Something Deeply Hidden

I recently read Something Deeply Hidden by Sean Carroll (2019). The book hints at an ambitious undertaking to examine some profound ideas, including the derivation of space, time, and gravity from a proper understanding of quantum mechanics, but on this point it falls short. I suspect the real reason for the book is to lay out the case for the many-worlds interpretation of quantum mechanics. On this point, it succeeds brilliantly. I’ve always thought Everett’s approach to QM was the most intuitive and this book makes the clearest argument for it yet.

Some say that the many-worlds approach breaks Occam’s razor by positing millions of additional, parallel universes that can never be detected, but the reverse is closer to the truth. Other interpretations of QM need to posit additional, so far unseen mechanisms to “collapse” the wave function. Some believe it random. Others believe consciousness plays a role. After observation, what happens to the other parts of the wave? Many-worlds assumes only that the wave that once existed continues to exist even when parts of it no longer interact. The idea is that you and your instruments observe a particle in the quantum state you do because the part of the particle’s wave function in that state is entangled with your own, while the part of the particle’s wave function in other states are entangled with the other parts of your wave function.

Once this is thoroughly explained, Carrol moves on to speculate chaotically about where gravity might come from and be made compatible with QM. He mentions the idea that space could be emergent from an abstract sort of space where objects of similar values interact stronger than objects of dissimilar values. This would be indistinguishable from how we experience space. He subtly hints that the wave function of the universe has broken its symmetry, allowing “position” to exhibit locality in this way, but not “momentum.” These two attributes might actually be fundamentally the same, but momenta have lost their ability to interact when holding similar values. The problem is that he proposes no mechanism for this to happen, gives no reason why we have three dimensions of space, and gives no reason why this approach would be more insightful than simply assuming space as foundational.

Carrol mentions Ted Jacobson’s 1995 paper suggesting that the entropy of a region is proportional to the interactions it has with other regions (and therefore surface area), and therefore reducing entropy might reduce surface area, warping space not unlike gravity. The problem with this is that gravitational collapse actually represents an increase in entropy.

He mentions Stephen Hawking’s work and that of his successors suggesting that a black hole’s information is encoded on its event horizon, meaning that the information of a three-dimensional volume can be stored on a two-dimensional surface. The problem is that there is still a lot of debate about this.

He mentions conformal field theory and the proof that a quantum field operating in a five-dimensional spacetime with a negative cosmological constant is mathematically equivalent to a quantum field operating on the four-dimensional surface of such a spacetime. The problem is that our universe has a positive constant and only four dimensions that need to be representable by three, not five.

Finally, he points out that the more degrees of freedom a system has, the more entropy it has, and therefore the more energy it has, and therefore the more gravity it has (m=e/c^2). Because gravity does something weird to collapse three dimensions into two, the degrees of freedom of a volume of space is limited at the Plank energy. The implications are that Hilbert space is not infinite (though still enormous), and that there is a limit on how many “worlds” can exist in the wave function simultaneously. This is the same reason I have heard elsewhere for why the vacuum energy is not infinite.

He never did explain where gravity came from.

My main criticism is that too often he would take up to ten pages explaining the same simple concept over and over when I got it the first time, and then suddenly cover twenty steps in half a paragraph. It was jarring. I simultaneously felt really smart and really dumb.

My takeaway observation is that this book confirms what I have heard elsewhere of big-name scientists over the generations accusing each other of fuzzy thinking and conceptual errors when it comes to QM. It gives me hope that my ideas might be just as valid even though I’ve never had to compute an eigenvector in my life. If the scientists can’t support their models and they get attention anyways, why not me?

Four stars.