Or am I interpreting this wrong?
The energy isn’t actually vanishing, despite the language used in the abstract. It gets turned into heat. When the authors say the energy is vanishing, they mean from the string.
No, energy cannot be destroyed. It can, however, be lost from a system via interaction with the ambient environment by acoustic, thermal, viscous, impact, electromagnetic, gravitational, or other interactions.
Energy can be made inaccessible, however, by increasing local entropy such that it is impossible to extract all energy from a system; in terms of the Second Law of Thermodynamics, the temperature of your high temperature reservoir and low temperature reservoir would be the same so that you can’t pump energy from the former to the latter in order to do work. So, you still have all the energy, but no way to use it, kind of like being in the desert. As David Mamet says, “You don’t want to go there.”
Stranger
Technically speaking, energy must be conserved, but that doesn’t mean it can all be recovered.
If energy is lost to heat, as so much of it is, then it can’t usually be recovered. It probably just radiated infrared into outer space, and is lost to us.
Remember the laws of thermodynamics.
1: You can’t win.
2: You can’t break even.
3: You can’t quit.
thank you, didn’t know that one.
>Technically speaking, energy must be conserved
Actually, energy plus mass must be conserved.
No, mass is just one kind of energy. So if you add up all the energy, and then add the mass, you’re double-counting the mass.
And actually, so long as you’re looking at a closed system, and don’t change your frame of reference, mass is conserved as well. But in many systems, this might not be obvious.
Does it really have to be a closed system? I think mass is conserved as long as you’re consistent in defining you’re system. I’m trying to decide if that’s the same thing, but I don’t think so.
I’m not sure I see the distinction. If your system isn’t closed, then something is leaving it or entering it. If something is leaving or entering what you’re calling the system, then you’re not being consistent in what the system is.
It all hangs together if you carry it to the end. To expand on what Q.E.D. wrote, when the string is set into motion its fibers slide over one another and the friction heats the string. Heat is just the mechanical motion of the elementary particles in the string and is what causes the temperature of the string to rise. Let’s say the string was in thermal equilibrium with its environment, i.e. at the same temperature.
When the temperature of the rises it begins to lose heat to the environment by radiation, convection and conduction since heat moves from higher to lower temperatures. This heat added to the environment heats it up a little and the string cools down until it is again in thermal equilibrium. The energy that was in the motion of the string is now in the elementary particles of the string and its environment.
Believe it or not, the environment is the whole world whose temperature has gone up a little. Damned little but that doesn’t matter, it has gone up. The world was in thermal equilibrium with the rest of the universe before the string vibrated. That is, the energy intake of the world equaled the amount of energy being radiated by the world into the rest of the universe as heat. That equilibrium has been disturbed by the increase in the world’s temperature. So the radiation from the world increases a tad which cools it down and warms the rest of the universe.
All over the universe energy is being expended by and on various bodies and it all, sooner or later, shows up as heat. This warms the cooler bodies and cools the warmer bodies and eventually all of them will be at the same temperature, provided the universe lasts that long as we know it. Once they are all at the same temperature no more energy will be available for anything and everything comes to a halt.
Notice that the total amount of energy hasn’t changed. What was lost by the warm bodies is gained by the cool bodies. However, all that energy is unavailable because there is no temperature difference to transfer it from one place to another.
You’re right. There is no difference. To save myself some embarrassment I won’t even say what I was thinking.
can matter or energy going into a block hole be regarded as lost?
It’s “lost” in the sense that all trace of what it was is gone, but in the sense referred to in the conservation laws, a black hole still has mass, and that mass increases just as it should when you toss stuff into it. So, for instance, if you had a black hole with twice the mass of the Sun, and you tossed the Sun into it, you’d end up with a black hole with three times the mass of the Sun.
So you don’t believe Hawking (among others)?
As I understand things, which isn’t much, black holes emit radiation (Hawking radiation) as a result of quantum effects. It might be compared to tunneling where even though the work function of a surface exceeds the energy of the electrons in it, there is a non-zero probablility that an electron from inside will appear outside the surface.
So, as has been said, the energy that goes into a black hole shows up as mass. The black hole gradually evaporates as a result of Hawking radiation. The sum of mass and the Hawking radiation is equal to the total mass-energy that went into the black hole.
I think that’s close enough for the layman.
I guess I should say that the comparison to electron tunneling was illustrative only. Black holes leak photons and not electrons. The radiation is thermal radiation.
Well, it’s conceivable that subtle correlations in the Hawking radiation might preserve the information, but Hawking at least has not made a very strong case for that. And even if the information is preserved in such a way, it’s a lot more thorough as a means of destruction than, say, burning something, dissolving the ashes in acid, and then eating the resulting sludge. So for layman’s purposes, I think it’s safe to say that the information is destroyed.
And David, black holes can radiate electrons, or in fact any particles. It’s just highly unlikely for any particle with a mass significantly higher than the black hole’s temperature. For black holes of stellar size, the only particles light enough to be radiated are photons and gravitons, and possibly (though unlikely) the lightest neutrino, but a smaller, hotter black hole could certainly emit electrons, or even heavier particles.
That’s interesting. I would think that the only thing that could radiatewould be a massless “particle” like a photon. As soon as anything with mass popped up outside, it would be pulled back in.
Gravity is coupled to momentum, not mass. Photons have no rest mass, but they damn sure have momentum.
The rough idea is that Heisenberg lets “virtual” particle-antiparticle pairs pop into and out of existence, as long as they’re gone before too much time elapses (uncertainty relation sez how much time that is). If it happens right near a black hole, one might get sucked in, and to conserve momentum the other one gets kicked away. Not much, but just enough to keep it outside the event horizon.