So many entry-level explanations of quantum mechanics start with classical physics, waves, particles, the double-slit experiment, etc. and then jump straight to infinite-dimensional Hilbert spaces. In my opinion, there's way too much conceptual baggage that comes with these concepts [0].
As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems [1]. The math is accessible at a pre-calculus level, and the most "counter-intuitive" aspects of QM (interference, the uncertainty principle, entanglement) make perfect sense in this framework. I think it's the best starting point for understanding what QM really says.
[0] That's not to say they aren't important historically or for a complete understanding of QM. I'm talking about conceptual understanding for someone, especially an amateur, encountering QM for the first time.
[1] Chapter 2 of Nielsen and Chuang is what did it for me. It's heavygoing if you've never seen linear algebra before, but I don't know of a clearer explanation of the postulates of quantum mechanics.
"A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry" by Peter Szekeres has several chapters on linear algebra early on, starting with sets and groups and including tensors (which you absolutely need for QM).
Nielsen and Chuang's "Quantum Computation and Information" Chapter 2. (Available online, but legality depends on where you live)
If you're interested primarily in QM rather than linear algebra, I'd recommend not working through all of Axler, but instead using Nielsen and Chuang to learn about qubits and observables, and using Axler to fill in the gaps.
not sure about its specific applications to quantum mechanics, but I worked through MIT OpenCourseWare's Linear Algebra class (taught by Gilbert Strang) and I thought it was amazing. The lectures are very very good.
If we've learned anything from modern physics, it's that our regular intuitions are often wrong. The framework makes perfect sense mathematically, and it makes the right predictions experimentally. It's still controversial how exactly the framework relates to reality, which is where you get into interpretations of quantum mechanics.
One of my favourite examples of this pedagogically is how kinetic energy is quadratic with velocity. It's easy to tie into things people think they understand, like braking distance. Our intuitions are wrong even in shockingly simple problems.
The dialogues of the author engages with various personas and the reader that are interspersed as Prelude and Interludes are really enlightening.
For example:
Classical Physicist: Can one seriously speak about an object without having an idea of what it looks like? Isn’t it strange that we study, for example, the behaviour of an electron in a crystal while we don’ t even know what an electron actually is?
Author: I don’t agree that we don’t even know what an electron is. I have just indicated a number of precisely determined characteristics and properties of an electron. More detailed properties of microparticles in general and electrons in particular were considered in the preceding sections of the book (and will be considered in the following sections). In fact, we know quite a lot about the electron and know, in particular, about its behaviour in a crystal. This is evidenced by the large number of semiconducting devices fabricated and used by us in practice. As you will see, the absence of a “physically intuitive” model of the electron has in no way turned out to be a serious obstacle. We may even go a step further and state that an understanding of natural phenomena in which Planck’s constant plays an important role is possible only through a significant rejection of a graphic description. By the way, this idea was given by Heisenberg, in whose works much attention was given to questions of the use of physically intuitive methods.
Classical physicists had conceptual difficulty when something stopped behaving as "body" even macroscopically. For example when they tried to determine coefficient of friction of pure coper, throughly cleaned, in vacuum to prevent any oxidation, the surfaces cold-welded together. The copper did not get the memo that it is supposed to be two physical bodies.
Somewhat related: a book that really helped me is Picturing Quantum Processes
by Bob Coecke. It's a visual representation of quantum processes, which really helped me understand the concept
It stands out as not too common a sight for books, so having two like this, more or less in the same style, on the same topic, both posted in this thread, is amusing. Maybe it's not that rare and I'm just not reading enough books from academics for whom a book is like a weird long paper with hand-holding for amateurs.
Finished reading this book not too long ago, one of my top three textbooks. An absolute joy to read full on great insight.
Not sure how it feels to a beginner, but to someone with a good deal of familiarity in the field it put everything in such a nice tight conceptual package.
"This rather fanciful interpretation of Quantum Physics has now become accepted by many theoretical physicists as being more satisfactory than the Copenhagen interpretation, despite the fact that the mechanism which causes the splitting of the Universe is not explained in any more detail than wavefunction collapse. As you can probably tell, I am in the minority of physicists who finds the Many Worlds interpretation dificult to accept, and not particularly illuminating."
I think these lectures are a good intro to QM. This statement feels very emotional though. Many-worlds just states there is no such thing as wave function collapse. The many worlds are a logical conclusion following. Copenhagen simply refuses to elaborate to when wave-function collapse happens, which to me is not a complete theory.
You could have some critique of many-worlds in relation to statistics, although I think many people have given quite satisfactory explanations.
Many worlds is just bare bones QM.. If any other theory is proposed, it should be falsifiable (like pilot wave theory for example). Doesn't mean it won't be difficult to measure.
My interpretation of the interpretation is that the universe is a giant constraint resolution system. Particles are free to be anywhere randomly as long as they do not randomly interact with other particles. As soon as they interact they have fewer "degrees of freedom", since now they interacted. When they interact with anything macroscopic they have no freedom left. Makes sense to me anyway.
Decoherence isn't an interpretation, but an experimentally established fact. What makes interpretations interpretations is that they cannot be experimentally distinguished (or in some cases, can only be with great difficulty). That said, the study of decoherence has certainly made aspects of the measurement problem easier to come to terms with, which in turn has bearing on the intuitive draw of some interpretations over others. In particular, it helps answer when universes should be said to "split" in MWI (though, as many will rightly tell you, that's not a complete solution to the measurement problem, as decoherence is still unitary--i.e., there's no in-principle irreversibility there).
Decoherence gets you a diagonal density matrix description of the world. It doesn't get you a single-state description of the world. Going from "There are many parallel universes" to "and we are in one of them" still takes a lot of handwaving.
But we're not in one of them. We're in all of them. Yours is a misunderstanding of how it feels to be in a quantum superposition. There's no component of the wave function in which Schrodinger's cat experiences anything other than being alive or being dead. There's no component in which it feels like it's in some ghostly combination of both outcomes. Both components of the wave function exist in superposition, and to the extent that they are decoherent, they do not interact and do not even notice that they have company. I don't mean this only as an academic statement; it's also true of you and me, at this very moment.
- That humans can't be put into quantum superpositions, or
- That a human being in a quantum superposition of two states A and B would feel at all to that human like being in a quantum superposition of two states A and B, when neither of those states is "a human feeling like they're in a superposition of two states A and B".
Follow this to its conclusion, and you end up with a superposition of A and B meaning: "the universe is in a superposition, containing a component where a human believes that they're in state A, and a component where a human believes that they're in state B. Within both branches, the human thinks their wavefunction collapsed in that state". This is exactly the way that all interpretations of QM already understand things to work with particles in superpositions.
Decoherence only hides entanglement by having the entire world go into a complex superposition. It's entirely compatible with MWI. Decoherence does not resolve the measurement problem on its own. It's not a separate interpretation. It only provides us a mathematical reason for why the world appears classical.
Many-worlds is an interpretation and not a theory. It makes no additional predictions beyond what QM does.
Believing in any interpretation (or shutting up and calculating) is purely emotional; it has no scientific content.
But if what you want is understanding, you want a good explanation. (Or to quote TheOtherHobbes from elsewhere in these comments, a reasonable metaphor: https://news.ycombinator.com/item?id=50220700)
If you only like predictions and disparage explanations, I might start calling you names, specifically instrumentalist.
Here you are taking "good explanation" and combining it with the term "just so story" which indicates a bad (arbitrary) explanation. So you cast doubt on the idea that explanations can be good. What's this, sabotage?
fasterik 7 hours ago
As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems [1]. The math is accessible at a pre-calculus level, and the most "counter-intuitive" aspects of QM (interference, the uncertainty principle, entanglement) make perfect sense in this framework. I think it's the best starting point for understanding what QM really says.
[0] That's not to say they aren't important historically or for a complete understanding of QM. I'm talking about conceptual understanding for someone, especially an amateur, encountering QM for the first time.
[1] Chapter 2 of Nielsen and Chuang is what did it for me. It's heavygoing if you've never seen linear algebra before, but I don't know of a clearer explanation of the postulates of quantum mechanics.
wwarner 5 hours ago
BobbyTables2 1 hour ago
The classic double-slit experiment is kinda bizarre when one considers the “single electron” case.
mattm 6 hours ago
d_tr 9 minutes ago
I loved it.
fasterik 6 hours ago
Axler's "Linear Algebra Done Right" https://linear.axler.net/LADR4e.pdf
Nielsen and Chuang's "Quantum Computation and Information" Chapter 2. (Available online, but legality depends on where you live)
If you're interested primarily in QM rather than linear algebra, I'd recommend not working through all of Axler, but instead using Nielsen and Chuang to learn about qubits and observables, and using Axler to fill in the gaps.
GlibMonkeyDeath 6 hours ago
brooke2k 4 hours ago
anotherpaulg 2 hours ago
Quantum Processes, Systems, & Information by Benjamin Schumacher and Michael Westmoreland is another good treatment along those lines.
podocarp 6 hours ago
fasterik 6 hours ago
hansvm 4 hours ago
SJC_Hacker 2 hours ago
wnoise 4 hours ago
the-mitr 14 hours ago
Basic Concepts Of Quantum Mechanics by L. V. Tarasov
https://archive.org/details/tarasov-basic-concepts-of-quantu...
The dialogues of the author engages with various personas and the reader that are interspersed as Prelude and Interludes are really enlightening.
For example:
Classical Physicist: Can one seriously speak about an object without having an idea of what it looks like? Isn’t it strange that we study, for example, the behaviour of an electron in a crystal while we don’ t even know what an electron actually is?
Author: I don’t agree that we don’t even know what an electron is. I have just indicated a number of precisely determined characteristics and properties of an electron. More detailed properties of microparticles in general and electrons in particular were considered in the preceding sections of the book (and will be considered in the following sections). In fact, we know quite a lot about the electron and know, in particular, about its behaviour in a crystal. This is evidenced by the large number of semiconducting devices fabricated and used by us in practice. As you will see, the absence of a “physically intuitive” model of the electron has in no way turned out to be a serious obstacle. We may even go a step further and state that an understanding of natural phenomena in which Planck’s constant plays an important role is possible only through a significant rejection of a graphic description. By the way, this idea was given by Heisenberg, in whose works much attention was given to questions of the use of physically intuitive methods.
rini17 13 hours ago
rramadass 7 hours ago
Also checkout Tarasov's other books - https://mirtitles.org/?s=Tarasov Relevant here are his books on Probability and Lasers.
The Physics of the "very small" is essentially probabilities applied to Atomic, Molecular and Optical (AMO) domains where light and matter interact.
the-mitr 3 hours ago
bobvanluijt 18 hours ago
yboris 17 hours ago
newsy-combi 16 hours ago
internetter 11 hours ago
newsy-combi 4 hours ago
wasabi991011 3 hours ago
Not sure how it feels to a beginner, but to someone with a good deal of familiarity in the field it put everything in such a nice tight conceptual package.
rramadass 14 hours ago
dbvdh 15 hours ago
I think these lectures are a good intro to QM. This statement feels very emotional though. Many-worlds just states there is no such thing as wave function collapse. The many worlds are a logical conclusion following. Copenhagen simply refuses to elaborate to when wave-function collapse happens, which to me is not a complete theory.
You could have some critique of many-worlds in relation to statistics, although I think many people have given quite satisfactory explanations.
Many worlds is just bare bones QM.. If any other theory is proposed, it should be falsifiable (like pilot wave theory for example). Doesn't mean it won't be difficult to measure.
linuxhansl 10 hours ago
My interpretation of the interpretation is that the universe is a giant constraint resolution system. Particles are free to be anywhere randomly as long as they do not randomly interact with other particles. As soon as they interact they have fewer "degrees of freedom", since now they interacted. When they interact with anything macroscopic they have no freedom left. Makes sense to me anyway.
monktastic1 9 hours ago
rcxdude 9 hours ago
kgwgk 8 hours ago
mitthrowaway2 7 hours ago
podocarp 6 hours ago
mitthrowaway2 1 hour ago
- That humans can't be put into quantum superpositions, or
- That a human being in a quantum superposition of two states A and B would feel at all to that human like being in a quantum superposition of two states A and B, when neither of those states is "a human feeling like they're in a superposition of two states A and B".
Follow this to its conclusion, and you end up with a superposition of A and B meaning: "the universe is in a superposition, containing a component where a human believes that they're in state A, and a component where a human believes that they're in state B. Within both branches, the human thinks their wavefunction collapsed in that state". This is exactly the way that all interpretations of QM already understand things to work with particles in superpositions.
kgwgk 6 hours ago
goatlover 9 hours ago
EvgeniyZh 11 hours ago
card_zero 11 hours ago
If you only like predictions and disparage explanations, I might start calling you names, specifically instrumentalist.
spolitry 4 hours ago
card_zero 4 hours ago