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I understand that the act of measuring a particle actually changes it. My question is, is that because our method of measuring is crude, and is it theoretically possible to determine the spin without changing it,

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    $\begingroup$ Say the particle's initial wavefunction is a combination of up and down states. Once you measure spin, say along one particular direction the answer is either up or down. Not any intermediate number. And the wavefunction instantly collapses to that spin state. Measurement in QM is probabilistic. You need to measure say 10000 times with an ensemble of particles in the same state to come to the conclusion. $\endgroup$ – sbp Oct 6 '17 at 16:13
  • $\begingroup$ Changes it for how long? It immediately goes back to a superposition of states. $\endgroup$ – user167453 Oct 6 '17 at 16:17
  • $\begingroup$ If you agree to ensemble interpretation of quantum mechanics. Best way to interpret measurement process is procedure for acquiring the information about the state of the system. Once you find certain observable is measured and found to have a certain value, then you specify the system with the state accordingly. To completely specify the state a complete set of observables need to be measured. Collapse interpretation in the context of entangled systems make things messy to imagine. $\endgroup$ – Sunyam Oct 6 '17 at 16:54
  • $\begingroup$ @Countto10 This depends on the Hamiltonian. If the outcome of the measurement is an eigenstate of $H$, then resulting state will remain in this eigenstate as a result of the hamiltonian evolution since the time-evolution of eigenstates of $H$ just adds a time-dependent overall phase. $\endgroup$ – ZeroTheHero Oct 6 '17 at 19:14
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    $\begingroup$ @Countto10 no worries. Your intuition was good and would be valid if not for the exception of measurement yielding an eigenstate of $H$. $\endgroup$ – ZeroTheHero Oct 7 '17 at 15:00
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There is nothing like (yet) spin measurement at quantum level. It is spin alignment, or spin anti alignment.

Therefore, needless to say, alignment/anti alignment would not be possible without changing it unless the particle already (coincidentlly) happens to be in that state, which you would not be able to know, unless you had already aligned it that way via previous attempt(s).

There is no act of spin measurement, rather it is act of spin alignment/anti-alignment.

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is it theoretically possible to determine the spin without changing it,

No, the act of measurement itself perturbs the state of the particle. After you're done measuring the particle's spin you'd never be able to answer what the state of the particle was just before measurement. In quantum mechanics, we don't measure one particle because that doesn't give you any thing. The measurement is done on a collection of the same particles, called an ensemble, which are in the same state.

For example, say there are only 3 possible states that the state wavefunction can collapse into. If you measure the system 1000 times and you get particles in state A for 50 times, the same in state B, and finally 900 times in state C, then the probability of finding the particle in state C is 90 percent. That's how a measurement is done in quantum mechanics.

Also according to QM a particle doesn't have, for example, a precise position just before you measure it, it's the measurement process that restricts it to one particular state, which is determined by the statistical weighting of the wavefunction.

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  • $\begingroup$ That's not completely correct as there are so-called non-demolition measurements (en.wikipedia.org/wiki/Quantum_nondemolition_measurement) that do not increase the uncertainty as the result of measurement. See for instance this question physics.stackexchange.com/questions/353142/… keeping in mind this type of experiment has not yet been done for spin. $\endgroup$ – ZeroTheHero Oct 6 '17 at 19:12
  • $\begingroup$ @ZeroTheHero Thanks for your comment. I will update the answer and add a few lines about quantum nondemolition measurements. $\endgroup$ – dirac16 Oct 6 '17 at 19:28

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