Marginal Space

“Quantum mechanics isn’t magic. It is the most comprehensive view of reality we have. As far as we currently know, quantum mechanics isn’t just an approximation of the truth; it is the truth. That’s subject to change in the face of unexpected experimental results, but we’ve seen no hints of any such surprises thus far,” writes the physicist Sean Carroll in his book Something Deeply Hidden:: Quantum Worlds and the Emergence of Spacetime.

Quantum mechanics is probably the most fascinating part of physics, and it has faced deep controversies and debates since its origin. It is an interesting subject, even though there are many things that are highly confusing about it. I am just an honest autodidactic who wants to study quantum mechanics from textbooks and eventually to learn enough to think deeply about the foundations of quantum physics. I do not understand all the subtleties about it, but any lack of understanding it can be forgiven, as–to quote Richard Feynman- no one understands quantum mechanics. (Well, maybe a few do.)

I liked the book. It is well written, and Sean Carroll does a fantastic job of describing the Many-Worlds interpretation. He also provides a framework for thinking about quantum gravity; provocative and extremely speculative but very interesting.  This is not really a review; just a few thoughts about the things that I find fascinating and writing is a way to better understand the topic in question and acquire new knowledge.

The book has three messages. The first is that quantum mechanics should be understandable. The second message is that physicists have made real progress toward understanding. The third message is that the foundations of quantum mechanics matter, not just for the integrity of science, but to understand “the nature of spacetime itself, and the origin and ultimate fate of the entire universe.”

Quantum theory is the most successful scientific theory humanity has ever devised. It is the physics of tiny, but it goes well beyond that. It explains virtually everything about the universe. The problem with quantum physics is what it is telling us about the physical world around us. I will try to explain this as I understand it- and I am not sure I understand it completely. The problem in quantum mechanics is that particles exist normally in a superposition of possibilities described by the wave function, rather than positions and velocities. The idea behind the wave function is that an electron is not really in an orbit around the nucleus of an atom as it widely described; it rather looks like a wave spread out around the atom. The equation that govern how wave functions evolve is the Schrödinger equation. We can express it in words as: “The rate of change of a wave function is proportional to the energy of the quantum system,” Sean Carroll writes. As far as we know, Schrodinger’s equation is right and one of the fundamental rules of nature.

 When we use the Schrödinger equation to measure the wave function of an emitted electron, it looks like a spherical wave coming out in all directions But, when you look at it you never see a wave. What you see is straight lines and trajectories, as if the electron is a particle again. So, the way particles behave when they are in the wave function is not the same way they behave when you are looking at them. Something happens when we look, strange as it may sound, the very act of watching affects reality. But what is that?

Physicists have not yet solved this mystery, and the strategy they follow (most of them, anyway) since the 1920s, is “shut up and calculate,” says Carroll. To explain what is happening they invented the idea of the “collapse of the wave function.” They said that particles obey the Schrödinger equation when we are not looking at them, but, when we try to measure them -that is to observe the interaction of the particles with something in the physical universe- the wave function changes and instead of predicting what will happen it predicts the probabilities of different things happening.

This came to be known as the Copenhagen Interpretation of quantum mechanics and developed by Niels Bohr and Werner Heisenberg and a few others. This interpretation was the reason for the famous debate between Einstein and Bohr. In Einstein’s opinion, this interpretation had severe deficiencies; he believed that “something deeply hidden, had to be behind things.” This is also the reason for the title of this book. But Bohr and his friends won the public relations debate and the Copenhagen Interpretation, which basically takes the observer out of the equation, remains the mainstream approach.

Sean Carroll objects the Copenhagen interpretation to quantum mechanics. In his book, he presents alternative approaches that have been developed over the years, but his favourite (and my favourite too) is the idea known as Many-Worlds, which first proposed by the physicist Hugh Everett in the 1950s. Simplicity is a wonderful thing. And the Many-Worlds interpretation is wonderfully simple. Hugh Everett, who received and lot of criticism and left the field after finishing his doctorate degree, said two things. First, the wave function represents reality. Second, the wave function obeys Schrödinger’s equation. That’s it. No other rules exist. The only problem with this interpretation is that it does not seem to match with our experience about the nature of reality.

Everett said that there are two things that we have not considered in quantum mechanics. The first one is the observer. In the Copenhagen interpretation, the observer is not part of the wave function. Bohr and his team separated the observer from the quantum system. But that is not right, argued Everett because the observer, you yourself, me, or a cat, is made of atoms, and atoms obey the rules of quantum mechanics, the observer, therefore, is also a quantum mechanical system, hence, part of the wave function of the universe. The Schrödinger equation, therefore, applies to particles and the observer alike.

The other point is entanglement. If I have understood it correctly, entanglement means that particles are not independent from each other. Let’s try to explain this with an example. We have two electrons. Electrons possess a quantum feature called spin. In the presence of a magnetic field, electrons may exist in two possible spin states, usually referred as spin up and spin down. Until they are measured, that is until they are observed, we don’t know which way they are, it could be either up or down. There is a 50/50 chance that electron A might spin up or spin down. There is also a 50/50 chance that electron B might spin up or spin down. Until they are observed, they are in a superposition of both. But we know that the two electrons are not spinning the same way. If we measure electron A and it is spinning up, we know that electron B is spinning down. If electron A is spinning down, then electron B is spinning up. That is entanglement. What is happening to electron A is entangled with what is happening to electron B.

So, the electrons are in a superposition of up and down, but there is only one wave function, and the observer, which is also quantum, is part of the wave function. So, the state of the electrons entangles with that of the observer. And now, let Schrödinger equation do its job, said Everett. What happens then is that the wave function evolves to a superposition with the observer seeing electron A spinning up and electron B spinning down and with the observer seeing electron A spinning down and electron B spinning up. The observer is also in a superposition.

Of course, this is not the way we experience things in the real world. What’s happening then? The explanation is decoherence, a process, when microscopic objects, like an electron, entangled with its environment. It comes with universe altering consequences. Decoherence causes the wave function to split and evolve separately. There is no collapse of the wave function, only two different branches, two different worlds, that obey the Schrödinger equation, but they are not connected in any way. The observer also branches into two copies. One copy sees electron A spinning up and electron B spinning down. The other copy sees electron A spinning down and electron B spinning up. This is the “Many-Worlds Interpretation.”  

There are a lot of questions about the Many-Worlds Interpretation, most of them are answered in the book. The most common question is: How many worlds are out there? The answer to this is that we don’t know, but there must be infinitely many worlds, says Sean Carroll. But we don’t know anything for sure.