Have you ever suddenly glimpsed at a timepiece with a second hand or some other visual display of seconds ticking off, and the first second seems to last like a second and a half?
Whay does that first second seem longer than others?
My theory has always been that we begin to move our eyes toward the watch or clock just as the previous second ticks off, and then our minds consider the amount of time between our deciding to look at the clock and our eyes actually settling on the clock as part of the amount of time we were actually looking at the clock.
In other words, we really only see one second, but we think we’re seeing more.
I too have noticed this, but I’m not sure that theory is right. I just looked a few times and thought: “Isn’t it odd how you never look just before the hand moves”, but then on the third or fourth time, I looked and the hand moved almost immediately.
But - and here’s the weird thing - the next full second seemed longer than the subsequent seconds. What is going on? 
You are still precieving the second? Like, when you first look, it seems so long because you are waiting for perception to set it. After a few go rounds you get used to this perception. Kind of like when you first watch a movie and it goes on forever yet the second viewing seems unbelievably fast. Something like that?
I’ve noticed this too.
I’ve always chalked it up to your mind averaging out the random times that the first partial second takes, given all the times you’ve noticed it before. In other words, your brain is used to paying attention to that first second; and it takes a half-second, on average, to pass.
You then build up a semi-conscious expectation for the hand to move after half a second, and if it takes longer (closer to a full second) you become aware of it and notice it distinctly. If the first partial second is about half a second, you don’t notice it as unusual, and it just further reinforces that sense of average timing. And if it’s significantly shorter, your brain automatically discards that, because it’s not valid for becoming a part of your mental average. The hand moves so quickly that your mind views the partial second before as “not enough data.” The whole phenomenon is a sort of confirmation bias, or at least a self-reinforcing bias.
This is my own hypothesis, and not any sort of tested theory.
I’ve noticed this too (I think it is quite a well-documented perceptual quirk).
Our sensory peripherals bombard our brain with a lot of different kinds of data; our brain assembles it into a workable approximation of reality, but all sorts of shortcuts and cheats are built in. For example, I was watching fireworks the other day and only after I consciously noted that the flash should precede the bang(for distant objects) did I actually perceive it that way; right up until the realisation, I was perceiving them simultaneously.
We tend to think of our perception as being sharp and instantaneous, but it may actually be the case that everything is a bit smeared/blurred together and that our brains just pick out what seems to be the most pertinent data and sequence.
The reason for this is intertia. According to the laws of quantum physics, the watch hand does not start moving until it is observed. So it takes a bit longer for it to accelerate up to speed, hence the initial pause.
/psuedo-scientific-babble-mode-off
Close, but not quite - although you’re essentially correct about the observer effect, it’s because the software in which our universe is simulated is event driven - on the first instance of an event, the handler code must be loaded into memory, causing a slight delay.
There is nothing in Einstein’s equations or the physics of time which explains or even alludes to our perception of time. It has even been proposed that this experience of a “flow” from past to future is simply a useful neurological characteristic which ultimately yields more prey since the creature that can “predict” the motion of the prey has an advantage over the one which lives solely in the “present” (or even a few milliseconds in the “past”) and thus can only calculate the prey’s movements based on what has already happened.
The mind appears to have different “modes”. When we absently look at a clock, the more “regimented” mode enforced by the clock’s perfect regularity might conflict with the more “liquid” mode of our everyday daydreaming, leading to some difficulty in resolving how long the second hand stayed still for.