A “deafening silence” is a striking absence of noise, so profound that it seems to have its own quality. Objectively it is impossible for one silence to be any different from another. But the way we use the phrase hints at a psychological truth.
The secret to a deafening silence is the period of intense noise that comes immediately before it. When this ends, the lack of sound appears quieter than silence. This sensation, as your mind tries to figure out what your ears are reporting, is what leads us to call a silence deafening.
What is happening here is a result of a process called adaptation. It describes the moving baseline against which new stimuli are judged. The way the brain works is that any constant simulation is tuned out, allowing perception to focus on changes against this background, rather than absolute levels of stimulation. Turn your stereo up from four to five and it sounds louder, but as your memory of making the change rapidly fades, your mind adjusts and volume five becomes the new normal.
Adaptation doesn't just happen for hearing. The brain networks that process all other forms of sensory information also pull the same trick. Why can't you see the stars during the daytime? They are still there, right? You can't see them because your visual system has adapted to the light levels from the sun, making the tiny variation in light that a star makes against the background of deep space invisible. Only after dark does your visual system adapt to a baseline at which the light difference created by a star is meaningful.
Just as adaption applies across different senses, so too does the after-effect, the phenomenon that follows it. Once the constant stimulation your brain has adapted to stops, there is a short period when new stimuli appear distorted in the opposite way from the stimulus you've just been experiencing. A favourite example is the waterfall illusion. If you stare at a waterfall (here's one) for half a minute and then look away, stationary objects will appear to flow upwards. You can even pause a video and experience the illusion of the waterfall going into reverse.
It's a phenomenon called the motion after effect. You can get them for colour perception or for just lightness-darkness (which is why you sometimes see dark spots after you've looked at the sun or a camera flash).
After-effects also apply to hearing, which explains why a truly deafening silence comes immediately after the brain has become adapted to a high baseline of noise. We perceive this lack of sound as quieter than other silences for the same reason that the waterfall appears to suck itself upwards.
So while it is true that all silences are physically the same, perhaps Spinal Tap lead guitarist Nigel Tufnel was onto something with his amplifier dials that go up to 11. When it comes to the way we perceive volume, it is sometimes possible to drop below zero.