$^\dagger$My Commentary
First of all, I am a very big fan of Sean Carroll and in general many of the fantastic science and technology communicators in the 21st century. As a society we are in debt to their efforts and time in aiding in understanding the fascinating and intriguing universe we live in. What I enjoy about Sean Carroll's approach to communicating physics concepts and topics is his unmatched clarity in delivery and pace of speech. If you've every listened to his podcast (Mindscape) or others that he has been a guest on, you know what I'm talking about. His most recent popular physics book titled "Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime" continues his trend of excellence in science communication.
In this book, Sean focuses on the foundations of quantum physics and how we ( the community scientist) have become complaisant with the "shut-up and calculate" mentality when dealing with the quantum realm. The issues stems from the early pioneers of quantum mechanics who could not make sense of the predictions from the mathematics and the experimental observations, namely, that the quantum object/information we call the wavefunction, does not manifest as described by the math when measured in the lab. Lets throw some math into the mix just to make things clear. In nonrelativistic quantum mechanics we have an equation which describes the relationship between the time evolution of the quantum state (i.e. wavefunction) to the evolution of energy content of a system given that quantum state; this is the what we are told the infamous Schrödinger equation:
$$ i\hbar \frac{\partial} {\partial t} | \Psi \rangle= \hat{H} | \Psi \rangle$$
The quantum state function, $\Psi$ is called the wavefunction because in many cases it has a functional form that reassembles wave-like characteristics. This wavefunction differs from our intuitive notion of classical waves in that the amplitude is a complex number. Sean Carroll's argument is that the wavefunction is all information needed to describe a quantum system. Furthermore, he argues that we take this equation at face value for what it tells us, namely, that given a quantum wavefunction we can describe its evolution deterministically. This is a key statement, because in popular science you may hear that quantum mechanics is a probabilistic theory, that is only true if we are concerned with knowing additional information about the system using the wavefunction. For example, if we want to know the position, momentum, or energy then we can only speak in terms of probabilistic outcomes of those observable. But the wavefunction always evolves deterministically via the Schrödinger equation. For example if we want to know the probability expectation for observing or measuring the momentum of a wavefunction describing a particle, we would write something down like:
$$ \langle \Psi | \hat{p} | \Psi \rangle $$
this equation provides us with a mathematical result about the momentum representation of the wavefunction in a probablistic manner. It is beyond the scope of my intent for this blog but the reason we can't say that the observed momentum of the wavefunction $\Psi$ is exact, is related to the fact that the wavefunction is a superposition of equally valid solutions in what is known as Hilbert space.
Now the main focus of the book is on an alternative understanding for the measurement catastrophy in quantum physics, that is to say, when experiments are performed on quantum systems we don't get the entire probability distribution of the wavefunction for an observable/expectation as an output. What we get is a single data point from that sampling space. If we conduct enough experiments, then of course we recover the distribution. But why don't we get the entire wavefunction probability when we measure? The historical and mainstream thought on this is that something happened by which when an observer (e.g., the human eye or a digital sensor) measured the quantum state/wavefunction so that it "collapased" into a single value. Now you say "What do mean? What forced the function to collapse?", yes this is indeed a strange phenomena. The Schrödinger equation nor any other mathematical interpretation tells us anything about a wavefunction "collapse". For many years I never really thought about this, but more recently it really is bothersome that a quantum state just "collapses" to a single value as if something forced it for which we don't know anything about. Albert Einstein's thought on this was that the forced collapse is due to local hidden variables; things we are unable to identify as being part of the system and are locally causal.
Now Sean Carroll's approach is more epistemic, we know we have this quantum mathematical object called the wavefunction and every thing in the universe can be described by it, so what happens when the quantum system I am describing interacts with an observer who is also treated as being a quantum system. The outcome is that we get parallel quantum states that are very much deterministic and in existence, but having different probabilistic outcomes (I think this is how I understand it?). In other words, the act of quantum systems interacting produces many outcomes that in a sense occur in parallel worlds, hence the many worlds. To be clear we don't need to think of the same physical space being occupied, but rather that in some abstract representation of many isolated outcomes have occurred with validity. This approach goes by the Everettian or Many Worlds interpretation.
The main tenants of the the many worlds argument are 1.) we should not try and interpret the meaning of the Schrodinger equation but just follow the mathematics as providing what is real and 2.) don't select which systems behave quantum mechanically, assume every physical object in the universe can be described by a quantum state.
Although I very much appreciate Sean's insight and excellent introduction to this foundation quantum physics vantage point, my own human bias doesn't want to agree. Its not that I don't think its a valid understanding of the outcomes of the Schrodinger equation, but more that it leaves me wondering about the other "branches" of the wavefunction. For example, can one roll-back time to traverse a new branch? This should be possible since the time evolution operator in the Schrödinger equation is a unitary operator.
There are two things I should mention, 1.) I'm not a quantum physicist by training so my understanding of the topic could have gone wary, 2.) I haven't finished the book.
$^{\dagger}$ I haven't finished the book yet so this is a partial commentary.
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