Alice gets reactions

Problem

I asked this question of a lot of people, including professional physicists, without ever getting a satisfactory answer:

To an outside observer, a particle such as Alice dropped into a black hole never passes the event horizon. So, to that observer, the mass of the particle would never be added to that of the black hole.

How then can a black hole ever grow?

Common reactions

Here is a summary of the most common reactions to the question, with my reasons for rejecting them as good answers:

Invoke quantum mechanics: “Particles cross the event horizon by quantum tunneling.”

This is easy to say, but the details of making a concrete argument in a mixture of quantum mechanics and general relativity are very hard. I have never seen these details worked out, and I don’t think they have been.

Furthermore, general relativity and quantum mechanics are widely regarded to be theories about different things, almost incompatible. There are very few examples of successful applications of the two. So I would question the validity of such an argument, without carefully examining the details.

At the time when I was asking the question, black holes were pretty theoretical. (Now I am fairly convinced of their existence, having seen the observations of the super-massive black hole at Cygnus X-1, etc.) It wasn’t as though we had observed a black hole gaining mass, and needed to explain the phenomenon. The theoretical proposal was in general relativity—why do we need to invoke a further theory to defend it?

“Never mind observation. It is unimportant once you understand the mathematics.”

This is typical of the popular “realist” subculture among physicists. They hold that the mathematics dominates the physical universe, which merely follows mathematical laws.

This view is an embarrassment to physics and math and science in general, and a sure sign of incomplete education. But I have heard such things from the mouths of some very bright and successful physicists.

Humility is in order. The universe is what it is—we do our best to explain our observations of it using mathematics.

But I think that this reaction was emotionally equivalent to the next one:

“We (or you) shouldn’t ask these sorts of questions.”

What would you call this? I guess the guys who responded this way thought they were practicing tough love. I call it bullying and cowardice.

It turns out that there is a very interesting resolution of the problem. It hangs on a revision of what is meant by “observation”.