## Tuesday, June 09, 2015 ... //

### Von Neumann-Wigner interpretation was just "verbally spiced" original Copenhagen

Is the hamburger in your stomach a part of you?
And can your brain predict its own future behavior?

In a discussion about the tiny added value of QBism, Gordon made an interesting point: that my "interpretation" of quantum mechanics is equivalent to Wigner's, after all. If you want to see what kind of an "interpretation" he means, open

Von Neumann–Wigner interpretation (Wikipedia)
It's the interpretation summarized by the slogan "consciousness causes collapse of the wave function". The point of John von Neumann and Eugene Wigner was that only "consciousness" is the level of physical reality where the outcomes of the measurements become sharp.

Is it controversial? Is it right? Is it new? Is it Copenhagen? No. Yes. No. Yes.

Wigner and von Neumann just "spiced" the same rules that the Copenhagen school – I mean Heisenberg, Born, Jordan, and especially Bohr as the unifying guru – clearly articulated and what must be understood as the Copenhagen interpretation unless we rewrite the history.

So like QBism, the von Neumann-Wigner interpretation is another system of ideas whose physical beef is the same as the original Copenhagen interpretation; but that differs in the emphasis, wording, and emotions.

What we want to understand is the demarcation line (also known as the Heisenberg cut) between the observer and the observed; or the part of the world described by sharp $c$-number values of observables that are sometimes a bit misleadingly referred to as "classical physics" (we don't need to use any classical dynamical laws that wouldn't follow from quantum mechanics); and the world of $q$-number operators where quantum superpositions are essential.

Three universal facts of quantum mechanics are that
1. this Heisenberg cut has to exist if anyone wants to use quantum mechanics at all
2. sufficiently microscopic or coherent degrees of freedom that have a potential to quantum interfere must be on the "quantum" side of the cut
3. the perceived values of the measurement that an observer uses to verify quantum mechanics have to be on the "classical" side of the cut
That's it. Those are the truly important rules. Heisenberg, Bohr, Dirac, Jordan, Born, as well as Wigner and von Neumann would agree. They may have used different words about other aspects but the differences were unphysical – which means that even in principle, there can't exist an operational procedure that would decide which of the nuanced statements are right and which of them are wrong.

Apparatuses, eyes, nerves, and brain

Classical physics describes the whole Universe as a mechanical machine that exists independently of observers. But even if we want to apply ordinary classical physics, we need to measure some quantities. Is it straightforward? Are there similar subtleties to those by which people have wasted so many decades of time in the quantum context? Let's see.

Let's assume that you want to predict the position of Mars. So you measure the location and velocity on Mars in the telescope, or something like that. To do so, you need some machinery: a telescope, an eye, a lens in the eye, a retina, nerves from the retina to the brain (getting enough energy from the blood), and the brain itself (which works, and one assumes that some "mind" or "consciousness" exists thanks to this activity, whatever these words exactly mean).

You should notice that the telescope and the eye are analogous. The telescope is a man-made gadget and the eye was created by Mother Nature. But this is clearly just a technical difference. Any physically sensible approach should be able to treat these two objects in the same way. If you consider the telescope to be just some "external machine", you must be allowed to consider the eye a "machine", albeit a biological one, too. And if you can consider the eye to be a part of the "observer", the telescope may be his part, too.

Galileo Galilei began to use telescopes intensively and the Catholic Church found this method controversial for a while. Can the observations from the telescopes be considered as real and as reliable as those made with naked eyes? I bet that almost all of us think that it is a stupid question. But historically, it was a source of a genuine controversy in the church. The church ultimately agreed that Galileo was right and telescopes were kosher.

Why would it be silly not to trust the telescope? Well, you may look at many things with the telescope and with the eyes and whenever both of them give you a clear answer about something you may see, the answers will coincide. At the same moment, the telescope can distinguish details that can't be distinguished by the naked eye. It follows that the telescope is giving us more information and all of its information agrees with the information we consider "reality" whenever we know what the "reality" is. The telescope is giving us some new data and if we're curious, we should be interested in the meaning and patterns of these data, just like we are curious about the things we see with the naked eyes. And because the telescope data agree with the eye data whenever both of them are well-defined, we may consider the telescope data to be "the same reality" that we saw with our eyes.

I think that you agree that I am too talkative. The telescope clearly is just an extension of the eye. Its inner working is analogous to the inner workings of the lens in the eye. If it is legitimate for us to collect the information that went through the natural lenses, it must be legitimate for us to acquire the truth transformed by man-made lenses, too.

We may scientifically explain how telescopes work. The explanation boils down to a description of the lenses and the law of refraction governing them. We ultimately think of beams or photons that go through the lens. Similarly, we may describe how the eye works. Some biophysics tells us how the retina sends impulses when the photon arrives. And how nerves transmit the information. It's a bit different than wires in a computer but it can't be metaphysically different.

When someone tells us how to apply classical physics to calculate the motion of Mars, he must also tell us things like the following: "You have to measure the location of Mars in the telescope." Do you agree? You couldn't verify whether the laws of classical physics (or Kepler's laws) are correct if you didn't know that you must find out the locations and/or velocities. But let's be as annoying as the "interpreters" of quantum mechanics. We were told:
You have to measure the location of Mars in the telescope.
That sounds great. But what does it mean "to measure"? And what does it mean "you" (which becomes "me" from your perspective; I hope that you've learned to switch in between these two conventions or vantage points back in the kindergarten). Bill Clinton would also ask what "is" means but I deliberately omitted the verb in the quote.

Note that even in classical physics, one needs a measurement theory for the full set of rules how to apply the laws of classical physics. To verify Kepler's laws, we need to know that the planet really sits at a given place or another place. But how can we be sure that "we know" the number? And what are "we", after all?

These questions are never discussed in the context of classical physics because no one needs a special lesson how to apply the laws of classical physics. Everyone seems self-confident and know what it means. But if you are strict and fair, even in the classical framework you have to ask all the questions that people love to repeat in the quantum context in order to deliberately spread fog and (in their flawed opinion) undermine quantum mechanics.

For example, when do we really know the position of Mars in the telescope? Do we know it even if we don't look? Or do we know it when the photon from Mars arrives to the telescope? To the eye? To the retina? When the electric impulse is sent to the retina? When it arrives to some brain cell? Or later, when the brain cell sends it all over the brain and other cells perform some manipulation with the information?

We could annoyingly ask all these questions but people don't ask them in the classical context because they know that these technicalities are no helpful for the understanding of the Kepler's laws. Kepler's laws are about the planets out there, not about the neverending discussions on the definition of "knowing" and its possible relationship with processes in biology or neuroscience.

Well, let me tell you something: these details of the inner working of the observer are equally irrelevant for a quantum understanding of external objects, too!

That's why the question about the "demarcation line" of the observer isn't physical. The purpose of classical physics is to describe things like the motion of Mars; the purpose of quantum physics is to describe things like the spectrum of an atom. So it's just silly to focus on the transmission of the information between the eyes and brain cells etc. We simply want to trust the eyes and the brain cells. If the brain cell "looks like" it has just learned something, we want to trust that it's because something in the external world really behaved like that.

We don't need to trust our organs. When we are drunk or high, it is reasonable not to trust everything you see. But the trust is a necessary condition for our ability to apply the laws of classical physics. The same comment holds in quantum mechanics. We must trust the inner workings of "us", including the brain and eyes or some other senses, that what we apparently perceive is really logically connected to some external properties. Without this trust, we simply can't know any coordinates and velocities and we can't predict things.

Where does the observer end?

Who is "you" in the sentence "you must first determine the location of Mars"? Is it just the brain? Or just some patterns in the brain? Or does it include the skull? The eye? Other organs? The rest of your body? The hamburger in your stomach? The air in your lungs? The feces you left in McDonald's? The dead cells on the surface of your skin? Dental fillings? The hair that you lost in the Grand Canyon in the recent hour? The photons from the Sun that your nail reflected 20 minutes ago and that are just approaching Mars now? Are they "you"?

Moreover, when the prescription to apply classical physics talks about "you who has to measure the position", may "you" be someone without a PhD? Your friends? Family? Kids? Women? Chimps? Birds? Bacteria? Computers?

There are many, many questions like that. And in a full "recipe to apply or verify classical physics", one could demand that all these questions and many others are answered because the recipe says things like "you need to know the location of Mars". Again, people learning classical physics are not this annoying because they understand that the focus of the theory – what it explains – is the external world, the planets.

But exactly the same thing is true in quantum mechanics. It is a theory with which you should study external objects. It is not a theory inviting you to spend 90 years by meaningless questions where "you" end and whether the hamburger in your stomach or the eyeglasses that you need to see sharply are a part of "you". Yes, no, it just doesn't affect our description of the external objects! We must trust that whatever is the inner architecture or definition of "us", we can measure (find the value of) the observables that quantum mechanics needs to know for us to predict things.

This insanely overrated "measurement problem" mystery isn't really new in quantum mechanics. You would need it in classical physics if you were careful enough to include instructions how the classical theory should be used.

In these respects, the only difference between classical and quantum physics is that classical physics may also be understood as something else than a recipe to observe, use, and predict data. Classical physics may also be understood as a one-to-one faithful picture of the external world that doesn't need any observers. Well, quantum mechanics cannot. Quantum mechanics generalizes the "interpretation" of classical physics which is the classical physics including the full manual how the theory should be used to make predictions! Only that "kind" (operational kind) of classical physics may be generalized to quantum mechanics. So in quantum mechanics, it is important to specify what the observer knows and what he doesn't. There just can't exist any "perfect observer" in quantum mechanics that would make all imperfect observers redundant or irrelevant or obsolete. Such a "perfect observer" could have been imagined in classical physics but it is not allowed in quantum mechanics. Predictions always need some of this "imperfection".

Different physicists demarcate "you", the "observer"

So the separation of the world to "the observer" and "the observed" is an unavoidable part of the quantum recipe to make predictions. The theory needs to be told what was measured – which information was collected – and the user of quantum mechanics must be sure that he trusts this information (or the sources from which this information was obtained).

Where the observer "ends" is exactly as inconsequential a question as the question whether the air in your lungs is "you". You may find the information about the external world by any conglomerate of your organs, machines, and other elements. You may consider them to be a part of "you" – the "observer" – or not. It doesn't make any difference as long as the combination of organs and machines works. And you need to be sure that it works. It has to be trustworthy and you must know it. If it is not, you won't be able to verify the laws of physics, anyway.

That's why the questions about the "demarcation line of the observer" (the precise location of the Heisenberg cut) are so silly. They just don't matter for the questions that the physical theory is supposed to explain and predict. They don't matter as long as your "collection of organs and machines" is good enough for you to be able to reliably use the laws at all! And if it is not, too bad for you. Then it makes no sense to talk about which laws of Nature are valid. You can neither prove them nor disprove them.

Concerning the "demarcation line" (Heisenberg cut), Wigner and von Neumann just loved the extreme choice that not just the telescope but also the eyes, the nerves, and other things sit on the "observed object" side of the Heisenberg cut; and only the bare minimum, the minimum consciousness, some minimum portion of the brain, is included in the "observer". Everything in the external world evolves to superpositions in the exact description – so it's true for the states of the nerves and other things. Only the portion/level of the brain that really carries the consciousness "collapses" and detects the sharp $c$-number values of the observables. Because of the entanglement between the external objects, nerves, and the state of your consciousness, the "collapse" of your state of your consciousness automatically involves the "collapse" of the properties of the external objects and your nerves.

And as always, the collapse is effectively one step in the Bayesian inference, although expressed in the quantum formalism. The wave function is a version of (a template for) a probability distribution and the collapse means that the "consciousness has learned something". It is not a collapse of a classical object that could be further decomposed to some more elementary processes.

These views were associated with Wigner and von Neumann and their usage of the word "consciousness" made their comments provocative and famous in the broader scientific public. But these two men were in no way authors of the physical idea behind these comments. The physical ideas were nothing else than the original, orthodox, Copenhagen interpretation of quantum mechanics! In particular, Heisenberg said things directly equivalent to Wigner and von Neumann (years before them)
Werner Heisenberg maintained that wave function collapse, "The discontinuous change in the probability function," takes place when the result of a measurement is registered in the mind of an observer.
He may have used the word "mind" instead of "consciousness" but the claim was clearly completely equivalent. Most likely, we can't decide whether he said "mind" or "consciousness" because the first time he spoke, he almost certainly described these things in German!

There was no disagreement whatsoever between Heisenberg on one side and von Neumann or Wigner on the other side when it comes to these matters. What about Bohr? Bohr didn't sharply disagree, either. He just preferred to emphasize that none of these questions is physical. Physicists shouldn't spend time with the question "where the observer ends" because it has no observable consequences.

One can make a choice. Many choices are practically equivalent. The eye or the apparatus (and perhaps all other safely macroscopic and decoherent objects around them, or in the Universe) may belong to the observer or not. It just won't make a difference. Whenever it would make a difference, it means that there is no one who can measure the observables reliably. And that would imply that the laws of quantum mechanics couldn't be verified, anyway. So it would be operationally meaningless to say that they are right or wrong!

So the von Neumann-Wigner "interpretation" was just an early example of the excessive babbling about quantum mechanics that doesn't really help one to understand physics any better. At least, it was a correct "interpretation" (like QBism) – just a spiritually worded, provocative version of the Copenhagen "interpretation". Incorrect "interpretations" began to spread decades later. But it was useless, too.

A classical brain predicting itself

I want to share one more playful observation that I made and was amused by when I was 7 or so, a decade before I understood quantum mechanics well enough to feel certain about it. Try to get to the same mental state. I was imagining that the world is governed by some "classical" theory although at that time, the classical laws I was imagining were even more primitive than the laws of Newton's mechanics.

The model I had in mind was that you had solid bodies defined by some shapes (each point of the space is either black or white, and the boundaries between the regions are sort of smooth) and they were colliding with each other like billiard balls or something. At that time, it looked "enough" to produce an interesting world, so I believed that these should have been the laws of Nature.

(Note how silly this reasoning is: But it's the same reasoning that leads the people to believe that the world is fundamentally classical. They impose a very small number of easy constraints – not all experimental constraints – and the classical theory seems OK for these constraints, so they just decide that it must be the right framework and no extra empirical evidence may change their mind or convince them that they are wrong! This is not science. In science, when an observation – even a previously unknown observation – contradicts your assumptions, your assumptions are proven to be wrong.)

OK, let me get to the point. The question is whether you may predict your own future decisions in this classical world. That's subtle. To predict what your brain will do, you have to know the state of the brain exactly. But how do you learn that? You need an external machine that measures all pieces of your brain, whatever the organization of the degrees of freedom was.

But if you want to use this external machine, your brain needs to interact with it and the interaction will inevitably go in both directions. At least my laws (and any realistic laws) immediately implied that the interactions went in both directions. You need to start the machine that measures your brain, press the buttons, but if you do so, the machine will influence your body and brain, too. (Well, the main influence of the machine on your body that actually matters is the moment when the machine informs you about the prediction.)

Things are getting tougher. You want to predict your brain but you need an external machine that measures the brain. But because this external machine will affect the future of your brain as well, you need to know the initial conditions for that machine, either. So you need an extra second machine that measures the first one... and so on. Indefinitely. You can never stop.

The punch line is that you just can't exactly predict your own brain, not even in principle. That's good because if you could do such a thing, you could deliberately prove that the laws of physics are internally inconsistent. In 2010, you could calculate whether you would vote for Obama or Romney in the next elections. The computer would inform you about the prediction before the elections. And then (because you have the free will – or the sense of humor) you could deliberately vote for the other man which would prove that the prediction doesn't work! That's another, consistency-based proof that you can't exactly predict your own behavior.

Back in 1980, I was sort of amused by these childish and interesting observations. The same conclusion – that you can't exactly predict your own brain – could have been derived "microscopically", by piling machines that measure the initial conditions of the brain and of each other; or "macroscopically", by consistency checks in a world with the free will.

But why do these games appear in a text about the foundations of quantum mechanics? Because even in this classical setup, one can see that the predictions must be limited to apply to the external world and if you try to produce predictions even for yourself, the observer, the inner world, you will face contradictions.

In other words, even in the classical framework, you should better separate things to the external world that may be studied and the internal world that you cannot exactly study – but you must trust that it works (and it should work!). Your internal world may be studied by others, however, because for them, it is a part of the external or "observed" world.

Summary

I have repeated the same ideas – several ideas – in different words. Von Neumann and Wigner have just "spiced" the Copenhagen interpretation with some provocative words but they haven't changed an epsilon about the ways how quantum mechanics made (any) prediction and they weren't the original discoverers of any of these laws.

Also, the question "where is the demarcation line of the observer" is about as physically meaningless as the question "whether the air in your lungs is a part of you". The "positivist" realization that similar questions that can't be decided by an experiment, not even in principle, are physically meaningless was appreciated by all founders of quantum mechanics and by Niels Bohr in particular.

And that's the memo.