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wouldn't it only fly into space if it's velocity was in that direction? And....wouldn't it interact with everything along it's path? I mean..it wouldn't be qu

by rnovak 11y ago

wouldn't it only fly into space if it's velocity was in that direction? And....wouldn't it interact with everything along it's path? I mean..it wouldn't be quantum tunneling correct? (I've only taken rudimentary physics related to standard mechanics and electricity/magnetism). But it seems to me, since the LHC is underground, it would have a decent probability of hitting something along it's path to space, or am I way off?

evanpw 11y ago
It would hit things, but that just means that it would drill a hole a couple of atoms wide as it passed through the earth and exited the other side.
- rlpb 11y ago
  What would be the mass of matter that it captures as it passes through the Earth? That matter has a momentum of zero relative to the Earth[1] and the total momentum of the black hole would therefore be reduced as it drills through. Would this loss of momentum be enough to reduce its velocity below Earth's escape velocity? I guess it depends on the length of the "drill hole", the mass of the original black hole before it left the vacuum in the lab, the size of the event horizon and the original velocity? [1] Technically I suppose it has some momentum due to the rotation of the Earth but I assume that's not significant. If it were significant, it would just mean that there's are "good" and "bad" directions for the escape so a worse case scenario could only get slightly worse, not better.
  - drdeca 11y ago
    Are you sure that the total momentum would be reduced? The mass would increase (unless the hawking radiation is fast enough to counteract the mass it is absorbing, which I don't know), so unless something had other forces on it, it would slow down somewhat... but unless some stuff outside of it has momentum significantly changed, I would think that the momentum would stay the same? (assume a frame of reference where the matter it is passing through has roughly no momentum to start with)
    - ars 11y ago
      > I would think that the momentum would stay the same? Momentum is mass times speed, the momentum would stay the same, but since the mass is going up the speed has to go down. It would stop pretty quickly actually. "Friction" type interactions with matter it did not eat would also bleed energy.
      - pdonis 11y ago
        > Momentum is mass times speed Only in the non-relativistic limit. We're talking about a hole that starts out with ultrarelativistic velocity, so its momentum is not mv, it's gamma * mv, where gamma = 1 / sqrt(1 - v^2). For v close to 1 (meaning the speed of light), gamma can easily be a thousand or a million, meaning the actual momentum of the object is a thousand to a million times what the non-relativistic formula would make you think. > It would stop pretty quickly actually. I think you need to show some calculations. If the hole starts out moving at the typical velocities of particles in an accelerator experiment, it would need to absorb thousands or millions of times its starting mass to be slowed down to less than Earth escape velocity, let alone to be stopped. And at its starting speed it would take less than a twentieth of a second to pass through the entire Earth.
        ars 11y ago
        > Only in the non-relativistic limit. That's only if use non-relativistic mass which you should not be doing anyway. In any case it's still proportional to mass and velocity - the gamma factor does not change that. > meaning the actual momentum of the object is a thousand to a million times what the non-relativistic formula would make you think. You are missing parts of the interaction. Say it eats an atom - it has to accelerate that atom to the same relativistic velocity - meaning that new atom now has EXACTLY the same gamma as the black hole, and steals just as much momentum as if gamma was 1. Or in other words the gamma factor is completely irrelevant for these calculations, it cancels out. > it would need to absorb thousands or millions of times its starting mass to be slowed down to less than Earth escape velocity As I've shown you, this is incorrect. It only needs to absorb mass similar to its own rest mass. > And at its starting speed it would take less than a twentieth of a second to pass through the entire Earth. That is also irrelevant. The only thing that matters is its "width", i.e. how many of the particles it interacts with does it eat.
  - pdonis 11y ago
    > Would this loss of momentum be enough to reduce its velocity below Earth's escape velocity? Highly unlikely. If the hole starts out moving at nearly the speed of light, it will spend less than a twentieth of a second passing through the Earth. That's not enough time for it to absorb much matter, and it would have to absorb many times its starting mass (quite possibly thousands or even millions of times) to be slowed down from nearly the speed of light to less than escape velocity.

by rnovak 11y ago

evanpw 11y ago

It would hit things, but that just means that it would drill a hole a couple of atoms wide as it passed through the earth and exited the other side.

rlpb 11y ago
What would be the mass of matter that it captures as it passes through the Earth? That matter has a momentum of zero relative to the Earth[1] and the total momentum of the black hole would therefore be reduced as it drills through. Would this loss of momentum be enough to reduce its velocity below Earth's escape velocity? I guess it depends on the length of the "drill hole", the mass of the original black hole before it left the vacuum in the lab, the size of the event horizon and the original velocity? [1] Technically I suppose it has some momentum due to the rotation of the Earth but I assume that's not significant. If it were significant, it would just mean that there's are "good" and "bad" directions for the escape so a worse case scenario could only get slightly worse, not better.
- drdeca 11y ago
  Are you sure that the total momentum would be reduced? The mass would increase (unless the hawking radiation is fast enough to counteract the mass it is absorbing, which I don't know), so unless something had other forces on it, it would slow down somewhat... but unless some stuff outside of it has momentum significantly changed, I would think that the momentum would stay the same? (assume a frame of reference where the matter it is passing through has roughly no momentum to start with)
  - ars 11y ago
    > I would think that the momentum would stay the same? Momentum is mass times speed, the momentum would stay the same, but since the mass is going up the speed has to go down. It would stop pretty quickly actually. "Friction" type interactions with matter it did not eat would also bleed energy.
    - pdonis 11y ago
      > Momentum is mass times speed Only in the non-relativistic limit. We're talking about a hole that starts out with ultrarelativistic velocity, so its momentum is not mv, it's gamma * mv, where gamma = 1 / sqrt(1 - v^2). For v close to 1 (meaning the speed of light), gamma can easily be a thousand or a million, meaning the actual momentum of the object is a thousand to a million times what the non-relativistic formula would make you think. > It would stop pretty quickly actually. I think you need to show some calculations. If the hole starts out moving at the typical velocities of particles in an accelerator experiment, it would need to absorb thousands or millions of times its starting mass to be slowed down to less than Earth escape velocity, let alone to be stopped. And at its starting speed it would take less than a twentieth of a second to pass through the entire Earth.
      - ars 11y ago
        > Only in the non-relativistic limit. That's only if use non-relativistic mass which you should not be doing anyway. In any case it's still proportional to mass and velocity - the gamma factor does not change that. > meaning the actual momentum of the object is a thousand to a million times what the non-relativistic formula would make you think. You are missing parts of the interaction. Say it eats an atom - it has to accelerate that atom to the same relativistic velocity - meaning that new atom now has EXACTLY the same gamma as the black hole, and steals just as much momentum as if gamma was 1. Or in other words the gamma factor is completely irrelevant for these calculations, it cancels out. > it would need to absorb thousands or millions of times its starting mass to be slowed down to less than Earth escape velocity As I've shown you, this is incorrect. It only needs to absorb mass similar to its own rest mass. > And at its starting speed it would take less than a twentieth of a second to pass through the entire Earth. That is also irrelevant. The only thing that matters is its "width", i.e. how many of the particles it interacts with does it eat.
- pdonis 11y ago
  > Would this loss of momentum be enough to reduce its velocity below Earth's escape velocity? Highly unlikely. If the hole starts out moving at nearly the speed of light, it will spend less than a twentieth of a second passing through the Earth. That's not enough time for it to absorb much matter, and it would have to absorb many times its starting mass (quite possibly thousands or even millions of times) to be slowed down from nearly the speed of light to less than escape velocity.