Faster than light travel

[Umbran]

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.

 

[tomBitonti]

If an object is accelerated forever, it will gain infinite kinetic energy. This would violate the 1st law of thermodynamics. Black holes make me more than comfortable.

Note that a thing can (theoretically) accelerate forever tending to a finite velocity. As long as the amount of acceleration decreases over time. A point falling towards the event horizon of a black hole, once it gets close enough, to a distant observer, actually appears to decelerate forever, slowing due to special relativity and the relative position of the observer as the horizon is approached.
Thanks!
TomB
PostScript: Just found this, which has some interesting insights:

Waterfall

jila.colorado.edu

"A former student once called the ergosphere the place where little children come from, because nothing can remain at rest there. "

 

[shawnhcorey]

Note that a thing can (theoretically) accelerate forever tending to a finite velocity. As long as the amount of acceleration decreases over time. A point falling towards the event horizon of a black hole, once it gets close enough, to a distant observer, actually appears to decelerate forever, slowing due to special relativity and the relative position of the observer as the horizon is approached.
Thanks!
TomB
PostScript: Just found this, which has some interesting insights:

Waterfall

jila.colorado.edu

"A former student once called the ergosphere the place where little children come from, because nothing can remain at rest there. "

Note the word "appears". Yes, if you assume space is flat, it appears to decelerate. But space is not flat. In reality, the object is constantly accelerating and the acceleration keeps increasing.

 

[shawnhcorey]

Yes Umbran, the 1st law cannot be violated. But black holes appear to do so. So something is wrong.

 

[Umbran]

Yes Umbran, the 1st law cannot be violated. But black holes appear to do so.

I have already outlined how they don't do so. There is no violation.

 

[shawnhcorey]

I have already outlined how they don't do so. There is no violation.

No, you have no stated where all that energy is coming from.

 

[Umbran]

No, you have no stated where all that energy is coming from.

In a very real sense, it is a figment of your imagination, and doesn't exist, so it does not "come from" anywhere. There is no finite time at which this energy can be observed in the universe, which makes it a non-physical fiction, a bedtime story to scare children. Where does the energy for the body of Peter Pan come from?

The above is technically correct, but I expect it won't satisfy you. So, I have another, equivalent phrasing.

In an imaginary sense (and, I mean this in terms of the actual math - it is quantum mechanical, so imaginary numbers are involved) the energy is borrowed from the vacuum, and returns to the vacuum when the falling item joins with the singularity (which, despite your protestations, it does do), leaving the overall system of rock + hole with the same mass-energy it started with. This is the usual source for internal, non-physical energies that crop up in math from time to time.

 

[shawnhcorey]

An object falling into a black hole will be accelerated forever. That means its KE is always increasing. That energy must have a source.

A black hole starts as a very large star. Anything falling into the star has a maximum speed when it hits the surface. This means it has a maximum KE.

Then the star goes supernova and leaves a black hole. There is no limit to the KE an object falling into a black hole can acquire. So where did this energy come from?