\rangle + |x_-\rangle)$. [Recall that](https://en.wikipedia.org/wiki/Pauli_matrices#Eigenvectors_and_eigenvalues) $\frac{\sqrt{2}}{2}(|x_+\rangle + |x_-\rangle) = |z_+\rangle$. If we measure the *z*-spin, we will therefore always get $|z_+\rangle$. On the other hand, if we had a *classical* mixture of $|x_+\rangle$ and $|x_-\rangle$, then each component would give a 50% chance of $|z_-\rangle$, and so too would the overall mixture.

One can think of this as the two x components "destructively interfering" to cancel out the $|z_-\rangle$ possibility:

$\langle\psi|z_-\rangle$
$= \frac{\sqrt{2}}{2}(\langle x_+|+\langle x_-|) |z_-\rangle$
$= \frac{\sqrt{2}}{2}(\langle x_+|z_-\rangle + \langle x_-|z_-\rangle)$
$= \frac{\sqrt{2}}{2}(1 + -1)$
$= 0$

Now suppose our state becomes entangled with a second particle: $|\psi\rangle = |x_+\rangle|x_+\rangle + |x_-\rangle|x_-\rangle$. If we measure both particles along the z axis, how often will we get $|z_+\rangle|z_-\rangle$?

We can rewrite this state:

$|x_+\rangle|x_+\rangle + |x_-\rangle|x_-\rangle = |z_+\rangle|z_+\rangle + |z_-\rangle|z_-\rangle$

To see that we would **never** get the first particle in $z_+$ and the second in $z_-$. On the other hand, if we had a *classical* mixture of $|x_+\rangle|x_+\rangle$ and $|x_-\rangle|x_-\rangle$, then each case **would** produce a $|z_+\rangle|z_-\rangle$ result (and thus so would the mixture):

1. $|x_+\rangle|x_+\rangle$
$= (|z_+\rangle + |z_-\rangle)\otimes(|z_+\rangle + |z_-\rangle)$
$= |z_+\rangle|z_+\rangle + \boldsymbol{|z_+\rangle|z_-\rangle} + |z_-\rangle|z_+\rangle + |z_-\rangle|z_-\rangle$

2. $|x_-\rangle|x_-\rangle$
$= (|z_+\rangle - |z_-\rangle)\otimes(|z_+\rangle - |z_-\rangle)$
$= |z_+\rangle|z_+\rangle - \boldsymbol{|z_+\rangle|z_-\rangle} - |z_-\rangle|z_+\rangle + |z_-\rangle|z_-\rangle$

Therefore, knowing the results of *both* particles can differentiate the superposition from the classical case. (Also notice the positive sign before the term in case 1 and negative in case 2 -- this is what causes interference for the superposition.)

But what if we look at either particle alone? How often will a single particle end up in $z_-$? Looking at the rewritten state above, we see that each result happens 50% of the time -- which is exactly what we got for the *classical* single-particle case. In other words, each particle by itself does not appear to be in a superposition. To get "interference" effects, you must look at *all* particles together.

For a fuller treatment, read about density matrices and mixed states.