The Heisenberg's foolish isospin
There is no Coulomb repulsion between two neutrons. But in short distances of the range of 10-15m (as for instance within the nuclei) there is a strong attraction between two neutrons, thanks to the actuation of the strong force.
However, there is no dineutrons in nature. Why?
After all, when two neutrons approach one each other within a nucleus, they would have to form a dineutron, and would never separate anymore.
So, dineutrons would have to exist in abundance in nature.
In order to explain why dineutrons do not exist, Heisenberg proposed the isospin concept.
It is something like a mathematical theorem.
Actually Heisenberg's solution solved nothing. Because a force of attraction between two neutrons can be neutralized only by a force of repulsion.
Only a force can oppose to another force.
Heisenberg isospin does NOT produce a force. A mathematical concept cannot produce a force.
What Heisenberg did was only to describe, in mathematical language, that dineutron is never formed.
So, he did not explain the PHYSICAL CAUSE of the phenomenon, ie, his solution did no show what produces the force of repulsion between two neutrons, which wins their force of attraction, and make them to separate one each other.
Heisenberg actually introduced a new method in the development of Theoretical Physics. He was sure that Physics cannot have metaphysical concepts.
OBS: in Physics, methaphysical concepts are those ones that derive from our hope on how the laws of nature must be. For instance, it makes no sense to suppose that the time can run back to the past. So, it's a metaphysical belief to consider that time reverse cannot exist in a theory of Physics.
Heisenberg claimed that Physics must be free of metaphysical concepts, and only observable quantities can be considered in any theory of PHysics (observable quantities are those submissed to be measured in experiments).
Einstein was the first one to claim against that arbitrary way of developing a theory, and Heisenberg replied to him that he, Einstein, was the first one to do that in his relativity, by refusing metaphysical concepts.
Heisenberg new method was successful for the development of Theoretical Physics.
But we realize that Heisenberg's method introduced in Physics some sort of solutions where fundamental physical causes are missing.
One example we saw here, when we discussed the spin-interaction force. The paradoxical aspect of the spin-interaction appeared just because the theorists have followed the Heisenberg's method, where some physical causes of the phenomena are not taking in consideration.
So, as some physical causes existing in Nature are not taking in consideration, the theorists try to replace them by abstract mathematical concepts, as Heisenberg did by introducing the isospin concept.
Now we realize that, after a long period of successfull development along the 20th Century, Heinsenberg's method is finally collapsing, because now the physicists are working within a deeper level of research, where those physical causes, neglected by Heisenberg's method, cannot be neglected anymore.
The LHC will show us the faillure of Heisenberg's method, in upcoming years.
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I don't understand most of what you're getting at above but I just thought I'd point out that Heisenberg's version of isospin isn't all that similar to what nuclear (and particle) physicists use today. Wigner's model (not sure that's really the right word) is much closer.


