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Faradave
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I’m a layman who has reviewed some popular literature on QM. Apologies in advance for my naivety.
I’m of the impression that the quantum spin (±½) of an electron can be determined as it travels through a Stern-Gerlach apparatus (SGA) for the single direction in which the SGA is aligned (say, along the X-axis). Spin along other axes is a superposition of those states, with amplitudes corresponding to the angle departing from X. Spin is also said to be complementary. Spin measurement along different axes is mutually exclusive. For example, “A particle cannot have definite values for both X and Z at the same time.” [ref]
It seems possible, at least in theory, to obtain values for both X and Z spin at the same time by the following method. Please let me know where it goes wrong.
1). Two electrons are prepared in an entangled, total-spin-zero state (each has spin opposite the other).
2). Two SGAs are oriented perpendicularly, one X-axis aligned and the other Z-axis aligned.
3). Each entangled electron is sent simultaneously through one of the perpendicular SGAs.
4). Spin X is determined for one electron while spin Z is determined for the other, at the same time.
5). Each electron had spin opposite the other, so spin X and spin Z of both electrons were simultaneously determined.
I’m of the impression that the quantum spin (±½) of an electron can be determined as it travels through a Stern-Gerlach apparatus (SGA) for the single direction in which the SGA is aligned (say, along the X-axis). Spin along other axes is a superposition of those states, with amplitudes corresponding to the angle departing from X. Spin is also said to be complementary. Spin measurement along different axes is mutually exclusive. For example, “A particle cannot have definite values for both X and Z at the same time.” [ref]
It seems possible, at least in theory, to obtain values for both X and Z spin at the same time by the following method. Please let me know where it goes wrong.
1). Two electrons are prepared in an entangled, total-spin-zero state (each has spin opposite the other).
2). Two SGAs are oriented perpendicularly, one X-axis aligned and the other Z-axis aligned.
3). Each entangled electron is sent simultaneously through one of the perpendicular SGAs.
4). Spin X is determined for one electron while spin Z is determined for the other, at the same time.
5). Each electron had spin opposite the other, so spin X and spin Z of both electrons were simultaneously determined.
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