After reading these ~350 pages I now feel like I know less about Quantum Mechanics (QM) than before I started. There were times when some of the concepts were beyond my comprehension (e.g. Popescu-Rohrlich boxes) but hopefully with some more reading and research, I’ll be able to understand them.
Ball starts to say, fundamentally that the crux of QM is that measurement on a system affects the outcome of measurements on the system itself. Quantization is not a requirement for QM. The book did solve a long held mystery of mine. How did Schrödinger come up his famous, eponymous, wave equation. He took the equation for waves and tweaked it using intuition, to what he thought would apply to particles. Miraculously it worked. Squaring the wavefunction of an object gives you the probability of finding the object at a given position when measured. QM is often misunderstood as a theory governing things only very small. However, entanglement shows that quantum effects can propagate over vast distances (non-locality).
Schrödinger’s cat, commonly misunderstood, is dispelled with swiftly in many ways. Firstly, in the way that Tegmark explains, the cat will die if in a vacuum, otherwise it’ll interfere with air molecules (the environment) and decohere and no longer exhibit quantum effects (wavefunctions of macroscopic objects can’t interfere or exist in a superposition if they aren’t coherent). Further, the notion of a superposition of dead and alive states is meaningless, unless we define what they mean in quantum terms and then calculate the wavefunction. As an aside, Ball explains that superpositions aren’t fragile. As they “decohere” their quantumness spreads out into the environment creating a large entity. System and environment merge into a single superposition. This effectively destroys the superposition as we can’t discern it anymore by looking at a small part of it.
Interestingly, physicists are actually trying to do this experiment dubbed Schrödinger’s Kittens, albeit with much smaller matter – water bears (think around mesoscale/millimeters).
QM teaches us that the order in which we do things (e.g. measurements) matters (non-commutable) dubbed Quantum Contextuality. In classical physics it doesn’t matter. This partly explains the double slit experiment, you are in effect doing two different experiments to elicit a classical or quantum outcome. In terms of the uncertainty principle, this explains why we get the results we do. You can’t know all the details of a quantum system, the more you measure, the more it will decohere. Until eventually it behaves as a classical system only.
The Many Worlds Interpretation (MWI), was devised as a way to deal with apparent wave function collapse and where it goes afterwards. So now you’ve created an even bigger problem, of a parallel universe, rather than the smaller problem of wavefunction “collapse”. Ball says the MWI is false because it cannot deal with the transfer of consciousness (to other “yous”) after universe splitting, as it depends on user experience. Arguments I find more compelling are as follows: science has always told us that the very fine details don’t matter and they should hardly be splitting universes. Proponents of MWI feel uncomfortable with proposals such as, Quantum Russian Roulette (if MWI is correct they shouldn’t). Finally for me personally, we can’t do an experiment to prove MWI correct, so it is unscientific in this regard. MWI does not tell us how the splitting occurs, only that it does.
I was pleasantly surprised to find several pages devoted to quantum computing (QC). Ball says that QC won’t necessarily revolutionise home computing. Although they may solve P=NP type problems quicker, breaking current encryption methods easily, they wouldn’t really speed up things modern computers already do well. QC is a long way off anyway, currently they can just about find prime factors of 21. It was interesting to learn how they worked.
Ultimately, Ball concludes QM is a theory about the representation and manipulation of information. Further, that the theory needs rewriting from the bottom up (Quantum Reconstruction) so that it’s not about waves or particles. That if you start with a few fundamental rules, properties do emerge that describe behaviour of quantum objects.
Concluding, Ball condenses QM down to 3 axioms:
1. You can’t transmit information faster than light (no-signalling)
2. You can’t deduce or perfectly copy the information in an unknown quantum state (no-cloning)
3. There is no unconditionally secure bit commitment (relating to cryptography)
Much of the problems talking about QM come from language. In that, we lack the vocabulary to accurately describe properties of quantum objects. We have to borrow words such as spin and entanglement.
Entanglement could be the key to the long-standing mystery of how to reconcile quantum mechanics with he theory of gravitation as supplied by general relativity
‘here it is a particle, there it is a wave’
‘if we measure things like this, the quantum object behaves in a manner we associate with particles; but if we measure it like that, it behaves as if it’s a wave’
‘the particle is in two states at once’
‘if we measure it, we will detect this state with probability X, and that state with probability Y’
What the MWI really denies is the existence of facts at all. It replaces them with an experience of pseudo-facts (we think that this happened, even though that happened too). In so doing, it eliminates any coherent notion of what we can experience, or have experienced, or are experiencing right now. We might reasonably wonder if there is any value – any meaning – in what remains, and whether the sacrifice has been worth it
When someone explains something in a complicated way, it’s often a sign that they don’t really understand it. A popular maxim in science used to be that you can’t claim to understand your subject until you can explain it to your grandmother.
The key difference between classical and quantum mechanics is that the first calculates trajectories of objects while the second calculates probabilities (expressed as a wave equation)