Measuring spin on electrons prepared in various directions

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SUMMARY

This discussion centers on the measurement of electron spin using a spin measuring device, specifically a Stern-Gerlach device. Two batches of 100 electrons are prepared with equal distributions of spin along the x and y axes. The key conclusion is that the time intervals recorded by Alice during the measurement process are independent of the initial spin state of the electrons, meaning she cannot determine which batch she is working with based solely on these intervals.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly electron spin.
  • Familiarity with the Stern-Gerlach experiment and its implications in quantum measurement.
  • Knowledge of photon emission probabilities in quantum systems.
  • Basic concepts of measurement theory in quantum physics.
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  • Research the mechanics of the Stern-Gerlach device and its role in quantum measurement.
  • Explore the relationship between electron spin states and measurement outcomes in quantum mechanics.
  • Investigate the implications of measurement independence in quantum systems.
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Physicists, quantum mechanics students, and researchers interested in the measurement of quantum states and the behavior of particles in magnetic fields.

Jeronimus
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Let's say we have 200 electrons.

The first batch of 100 of those electrons are prepared in a way that 50% are UP in the x-axis while 50% are DOWN in the x direction. The order is unknown.

The second batch of 100 electrons are prepared in the same manner but in the y axis.

Bob picks one of the two batches randomly and sends it to a spin measuring device.


Alice runs the batch sent to her through the spin measuring device, and checks for the x spin of all 100 electrons.
Alice writes down the time interval it took for the device to figure out the spin for each of the electrons individually.

Then she does the same for the other batch.


Is it possible for Alice to figure out which of the two batches she was working with, simply by looking at the time intervals it took the machine to figure out the spin of each electron?

From what i read, a spin measuring device is basically a magnetic field you put the electron in, and which then has a certain probability to emit a photon or not to emit a photon within a given time-frame.
Does the average time-frame it takes depend on the initial alignment of the electron or is it the same no matter which direction the electron was prepared in?
 
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Jeronimus said:
Is it possible for Alice to figure out which of the two batches she was working with, simply by looking at the time intervals it took the machine to figure out the spin of each electron?
no.
From what i read, a spin measuring device is basically a magnetic field you put the electron in, and which then has a certain probability to emit a photon or not to emit a photon within a given time-frame.
Does the average time-frame it takes depend on the initial alignment of the electron or is it the same no matter which direction the electron was prepared in?

Google for "Stern-Gerlach device", and to the limits of our ability to measure these things, the time to get a measurement out of the device is independent of the initial spin state of the incoming particles.
(It's also worth taking a few minutes to think about how you would define the end points of this interval)
 

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