The pint is that the KE is forever increase, with no known source. That violates the 1st law.

The quanta cannot tunnel into the singularity. They are too far away. The probability of them doing so is almost zero.

The probability of tunneling is

*almost* zero, at any particular moment. But there's two things to remember:

1) the probability increases as energy increases. So, as you like to keep noting that the energy goes to infinity, so, then, does the probabilty approach certainty, because the barrier height is fixed.

2) Long before that certainty, though, we note that

*almost* zero probability at any particular moment means a certainty over "forever". So, eventually, it happens.

The universe is a closed system because we can see a fixed distance into the past. All the energy we see back to the big bang is finite.

We don't see all the way back to the big bang. As you look back in time, the universe eventually becomes opaque before then. We also don't even see the entire universe. We only see a

*visible* universe, limited by lightspeed. There's no indication I'm aware of that the physical universe is not infinite in extent, meaning that the energy overall may well be infinite. There's not a lot of win to be had in discussing the thermodynamics of a system with infinite energy...

We also don't see into black holes. Beyond the event horizon is, for many intents and purposes, outside the visible universe, and possibly outside the physical universe.

Or would be if there weren't any black holes.

Interesting point - I said the interior of the black hole is thermodynamically an open system. That's true. However, that open state is one-way. The only things that can come out of a black hole are the mass/energy, charge, and information that went in, and that only by Hawking radiation. Other than that, black holes are Las Vegas - what happens inside them stays inside them. That'll be important in a minute.

Upthread, I mentioned that I sometimes edit and use simplified language to keep things simple an comprehensible. Well, now we have to be more accurate as we invoke the First Law of Thermodynamics. It does

*NOT* say, "you cannot have infinite kinetic energy". It says that, in a closed system, energy cannot be created nor destroyed. However, we note that it

*can* be transformed.

So, let us consider a closed system that contains one black hole, and one rock. We drop the rock into the black hole. And you say, well, that rock now accelerates infinitely toward the singularity, develops infinite kinetic energy, and breaks the first law!

Then I ask - what was the rock's potential energy of position at the start of the experiment? I answer for you - the rock starts infinitely far from the singularity, so its potential energy of position was

*infinite*! No energy is being created!

Moreover, we can be even more strict, and note that the First Law really says that you cannot get more energy (as work) out of a closed system than you put into it. And now Black Hole Las Vegas comes up. I cannot

*extract* any of that kinetic energy from inside the black hole. Inside the event horizon, all world lines point inexorably inward. There is no path out for that energy. Thus, the First Law still holds.

Signals from above the event horizon get red-shifted. There are no signals from the event horizon or below it. Nothing can escape the event horizon.

Yep. Exactly. For that reason, that which goes on inside the event horizon cannot violate the First Law of Thermodynamics.