Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime

[Demystifier]

E.g., it's impossible to talk about spin 1/2 without the idea of the rotation group and its covering group and representations of groups on a Hilbert space.

Historically, both Pauli and Dirac described spin 1/2 without groups and their reps, so I wouldn't call it impossible. But of course, their descriptions are mathematically abstract too.

 

[vanhees71]

Interesting. Which papers by Pauli and Dirac are you referring to? I guess they used the Lie algebra (aka angular-mometum matrices/operators) of the rotation group and didn't bother much with finite rotations? That's of course indeed as abstract as the use of the groups.

BTW: Pauli was the first who really gave a valid argument, why orbital angular momenta have no half-integer-spin representations. This is missing in almost all modern textbooks, which simply make a hand-waving "uniqueness argument" for the wave function, which is flawed, because a pure state is not represented by a wave function but a wave function modulo a phase factor, which is the reason why half-integer spin representations make physical sense in the first place ;-)).

 

[Demystifier]

Interesting. Which papers by Pauli and Dirac are you referring to? I guess they used the Lie algebra (aka angular-mometum matrices/operators) of the rotation group and didn't bother much with finite rotations? That's of course indeed as abstract as the use of the groups.

My point is that they didn't use the language of Lie groups and algebras. They worked with some matrices, but they were probably not aware that those matrices are reps of Lie algebras. Similarly, someone working with position and momentum operators in elementary QM does not need to know what is Heisenberg algebra.

 

[Demystifier]

In quantum theory it's impossible to use such "intuitive pictures" but you need a pretty abstract mathematical machinery to even talk about quantum phenomena adequately.

It's impossible in minimal interpretation of QM. But that's exactly why some physicists find useful to think about non-minimal interpretations, to create some intuitive pictures associated with the abstract mathematical machinery. The many-world interpretation, which is the main subject of the book we are supposed to discuss here, is one such mental picture that some physicists find intuitive. Perhaps a popular science book is not a good place to learn something about quantum formalism, but it can be a good place to learn something about quantum interpretations.

 

[vanhees71]

My point is that they didn't use the language of Lie groups and algebras. They worked with some matrices, but they were probably not aware that those matrices are reps of Lie algebras. Similarly, someone working with position and momentum operators in elementary QM does not need to know what is Heisenberg algebra.

I'm pretty sure that Pauli knew very well, what angular-momentum operators have to do with rotations and representations of the rotation group. He obviously also knew about dynamical symmetries, i.e., the additional dynamical symmetries of the Kepler problem enabling him to solve the hydrogen energy eigenvalue problem in matrix mechanics (before Schrödinger with his wave-mechanics approach!).

The Heisenberg algebra is of course a very unjust misnomer, i.e., it should be named "Born algebra", because indeed Born was the first to write down the commutation relations for position and momentum and recognized the algebraic scheme behind Heisenberg's Helgoland paper ;-)).

 

[Demystifier]

The Heisenberg algebra is of course a very unjust misnomer, i.e., it should be named "Born algebra", because indeed Born was the first to write down the commutation relations for position and momentum and recognized the algebraic scheme behind Heisenberg's Helgoland paper ;-)).

I was not aware of this, but it's consistent with the Stigler's law. https://en.wikipedia.org/wiki/Stigler's_law_of_eponymy

 

[vanhees71]

Well Greenspan's biography of Born is very revealing concerning the behavior of Heisenberg!

 

[martinbn]

I was not aware of this, but it's consistent with the Stigler's law. https://en.wikipedia.org/wiki/Stigler's_law_of_eponymy

That's known as Arnold's principle.

• The Arnold Principle: If a notion bears a personal name, then this name is not the name of the discoverer.
• The Berry Principle: The Arnold Principle is applicable to itself.

 

[Lord Jestocost]

The many-world interpretation, which is the main subject of the book we are supposed to discuss here, is one such mental picture that some physicists find intuitive.

Maybe, the many-world interpretation is one such mental pictures that some physicists find intuitive. Nevertheless, the essential question is swept under the rug. There is only an illusion of probability of outcomes of quantum measurements. The many-world interpretation is deterministic about things we never see and fails to predict the probabilistic events we do see.