## Saturday, July 05, 2014 ... /////

### Quantum mechanics doesn't really imply solipsism

The subjective character of certain processes doesn't mean that there aren't other subjects

Stubborn warriors against proper quantum mechanics often like to say that the theory, as it's stated, is incomplete, incorrect, or ludicrous because it leads to "solipsism" and that's why one of their "fixes" is needed. Wikipedia defines this meme as follows:

Solipsism (/ˈsɒlɨpsɪzəm/ from Latin solus, meaning "alone", and ipse, meaning "self") is the philosophical idea that only one's own mind is sure to exist. As an epistemological position, solipsism holds that knowledge of anything outside one's own mind is unsure; the external world and other minds cannot be known, and might not exist outside the mind. As a metaphysical position, solipsism goes further to the conclusion that the world and other minds do not exist.
You see that the idea has several "flavors". Its "epistemological" edition (=one related to the "philosophy about knowing") only talks about "things that are sure to exist" while its stronger, "metaphysical" version flatly says that the world and other minds do not exist. So different interpretations of this vague musing of philosophers are more right or more wrong than others. Science isn't obliged to say that philosophies like that have to be either sharply right or sharply wrong, and they're excellent questions in any case. Instead, science usually does say – and this is no exception – that philosophies are mixed bags with some vaguely right things and vaguely or sharply wrong things. This identifies this philosophy – and philosophy in general – as pretty much worthless ill-defined noise that is at most emotionally interesting but that isn't a good starting point to properly understand Nature, especially because it hides lots of fundamental misconceptions (and decorates and defends them with pompous linguistic constructs).

The haters of the new framework for physics that was concisely formulated and developed in Copenhagen like to use the word "solipsism" as an expletive of a sort that is supposed to defend their own views. This approach implicitly assumes the following classification of the basic possible frameworks how to think about Nature or the world or reality or everything and anything:
Their scientific, intrinsically 19th century world view (there is objective reality described by a set of objectively well-defined numbers that obey certain objective laws of physics)

Unscientific, metaphysical, religious beliefs
I wrote the first entry in bold because that's the type of thinking that is considered – in this case, considered by the anti-quantum zealots – to be correct. However, the 20th century physics has shown something completely different.

It has shown that the first world view is also completely wrong when it comes to the scientifically correct description of most phenomena in Nature, especially those in the microscopic world. Classical physics has really been ruled out so the original bold face has to be removed:
Their scientific, intrinsically 19th century world view (there is objective reality described by a set of objectively well-defined numbers that obey certain objective laws of physics)

???

Unscientific, metaphysical, religious beliefs
I added the question marks in the bold face because open-minded, scientifically inclined people would realize that when one scientific theory is ruled out, it does not mean that there cannot exist any correct scientific explanation. Of course, the correct description does exist even though its laws were unknown before the mid 1920s. These laws of modern physics are fundamentally different from all previously existing types of descriptions that people knew from classical physics; but they're still fundamentally different from religions and other spiritual non-quantitative approaches to Nature, too.

Well, around 1925, the correct and successful way of thinking about the processes anywhere in Nature – and in the microscopic world in particular – has led to the following clarification of the question marks:
Their scientific, intrinsically 19th century world view (there is objective reality described by a set of objectively well-defined numbers that obey certain objective laws of physics)

Quantum mechanics (the description of relationships between observations or intrinsically subjective perceptions that any object may use to produce probabilistic predictions about the outcomes of future measurements given some knowledge of the previous ones)

Unscientific, metaphysical, religious beliefs
If we categorize the basic ways of thinking about Nature into these tight (but oversimplified) boxes, then indeed, the correct theory is something entirely new, something "in between" classical physics as we knew it and some spiritual ideas.

But quantum mechanics is really new. Just because its foundations disagree with both or all "candidate theories of everything" doesn't justify the statement that "quantum mechanics belongs to the second camp" (the camp we don't like). It doesn't belong to any camp that existed before 1925. Even the statement that it is "in between" is just a simplification, a projection to the lower-dimensional space of properties that were analyzed before 1925. The truth is that quantum mechanics is completely new in certain ways so it is separated from the center of the line interval between "classical physics" and "spiritual traditions". It is separated in completely new directions or dimensions of the "space of ideas", dimensions that hadn't previously been even considered.

Obviously, solid science we possess after the discovery of quantum mechanics confirms many insights that scientists made in the era when classical physics was in charge of physics as a discipline. Quantum mechanics is the accurate theory for those "old" phenomena as well but classical physics is "also" pretty good. It is a good approximate theory and this fact may be demonstrated using the tools of quantum mechanics only. So Newton's or Kepler's laws of planetary motion are still OK. These theories worked in that context before quantum mechanics was born and it couldn't have been a coincidence. Quantum mechanics also allows us to calculate the errors caused by the approximation (classical physics) and these errors generally become larger (and the conceptual errors become more visible) if we consider ever smaller objects.

Let me pick another example of a theory that wasn't overthrown by the quantum revolution. Darwin's theory of evolution. Darwin and other advocates of the theory would probably think that the laws governing the fights between two animals were deterministic and agreed with the framework of classical physics. But this very specific, strong assumption isn't really needed for evolution to work. Evolution works even if the basic laws of physics are probabilistic and "designed for an observer". Nothing changes in practice.

One of the implications of evolution is that you, assuming that you are a human (apologies to robots, kittens, and extraterrestrial aliens who are following my blog), are a descendant of common ancestors of all humans, chimps, and other nations and species. The difference between your body and your brain on one side; and the body or the brain of someone else is just quantitative or gradual in character. There isn't any "metaphysical gap" between you and me. Our brains basically work in the same as way as well. Every fundamental enough, conceptual, metaphysical claim about me has to hold for you, too. And vice versa.

The common ancestry and evolution may be defended in the quantum framework as well and the proof is pretty much the same. If one wants to be kosher, some sentences have to be reformulated so that they don't implicitly assume classical physics. But the essence of Darwin's evolution theory has never assumed any particular technical statements about classical physics. It's sort of obvious that everything works in quantum physics, too. DNA may get replicated. Proteins may still be built according to the DNA code in quantum physics – one could actually argue that these things such as discrete information in the DNA would never really arise in a classical world.

The probability (and it's ultimately the same concept as the probability we have anywhere in quantum physics) of survival (=a Hermitian projection operator on the Hilbert space) still depends on certain features of the organism that quantify how well the organism deals with the resources and energy, how quickly it runs, how cleverly it thinks when it wants to eat others, and so on. All these things are hopefully obvious. The conclusion is that:

Quantum mechanics applied to life processes demonstrably implies that you are not metaphysically special. I am not metaphysically special, either.

That's an aspect of modern physics in which the old science was just fine. But the statement above does not imply that the right laws of physics are objective in character, i.e. that they describe some objective reality given by objective numbers that all humans must always exactly agree about. I have already discussed why this implication is wrong. A proof of this implication would effectively have to assume that classical physics is the only possible scientific theory of Nature. But it is not.

Instead, quantum mechanics allows one to calculate the probability that an observer will measure or perceive the outcome $L_i(t_{\rm future})=\ell_{i,k}$ of a particular observable $L_i(t_{\rm future})$ assuming that the observer knows some facts about some other observables in the past, $L_j(t_{\rm past}) = \ell_{j,m}$. If he does, he effectively knows the pure state $\ket{\psi(t_{\rm past})}$ which allows him to make the prediction using the usual quantum formulae involving the unitary evolution and Born's rule. Alternatively, the knowledge about the observables in the past may be incomplete and therefore probabilistic. In that case, the predictions are not extracted from a pure state $\ket\psi$ but from a density matrix $\rho$. The density matrices describe the most general type of knowledge that one may in principle possess about the objects in Nature.

Indeed, quantum mechanics isn't talking about the patterns in the "objective state of the world". It talks about patterns and regularities (expressed via conditional probabilities of many types) linking different pieces of knowledge about the state of objects. And this knowledge is intrinsically and unavoidably subjective at the fundamental level. This is a fundamental deviation of modern physics from the 19th century (and older) classical physics. But this deviation doesn't mean that everyone who defends modern physics is "on par" with witches or priests or psychics or anyone of that kind. Instead, the adoption of the rules that ultimately refer to the subjective measurements is a critical component of a theory that agrees with the observations of the microscopic world.

As all good textbooks of quantum mechanics have to emphasize and clarify in one way or another, it is critically important that one avoids the assumption that even before the measurement, any of the quantities that may be observed later already have some objective, particular values. Such an objective well-definedness of things that are measurable but before they are measured is prohibited in quantum mechanics because of the uncertainty principle. The set of observables that may be measured is diverse – any Hermitian linear operator is a good observable – and they refuse to commute with each other.

If two observables such as $x$ and $p$ have a nonzero commutator, it just means that they can't have well-defined values because the ordinary values, the $c$-numbers, do commute with each other. So that would be a contradiction. It is not just observables with some continuous spectrum or units that refuse to commute with each other. Two general Hermitian projection operators $P_1,P_2$ also refuse to commute with each other which implies that the answers to two general meaningful Yes/No questions can't simultaneously have well-defined values, either.

Careful physics – and science in general – requires one to abandon the unshakable belief in entities that can't be observed. This attitude – one that philosophers would associate with the words such as "positivism" or "instrumentalism" – became extremely important already when relativity took over in 1905 and its importance has further increased during the quantum revolution.

(By endorsing the words "positivism" and "instrumentalism" used by philosophers, I am not attempting to pay lip service to everything that all philosophers have ever sold under these brands. Recall that philosophers offer at most mixed bags of noise. I mean the interpretation of these words by a competent, not confused, physicist who finds these words useful to describe some actual properties of the validated physical theories he knows well.)

Even the anti-quantum warriors should be able to realize why it is important to respect the principles of positivism. It's really needed to get rid of some mistakes associated with the religious and other spiritual ways of thinking about the world. People may believe in divinities. But as long as these divinities don't influence anything that may be measured or perceived or verified, they don't really exist in the scientific sense. And as soon as we make the divinities able to influence something measurable, these divinities become standard scientific hypotheses that may be tested. In most cases, such "divinities who climbed down to the Earth" may be ruled out within seconds. It's not possible to eat a cake and have it, too. Either your concept or divinity doesn't influence the doable measurements at all, in which case it is scientifically meaningless; or it does affect some of them, in which case it makes predictions – at least in principle – that allow one to falsify the concept.

Allah is an example of such a divinity that a scientist should be ultimately able to kick out of his thinking about science. But what the anti-quantum warriors don't want to hear is the fact that the "objective reality" that knows about everything and that everyone must be able to agree with is also such a divinity that doesn't belong to viable modern science.

The objective reality in the sense of classical physics has been ruled out exactly as safely as Allah, if not more so. Some people want to believe that this can't be possible and they get very sensitive when you inform them that their world view has been known to be wrong for roughly 90 years. But it's just what science has done. It has shown that the paradigm of classical physics is approximately as far from being able to faithfully and accurately describe the phenomena in atomic physics as the religious teachings. As we said, the truth is in the middle – or more precisely, it is separated from the middle in a direction that was unknown before 1925.

Quantum mechanics ultimately respects the "facts" as "subjective perceptions" only. As long as you don't really "perceive" (or "are aware of") the result of a measurement, you are not allowed to assume that the measured quantity or anything related to it has an objective state that would have to be agreed upon by everyone. This brings absolutely no loss of generality or the "increase of incompleteness" relatively to classical physics because even in classical physics that was fully compatible with the notion of objective reality, facts about the state of the real world – whose patterns, correlations, regularities, and evolution were described by the deterministic laws – were ultimately extracted from subjective perceptions.

So the subjective perceptions were always needed for us to "extract the results of measurements" which was needed to compare the theories with reality. Even in classical physics, everything that a scientist knew about the state of objects around him (e.g. locations of planets) ultimately depended on his subjective perceptions. Classical physics used to postulate an additional "auxiliary entity" in between the different subjective observations, namely the objective reality.

But like Allah, the "objective reality" is a divinity that isn't directly observed. The observations ultimately boil down to subjective perceptions – and this is the "modest level of solipsism" that quantum mechanics really endorses – and everything inserted in between are just theories and theoretical constructs that are meant to connect the different observations, the different subjective perceptions. They're parts of "theories" and "theories" may often be ruled out or replaced by better ones. Classical physics along with the notion of objective reality was one such theory – or a class of theories. This whole insertion was falsified and replaced by another theory, quantum mechanics.

Quantum mechanics connects the measurements "more directly". It just abandons a particular assumption – classical physics with the objective reality – about the ideas that are inserted in between the measurements to logically connect them. And it replaces this "heart of physics" with a completely new organ. Some people just can't swallow the fact that their favorite divinity has shared the fate with Allah or the tooth fairy. But they can't change the fact that this is demonstrably what has happened.

The information contained in the state vector or the density matrix is intrinsically subjective. In particular, the "collapse of the wave function" isn't any objective process at all. It only occurs in one's mind – using many thought experiments and metaphors, Heisenberg, Jordan, Born and friends would emphasize this point all the time so it's silly if someone in 2014 tries to present himself as the "discoverer" of these conceptual ideas.

The "collapse" is just the complex, quantum counterpart of the step in which we switch from the original probability distributions for all observables $\rho(x,y)$ to the simpler conditional probabilities $\rho(x_{\rm measured,fixed},y)$ in which the "already falsified possibilities" have been erased and only the already known value of $x$, namely $x=x_{\rm measured,fixed}$, is allowed as the argument of $\rho$ because the other values of $x$ are no longer relevant (they are no longer possible).

This collapse is just an observer's way to simplify the future predictions. He could still remember the whole probability distribution and to take the known facts into account right before every new prediction. The thought experiment involving Wigner's friend (who observes Schrödinger's cat and both are confined in a box) makes it clear why the wave functions (and similarly density matrices) are ultimately subjective. Wigner's friend already observes the cat and views the result as a fact – a fact that may be treated similarly to the treatment in classical physics (but quantum mechanics doesn't require any new "classical addition"!). However, for Wigner himself, the friend is just a bound state of many protons and electrons (emotions aside) so it or he or she evolves into general linear superpositions of macroscopically distinct (as well as similar) states. So Wigner and Wigner's friend may use descriptions in which the wave function "collapses" at different moments. Wigner's friend's wave function for the cat (and his own brain) collapses when he sees the cat; the wave function for the whole box used by Wigner "collapses" later, when Wigner actually looks.

This is no contradiction. There is no reason why the two men should agree about the "moment of the collapse". Those are subjective processes. Wigner's friend's subjective processes are not "directly accessible" by Wigner (and vice versa, although this thought experiment focuses on one side of the relationship only). Only the subjective processes' measurable consequences are accessible and they're only accessible by (and at the moment of) measurements. The moment of the collapse itself cannot be objectively measured because it's a purely subjective process used by a particular observer who uses a particular state vector. When it comes to the properties of the cat that may be measured, both Wigner and his friend will agree about the outcomes. I have discussed this issue in a closely related blog post, Why subjective quantum mechanics allows objective science.

In particular, it's true – and this fact is provable within quantum mechanics, due to various demonstrable correlations that are implied by the laws of quantum mechanics – that once both Wigner and Wigner's friend look at the particular cat, they will agree whether it's alive or dead. If they measure the livelihood of many cats prepared in the same initial state, they may empirically estimate the probability that the cat is alive at the end of the well-defined experiment. They may also compare this predicted probability with a theoretical prediction – and the calculations they use to make the predictions may be similar or the same.

The subjective character of the "collapse" is needed to avoid violations of relativity. If the "collapse" were an objective process of any kind, the collapse needed to enforce the correlations that follow from quantum entanglement would have to involve the superluminal propagation of "real information", and that's simply not allowed by the Lorentz invariance.

Quantum mechanics does agree with the harmony between different observers' perceptions of different things that may be actually measured. But the agreement may only be checked – and predicted by quantum mechanics – after both men actually measure the quantity. Quantum mechanics doesn't guarantee any agreement between the two men's descriptions of an object before both men complete their measurement. That's no contradiction with anything because if you don't do measurements (or before you do your measurements), you can't disprove any statement about the measured quantity (or find any paradoxes).

In this respect, quantum mechanics fundamentally differs from classical physics. In classical physics, the agreement between the observers applied at all times, even before the measurements, and it applied trivially. It was true because of a very simple and strong assumption that classical physics made – namely that everything is fundamentally described by "objective reality at each moment" that all observers have to fundamentally agree about if they are accurate enough.

Quantum mechanics just refutes this assumption. The assumption is no longer correct. But it doesn't mean that everything in quantum mechanics depends on the observer or that quantum mechanics is just like a religion or the teachings of witches and psychics. It isn't. Unlike the teachings of witches and psychics, quantum mechanics agrees with all the observations. People could only find it because they carefully removed all assumptions of their thinking that couldn't have been really, operationally demonstrated – i.e. demonstrated by their true perceptions of the results of measurements. When this was done, people realized that the assumption of the objective reality in the classical sense had to be removed just like the tooth fairies. It's just wrong at the fundamental level.

The usual agreement between different observers about everyday life events still follows from quantum mechanics but it only follows as an approximation. According to quantum mechanics, the objective reality is an emergent, approximate concept.

To summarize, anti-quantum jihadists who say things like "you have to adopt my realist world view or 'interpretation', otherwise you are an evil solipsist" are just fooling themselves. It is not true at all that these are the only two possibilities. The true description of Nature, quantum mechanics, is wonderfully different from both of them and from anything else that people had considered before 1925. Quantum mechanics has carefully eliminated assumptions whose validity or existence cannot be operationally proven.

A detailed analysis of the processes in the microscopic worlds – including stable atoms, the estimates for the heat capacity of atoms, interference patterns produced by particles, quantization of energy carried by electromagnetic or other monochromatic waves, and so on – has shown that the notion of the objective reality in the sense of classical physics had to share the fate with tooth fairies.

The people who are trying to revive the objective reality – whether they are assuming Bohmian "real particles plus guiding waves" or various forms of "objective GRW-like collapses" or "many worlds" or any other classical visualization what's going on – are not closer than proper quantum mechanical physicists to genuine science. Instead, they are stubbornly defending the indefensible, a notion (of the objective reality) similar to a tooth fairy that cannot be extracted from our real perception of observations and that may actually be shown to be wrong by a careful enough (but not excessively complicated) analysis of several representative processes in the microscopic world.

The anti-quantum jihadists are doing nothing else than to defend their belief which is just another religion, as indefensible as many others if not more so. So the right analogy is one between the anti-quantum jihadists and other religious believers. Meanwhile, quantum mechanics – and science in general – is living its own life, happily demonstrating that certain theories or propositions are correct while others are wrong, whether someone likes it or not.

#### snail feedback (7) :

"[...]Wigner's friend's wave function for the cat (and his own brain)
collapses when he sees the cat; the wave function for the whole box used
by Wigner "collapses" later, when Wigner actually looks.

This is no contradiction.[...]"

IF, for Wigner, the wave function collapses to a different measured, fixed X as it did for Wigner's friend, there most definitely IS a contradiction (AKA the measurement problem).

There is no contradiction only IF, for Wigner, the wave function collapses to the same measured, fixed X as it previously collapsed for Wigner's friend.
For this to always happen, when the wave function collapsed for Wigner's friend, it must have collapsed for Wigner as well; the uncertainty Wigner has regarding the result of the wave function collapse merely reflects his own ignorance, not any ability of the wave function to collapse to another position as the measured, fixed X Wigner's friend saw.

reader Kimmo Rouvari said...

Don't you think that there exists a TOE and QM is only an approximation from it?

reader Luboš Motl said...

No, there is no contradiction. The actual facts described by the words "measurement problem" are no contradiction at all - or at most a contradiction between the reality correctly described by quantum mechanics on one side; and people's invalid assumptions that the world behaves classically on the other side.

reader Luboš Motl said...

No, TOE surely respects the postulates of quantum mechanics exactly. The TOE is a special particular quantum mechanical theory. I have no doubts about it whatsoever.

If, for Wigner's friend, the wavefunction collapsed to a measured, fixed X, and for Wigner the same wavefunction collapsed to a different measured, fixed X', then Wigner's friend 'reality' and Wigner's 'reality' will be different - which will be obvious when they meet and compare notes.

That's a contradiction - whether you call it the measurement problem or whatever.
Unless you actually subscribe to quantum mechanics as solipsism AKA the fuzzy concept of quantum mechanics creating different realities for each observer - contradictions between these realities be damned.

reader José Ignacio said...

QM predicts a probability of contradiction inversely proportional, roughly, to the number of atoms of the observers, and this extremely tiny quantity is equal to zero for all practical purposes.
You can see these affirmations in the book "Quantum theory: concepts and methods" by Asher Peres.