# Why two spin-$1$ bosons could not be in a spin $\frac{1}{\sqrt{2}}(|1,0\rangle-|0,1\rangle)$ state?

Consider two boson of spin $$1$$ without angular momentum. I'm seeing an argument that

"because those two particles were bosons, they must be symmetric under the exchange $$m_1,m_2$$. Thus they could not be in $$J=1$$ states such as $$\frac{1}{\sqrt{2}}(|1,0\rangle+|0,1\rangle$$)".

From appearance it kind of make sense, but then it doesn't, i.e. what if the spacial part of the wave function was asymmetric as well? Doesn't that resolve the issue?

Why two spin-$$1$$ bosons could not be in a spin $$\frac{1}{\sqrt{2}}(|1,0\rangle-|0,1\rangle)$$ state?

• Is the $+$ sign in the quote correct? Also: from the question it is not obvious whether $|1,0\rangle, |0,1\rangle$ refer only to the spin states or perhaps to the spin states of the particles in the same orbital. May 6, 2020 at 5:56
• I thought there was a second answer? May 6, 2020 at 18:36

Half spin particles at rest have a spin whose orientation does not change with time. When interacting with another half spin particle (e.g. electron-electron interaction in the same shell of an atom), they acquire a dependent state, which in turn does not change over time unless it is disturbed from the outside.

Particles with spin 1 have a spin that changes over time and are normally not able to assume a common state with other particles.

The component of such a particle's spin along any axis has the three eigenvalues −ħ, 0, and +ħ (where ħ is the reduced Planck constant), meaning that any measurement of its spin can only yield one of these values.

If you are not satisfied with this explanation - because it does not explain the nature of the interaction between the spins of the particles - read on.

Take the photon. It is part of the Standard Model of Elementary Particles and has spin 1. And now it gets a bit complicated, because the photon can be described in different ways, and some people don't like the one representation very much anymore. I’ll explain.

All light (EM radiation) consists of photons, and for polarized light it is clear that photons have oriented electric and magnetic field components. For radio waves it is also known that these electric and magnetic components change in time and space. From this it should be clear that each photon has an oscillating electric field and an oscillating magnetic field. This makes it obvious that two photons - especially those with different frequencies (wavelengths) - do not interact with each other.

So it’s all about the electric and magnetic field components that are behind the particles spin. Take the interaction of the two electrons in the same shell of an atom. Their electric fields are compensated by the nucleus. Their magnetic fields are interacting and they get oriented antiparallel. For particles with spin 1 that is impossible. Their magnetic fields are changing permanently. $$^1^)$$ $$^2^)$$

Two remarks outside the minutes

$$^1^)$$ Two photons of the same frequency and synchronized with their amplitudes (although the latter is probably not an absolute condition) could move in a common state with a periodic interaction of their field components. Would ist call bunching.

$^2$\$^) I refer to my question about MSE about how many dipoles (bar magnets) could be in balance in 3D. The question has no answer, but without mathematical proof it seems obvious that only 2 or 8 dipoles are possible. This corresponds to the number of electrons in the outer shell of noble gases in the first to third period of the Periodic Table of the Chemical Elements.