Sunday, March 25, 2018

What is real? An experiment with Wigner's friend Stephen Hawking

Half a week ago, I discussed Adam Becker's new book, What Is Real?, which is another attack on standard quantum mechanics or the "Copenhagen interpretation", if I use a slur popular among the haters of quantum mechanics. In the book, all the founders of quantum mechanics are villains or criminals who have organized a cabal that has forced the scientists of the 20th century to repeat claims that quantum mechanics was correct even though, in reality, the Earth was flat (as Mad Mike Hughes proved today by launching a rocket with himself in California; by the way, from the height of 1875 feet, he must have seen that the Earth was round and "terminated" at the distance of some 40 miles from him). Everyone who has opposed the cabal is a hero. The more alcohol he has drunk, the greater hero he is.

Peter W*it has published a blog post titled "What Is Real" which has attracted some 40 comments. If you want to participate in that discussion about "What Is Real", you must just accept the rule that any discussion about "what is real" will be ruthlessly suppressed. It reminds me of the elections in the communist Czechoslovakia: people could express their views about politics but any discussion about politics was ruthlessly suppressed. ;-)




OK, W*it takes the most no-nonsense attitude which is basically pro-Copenhagen and against various proposed sketched alternatives that don't make any sense or insist on debating physically meaningless questions. On the opposite side, there are people like (obviously) Tim Maudlin, Dieter Zeh, Lee Sm*lin, Mateus Araújo, Blake Stacey. A few people are somewhat neutral.




First, let us answer: what is real? It depends on what you exactly mean by real. But I actually know what these people mean by "real". By "real", they mean the observables – canonical coordinates and/or momenta and/or their functions – that have objective values at every moment and that evolve exactly according to the laws of classical physics. You may check that this is what every single critic of quantum mechanics (a "critic of Copenhagen") who also uses the word "real" means by "real".

They're both ignorant about modern physics and inarticulate so I helped them to formulate the precise definition of their problematic adjective "real". With this definition, the question
What is real?
has an obvious answer. Nothing is quite real because nothing in the Universe follows the laws of classical physics exactly. It's that simple: everyone who has some problems with quantum mechanics or who insists on the reality of the classical type is profoundly dumb, whether or not he tries to obfuscate this simple point. Instead of things' being objectively real, the "reality" of everything depends on observations and those are always in principle subjective or dependent on the observer, if you want to use a phrase that looks less "spiritual" but ultimately means exactly the same thing. And the evolution of the subjectively real things (observables) is dictated by the probabilistic laws of quantum mechanics which are strictly unequivalent to any laws based on classical physics.

You may observe things by listening to other people whom you trust, so with the assumption of trustworthiness, their publicized measurements are yours, too. But if you're reasonable, you know that this is just an approximation. You can't always trust others. Only what you have really observed by yourself are the empirical data that you may really trust. On top of that, you have to have good reasons to trust your own eyes, nerves, and your brain. And your gadgets and the computers that are used to evaluate the results. If any of these things fail, or if any gadget is hacked, even your own perceptions could be untrustworthy and wrong. Any failure of quantum mechanical predictions should be blamed on the hacked computers and erring brain, among other things, not on alleged problems with quantum mechanics.

But the idea that the empirically collected data are fundamentally subjective is really common sense. People just perceive different things. People know different things about the world. And you can't really make anyone – not even an idealized agent – know everything because \(p\) and \(x\) are physically meaningful yet impossible to know simultaneously, due to their nonzero commutator.

Once you accept this simple statement that observations are fundamentally subjective, everything is trivial. One defines the initial state for the quantum mechanical evolution by subjectively perceiving something – it's his subjective perception that he has perceived some observable to be equal to some eigenvalue – and with this assumption, the unitary evolution supplemented by Born's rule may be used to compute the probability of any future, equally subjective outcome of another observation. After that observation, the wave function is projected to the subspace of eigenstates corresponding to the measured eigenvalue, and it may be repeated as many times as you wish. All these things are done within a particular observer's perspective about what is empirically true about the state of Nature – and all that knowledge was obtained from subjective measurements.

There's nothing rotten in the eigenstate of Denmark.

Stephen Hawking's poker face

And you should accept the subjectivity of the observations. Stephen Hawking died. Before he died, we could have used him for a nice experiment that makes the point because Hawking was a nearly perfect realization of a poker face. He was conscious and aware of things but you couldn't know.

So we could have done experiments with him. For example, we could have used his eyes as the photographic plates in a double slit experiment. The photon or another particle propagates, the wave function spreads, we get a superposition of the particle at many points. When the particle hits Hawking's retina, the retina gets entangled with the particle.

But nothing really collapses. Just be a cold physicist. Stephen Hawking was just a piece of matter – sadly, especially now, he's just a collection of nuclei and electrons. So you don't know what Hawking has perceived – unless you try to attach some additional measurement apparatuses to his eyes, nerves, or brain. However, you won't do it because such an extra apparatus would change the experiment. EEG can't be quite done so that it doesn't disturbe the observed person at all – and it's an example of a more general claim. Every measurement changes the situation.

OK, so Hawking has seen the photon somewhere but your exact description must work with the superpositions that allow all locations of the photons – and the corresponding cells on the retina that were hit and excited and that are entangled with the photon's location. Again, just ask the question: Has the location of the photon collapsed to any particular point? If it did, you don't know what the location was. Hawking's face was a poker face and conveys no information – not even whether the photon landed in the left eye or the right eye. He needed minutes to write a sentence so you couldn't find out quickly.

On the other hand, you know that despite his poker face, he was conscious. His brain was similar to ours but perhaps more brilliant. It had to work analogously. It had to be conscious. So he was feeling something particular subjectively. You could replace the probability amplitudes for different locations of the photon by the probabilities only – you could forget about the relative phases and switch to a density matrix – but that would clearly prevent you from correctly predicting some very fine interference measurements that may still be done in the future. Any such pure-to-mixed evolution is just an approximation. Hawking himself believed up to 2005 that an evaporating black hole evolves from a pure state to a mixed state but it doesn't. The detailed information is stored in some fine correlations. Pure states evolve to pure states.

So the answer about the collapse is that from your subjective viewpoint, there has been no collapse because you have made no measurement. Hawking and the photon "are" in the superposition of the entangled photon and Hawking's retina (and Hawking's brain). But from Hawking's viewpoint, there has been a collapse, he feels something particular, and he takes this subjective perception as the starting point for his predictions.

The key assertion is that there is simply no contradiction between these two different descriptions of the "reality". The reality is subjective. He knows some particular position, you don't. People know different things. The superposition state that you use formally predicts a nonzero probability for any allowed position – so it's not strictly incompatible with a particular position that Hawking subjectively feels to be real. Non-orthogonal states are not mutually exclusive – that's why there is no contradiction.

The idea of classical physics that every physicist's knowledge about the state of the world is just some approximation of some centralized, objective, single, master collection of classical numbers that evolve according to classical laws is simply wrong. There exists no reason why it should be correct and it's not correct. Just before 1925, people believed it was correct (and people who are retarded by almost one century may believe it even in 2018) but because classical physics stopped working, there is no good reason to believe in its assumptions – just like there is no longer a good reason to believe in the assumptions of non-relativistic physics which has also failed and had to be replaced with relativistic theories (or creationism, Newton's gravity, or any other theory in science that has been superseded).

There's nothing "permanently mysterious" about quantum mechanics. Observers make subjective observations of observables, they subjectively know what they observed and what they may observe (and what they want to predict), and quantum mechanics can compute all the conditional probabilities "of a future outcome given the outcomes of some past measurements" using the unitary evolution operators and Born's rule. That's it. Their perspectives are never quite identical and there's nothing contradictory about that point. To write hundreds of pages about the measurement problem is just a sign of someone's stupidity or bigotry or both.

Fundamentally, the collapse is subjective and it's irreducible. There is nothing more to explain. The collapse of the wave function is just the complex amplitude-based counterpart of Bayesian inference. In Bayesian inference, the probabilities of hypotheses that have been ruled out by the new evidence drop to zero instantly. Why? What mechanism makes them drop? The learning itself. It's exactly the same in quantum mechanics. The amplitudes associated with the eigenstates linked to all the wrong eigenvalues – eigenvalues that weren't observed in the latest measurement – drop to zero. Only the right portion of the wave function survives because you learned something. If you have a brain and you learned something, the knowledge is stored in some atoms of your brains and other complicated stuff that depends on the context and that may be studied by additional observers (e.g. Amy Farrah Fowler). But quantum mechanics guarantees that all the predictions about the external world will be independent of the precise anatomy and physiology of your brain. What matters is that the information was learned by an observer – and that's why it effectively became a classical fact. But it's only a classical fact from a particular vantage point of the observer. This observer's brain may still be found in a superposition of different perceptions according to another observer. The "classical physics for all" with the objective data doesn't work.

Every attempt to add new classical or similar degrees of freedom to quantum mechanics is just dumb. They're not only ugly. If such degrees of freedom existed, atoms would have a much higher – probably infinite – heat capacity because they could carry much more than roughly one bit of information. There exists no empirical evidence for such new degrees of freedom. Surely if something like that existed, it would have to manifest itself in some situations. No situations like that are known because no such extra degrees of freedom exist. In the same way, no universal rules for a preferred basis exist. Not only these things seem to be non-existent empirically. There exist no convincing candidates about the particular character of these additions. Mathematically, there can't be any natural choice.

A statement by many of the many world advocates that it's wrong to add any new degrees of freedom or processes to quantum mechanics is right. But their statement that quantum mechanics with the usual minimal set of mathematical objects may be applied independently of observers i.e. objectively is wrong. Quantum mechanics is defined as a theory where subjective observers' observations are calculated using complex linear Hilbert spaces and Born's rule. If you use a theory that disagrees with the previous sentence, it's not quantum mechanics and it cannot work.

One reason why I don't think it's "right" to write a long book about these issues is that I don't think that they deserve it. The conceptual foundations of quantum mechanics is a section that deserves several pages – perhaps a dozen of pages – in a textbook of quantum mechanics. But it just doesn't deserve hundreds of pages. With hundreds of pages, one must unavoidably end up talking not about physics but about stupid claims that morons without knowledge, open-mindedness, and good intuition have made about physics. And these claims are something totally different than physics. With hundreds of pages, one unavoidably drops to some kind of comparative literature, a social science, if not humanities – to a pseudoscientific cesspool full of floating excrements and Maudlins and other similar objects. Every excrements or Maudlin comes in dozens of scents and flavors. They are almost the same and not quite separated from each other but they still insist of being better than the loosely attached neighbor. If you enjoy such stuff, you could write or read thousands of pages. But I don't enjoy it.

No comments:

Post a Comment