## Monday, August 10, 2020

### Positivism: relativity, QM just demand questions to be precise

Off-topic: A fun popular stringy talk by Cumrun Vafa from the last week, hat tip: Erwin

And translatable to well-defined properties of the sensory perception

The laymen usually refuse quantum mechanics – and jump on the bandwagon of moronic pseudoscientific fairy-tales such as Bohmian mechanics, many worlds, objective collapse, or even superdeterminism – because they are just overwhelmed by the very realization that the observer plays any role in the application of the theory.

The insight that observers matter sounds like "soul" or "religion" and materialists in a very broad sense (a set that happens to include many Catholic theologians, it turned out) just instinctively refuse it. But it is simply wrong to reject scientific propositions instinctively; it is wrong to clump and conflate them according to ideological criteria. Even if the quantum mechanical observers were "religion", it's not the same as "Islam" or something like that and your usual arguments against religions simply fail. They certainly fail. In fact, the basic postulates of quantum mechanics and demonstrably true.

As I have written many times by now, early 20th century physicists like Einstein and Bohr – who kickstarted modern physics – were great readers and admirers of philosophers of their time. And those philosophers just happened to be intelligent and scientifically literate in some cases – and they were probably lucky in some others. Philosophers obviously mustn't have any "right" to influence the direction in which science evolves – science has its own rules that are totally independent of the shaky authority of philosophers and their intrinsically unscientific method – but there's nothing wrong about a physicist who just happens to read a philosophical book. If there is any outcome of this "inspiration", it will still have to pass the scientific tests. Einstein and Bohr did read a lot of philosophical stuff.

The late 19th century philosophy was dominated by positivism founded by Auguste Comte. Ernst Mach had belonged to that school as well although he wanted to look more special when he was older. Positivism is just a "flavored" variation of empiricism: what may be known about the world is known from observations. Positivists made a small refinement: the observations really require sensory perception at the end. Everything we know is ultimately reduced to sensory perceptions. The real point is that if a sentence or a question can't be translated to a well-defined, "operationalist" statement about our perceptions (involving the senses), then it may be meaningless.

It may also be meaningful and scientific theories may use lots of concepts that can't be "seen", at least not directly, like quarks, but you can't "assume" that sentences that are disconnected from well-defined (elementary or composite) properties of the information detected via our senses are meaningful. At the end, what I am saying is really common sense – a variation of the dictum "a scientist should be precise and careful to say meaningful things". In particular, the sentence
the number five is green
is meaningless. It is silly to associate colors like green with numbers; colors should be reserved for objects that may be observed with our eyes (the color derives from the parts of the visible spectrum that are reflected or emitted by the object whose color is being discussed) and the number five lives in a more abstract world where we don't really use eyes to look at things. Well, if you follow the latest discoveries by "professors" who are intellectually equivalent to poultry, you know that the number five is green, after all. The number 4 is both red and white because 2+2=4 is an example of white supremacist patriarchy which can only be supported by oppressors who have swallowed the red pill. Everyone who is green (i.e. brain-dead) knows that 2+2=5 and that's why the number five is green, too.

OK, that wasn't meant to be a completely serious conclusion. "The number five is green" is a meaningless sentence. And so is
Faraway events A,B separated by distance $$\Delta x \neq 0$$ and time $$\Delta t\lt \Delta x / c$$ occurred simultaneously.
Just like you can't see the "color of the number five" by any experiment, you can't make a universal experiment that detects whether two events are simultaneous. More specifically, if you design such an experiment, it will depend on the speed (the reference frame) of the experimenter who was synchronizing the clocks across the space which is needed to determine whether events are simultaneous. Albert Einstein understood this important point in his 1905 special theory of relativity whose basic message was that the property
events A,B occur simultaneously
is too ambiguous or meaningless as it stands. And if you want to fix it, you need to extend it to
events A,B occur simultaneously according to a chosen reference frame (e.g. TRF).
In particular, the speed of the reference frame or "observer" in the sense of special relativity matters for the question whether two events are simultaneous.

Fine, many laymen who study physics hard enough reconcile themselves with this thesis – the simultaneity of events is relative (frame-dependent) just like the speed itself was obviously relative (you must say "speed with respect to what" because there's really no universally preferred "what"). There are still some objective quantities and truths in special relativity, the invariants etc. (Einstein considered the term Invariantentheorie for relativity to emphasize the properties that are not relative which makes them precious. But both relative and invariant quantities play their role in relativity. Relativity has made a larger number of concepts relative i.e. frame-dependent; and it has made the calculation of the invariant quantities more mathematical subtle, more constrained and thus more predictive, as well as more elegant than before.)

It's "easy" to accept the frame-dependence because the transformation between the reference frames is "straightforward enough" (the Lorentz transformation) and the set of allowed reference frames is as simple and "materialistic" as the set of possible velocity vectors $$\vec v$$. Quantum mechanics is harder because it requires a much greater degree of "refinement" of the questions – and pretty much all of them. Quantum mechanics tells you that the statement
the physical object A has some property, e.g. location equal to $$x$$
is meaningless in general, just like the statement about the simultaneity of events. It needs to be refined. Just like in relativity, you needed to add "according to which reference frame" to discussions about simultaneity, in quantum mechanics, you need to add "according to what observer" into all statements about the state of objects and the Universe, including statements about the positions, momenta, or angular momenta of particles, molecules, and everything else.

And the "observers" in quantum mechanics don't form a set that is as simple as the $$\RR^3$$ space of possible velocities $$\vec v$$ in relativity (the hyperbolic space $$H^3$$ may be a better way to imagine that 3-dimensional space). Instead, we really mean all possible humans and perhaps all possible animals, conglomerates of humans, intelligent computers, or anything else that may perceive any property of its (and indirectly of other objects). That's a much broader and less controlable space than $$\RR^3$$ and people just have a problem with it.

But at the end, this required refinement means nothing else than "you need to specify how you operationally measure the quantity you want to be discussed".

The truth could be at risk of becoming totally relative and spiritual – because when you start to study the Universe, you are not given the list of "all possible apparatuses that may be used to find the properties of objects". Classical physics has the property that you don't need to know anything about the measurement apparatuses because the properties of all the other objects in Nature (and the apparatuses as well, if those exist) are defined as some mathematical sets. You can talk about them without any attention to the set of possible apparatuses that are used to measure things. In classical physics, it may be assumed that all apparatuses and observations are composite or emergent objects or processes.

However, this subtlety is important in quantum mechanics where it's experimentally demonstrable that any measurement that extracts a nonzero amount of information does perturb the measured object. OK, so it still looks hard: if you study the hydrogen atom, it looks like I am demanding that you first learn all possible engines, devices, gadgets, and facilities that men (and a woman) have ever built or will ever build. It's not really possible, so you can't study the hydrogen atom by quantum mechanics, you could say. It seems hopeless.

But it is not hopeless. Why? Because quantum mechanics doesn't actually require you to study the actual experimental gadgets that may exist. The theory tells you what is the list of all possible unequivalent measurement procedures that extract some information about the hydrogen atom (or anything else). And this list doesn't care about the plastic round buttons or LCD displays that some apparatuses may have or not. Quantum mechanics tells you that for any Hilbert space $$H$$, the space of all linear Hermitian matrices (operators) $$L$$ acting on $$H$$ enumerate all possible "observables" which are the quantities that are found "to be equal to particular real numbers" once the appropriate apparatus does the right job. There may be various apparatuses measuring $$x$$ or a bit $$j_{z,i}$$, for example, a Finnish, a Swedish, or a Chinese one. These three gadgets are exactly but perfectly equivalent realizations of the measurement of these observables. Which one would you choose (e.g. in the case of bits from the 5G datastreams)? The Finnish one, of course. ;-)

So quantum mechanics is a very nice framework that immediately classifies all apparatuses that may be helpful to study an object – whose Hilbert space is known or constructed in some way. Quantum mechanics won't directly tell you how you should design the appropriate apparatus (and it surely doesn't build it for you if you are manually challenged) but it does classify all the options. The really new aspect of the universal postulates of quantum mechanics is that quantum mechanics, to be applied, requires an arbiter, an observer, who invests his or her trustworthiness and says that "a measurement has been done and I found $$x=2+2=4$$, for example". This statement, however subjective or human-dependent it may be, is needed to produce any predictions for experiments – that will be verified experimentally in the future, by another unavoidably subjective or human-dependent act.

The observer-dependence is different from classical physics but it is in no way unscientific or contradicting any scientific findings etc. Quantum mechanics with the observer dependence is really needed – and it is a much more correct foundation to build physics than the observer-independent classical physics turned out to be. It's really common sense: to be able to predict whether some observables will have some values, you need a precise enough definition that says what the observable really is and "who measured it". If you can't say "whether the right agent measured it" when you try to describe the initial state, it's unsurprising that similar vagueness or ignorance will exist about the final state, too.

And it's ultimately unsurprising that the theory, quantum mechanics, wants both the initial and final state to be described operationally so you really need a well-defined "framework to codify the truths" (ideally associated with a very reliable and precise experimenter and her apparatuses). Good science just needs experiments and you need to get your hands (or someone else's hands: it's enough for many of us) dirty.

Classical physics allowed the observer-independent description, a "realistic" model of the reality, which didn't need to discuss what are the possible apparatuses, observers, and perceptions at all because the truth was "objective". But one might say that intellectually limited people love it because they love to be indoctrinated and told what is the truth. They don't actually want to verify or measure anything which is why they have never collided with the idea that the method to extract the experimental facts might be subtle. They want to feel important by being obedient brainwashed sheep who are demanding other people around them to become obedient brainwashed sheep, too. In a herd of mindless sheep, the observer independence sounds tautologically true – because all sheep are obliged to copy the herd's opinions. But that principle of classical physics is not actually true in the world around us.

But science really doesn't work like that. The truth doesn't come from an objective authority. The truth comes from the experiments, from the sensory perception, and those have a subjective character, at least in principle. Quantum mechanics needs the user to know "who defines what counts as a measurement", it must be inserted as an input, otherwise the wave function cannot be known. The wave function is a mathematical object that may be calculated from the subjective sensory perceptions of some of the information about the initial state.

If you think about it, it is obvious that this subjective character of the statements about the observables just cannot be eliminated entirely. The application of the theory must be dependent on the observational data and if those are bad, the predictions will be wrong or inaccurate, too. Again, as I am saying from the beginning, the observer-dependence of quantum mechanics is just the positivist dictum "you are obliged to refine all statements about observables" because you must make it clear who (or which perspective) counts as the observer.

Observers, including humans and their apparatuses, are dirty, complex, insufficiently localized or well-defined objects. But that's really the reason why quantum mechanics must work the way it does. The observer (like a human) clearly causes something like the loss of most interference patterns in all nontrivial quantum measurements. But the observer can't be objectively encapsulated or defined – he or she or it isn't sharply separated from the rest of the world and we don't really know "who has consciousness" of the right type etc.

That is why this choice of the observer (it is "my wave function") must be inserted as a part of the input. At the end, it is not more qualitatively mysterious than the special relativity's relativity of simultaneity (e.g. the dependence of the simultaneity on the reference frame). You can't experimentally prove that "simultaneity is objective" and indeed, it's not. You should just understand that the same logic must be applied to the observer-dependence in quantum mechanics, too. You can't experimentally prove that the statements about any observables are objective or independent of observations. Why can't you prove it? To prove that something exists without observations, you're obliged to avoid all observations but if you avoid all observations, you can't prove anything about the Universe because it's science, stupid! ;-) That's why the statements about observables may be subjective and a refinement ("which observer") must be added to all propositions and quetions. And that's indeed how Nature works.

Everyone who understands that natural sciences are superior relatively to social sciences, humanities, and other pseudosciences must love this feature of modern physics. Many propositions involving the allowed words (like electron's location) are as meaningless as "five is green" if you don't specify the observer or some other refinements. Linguistics and humanities aren't actually enough to do physics: you need to pay at least some basic attention to the measurement process because natural science cannot work without it, whether linguists, humanity types, and anti-Copenhagen crackpots like it or not! The search for an observer-independent description of quantum phenomena is as stupid as the search for a universally preferred inertial frame. If you added this "only allowed and objective" vantage point, the theory would get worse, not better. The Lorentz symmetry and symmetries between observers and observables are the features that make relativity and quantum mechanics so beautiful and robust. They're the real reasons why good physicists are certain that the theories are right.

When it comes to the basic logic, the people who have problems with the genuine theory of quantum mechanics (pejoratively called Copenhagen) are doing the same type of a mistake and self-delusion as the anti-Einstein crackpots who will simply never accept that the simultaneity of events is relative. Once an intelligent person learns the general lesson that "previously seemingly objective statements may be subjective, relative, or they may require a clarification or additional experiment-related information to be inserted", he should be able for this mental step in many other contexts. He should be able to do the analogous step in the case of quantum mechanics, too, otherwise he isn't intelligent enough to learn profound lessons from Mother Nature.

And that's the memo.