I was going through a tutorial that explained the use of an NDX filter. Pictures taken of a busy street at slow shutter speeds with the filter on had only empty streets without any vehicles. How does this happen ? Shouldn't there be objects with blur instead of completely disappearing? Can someone please explain how this happens ?
The camera records light reflected or emitted by the scene being photographed. While the shutter is kept open during exposure, the camera accumulates light hitting the sensor as per the selected sensitivity and aperture.
Now, thinking about the camera recording light, you can consider what happens to different parts of the scene:
Considering a set exposure, #1 explains why the background appears and is sharp. #2 explains why people who are mostly still by slightly moving make it into the image but appear blurry. #3 explains why cars bodies do not show in long exposures and #4 explains why cars leave light-trails but are not seen themselves.
Now, this will happen with a normal exposure or using an ND filter. The only difference is what falls into the fast moving case. For a short exposure, an object must be moving quite fast not to contribute to the scene. For a long exposure, even a person walking can move enough within the frame not to make an imprint in the photo.
They're not gone completely, they are there with blur, but the effect a moving object has on the overall exposure is so small that we can't see it any more.
You could simulate this effect in Photoshop or other editing tools. Create an image with a black background and put a white dot or mark in the centre and apply increasing amounts of the motion blur tool. Eventually you reach a point where you can't see the white dot any more because the effect it has on the brightness of that area is negligible.
Or you can often see this effect multiplied in seascape images done with the ND filter. Because the sea never settles on one point it just becomes a mist, where the exposed rocks which are static, show through sharply.
This is what's happening in a long exposure with the ND filter, the length of the blur 'trail' of any object is so long that it doesn't visibly affect the exposure.
This is a spot with differing amounts of motion blur applied: