One of the interesting side effects of putting a bunch of solar panels on my roof was the shade they provide (they sit about 4" above the roof) and that small gap of air made the attic significantly cooler than before the panels were installed. With these on the 'north side' of the roof (not with water plumbing, just providing a 5 degree C temperature difference) that would be helpful in the Bay Area.
Shingles or metal directly on a roof heats the house substantially but is cheaper (costs less in labor). That is why we still do it. (Just like dark roofs look "nice" so we still do that too).
Putting the shingles directly on the roof has benefits like keeping water out, and a floating roof (like my panels) is much more susceptible to wind damage (either to create a sail out of them). The 'old school' fix was of course sod roofs. If you put enough thermal mass between the roof and the interior you avoid significant heating.
The point of jackets, mittens, and scarves is to retain as much of that radiant heat as possible, keeping us warm on winter days.
This is AFAIK not how clothing works - excepting special ones like space suits, firemen suits, etc. Clothes are primary to prevent convective cooling, not radiative cooling.
5C cooling in Bay area may be enough for most of the summer outside of top heat days in Jul-Sep. If that is substantially cheaper than installing AC, it could be a good solution for most homes and save lots of energy.
Also I was wondering what the effect of plain old mirrors on people's roofs would be. The point being to reflect the sunlight of course.
Mirrors don't work in the way you're suggesting because they don't provide enough of a shift in frequency in the energy they rebound (though they would act as an effective shade). For active cooling strategies, what you want is a material that can take the infrared frequencies from a heatpump, and shift them to the specific frequencies that make it hard for the atmostphere to absorb (similar to the use of phosphors in lighting for the visible spectrum).
Edit: I clearly didn't read this particular article closely enough, and the process they're measuring is actually a passive cooling system, which shows the material, or at least it's shade to be cooler than ambient temps. You could still use this material in conjunction with simple radiators to get better performance from a heat pump though.
The sun can hit the roof all day and it will not heat a normal house...so many layers in between and the heat will not reach below.
IMO it's just a matter of time before we use the sun to offset its effects on homes and offices. A super sunny day gives us a lot of power we could use to cool what the sun is heating. They coincide perfectly for a lot of hours.
This is completely false. An attic that's heated up to 130+* will have a significant impact on the temperature of the house it's attached to unless you use an uncommonly ridiculous amount of insulation. This is why things like attic fans are so effective in reducing AC load...
The earth already emits massive amounts of energy back into space. Nearly all the energy received from the sun is reemitted back into space, if this didn't happen the earth would quickly burn up. Adding reflectors won't make a huge difference as this energy would go back into space anyway.
EDIT: Of course, we would have to significantly alter the albedo, which is probably not possible with rooftop panels alone.
From the article, it doesn't look like increasing albedo is the researcher's goal for these devices. It looks like they're doing this to reduce air conditioner energy usage, which would reduce CO2 emissions from fossil fuel burning power plants.
Also, the earth's temperature is never really in equilibrium in the first place, as it's always heating or cooling due to the day-night cycle or seasonal axis tilt.
Delete "per hour". The watt is already a unit of energy per unit time (1 joule per second, specifically). So 12 trillion watts is the same as 12 trillion joules per second.