# Uncertainty Principle versus spin alignment

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• hvo
In summary, the magnetic moments of atoms are affected by the uncertainty principle, limiting the knowledge of the spin and orbital angular momenta of electrons. However, the magnitude and projection along a z axis can still be determined. This z axis is chosen by convention, allowing for the simultaneous determination of the magnitude and component of the spin angular momentum along any direction.
hvo
TL;DR Summary
How can spin vectors be perfectly parallel/antiparallel if uncertainty principle says neither its direction and magnitude can be determined simultaneously?
Hello,

So I know that the magnetic moments of atoms are dependent on the spin and orbital angular momenta of its electrons. Both of these quantities are limited by the uncertainty principle so that neither of their direction and magnitude can be known simultaneously with arbitrary precision. The only quantities that aren't restricted by the uncertainty principle are the magnitude and the vector's projection along a z axis.

So how can magnetic moments align parallel to one another? I've tried to read lectures and books on this but none mentioned the uncertainty principle and they all have pictures of perfectly aligned spins. I've considered that these vectors I see in textbooks are actually projections along a common axis, but then why is spin wave considered a separate phenomena?

hvo said:
Both of these quantities are limited by the uncertainty principle so that neither of their direction and magnitude can be known simultaneously with arbitrary precision.
The direction of the angular momentum vector is is not known exactly, only the z-component of the direction is known. That's allowed by the uncertainty principle.

(And why is the z-component of the angular momentum the one that we know? That's just by convention: we we pick the one direction in which we will choose to know the exact value of the component in that direction and call that direction the z axis).

Since ##\left [ {\bf S} ^2, S_z \right ]=0##, then the magnitude of the spin angular momentum and its z-axis component can be simultaneously determined. As @ Nugatory mentioned, the direction of z-axis is chosen by convention. In fact, ##\left [ {\bf S }^2, S_{\hat n} \right ]=0## where ##S_{\hat n}## is along an arbitrary direction, so the magnitude of the spin angular momentum and its component along arbitrary direction can be simultaneously determined.

Last edited:
vanhees71

## 1. What is the Uncertainty Principle and how does it relate to spin alignment?

The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle. This principle also applies to the spin of a particle, meaning that it is impossible to know the exact spin direction and the exact spin magnitude at the same time. Therefore, the Uncertainty Principle has a direct impact on spin alignment.

## 2. Why is spin alignment important in quantum mechanics?

Spin alignment is important in quantum mechanics because it is a fundamental property of subatomic particles. It affects how particles interact with each other and how they behave in different situations. Spin alignment is also crucial in technologies such as magnetic resonance imaging (MRI) and quantum computing.

## 3. Can spin alignment be controlled or manipulated?

Yes, spin alignment can be controlled and manipulated through various methods such as applying magnetic fields or using laser beams. This allows scientists to study and harness the properties of particles with specific spin alignments, leading to advancements in technology and understanding of the quantum world.

## 4. How does spin alignment affect the behavior of particles?

Spin alignment affects the behavior of particles in a variety of ways. For example, particles with opposite spin alignments can attract each other, while particles with the same spin alignment can repel each other. Spin alignment also plays a role in the stability and energy levels of atoms and molecules.

## 5. Is there a limit to how precise spin alignment can be measured?

Yes, due to the Uncertainty Principle, there is a limit to how precise spin alignment can be measured. This limit is known as the quantum limit and it is determined by the inherent uncertainty in the measurement of a particle's spin. However, advancements in technology have allowed for increasingly precise measurements of spin alignment, pushing the boundaries of the quantum limit.

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