# Confusion over spin measurements

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• etotheipi
In summary, the discussion is about the spin example in the Theoretical minimum and how a spin with a z component of +1 behaves when rotated 180 degrees. It is mentioned that the orientation of the detector's axis does not affect the measurement, and this relates to the idea of symmetry in the universe. The analogy of measuring the z-coordinate of position is used to explain this concept further.
etotheipi
TL;DR Summary
Sorry if this question has popped up before.
I will refer to the spin example outlined in the opening chapters of the Theoretical minimum.

Suppose we prepare a spin with a z component of +1. If we rotate the apparatus about 180 degrees, the ‘classical component’ of the prepared spin vector along the new axis of the detector is -1, so every time we make this new measurement the apparatus will show -1.

However, does this still mean that the z component of spin is +1, since a negative spin relative to a detector oriented in the negative z direction of our arbitrarily defined coordinate system seems to imply that the spin vector is pointing in the positive z direction?

I ask since he later goes on to say that the up and down states are orthogonal since if we prepare a spin with say a +1 (up) z component, there is a 0% probability of measuring a -1 (down) z component.

This only makes sense to me if we say that, assuming a +1 z spin has been prepared, however we measure the z component immediately after (regardless of whether the apparatus points in the positive or negative z directions) we will get the original spin with 100% probability, so if we flip the apparatus over 180 degrees we will always measure -1, which consequently corresponds to +1 in the positive z direction?

Sorry if I’m messing anything up here!

etotheipi said:
Summary: Sorry if this question has popped up before.

I will refer to the spin example outlined in the opening chapters of the Theoretical minimum.

Suppose we prepare a spin with a z component of +1. If we rotate the apparatus about 180 degrees, the ‘classical component’ of the prepared spin vector along the new axis of the detector is -1, so every time we make this new measurement the apparatus will show -1.

However, does this still mean that the z component of spin is +1, since a negative spin relative to a detector oriented in the negative z direction of our arbitrarily defined coordinate system seems to imply that the spin vector is pointing in the positive z direction?

I ask since he later goes on to say that the up and down states are orthogonal since if we prepare a spin with say a +1 (up) z component, there is a 0% probability of measuring a -1 (down) z component.

This only makes sense to me if we say that, assuming a +1 z spin has been prepared, however we measure the z component immediately after (regardless of whether the apparatus points in the positive or negative z directions) we will get the original spin with 100% probability, so if we flip the apparatus over 180 degrees we will always measure -1, which consequently corresponds to +1 in the positive z direction?

Sorry if I’m messing anything up here!

I think the answer is yes!

Theoretically, when you turn your apparatus upside-down you are still measuring the same thing. The only thing you are doing is reversing the directions you call ##\pm##.

This actually relates to the fundamental idea of symmetry of the universe. There is no intrinsic orientation of a z-axis. Up and down are the same physical axis, with only a different sign convention.

A rough analogy is if you measure (classically) the z-coordinate of position. It's the same measurement, whether your z-axis is up or down. But, it is different from measuring the coordinate along any other axis.

etotheipi
PeroK said:
I think the answer is yes!

Theoretically, when you turn your apparatus upside-down you are still measuring the same thing. The only thing you are doing is reversing the directions you call ##\pm##.

This actually relates to the fundamental idea of symmetry of the universe. There is no intrinsic orientation of a z-axis. Up and down are the same physical axis, with only a different sign convention.

A rough analogy is if you measure (classically) the z-coordinate of position. It's the same measurement, whether your z-axis is up or down. But, it is different from measuring the coordinate along any other axis.

Thank you, that’s a really nice way of putting it!

## 1. What is spin in physics?

Spin is an intrinsic property of elementary particles, such as electrons and protons, that describes their angular momentum. It is not the same as the physical spinning motion of a macroscopic object, but rather a quantum mechanical property that can take on discrete values.

## 2. How is spin measured in experiments?

Spin can be measured through various experimental techniques, such as scattering experiments or spectroscopy. These experiments involve interacting with the particle and observing the resulting changes in energy or momentum, which can then be used to determine the particle's spin value.

## 3. Why is there confusion over spin measurements?

One reason for confusion over spin measurements is that spin is a quantum mechanical property, and as such, it does not have a classical analog. This can make it difficult to conceptualize and understand, leading to misunderstandings or misconceptions.

## 4. Can spin measurements be changed or manipulated?

No, the spin of a particle is an intrinsic property and cannot be changed or manipulated. However, it can be influenced by external forces, such as magnetic fields, which can cause the spin to align in a certain direction.

## 5. How does spin relate to the Pauli exclusion principle?

The Pauli exclusion principle states that no two particles can have the same set of quantum numbers. Spin is one of these quantum numbers, and it determines the allowed values of other quantum numbers, such as energy levels. This principle plays a crucial role in understanding the behavior of particles in atoms and molecules.

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