Collapse or solipsism: pick your poison

Why decoherence and MWI do not solve the measurement problem

Intro

We consider a Schrodinger’s Cat style experiment.

There is a point in time before which you cannot say that there is an answer, and after which you can. Therefore, there is a point in time when this answer first comes into being. This transition either happens due to some collapse mechanism, or upon your encountering the experiment. And nobody likes collapse.

This conclusion is not rectified by either decoherence or many worlds, though it is very tempting to think so. This note is the result of trying to clarify my own thinking. I hope it is of some use to others.

Caveats

I am not a physicist but a software engineer with a little background in quantum information science.
The title is purposely provocative, but not far from the conclusion.
If you disagree with what I have to say, please feel free to write me (email at bottom).

Superposition, interference, and entanglement: a recap

Suppose we have a single particle that’s in a superposition of two states[1]. We can do what’s called an interference experiment[2] on it to demonstrate that it’s really in a superposition, and not just “in one state but we don’t know which.”

If it interacts with another particle in such a way that the second particle’s behavior depends on the first particle’s state, then the two are said to be entangled. They are in superposition together.

For example, if the first particle was in a superposition of “moving left + moving right,” and it bounces off a stationary particle, then the two may end up in “first particle moving right and second moving left + first particle moving left and second moving right.”

This is just the conservation of momentum applied to each branch separately. In a sense, that’s all entanglement is: when the usual laws of physics are applied to each branch of the superposition, it generally results in different outcomes for each branch. Then knowledge about one of the particles tells you something about the other particle[3].

At this point, if we have full control over both particles, we can still demonstrate superposition on the pair. If we only have control of the first particle, however, an interference experiment would show nothing[4]. Whether or not we actually try that interference experiment, the behavior of the first particle would look classical (as though it were in one state, even if we don’t know which).

The information we need has “leaked into” the second particle, and can only be recovered by gaining control of it.

Decoherence

If the particles encounter a detection device, that device’s whole job is to leak information in a big way. In one branch, the alarm should be blaring, and in the other, it is silent. That’s trillions of particles that are in on the entanglement together.

Even if there’s no explicit detection device, if stray air molecules or photons encounter the pair, they will carry away information (which potentially propagates away at the speed of light), acting as a sort of detector. If the “detector” is a device that kills (or doesn’t kill) a cat, then the unfortunate cat becomes a kind of detector.

In either case, we would need control of all of those particles in order to demonstrate the superposition that they all belong to, or to undo most of the entanglements so that we can demonstrate interference on a much smaller subset. But that’s virtually impossible with current or foreseeable technology[13].

Since we normally only have precise control over a tiny subset of these particles, we cannot demonstrate interference.

That’s basically what decoherence is. It’s a way of explaining why macroscopic systems don’t “look quantum” (e.g., they do not show interference patterns)[15].

“Whenever a quantum system gets entangled with another system, its coherence is reduced. However, the term ‘decoherence’ is typically reserved to situations in which the loss of coherence is effectively permanent and difficult to reverse or avoid.”

But while the branches of the superposition cannot interfere in practice, it does not deny that they are there in principle. And if the superposition is still there in principle, then it is not valid to say that there is just one outcome – even if it’s a perfectly good approximation for all practical purposes.

This is why decoherence does not solve the measurement problem[5].

The measurement problem

So when should we be allowed to say that the first particle really has a definite value? This is the heart of the measurement problem, and we’re not going to solve it here. But note that we can put an upper bound on the problem.

Namely, when I see the result, I ought to be able to say that there is a result. If I encounter a decomposing cat, I would really like it to be meaningful to say “this cat is really dead.”

It is not enough that my friend sees it – for all I know, she is merely part of the superposition, however impractical it may be for me to demonstrate. On the other hand, if my friend sees it and tells me, then this is as good as me seeing it myself. Either way, the superposition has grown to involve me.

Early in the experiment, there was no meaningful sense in which there was just one result. Now, there clearly is a meaningful sense. When did that sense come into being?

It’s easy to slip into thinking that maybe decoherence makes the result slowly come into existence or something, but this is not good enough: as we saw, decoherence never denies the reality of the superposition, so it never causes there to be just one answer in principle. And yet I want to say there is one answer in principle, because… dead cat.

Collapse

One explanation might be that there is a “collapse” that happens somewhere. The problem is, there’s not much theoretical or experimental evidence of such an event happening anywhere, and anyway it would violate the time-reversibility of physics. Suffice it to say that nobody likes this idea very much[6].

Nonetheless, the term “Copenhagen interpretation” is frequently used to describe a vague idea in which collapse probably happens somewhere, somewhen, somehow, and it continues to be a favorite of physicists for mostly practical reasons.

I think Copenhagen is completely ill-defined, and shouldn’t be the favorite anything of any thoughtful person – Sean Carroll, “The most embarrassing graph in physics”

Recall that we put an upper bound on when this “collapse” must happen: by the time we see it. So either we must be able to cause it, or it must happen at tiny scales (preventing us from getting inside the boundary)[7].

It is also worth noting that some researchers are looking for evidence of irreversible decoherence[16]. If such a thing is found, it should be physically indistinguishable from a “real collapse”: the branches cannot interfere in principle, and so within each branch it looks like there suddenly became one final answer.

Many worlds to the rescue?

A more modern interpretation is that collapse never happens. Instead, we must widen our lens.

From a “God’s-eye view,” the superposition simply grows to include us. In one branch, a copy of us sees one result, and in another branch, another copy sees the other result. This is called the “many worlds interpretation” (MWI). In this interpretation, the state vector never collapses.

There are various descriptions of when exactly worlds “branch,” but the most common is that they “effectively branch” when decoherence is “effectively irreversible.” This is imprecise, but luckily the state vector is all we need for analysis, and it is still a superposition.

Now consider how things look for any single “copy” of you. This shouldn’t be too onerous, since are always just “one single copy of you.”

If a collapse never happens, then the boundary between which there is no answer, and which there is an answer, is when you see it. The answer somehow “comes into being” when you see it.

This is another place where people seem to lose the plot. Let’s look at some common objections:

Q: Big deal, you discover the answer when you encounter it.
A: Since we’re denying collapse, the theory is clear that there was no answer before you encountered it. It’s in a superposition, which you can verify in theory. And there’s no other reason to believe there’s an answer.

Q: From a God’s-eye view, it is still in a superposition, so there is never a point at which there becomes just one answer.
A: Yes, but from your perspective, there is a point where you can say there is an answer. And with sufficiently advanced technology, you should be able to discover that this happens only when you, personally, encounter the system.

Q: But if it’s still in a superposition, then someone still outside the system can theoretically undo your entanglement, and so your answer is not really a “final answer.”
A: Again, true but irrelevant. There is still a moment where an answer “pops into being,” regardless of whether it can later pop out of being[12].

Whether or not there is a “real collapse,” and regardless of interpretation, from your perspective, there is a point at which an answer “comes into being” – where there is an answer now but wasn’t before.

In addition, though we might be able to say now that the cat has been dead for some time, even that fact wasn’t meaningfully true a moment ago. The present and past truth of the cat’s fate come into being simultaneously.

If you accept MWI and not collapse, then you must also accept that this “moment of truth” happens with you. You are the only observer in your branch of the universe – i.e., in the world[8].

Not quite solipsism, but not very far, either.

Other possibilities

Our picture would be incomplete without mentioning the possibility that QM is wrong, and some modification is needed. This is the idea behind theories like de Broglie - Bohm. None of these is very popular yet.

A note on consciousness

Sometimes people misunderstand and think that detectors have to be conscious. As we saw, this is of course wrong. Any physical system that entangles with the experiment is a “detector.”

On the other hand, some people then conclude that since I also only entangle with the system, and I am just another detector, consciousness has nothing to do with quantum mechanics.

IMHO, this is just as misguided.

Recall the “upper bound” we placed on the (apparent) collapse: it is when “I see the result.” If you try to make precise what you mean by those words, you will discover that you are trying to make precise the statement that you become conscious of the result.

The “collapse” may happen before this point (e.g., you can claim that it happens in unconscious parts of your brain), but somehow it never happens after. This is what it means for there to be a measurement problem: somehow, by the time I become aware of the result, I must say that there really is one.

I am of course free to try to extrapolate this conclusion to other physical systems (such as detectors or other people), but they either end up in different worlds or cause collapse in mine (or ours).

Also see Ed Witten’s thoughts [14].

A personal note

I might as well share my own views here. Feel free to disregard or mock them as you see fit. I will only give a rough sketch; a longer piece with more details is in the works.

Consider various philosophical conundrums:

Last Thursdayism: there is no way to know whether the past really happened[9].
The problem of induction: the principle of induction relies on circularity, and thus any certainty that the laws of physics will continue to operate tomorrow is unjustified[10].
The problem of other minds: there’s no way to be sure that anyone else is conscious[11].

These all find convergence in a simple (if radical) idea: namely, that your experience of the world is the world. It is not that consciousness is a property you have (and that nobody else does). It is that consciousness is the very “fabric” of all the sights and sounds and ideas you experience, and they together make up the thing you call “the world.” Look around and make this shift in perspective. Sounds are manifestations of a luminous property called “consciousness.” If it helps, compare the presence of sound with its absence. This presence that constitutes sound is consciousness.

You are not conscious; your body, thoughts, personality, etc. are always a content of consciousness.

Sometimes this fabric manifests as the perspective you call “my friend’s conscious experience.” This happens neither in parallel with yours, nor sequentially, but in a sense, beyond time. You only ever experience your own projections of other people.

The truth comes into existence when “you become conscious” of it because consciousness is the world.

As for why there are all the perceived regularities called “physics,” these are all occurring in much deeper layers of mind than our profoundly distracted minds normally have access to. But they are not beyond conscious reach in principle. This is the entire point of certain contemplative traditions, though they are frequently misunderstood. There are things you cannot prove because if you stopped doing them, they would stop happening, in a physically meaningful sense.

More will have to wait til later.

About the author

I’m not a physicist, but a software engineer with a little background in quantum information science. I’m also deeply committed to contemplative practice, having spent months at a stretch in retreat.

Notes and references

Note that with some observables, such as spin, the particle can be in a definite state and still be in a superposition with respect to another observable. For example,

|z_-> = sqrt(2)/2 * ( |x_+> + |x_-> )

This says that when a particle is spin-down along the z-axis, it is in a superposition along the x-axis. See Pauli matrices. 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 (see [2]).
Consider a qubit in state |psi> = |0> + |1> measured with respect to the following basis:

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

Note that 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 and are said to “destructively interfere.”
Consider the case of a perfectly elastic collision where the two particles have the same mass. Then, when the first particle “bumps into” the second, the first will stop. The resulting state will be “first particle stopped and second moving left + first particle stopped and second moving right.” In this case, knowing the first particle’s motion does not tell you anything about the second particle’s, and the two momenta are not entangled.
Continuing from note [2]:

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 |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> or by undoing the entanglement). This requires control of both systems.

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.
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.

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].

See also this answer.
Leonard Susskind, relating how he and Nobel laureate Gerard ‘t Hooft disproved an idea of Stephen Hawking:

In fact, I think of it as more basic than any of the other principles of physics. The most basic principle of physics is that distinctions never disappear.

Nonetheless, there are modern “objective collapse” theories like GRW. But they seem not to be very popular.
Or we discover we can get inside the boundary and experience something very strange. But this is just sci-fi right now.
Nobel laureate Eugene Wigner is most (in)famous for his idea that consciousness causes collapse. What’s less well known is that he probably did it to avoid approximately the same conclusion we’re arriving at:

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.
I don’t have space to argue it in the footnotes, but it’s much worse than “I can’t know whether the past really happened.” All attempts to support that the past really happened (e.g., by invoking physical law, or trying to justify Occam’s Razor) end up presupposing the past. Because all attempts to justify the past end up being circular, there’s no way to say that a real past is even “more likely.”
Again, hard to justify in footnotes, but read the whole article. It is commonly understood to mean “we cannot be certain of the future,” but it cuts far deeper than that.

If Hume is right, the belief that the sun will rise tomorrow is as unjustified as the belief that a million mile wide bowl of tulips will appear over the horizon instead. We suppose the second belief is insane. … But then the onus is on these defenders of “common sense” to show precisely what is wrong with Hume’s argument. No one has yet succeeded in doing this (or at least no one has succeeded in convincing a majority of philosophers that they have done so).

Also see

[Wheeler would] say things like, “In the end, the only law is that there is no law.” There’s no ultimate law of physics. All the laws of physics are mutable and that mutability itself is a principle of physics. He’d say, there’s no law of physics that hasn’t been transcended. I saw this, and I remembered my joke about how the laws of physics must be wrong, and I was immensely attracted to this idea that maybe ultimately there actually are no laws of physics. What there is in place of laws, I didn’t know. But if the laws weren’t 100 percent trustworthy, maybe there was a back door to the stars.

– Christopher Fuchs, discussing his advisor, physics titan John Archibald Wheeler.
Sometimes it is argued back that there is no way to know whether even you are conscious. Again, I cannot do it justice here, but I might as well try.

Look and/or listen around you and try to answer, as innocently as possible: doesn’t it definitely seem as though something is happening? Not probably but definitely? Forget about whether it is possible to know what is “actually” happening.

This is a different kind of certainty than you can have about metaphysical hypotheses like space and time. It does not depend on reasoning. If you find yourself becoming unsure of this fact, just let go of reasoning for a moment and “look again.”
Recall the final part of note 4. As with any physical system, your entanglement can fall along a spectrum. If you are asleep when the result reaches you, and your body/brain states in the two cases are nearly indistinguishable, then the coherence of the rest of the system (excluding you) is only partially lost: you can still show most of the interference, in principle.

This naturally leads to the question of whether something like a quantum eraser experiment should be theoretically possible: restoring the cat’s superposition by completely “forgetting” it. This is pure sci-fi today.
Though it should be noted that we have done this with at least trillions of carefully controlled atoms. See, e.g. here.
Edward Witten, towering genius of physics:

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.
It also may help solve the preferred basis problem, but that is beyond the scope of our discussion.
This is an interesting paper.