So one would just need to reduce the air pressure on an object and see if it weighs less?
No, this is where it becomes difficult and has to be done the right way.
Measuring a weight at sea level and then carrying the scales and weighted object up a sky scraper to measure again will produce a marginal effect, making it appear that the weighted object is slightly lighter at that height if the scales are not calibrated and it has to be done properly to show that weight would not physically change.
So then don't travel to different elevations. Use vacuum chamber to get less air pressure. A weight and a precision scale, one reading at ambient air pressure, and then another at reduced pressure.
One problem.
How do you calibrate a scale then put it inside a vacuum chamber to extract air and then calibrate again?
At least the sky scraped solves this problem.
We have a four figure balance in the glove box at my university. We use it to weigh out extremely reactive substances in a vacuum and it is calibrated by the same weights whether or not it is inside the glove box. It makes no difference whether it is under the vacuum or if the scales are outside the glove box.
I know you won't believe me but I felt I should chip in because I actually have first hand experience with this. Furthermore, if you place a calibrated set of these extremely sensitive scales into the glove box (calibrated at atmospheric pressure and reads 0.0000 g when tared) and then apply the vacuum, the scales will stay at 0.000 g the whole way down until the maximum vacuum is reached, which is about 0.1 mbar - that's about 10,000 times less pressure than outside the box.
Conversely, it's also possible to flood the glove box with an inert gas such as argon, which usually results in a pressure greater than atmospheric within the box. We do this when there is an intention to conduct an experiment within the box but without the desire to have reduced pressure (as many common solvents would simply boil at such reduced pressure). Just the same way as the scales stay at 0.0000 g as pressure is reduced, it also stays at 0.0000 g as pressure is applied.
Again, you won't believe me, but that's how it is.
The scales may stay at zero but that doesn't mean they will be at zero, only that they say zero.
Why?
Because scales calibrated at sea level atmospheric pressure to read zero, will read zero because the pressure is already bearing down on the plate of the scale in some capacity....BUT...in an evacuated chamber they cannot be calibrated with any accuracy other than guess work, because having them at zero at sea level atmospheric pressure, means they go into the chamber reading zero and once evacuation starts, they will still read zero, yet the pressure on the plate will be marginally released...UNLESS the scale shows that reverse discrepancy, so it can be calibrated from that point on with the gloves that will by that time, look like inflated fingers with little flexibility.
Yes - the scales can go negative. If something particularly heavy is on them (say, a 500 ml round-bottomed flask with some chemicals in it) and it is quickly removed, the scale will easily oscillate between negative and positive weights until it reaches zero again for a few moments.
Alternatively, (and I have done this as well), you can 'zero' the balance with something already placed on it (like an empty flask, ready to weigh something into it). Remove said item, and voila - the scale will go into the negative by exactly whatever the flask weighs.
Honestly Scepti, I'm heavily experienced with this and you're simply wrong. You won't like that, but you are.
Also, unlike many other things, I
do actually have first-hand experience with what I'm talking about and I can 100% verify that pressure has absolutely no bearing on the weight of an object what-so-ever. There is no guess work - I have
literally zeroed the plate before the vacuum is applied (I have done it many times) and when the vacuum is applied, the plate does not drop into the negative. When I flood the chamber with argon, I must firstly evacuate it of air (so basically put it under vacuum), then I flood it with argon which typically goes to a pressure a little above atmospheric (then I repeat the process twice more to make sure there is no air in there) and the scales will
literally sit at zero the whole time (until I place something on the scale).
The 200 g calibration weight (it weighs 200.0000 g exactly) will weigh exactly that regardless of the pressure. You're just wrong. If you refuse to believe me then fine. I can't convince you of the fact we are not encapsulated by a giant ice-dome, I've come to peace with this. However, if I cannot convince you that pressure has absolutely no bearing on the weight of something, given it is something that I have personally dealt with so many times - then I give up.