Wednesday, August 21, 2019

QM "also" applies to the Universe

Critics of quantum mechanics are wrong about everything that is related to foundations of physics and quite often, they please their readers with the following:
Physics has been in a crisis since 1927. You can help to end it if you accept [all the fragmented pottery I am writing now]. Amen.
That's what you can read on the front flap of a new book by a Californian would-be quantum physicist.

You may see that they 1) resemble fanatical religious believers or their postmodern, climate alarmist imitators or the typical propaganda tricksters in totalitarian regimes. They tell you that there is a crisis so you should throw away the last pieces of your brain and behave as a madman – that will surely help. 2) They are just an extension of the anti-string demagogues who are saying pretty much identical sentences but with years such as 1968 or 1974 or 1984. 3) Their thinking is totally irrational because whether a problem with physics exists is surely independent of the question what a lay reader believes. But they want to make the obedience of a reader who doesn't really understand anything to be central for the health of science, for the presence or absence of crises! This has nothing to do with the rational thinking about the world although it's relevant for the profits from the trash by which they flood the bookstores.

In reality, the years 1925-1927 brought vastly more true, vastly more solid, vastly more elegant, and vastly more accurate foundations to physics, foundations that are perfectly consistent and that produce valid predictions whose relative accuracy may be \(10^{-15}\) (magnetic moment of the electron).

On the new postulates of quantum mechanics, people have built atomic and molecular physics, quantum chemistry, modern optics, lasers, condensed matter physics, superconductors, semiconductors, graphene and lots of new materials, transistors, diodes of many kind, LED and OLED and QLED panels, giant magnetoresistance, they are building quantum computers that would make the quantum revolution even more essential. They have extended theories of the nuclei, subnuclear physics, found and understood new elementary particles, and unified them within unified field theories and especially string theory which has also allowed them to study the black hole entropy, evaporation, and topology-changing quantum processes in the spacetime, aside from many other things.



The brain defect that makes someone say that "physics has been in a crisis since 1927" must be severe and it is probably incurable. Other "critics" – if I kindly avoid musings which of these inkspillers belong to special facilities that Germany was building some 80 years ago – will tell you:
Everett, an unjustly fired progressive, was fighting a heroic battle against the reactionary Niels Drumpf Bohr and Werner Drumpf Heisenberg and their deplorable supporters.
That idea appears in another real book.

Nice but not really. Everett was just a lousy student and a crank who showed the lack of potential to understand, or contribute to, fundamental physics so he just couldn't have gotten a job in that field when the meritocracy was still a thing – while some unhinged destructive activism wasn't widely praised yet. Niels Bohr and Werner Heisenberg were top and revolutionary 20th century scientists. And making conditions in which physics decisions are made according to politics – and even emotional political instincts – is just incredibly bad.

But books – and many books – with similar outrageous claims are really filling bookstores these days, they are being pushed down the readers' throats, and people are even being blackmailed when they point out that these books are pure garbage.



But many such deeply confused yet radical people including their listeners will often produce the following objection:
There must be something wrong with quantum mechanics (or with the "Copenhagen Interpretation") because it can't be applied to the Universe, can it? There were no observers in the Universe some time ago so there was no one who could have made the collapse and that's such a catastrophe.
Quantum mechanics is the new foundation of all of physics and physics studies "things" including the Universe.

In fact, the Universe is quite a characteristic thing that is studied by physics, isn't it? When a layman tries to describe what a theoretical physicist studies, the layman may often say "the Universe", and for a good reason: physics ultimately describes everything that physically exists – the Universe – and by talking about the whole Universe, i.e. about the maximally long distance scales, we really nake it clear that we don't want to be satisfied with any approximate laws whose validity is confined to some intermediate scales. Sheldon Cooper also defined a theoretical physicist as a man who understands all the important things in the Universe.

Quantum mechanics says that the wave function is indeed evolving into an increasingly diluted superposition of an increasingly diverse collection of alternative histories – and any unambiguous outcome is only produced with the help of a random generator, and only in the presence of an observer who just makes an observation. The collapse of the wave function is just a mathematical description or reflection of the observer's new knowledge about the state of the physical system – e.g. the Universe.



Now, an extreme example. This is a map of the temperature of the CMB (Cosmic Microwave Radiation, a lot of photons in the Universe identical to those emitted by "warm" objects whose temperature is just –270 °C) as detected by the Planck satellite in 2013-2018. The COBE satellite and WMAP previously produced less sharp versions of the same picture in 1992 and 2003, respectively.

We should ask: Does quantum mechanics say that before these satellites have measured these pictures, the precise information about the Universe that is shown on these pictures "didn't exist"?

There were no Czechs who could check 1400 years ago, no Slavs 1600 years ago, no whites 20,000 years ago, no homo sapiens a few million years ago, no homo 7 million years ago, no mammals 350 million years ago, no life on Earth 4.4 billion years ago, no Earth 4.6 billion years ago, no nuclei when the Universe was much younger than 3 minutes etc. At a sufficiently early moment, there was no one who could make the observation of this particular picture or a highly correlated one.

The answer is that quantum mechanics mainly says that it was meaningless or impossible to talk about any particular image describing the CMB before the observers looked. Quantum mechanics really says that the precise map of the CMB temperature was unknown. Everyone knows that the previous sentence is uncontroversial. If there are no agents that are smart and skillful enough to "know", something remains "unknown".

But the critics of quantum mechanics aren't satisfied with that. They may say:
You just said that the CMB map was unknown but you also mean that it didn't exist, it was unknowable, right? And that's the blasphemy!
Right. Quantum mechanics says that in the absence of observers, data such as the information about the CMB map is also unknowable – because the observers are actually a necessary but not sufficient condition for something to be known. Because they are a necessary condition, you may prove that their absence not only means that things are unknown but indeed, they are unknowable, too.

Concerning the existence, it's a particularly problematic verb in these discussions. What can we mean by saying that something exists? If we want to meaningfully define the bits of information saying "whether something or something else exists", we need an operational definition that may be done – at least in principle – to decide whether it exists or not. In this case, the "existence" might mean that in principle, there could have been an observer who actually knew the CMB map – even before there were any humans.

Well, there could have been life on another planet in the Universe that was born long before the Solar System was formed. These early observers could have observed the CMB before humans. And if we could talk to them or find traces of their observations, we would unavoidably find out that their maps are compatible with ours. Quantum mechanics guarantees this compatibility. In quantum mechanics, the observation of the CMB directly and the observation of the results done by another careful trustworthy observer in the past boil down to nearly identical observations so quantum mechanics prevents you from getting completely different results.

On the CMB map, you may see a lot of noise. The temperature is really some 2D random-walk-like function of the two angular coordinates \((\theta,\phi)\) labeling the direction where we look. Where did these random numbers come from? Well, quantum mechanics is the correct theory of everything so all the data describing the state of things that exist – anywhere in the Universe including "the Universe as a whole" – must be obtainable from quantum mechanics.

Yes, quantum mechanics helpfully has the ability to produce random numbers. Is the quantum mechanical random generator responsible for the chaotic CMB map as well? Yes, it is. It has to be. In fact, assuming that the cosmic inflation was at least spiritually right, and it almost certainly was, the random function describing the temperature \(T(\theta,\phi)\) of the sky came from a wave functional of the inflaton – a function of infinitely many real variables describing a probability distribution for functions on the sphere.

How does it work? If you look in a direction given by \((\theta,\phi)\) now, you only see photons that were emitted "at the right moment". If you assume that all the photons were emitted roughly 300,000 years after the Big Bang when the Universe became transparent because most electrons finally "settled" and teamed up to create atoms along with the nuclei, you must look at the sphere around us whose radius is morally "13.8 billion years minus 300,000 years", although this description can't be taken literally. That sphere was much smaller than it is today (in meters) when the Universe was 300,000 years old.

We want to say something about the temperature of the photons on that sphere at the moment when the Universe was just some 300,000 years old – because that is the temperature that Planck observes like \(T(\theta,\phi)\). Almost nothing nontrivial has occurred in the subsequent 13.8 billion years – the photons were just propagating freely towards our telescopes where a tiny fraction of them is caught. That free propagation means that the measurements of the CMB that we do today are almost equivalent to similar measurements that could have been made when the Universe was 300,000 years old. The intertemporal dictionary is almost trivial.

Why was there a variation of the temperature those 300,000 years after the Big Bang? There was always some variation of the temperature, basically the same, but it didn't change much since a tiny split second after the Big Bang where the temperature was basically an increasing function of the inflaton \(\Phi(\theta,\phi)\). The inflaton field didn't have the same value at all places of the Universe. Fields – and they're ultimately quantum fields if you look carefully – just oscillate.

Imagine you recall the first lectures of a quantum field theory course and write the free field \(\Phi\), the inflaton, as a sum over the momenta \(\vec k\) of the creation and annihilation operators. You will be reminded that a free field is mathematically equivalent to an infinite-dimensional harmonic oscillator. This oscillator has infinitely many copies – labeled by \(\vec k\) – of the position and momentum \(x,p\) from the ordinary harmonic oscillator. Here, the positions and momenta \(x_k,p_k\) are associated with values of the 3-dimensional vector \(\vec k\) – and these \(x_k\) or \(p_k\) are related to the field \(\Phi\) by being the Fourier transform of \(\Phi\) or \(\partial_t \Phi\) into the \(\vec k\)-basis, respectively. Some \(\vec k\)-dependent normalization factor may appear there, be careful.

The wave function of this infinite-dimensional harmonic oscillator from the Fourier modes of \(\Phi\) is the Gaussian\[

\Psi \sim \prod_{\vec k} \exp(-C_{\vec k} x_{\vec k}^2/2)

\] I wrote the wave function in the \(x_{\vec k}\)-representation. The \(p_{\vec k}\)-representation would be a simple Fourier transform over infinitely many variables. Note that the Fourier transform of a Gaussian is another Gaussian – and their widths are inversely proportional to each other (as expected from the uncertainty principle, in fact, the Gaussian is the only wave function that saturates Heisenberg's inequality).

The coefficients \(C_{\vec k}\) inside the exponents are calculable – and of course, they have a very simple form for a free field. I leave these coefficients as an exercise for you.

You see that my \(\Psi\) is really a wave functional because it's a function of infinitely many variables \(x_{\vec k}\). The overall normalization is not too important – normalization factors don't matter much for wave functions – and to normalize the wave functional to unity, you would have to define your rules for the infinite-dimensional integral including the normalization and deal with some seemingly infinite or vanishing factors (that nevertheless cancel in the physical predictions).

At any rate, the product of Gaussians tells you that the probabilistic standard deviation of the variable \(x_{\vec k}\) is nothing else than \(1/\sqrt{C_{\vec k}}\). If you want to be God and pick a nice random representative of the functions \(\Phi(\vec k)\) or \(\Phi(\vec x)\) or \(\Phi(\theta,\phi)\), you just produce random numbers \(x_{\vec k}\) that are normally distributed with the aforementioned standard deviations, and interpret these numbers as the Fourier coefficients to actually compute the function \(\Phi\) as a sum over \(\vec k\).

When you write \(\Phi\) as a function of \(\vec x\) in 3D or the angles \(\theta,\phi\) – and you need at most a straightforward Fourier transform for that plus some simpler steps – you will get a random function that is qualitatively the same as the Planck map of the CMB. The funny point is that:

Indeed, COBE or WMAP or Planck may be viewed as the observers that made the observation for the first time and "collapsed" the wave functional – that previously included all possible similar maps from the distribution – to the map that COBE, WMAP, Planck gave us, or a nearby compatible map.

The information about the CMB map was unknown just 30 years ago and it is known now. So these teams have "created some information" or "made some information known". Is that shocking? In this formulation, it can't be shocking. The problem with the folks who don't want to believe that quantum mechanics works is that they realize – and correctly realize – that the result of a measurement in quantum mechanics isn't "just" about the knowledge. The measurement influences the state of the system and, in this sense, helps to create a new reality.

So COBE, WMAP, Planck are suddenly claimed to be unbelievably powerful! Like the person who opened the box with Schrödinger's cat, they "create" the whole shape of the Universe. Note that the warmer spots in the CMB are those with a higher number of stars or galaxies, colder spots have a deficit of stars and galaxies, the whole particular appearance of the Universe was suddenly created by a few humans in COBE, WMAP, or Planck. Is it possible?

Again, calm down. They just made something "known". Before that, it was unknown and, assuming no other intelligent observers before us, "unknowable". But when something is "unknowable", it also means that it can't lead to any contradictions. That's the basic reason why quantum mechanics easily protects the consistency.

The more careful, relevant, and refined question is:
Can we assume that the particular Planck map "existed in the classical sense" before COBE, WMAP, Planck made their observations? Please!
Importantly enough, I was more accurate in the question than others. By "existence", as I made it clear, I meant "existence" of the information as imagined in classical physics. That refinement makes it a bit more clear what "existence" is supposed to mean. And it gives us a clue how to approach such a question: If the CMB map "existed" in the classical sense, it means that classical physics must have been a good enough approximation to describe these degrees of freedom. Was it?

The information about the modes \(x_{\vec k}\) whose calculation was sketched above has been imprinting into many other degrees of freedom – the density of hydrogen, stars, galaxies, photons – and this system is so chaotic that for all practical purposes, different values of the CMB map i.e. different collections of numbers \(\{x_{\vec k}\}\) were decohering from each other – already since the end of inflation or so, when the cosmic age was just a split second. Because of this decoherence, we may say that indeed, it is consistent to add the extra assumption that the values \(\{x_{\vec k}\}\) existed in the classical sense, at least since the split second after the Big Bang.

If you think about the (highly continuous) basis of the inflaton quantum field's Hilbert space (Fock space) in which different points in the infinite-dimensional space \(\{x_{\vec k}\}\) are the basis vectors, then we may say the following:
For the very long time, it was virtually impossible to measure the observables that are non-diagonal in this basis.
Because all the feasibly measurable observables are diagonal in the basis, the classical logic seems good enough for this space – at least since the end of inflation – and we may add the approximate axioms that the probabilities associated with different values of \(\{x_{\vec k}\}\) etc. are being added just like in classical physics, the quantum interference cannot affect anything that is measurable, and therefore the "story about the Universe" that classical physics would give us doesn't add any contradiction to quantum mechanics.

At the same moment, it's utterly pointless to add these "classical memes" to the quantum story about the Universe. By a classical meme, I mean the claim that the "particular CMB temperature map already 'existed' before COBE observed it". Well, it may have "existed" but this statement is utterly scientifically useless metaphysics because no one knew the CMB temperature map.

One way to parameterize the "surprise" about the need of observers is to say that COBE, WMAP, Planck look "too important" – they were "changing" the whole Universe. But that's overstating what they did. They just made something known – the particular CMB map they found had been a possibility before they observed it. The only thing that the experimental cosmologists "created by their free will" was the Heisenberg choice, i.e. the choice of the observables they wanted to measure, basically \(\{x_{\vec k}\}\). Did they have much choice? Well, I've already said that since the end of inflation, the assumption that \(\{x_{\vec k}\}\) "objectively existed" in the classical sense wouldn't allow to prove sharp contradictions. Only observables diagonal in this basis were feasible measurable – so COBE and others didn't have much choice.

Another reason why you should calm down is that the claim "COBE is the observer that made the collapse" doesn't really mean that "COBE was the objectively unique observer in the world who did it". Instead, quantum mechanics allows many observers to co-exist (including extraterrestrial colleagues of the Planck Collaboration who just got a new ET grant now). They have their own perspectives. Whenever they compare their results of measurements of the "same thing", they are guaranteed by the rules of QM to be compatible. But that plurality of observers is the actual reason why QM talks about observers at all. And that plurality makes a single observer less important in the "objective" scheme of the world. The idea that "COBE is cosmically important because it's COBE that did the collapse" is just another manifestation of the knee-jerk tendency to eliminate observers and make physics objective (classical) again, another manifestation of the misguided idea that the wave function is an objectively real wave. In quantum mechanics, the observer isn't unique so the collapse just can't be interpreted as a uniquely important event in the history of the Universe. The collapse of a wave function really does mean that the state of the Universe changes – but in general, it only changes according to the perspective of this particular observer who owns this particular wave function.

However, you should realize that the classical assumption about the "objective existence of the numbers \(\{x_{\vec k}\}\)" is only admissible since the end of inflation, a split second after the Big Bang, and there was preceding era - the inflation itself and perhaps some phenomena before inflation which are obviously hard to study, especially experimentally, because inflation has brutally weakened all the traces of such phenomena – in which the non-diagonal operators that were sensitive to the relative phases between the coefficients of the ket vectors \(\{x_{\vec k}\}\) were in principle important and measurable. What do you do then?

Well, in these very early epochs, it is indeed extremely important not to use any classical approximation – in which some values of \(\{x_{\vec k}\}\) are considered "objectively real" – because the probability amplitudes in front of various points \(\{x_{\vec k}\}\) in the infinite-dimensional space were quantum interfering with each other. Whenever the quantum interference could have impacted the Universe in any way, it is absolutely critical to describe the Universe quantum mechanically i.e. to avoid the assumption that a particular collection of values \(\{x_{\vec k}\}\) was "objectively correct". The information about \(\{x_{\vec k}\}\) during or before inflation could have only been described using the full-blown quantum mechanics and its wave functional.

The instinct "quantum mechanics can't work for the Universe, can it?" is clearly nothing else than another manifestation of the anti-quantum knee-jerk responses. People who say such things simply don't want to accept quantum mechanics as fundamentally more true than classical physics anywhere. At most, they want to treat it as some helpful illusion that must go away very soon, surely before important things – such as the Universe and the CMB – are discussed. Those things must be observer-independent and the classical framework must take over, right?

No. Not at all. Quantum mechanics is the fundamentally correct framework and it's classical physics that is inaccurate and/or whose range of validity is restricted. It's classical physics that is the illusion. And it's the idea that physics may be done without any reference to an observer that is fundamentally misleading and, whenever fundamental enough processes are discussed, producing absolutely incorrect claims about Nature. The precise description of the Universe needs observers, this fact is true even when the whole Universe is discussed, and it is "especially" true when extreme phenomena in the whole Universe are being discussed.



P.S.: Open and closed systems

Sometimes, extra confusion is added to the question "whether QM applies to the Universe" when it's mentioned that the Universe is the only closed system we can have etc. Note that we distinguish open, closed, and isolated systems that may exchange matter+energy, just energy, or nothing (with the rest), respectively. The Universe doesn't have any "rest" so none of these adjectives is strictly right. On the other hand, having no rest is basically equivalent to an "isolated" (or at least "closed") system because nothing is being exchanged.

(Well, the mass-and-energy conservation law – and there is only one once relativity is taken into account – is violated in cosmology so it doesn't make much sense to talk about the "banned exchange" – even in the absence of the "rest", the conservation law is violated.)

But there's no extra complication coming from an "isolated" system. That's the normal system we study in a simple physical analysis – whose description is expected to be complete because no unknown "environment" is bringing extra uncertainty. The Universe is pretty isolated which makes things simpler not harder to describe. However, the visible part of the Universe – bounded by the event horizon – may be open and we do expect related subtleties in quantum gravity, e.g. the horizon complementarity that means that (like in the black hole interior and exterior), the space-like separated fields don't quite commute as expected from QFTs if there's a horizon in between.

Another popular source of "deliberate confusion" is the observation that one has to divide the world to the observer and the observed and it should be "impossible" when we study the whole Universe. Well, again, there is no difference between the Universe and smaller systems. Quantum mechanics says that the observed data must always be evaluated from the perspective of an observer who lives next to the observed! The claim that we study the "whole Universe" cannot be used to get any exemption from the rule. In other words, to study the whole Universe "without picking any observer" is exactly as impossible as the probing of any other quantum system without any observer.

As you can see, the words "whole Universe" are often screamed to emphasize that "this time, the observer must finally really be banned" but it's another variation of the old ludicrous game. You just can't ban or sacrifice observers in quantum mechanics.

No comments:

Post a Comment