You've made the same fundamental mistake made earlier - assuming that the optics of the lens have somehow changed because of the size of the imaging sensor.
No, you have. A 52mm f/2 won't somehow magically get a 42.5mm entrance pupil when it projects its image onto a crop sensor.
The entrance pupil is what matters in determining which rays from the scene enter the lens and reach the sensor plane from a given angle, and thus in determining the depth of field, the bokeh size and the photon noise (given that the scene illumination and the exposure time are the same and the lens is sufficiently transparent) of the captured plane of focus.
The lens focal length to aperture size ratio is unchanged regardless of how much of the image the sensor picks up. The whole concept of x focal length on crop sensor = y focal length on full frame is little more than obfuscation designed to help us understand the difference between the two sensors, nothing more.
That's exactly what I am telling you but you are refusing to notice:
A 52mm f/2 lens on a crop sensor is
not "equivalent" in depth of field, bokeh effects and photon noise to a 85mm f/2 lens.
It is only equivalent in the field of view, but not equivalent in the entrance pupil size.
If you want to get a "lens equivalent" in
both the field of view and the entrance pupil size, you need to "change"
both the focal lens and the f-number.
If you're going to scold me about basic physics, then don't start by erroneously assuming that the imaging sensor is looking through the lens. It isn't. It's a recording device seeing an image that the lens projects onto it. Nothing more. The image circle is projected at a fixed size, which doesn't change, and the size of the imaging sensor means that it is recording a smaller portion of that image circle. The image isn't somehow magically concentrated onto the sensor as some people seem to think. By the thin argument of "relative" aperture, the lens isn't f/2.0 for full frame because the image circle is larger than what a full frame sensor sees as well. As well, if we go ahead and accept that the sensor is looking out through the lens, and that the size of the aperture carries meaning relative to the size of the imaging sensor, wouldn't a smaller imaging sensor against the same size aperture make it seem relatively larger? I only say this to make a point. Don't answer, because my same argument applies - it's flawed logic, just like everything else. The lens optics, focal length, and aperture are unchanged regardless of what you put them on. The variable is in how much of the image created by that lens is seen by the sensor. Trying to make it anything more than that is fundamentally incorrect. And the overcomplicated arguments that stem out from those flawed assumptions also don't hold up.
Too much of hot gas, but absolutely no content. A good illustration that you have no idea what you are talking about.