Yes, for example you might be able to measure the force against the magnet as it interacts with magnetic fields around the black hole, generated by swirling ionized gas. Or even knowing the mass of the magnet you could infer the mass of the black hole and thus its radius even though you could not see it, by measuring the weight of the magnet near it.

It would be difficult to implement any direct experimentation since the nearest black hole is thousands of light years distant; but a "Gedankenexperiment" or thought-experiment in the Einsteinian tradition could be conducted.

The mass of a large lightweight object is not simple to determine. For you must allow for the buoyancy* of the volume of air displaced by the volume of the item.

But having done so, you will have the true mass, not merely its weight on Earth.

[Its weight will also vary according to the force of gravity at that point. Even in a country as small as New Zealand, the gravitational force varies by about one part in a thousand. Right at the limit for commercial weight precision. ]

* This buoyancy concept needs thought. Consider a fish, which you must not leave out of the water for more than 10 seconds. And of which you desire to know the mass.

Now, this fish, when neutrally buoyant, will neither rise, or sink. Therefore it is equally dense as is the water. So its mass is the same as the mass of the volume of water that it displaces. (This is Archimedes idea.) So by measuring the volume of the fish, and knowing the mass of that volume of water, we have the mass of the fish - not merely its weight.

So we quickly move the fish to a new tank, and measure the increase in the level of the water, to know the volume occupied by the fish.

[You may wish to conduct the same mental experiment (gedankenexperiment) to find the mass of a perfectly spherical balloon, filled with Helium.]

"Schroedinger's Cat" is a Gedankenexperiment (German for "no funding available"*).

It runs something like this:

Suppose we have a box we cannot see through. Inside that box we place a cat, and a device containing a cyanide generator and a radioactive sample. The cyanide generator will be triggered if the sample emits radiation. We now seal the box and wait.

There is some chance that an atom in the sample will decay. Since we're doing this all in our imagination, we'll suppose that we have carefully chosen the material and the sample size so that there's a 50/50 chance that an atom will decay in one hour.

Schroedinger points out that, after one hour, the box contains a quantum superposition of states. That's a fancy term for saying that the cat inside is neither dead, nor alive, but half of each, kind of "smeared" into each other.

This was intended as a scathing criticism of the Copenhagen interpretation of quantum mechanics, which basically says that that a superposition of states only collapses into a definite state when it is actually observed (per Schroedinger, when the box is opened and we see either a 100% living or 100% dead cat).

A scientist named Wigner pointed out that this is not really a valid criticism using a different thought experiment usually called "Wigner's Friend". Wigner basically said let's get a bigger box and put a person in it instead. From our point of view (outside the box), there may be an uncollapsed "superposition of states", but to our friend (inside the box) there's no such thing: either he's alive or he's dead.

More to the point, the trigger that either starts the cyanide generator or does not can be counted as an "observer" in the Copenhagen interpretation. The real criticism of the (original) Copenhagen interpretation is that it doesn't define what the word "observe" means clearly enough.

* Actually, it means "thought experiment."