It's like the quantum number for spin-up/down was reset during the spin-left/right test. (reset from "up" to "?", please excuse my layman's language)
Yes. The notes have not explicitly reached this point, but that is what will be developed next. Testing x-spin resets z-spin to "?". We say they are incompatible observables, they cannot both possess definite values. (This will turn out to be the origin of the uncertainty principle.)
Most of the mathematics really boils down to precisely quantifying the many forms "?" can take and getting quantitative predictions from it.
In the "B" experiment this detection of spin-left/right is not made and the result of the second up/down test yields 100% "up". Even though the beam in the spin-left/right apparatus is split into separate spin-left and spin-right paths (since the equipment is exactly the same, functions just the same (minus the detector)) the quantum number ("up") from the first up/down test block was not reset by the left/right test block.
The only difference between the setup of the original and "A" experiments and the setup of the "B" experiment is that the original and "A" detect the left/right split while "B" does not.
Exactly. Essentially eliminating anything but the detection process as the source of the difference.
This is a "Double Slit" experiment for electron spin, yes?
Yes, it is the direct analogue of the Double slit experiment for spin. The unfortunate thing about the double slit is that to describe it you need advanced mathematics (Hilbert spaces, complex-valued partial differential equations). However for spin, the mathematics is far simpler, vectors and matrices.
So in a layman's analogy (not totally accurate but close enough for some understanding) is saying ...
"When the spin-left/right paths are detected the quantum number for spin-up/down is reset to "?" thus allowing the second up/down test to spread the results among the quantum probabilities" ...
Actually that's totally accurate. We only need to develop an understanding of the "?" state, i.e. are there different types of "?", how do we describe them mathematically.
This was a great idea, and I hope to refocus your topic below. Thanks for participating at EvC Forum in your spare time. You are a valued resource. ***********************************************************
I've been inspired by Dr. Adequate's series on Geology (an amazing thread), so I would just like to propose a similar introduction to quantum mechanics.
The only mathematics involved will be matrices and vectors.
EDIT: Vectors and matrices form the subject known as linear algebra, the amount of linear algebra necessary for the course will be explained in a separate pdf/post. To learn linear algebra you only need to know what a number is!
So the idea is that the topics would be something like: 1. Derive quantum mechanics from looking at the Stern-Gerlach experiment. Basically that all the features of Quantum Mechanics (e.g. Complex numbers, probabilities) naturally follow from taking a serious look at how the spin of electrons is affected by a magnetic field.
First Set Of Notes
2. Then, look into more depth at the framework we have derived. Deriving the uncertainty principle and entanglement for example.
3. Next, focus on the probabilistic aspects of Quantum Mechanics and their meaning. Proof of the Kochen-Specker theorem and other such results, which serve to prove how probability in quantum mechanics differs from normal statistics and probability.
4. Interpretations and Decoherence.
5. Quantum computing, as an application of the preceding four sections.
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