Preface

Quantum Mechanics is weird, but most people don’t appreciate exactly why it’s weird or just how weird it is. Those with a New Age bent seem to think that electrons must be conscious to explain the two slit experiment[12]. At the other extreme, many physicists seem to be of the opinion that consciousness has nothing whatsoever to do with QM. The truth is somewhere in the middle. To understand it precisely, some math is needed. Math footnotes are given at the end, but in this piece we try to communicate the essential point in words.

Caveat

I am not a physicist, but a software engineer who has some training in quantum information science. I am far from being an expert, but I can tell you a bit about density operators on Hilbert space (which is about all the math you’d need to work this all out yourself). Everything I say in the main section here is, to the best of my knowledge, accurate and reasonably well-accepted[9]. There are mathematical footnotes if you feel like going deeper.

As this piece is part of a series on metaphysical idealism, I will make some interpretations that may be hard to swallow. That section is indicated as speculation.

---

In a “Schrödinger’s Cat”-style experiment, there is a radioactive particle that does or does not decay. Both possibilities exist together in a superposition; neither is yet definite. The particle triggers (or does not) a device, which then kills (or does not) a cat. Now the particle, device, and cat are together in a superposition. As more pieces of the world (including people) encounter the system, they too join the superposition. You can think of the experiment as having two “branches,” corresponding to the two possible outcomes.

But we never see a world with two “branches”; we only ever see one result or the other. So what’s going on? Maybe the two branches “collapsed” into one somewhere?

When the experiment is still at the single or few-particle stage, it is easy to demonstrate the superposition, via an interference experiment. That’s how we know that small systems can be in superpositions. But doing so requires that we can precisely track every particle in the experiment. We’ve been able to do this with up to trillions of particles, and have no reason to believe that there is a fundamental upper limit.

As the experiment grows to entangle with many more objects (including air molecules and stray photons bouncing away at the speed of light), such control quickly becomes impossible in practice – a fact known as decoherence. This accounts for the loss of interference pattern in the well-known two slit experiment, which is not as “spooky” as some would have you believe[12].

Because of decoherence, it is practically impossible to demonstrate that a macroscopic system is in a superposition, but crucially, as far as we know, it never becomes impossible in theory[0][1] because a growing superposition continues to exist. So you cannot say that the cat has a well-defined fate, because the right experiment would give lie to that claim. Both branches still exist, even if you don’t have the technology to make them interfere.

Yet when you encounter the system[2], you never see a superposition – whatever that would mean. You always see one result or the other; the cat does have a single well-defined fate. This is the first point at which the theory predicts that you cannot do an interference experiment even in theory; when there is no longer a superposition from your perspective. You are the point at which the cat’s fate becomes definite in the place you call “the world.”

This is also the first time it has a well-defined history: one second ago, you couldn’t say “the cat is dead,” but now you can say “one second ago, the cat was dead”[3]. To put that in slightly different wording: one second ago the cat wasn’t dead, but now, it was dead.

This isn’t just a matter of interpretation, either; it has physical consequences. At this point it is impossible even in theory for you – or anyone else – to demonstrate superposition[4]. Again, this happens precisely when you encounter it. And what do we mean by “you” here? If your toe “sees” the result (and the signal hasn’t traveled up your leg), you can treat your toe as an external device just like any other. It just joins the superposition. And yet, once the signal reaches “you,” the story changes.

Why doesn’t this weird everyone out[5]? Because there are a few places it is easy to hide the weirdness.

First, because of decoherence, it’s easy to pretend that the superposition disappeared early on, long before it got to you[11]. Even once you accept that decoherence doesn’t solve it[6], it’s easy to say “well something must have ended the superposition somehow, somewhere, somewhen, because otherwise WTF.” In fact, this is roughly called the Copenhagen Interpretation, and it has been the party line for over a century, despite nobody having a clear definition of it[7].

Second, if we look at this from a “God’s-eye perspective,” then all that really happened was that you joined the superposition. Both branches still exist, with one “copy” of you seeing each result. You may see a dead cat, but a copy of you elsewhere in the multiverse sees a live cat. This is basically the Many Worlds Interpretation. But while God may not find any of this strange, it doesn’t make the situation any less weird for you.

From your perspective, you seem to be the sole “observer.” In an interesting (and physically meaningful) sense, this world is your world[8].

---

Some speculation

Everything I’ve said above is, to the best of my knowledge, accurate and reasonably well-accepted[9]. Now for some speculation.

Physicists tend to hate attempted associations between QM and consciousness, but notice that this whole problem exists solely because of the discrepancy between you seeing one result and the math suggesting many. If you try to pin down what it means to “see” a result, you will discover yourself trying to make precise what it means to be conscious of it. In this sense, the problem is very much about consciousness[10].

It seems I am not the only one who thinks so:

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 who colleagues casually call “head and shoulders above the rest” and “smarter than anyone else.”

So here’s another way of looking at the problem. According to the philosophy of Idealism, the whole world is made of mind-stuff. You never encounter objects; you experience colors, textures, etc., and infer from them that objects must exist. Yet all of what you call “the world” is made entirely of the stuff of consciousness.

From this perspective, it is hardly surprising that becoming conscious of a result coincides precisely with the coming-into-existence of that result: they are one and the same event. The reason this isn’t solipsism (the philosophy where all of reality is your personal dream) is that, as far as you can know, the same thing is happening to everyone else from their perspective as well.

It may seem impossible to prove whether Idealism or Materialism (the philosophy that the world is made of stuff) is true, but this is false. Your world is a dream, and you can prove this for yourself. Until more people do this, the whole thing will remain perplexing.

For quantum mechanics, all we really have to do (most people believe) is think about it in the right way. No elaborate experiments necessarily required (although they could help nudge us in the right direction, no doubt about that). But if anything, that makes the embarrassment more acute. All we have to do is wrap our brains around the issue, and yet we’ve failed to do so.

 

– Sean Carroll

---

Notes and references

[0] Roger Penrose (2004), The Road to Reality, pp. 802-803:

…the environmental-decoherence viewpoint … maintains that state vector reduction can be understood as coming about because the environmental system under consideration becomes inextricably entangled with its environment.[…] We think of the environment as extremely complicated and essentially ‘random’ [… but] there is no general principle providing an absolute bar to extracting information from the environment.[…] Accordingly, such descriptions are referred to as FAPP [For All Practical Purposes].

It should be noted that some are looking for “(in-principle) irreversible decoherence.” See this interesting paper. Nonetheless, no such mechanism has been found.

[1] There is also the possibility of “collapse of the wave function,” but very little reason to believe in such a deus-ex-machina. There’s very little experimental support for it, and it’s very ugly theoretically (being nondeterministic and irreversible, unlike the rest of physics).

Note that we have demonstrated superposition for at least trillions of (well-controlled) particles. See, e.g. here. As we do bigger and bigger experiments, the collapse hypothesis becomes less and less likely.

[2] Either directly or indirectly, such as via a friend telling you, or stray photons giving you information.

[3] Note the sense in which the history is not a record of what happened, but a retroactive story to make the present consistent.

[4] At least, in any way that could be shown to you while you still have knowledge of the cat’s fate. For your perspective to remain consistent, when you compare notes with anyone else, they will have seen the same result as you.

It is true that someone outside the system (i.e., not yet entangled with it) can still demonstrate superposition, but you are now part of the system they are experimenting on, and they cannot show you the result without something like quantum erasure, making you forget the original result.

[5] Or maybe it does weird everyone out.

I suspect that a substantial majority of physicists who use quantum mechanics in their everyday work are uninterested in or downright hostile to attempts to understand the quantum measurement problem.

 

– Sean Carroll

[6] The decoherence myth:

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.

If that is so, why do so many people think that decoherence has solved it? Consider this quote from Sean Caroll (bolding mine):

Once our quantum superposition involves macroscopic systems with many degrees of freedom that become entangled with an even-larger environment, the different terms in that superposition proceed to evolve completely independently of each other. It is as if they have become distinct worlds — because they have. We wouldn’t think of our pre-measurement state (1) as describing two different worlds; it’s just one world, in which the particle is in a superposition. But (2) has two worlds in it. The difference is that we can imagine undoing the superposition in (1) by carefully manipulating the particle, but in (2) the difference between the two branches has diffused into the environment and is lost there forever.

How many is “many?” And when has it become truly “forever?” This is a pure judgement call, unless someone discovers such a thing as in-principle irreversible decoherence. This is what allows you to pretend that the superposition disappeared early on.

[7] The most embarrassing graph in modern physics.

I think Copenhagen is completely ill-defined, and shouldn’t be the favorite anything of any thoughtful person

[8] Nobel laureate Eugene Wigner was (in)famous for his interpretation that conscious beings cause collapse, but we can see that he perhaps did it to avoid this stranger conclusion (in 1967):

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.

 …

However, to deny the existence of the consciousness of a friend to this extent is surely an unnatural attitude, approaching solipsism, and few people, in their hearts, will go along with it.

[9] I’ve made sure to run it by a few quantum physicist friends, and also the online community:

PhysicsForums

Physics StackExchange

Nobody has much concrete to say, either in support or objection.

[10] Sometimes it is argued that any object, including an unconscious detector, is an observer from its own perspective, and so consciousness has nothing to do with it. But to say that a detector has a perspective is to say that it is conscious. Maybe true, maybe false, but it changes nothing for you.

[11] See, for example, this piece of writing in Quanta Magazine (emphasis mine):

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.

As we’ve discussed, it doesn’t force it into one state or the other. The overall system is still in a superposition, but we are forced to model it as being in an unknown-but-definite state (like a classical hidden coin toss) for practical purposes.

[12] Especially New Age material, like this scene discussing the two slit experiment in the movie “What The Bleep.”

The electron decided to act differently, as though it was aware that it was being watched!!

When a billiard ball moves because it’s been struck, does it “decide” to move because it’s “aware” that it’s been hit? No. The situation is exactly analogous here. The electron behaves differently because of a purely physical effect.

But while the electron will not exhibit interference between the two paths, that does not mean that it has actually taken one path. The electron + detector (+ environment) are still in a superposition, and both branches still exist.

---

Mathematical footnotes: decoherence

This section is for those with some knowledge of QM who want to understand decoherence as simply as possible.

Consider a qubit in state |psi> = |0> + |1> measured with respect to the following basis:

{ |A> = |0> + |1>, |B> = |0> - |1> }

Because <B|psi> = 0, the result will never be B. This result can be interpreted as the result of interference. In particular, <B|0> and <B|1> (the “two paths” from |psi> to |B>) have opposite amplitudes (+1 and -1) and are said to “destructively interfere.”

For example, say we have a particle that’s spin-down along the z-axis. Note that it is in a superposition w.r.t. the x-axis:

|phi> = |z-> = sqrt(2)/2 * ( |x+> + |x-> )

The fact that measuring it in the z-axis will yield a definite result (spin-down) even though “it is in a superposition” can be seen as an interference effect.

Now let the qubit |psi> become entangled with a “measuring device”:

|psi'> = |0>|X> + |1>|Y> (with |X> and |Y> orthornormal).

If you calculate the probability of the left subsystem being measured as |B> and ignoring the second particle (e.g., by applying the projector P_B @ I), you will find that it is 50%, as would be predicted if the particle were in a classically indeterminate mixture of |0> and |1>. The interference has “disappeared” with respect to either sub-system alone. In the density matrix formulation, this is equivalent to taking the partial trace and noticing that the off-diagonal terms have disappeared.

On the other hand, because the overall system |psi'> is still just a superposition (in the tensor-product space spanned by { |0>|X>, |0>|Y>, |1>|X>, |1>|Y> }), we can still demonstrate interference on it (e.g., by noting that it is never measured as |0>|X> - |1>|Y>). But this requires control of both subsystems.

If the second subsystem is a stray photon that is now zipping away at the speed of light, we have no hope of catching it, and thus the remaining subsystem appears classical. This is decoherence in a nutshell.

Another interesting thing to note is that the interference on psi disappears only insofar as |X> and |Y> have a smaller inner product. In other words, there are degrees of entanglement. The more strongly the particles are entangled – the more that the second particle’s state gives information about the first’s – the less interference we can demonstrate.