I can't visualize spin I know that its not just a particle rotating

In summary, spin is a purely quantum phenomenon that cannot be visualized in a classical way. It refers to the number of times a particle's wavefunction must be rotated through the complex plane to return to its original value. It is often associated with a Riemann sphere in complex analysis, where each point corresponds to a physical state and the geometry is related to the probability of measuring spin up or spin down. This concept can be explored further in Roger Penrose's book, "The Road to Reality."
  • #1
Ezio3.1415
159
1
I can't visualize spin... I know that its not just a particle rotating about its axis... Then how do I think of it?
 
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  • #2
Unfortunately, you can't. It's a purely quantum phenomenon that doesn't have any classical analogue to use for visualization.

And as you say, it certainly isn't a particle rotating about an axis.
 
  • #3


Then we just think of it as a property of the particles...
 
  • #4


Ezio3.1415 said:
Then we just think of it as a property of the particles...

Correct.
 
  • #5
Ezio3.1415 said:
Then we just think of it as a property of the particles...

Yes. Essentially, it refers to the number of times you must rotate a particle's wavefunction through the complex plane to bring it back to it's original value.

A misconception is that it refers to the number of times you must literally rotate a particle to bring it back to it's original state, but this is false. 'Rotation' in the above context refers to an operator on the wavefunction in Hilbert Space.
 
  • #6


Thanks... :)
 
  • #7


It's a purely quantum phenomenon that doesn't have any classical analogue to use for visualization.

It might not have a classical analogue, but that doesn't mean that it can't be visualized mathematically, and this is particularly true for a spin 1/2 particle.

If you have a spin 1/2 particle, like the electron that is can be spin up or spin down, the Hilbert space is a 2-dimensional complex vector space. When you consider than multiplying by a constant give you the same physical state, you get a 1-dimensional complex projective space. This is the nothing but the Riemann sphere of complex analysis. Thus, the Riemann sphere can be associated to any system with a 2-d state space, which each point in the Riemann sphere corresponding to a physical state. And what's really interesting is that the geometry of the Riemann sphere is related to the probability of measuring spin up or spin down. For details, see The Road to Reality, by Roger Penrose, Chapter 22, I believe.

There seems to be some kind of similar picture for higher spin that he talks about, but I don't understand it yet.
 

Related to I can't visualize spin I know that its not just a particle rotating

1. Why can't I visualize spin?

Spin is a property of subatomic particles that cannot be visualized in the traditional sense. It is an intrinsic angular momentum that does not correspond to any physical rotation. Therefore, it cannot be represented by a spinning object like a top or a gyroscope.

2. What does spin actually look like?

As mentioned before, spin cannot be visualized in a physical sense. It is a mathematical concept that describes the intrinsic properties of particles. Some theories suggest that it may be related to the particle's shape or orientation in space, but there is no definitive answer to what it actually looks like.

3. Is spin only related to particles?

No, spin is not limited to subatomic particles. It is a property that can also be seen in macroscopic objects, such as planets and galaxies. However, the concept of spin in these cases is different from that of subatomic particles and is related to their rotation in physical space.

4. How is spin different from angular momentum?

Angular momentum is a measure of the rotational motion of an object around an axis. It can be visualized as the spinning of a top or a rotating planet. Spin, on the other hand, is an intrinsic property of particles that cannot be visualized in the same way. It is a form of angular momentum, but it is not related to any physical rotation.

5. Can we measure the spin of a particle?

Yes, we can measure the spin of a particle using various experimental techniques. For example, the Stern-Gerlach experiment is a classic method for measuring the spin of particles. Other techniques include scattering experiments, magnetic resonance imaging (MRI), and particle accelerators.

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