Equilibrium · polarisation · silence

Thermal Equilibrium & Random Phase

Every moment is precessing. The sample is fully magnetised. And the receive coil detects nothing at all, until you do something about it.

What this figure is for

Students reliably expect a magnet full of precessing protons to produce a signal. It does not, and this figure shows why. Each moment sits on a cone about B₀ with a random azimuth. Sum them: the transverse components cancel term by term, and all that survives is the small longitudinal excess that makes the sample magnetised in the first place.

Magnetisation is not signal. M_z is a constant vector along B₀. Faraday's law asks for a changing flux, so a constant M_z induces no voltage no matter how large it is.
Excitation creates phase coherence. Apply the 90° pulse. The pulse acts on every moment at once and with the same phase, which is what converts a random fan into an ordered one. Only then does the sum have a transverse component to detect.
The cone is a cartoon. A single proton is a quantum object and does not really sit at a fixed angle on a classical cone. What is rigorously true is the behaviour of the net vector, which follows the Bloch equations exactly. Use the cone to build intuition, then trust the sum.

Try this in class: before pressing anything, ask the room to predict the reading in “|M_xy| of sum”. It hovers near zero and gets closer to zero the more spins you add, because the cancellation is statistical: the residue falls off like 1/√N.