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Where would all of the heat go? I'm not really that into science, but even I understand the basic concept that energy can't be destroyed, only transferred. So where did all the energy go
When you get into quantum physics and the extremes of astrophysics and cosmology, the laws of physics as we know them will break down. The temperature they managed to reach is well beyond mere fusion (15,000,000 Kelvins at the center of our local nuclear fireball, and 2,000,000,000 Kelvins in this accelerator; that's an extra two digits we added on there).
This is my guess, but I think they could have created a flash of antimatter or neutrinos. Theoretically, mass
can be destroyed if it is replaced by its antiparticles (as a big simplification, think of atoms with positively charged electrons and negatively charged protons). This is what theoretically causes black holes to evaporate: the breaking down of matter into matter-antimatter pairs and firing the antimatter away.
I'm not entirely sure what physically created the heat, but if it was due to a collision of particles, I wouldn't be all that surprised if they created something for an instant that neared the limit of what matter could physically support (but no, I seriously doubt that a singularity was made).
As for where the energy would go, it is in the form of plasma and, to my knowledge, is contained in a magnetic field so it won't get in contact with the actual machine. Also, along the same lines I think it is in a vacuum. I don't know that the flash of heat would remain once the matter involved was basically obliterated into nothingness, given that it did not come in contact with the machine. "Heat" is basically energy. On Earth when you heat something, it will continue to radiate because the matter itself begins emitting radiation. If there is nothing to continue to radiate though, I don't think heat will remain. If this isn't right though, I'm not sure how it works.
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how did they even measure that temperature? I'm pretty sure there isn't something that wouldn't be melted by that, so how would they possibly record it?
Not positive about this, but they could have measured the wavelength of the radiation emitted. That's how they measure the temperatures of distant stars, and it's fairly uniform. We all produce heat and glow in infrared. When you get hotter stuff though, it'll creep up the spectrum from visible, to ultraviolet, to x-rays, to gamma rays, and then to 'cosmic rays' (basically anything with more energy than gamma rays). To put it into perspective, our sun peaks in the yellow end of the spectrum and 'visible light' (which is why that is what we can see; wouldn't be much use to see what the sun doesn't emit). Neutron stars and stars getting sucked into black holes emit a bit of x-rays. These wavelengths correspond to the energy (heat) which produced them, and that is my guess for how they measured this.
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China might be a bit ahead on fusion, but will we even need fusion with this? This looks to be an even better source of energy than fusion, but can it be applied to the energy industry?
It is unfortunately (or perhaps fortunately

) impossible with our current technology to maintain that kind of heat beyond a single flash, and I think it took a bit of work and precision for them to pull off this one event. I'm thinking that it could have more of a use in spacecraft though, as a form of propulsion for [probably unmanned] ships. We're kinda far from that though, lol, they don't even know how they did it to begin with.
All pyros should envy them.

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At least really small ones. Any one bigger than a basket ball would CONSUME US ALL!
Well, it all has to do with how much matter is in it, since all black holes are technically the same size: a point. The event horizon that is commonly referred to as a black hole's size is in direct relation to how much matter was consumed (the singularity's gravitational influence), and if one with a sustaining amount of mass were to collide with the ground, it would be all over.

If contained though, it would probably evaporate. But to tell the truth, if the entire planet were consumed by a black hole, it would probably all total up to an event horizon the size of a basketball.
But then again, if it is a 'microscopic' black hole like they plan, it would be gone about when it was created. Assuming the astrophysicists aren't confused (lol...), we should be ok. Either that, or there will be a tiny black sphere orbiting the sun for a little bit where Earth used to be. The moon will probably survive though.