what is the relationship between a spectrogram and the uncertainty principle heisenberg?
In Quantum Mechanics, state of system specified by a vector (wave function which is a vector in function space), and you could use different basis to represent this vector (imagine one vector in 2 different coordinate system which lead to different components in those coordinate system but they both represent the same vector). For systems composed from moving particles, one basis is the position basis and the second one is momentum basis. The transform between these two basis is the Fourier transform. Considering the wave function give us a probabilistic interpretation, to find the momentum or position of a particle you have to find the average and after that to have a sense about error, you have to find the standard deviation.
The Heisenberg Uncertainty principle, tell us the multiplication of position error and momentum error could not be smaller than some value, for any possible state of system.
Considering this is a property of Fourier transform you could extend that to signals where the signal amplitude and it's spectrum are different representation of same thing in different basis, and say multiplication of effective bandwidth of pulse (as standard deviation of power spectrum around central frequency) and the effective pulse width (as standard deviation of signal's power around it's center in time) could not be smaller than some value for every possible signal.