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What is the meaning of "in the same way as ~" in the following sentences,

Internal symmetries relate similar types of particles. For example, isospin relates protons and neutrons, which have the same spin, and about the same mass, but different charge. The proton and neutron form a doublet that transform into each other, in the same way as the 2 spin states of a spin 1/2 particle, hence the name "isospin".

? (Source: http://insti.physics.sunysb.edu/~siegel/particle.html)

Does "~in the same way as the 2 spin states" mean "The proton and neutron form a doublet that transform into each other. Each other in the same way is the 2 spin states of a spin 1/2 particle" ?

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I don't know much about 1/2 particles, but I would interpret that sentence to mean:

The proton and neutron form a doublet that transform into each other, in the same way as the 2 spin states of a spin 1/2 particle [transform into each other], hence the name "isospin".

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