What is a negative magnetic moment?

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Protons possess a magnetic moment of 2.8 μN, while neutrons have a negative magnetic moment of -1.9 μN, indicating an anti-alignment with the angular momentum. The negative sign suggests that neutrons respond differently in a magnetic field compared to protons, potentially affecting their orientation. Visual representations of magnetic moments can aid in understanding the distinction between positive and negative values. The discussion raises questions about the implications of the negative magnetic moment and how it affects neutron behavior. Overall, the negative magnetic moment of neutrons signifies a unique property in their interaction with magnetic fields.
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Protons have a magnetic moment of 2.8 μN, Neutrons have a magnetic moment of −1.9 μN.

What is the meaning of the negative sign? Does the Neutron go a different direction in a magnetic field? How do they know it isn't just upside down? Is there any kind of a visual picture of a magnet that would help someone understand the difference between a positive and a negative magnetic moment?
 
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I'm a bit rusty, but I think the negative sign means it's anti-aligned with the angular momentum. (Or vice versa.)
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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