The Current Arguments
[Someone] asked me to respond to several arguments for collider safety. I am quite familiar with two of them. Two are sort of new. They may even be definitive. I appreciate the chance to think about them.
1. If the LHC can create micro black holes, cosmic rays have been doing it for years and years.
2. If these micro black holes are stable, we are awash in them because cosmic rays are producing them.
A cosmic ray hitting an earth particle and creating a black hole is an example of an inelastic collision. Another example is two billiard balls that hit and stick together. If one billiard ball is moving rapidly (the cosmic ray) and the other is stationary (the earth particle) the resulting black hole would retain the momentum of the cosmic ray. A cosmic ray that can create a black hole has a lot of momentum. The resulting black hole would be relativistic, that is, it would be moving at a substantial fraction of the speed of light. There are reasons to think micro black holes would interact with matter at rates not greatly exceeding the rates of neutrinos. Neutrinos can zip right through earth, and right through a star. Very few hit anything. Hitting something will stop a neutrino, but not a black hole. A black hole will only accrete the particle it hits, slow minutely, and keep right on going. A relativistic black hole would have to accrete thousands of particles to slow below escape velocity from earth. The binomial probability of this many accretions ever happening (given that a single accretion is improbable), even in trillions of cases during the billions of years of the existence of the earth, is vanishingly small.
On the other hand, black holes produced by colliders are produced by two particles moving in opposite directions. Their momenta cancel, so they can be moving at zero velocity. Actually the collision of consequence is the collision of the quarks, which have large and randomly directed energy. Quark energy would rarely cancel precisely, so most collider-created black holes would also be moving at faster than escape velocity from earth. However, a few would not be moving that fast. They would travel in orbits that repeatedly intersect earth. If they were slow enough, they would travel in orbits within the earth. Instead of zipping through earth in a few seconds, they would have forever to accrete.
Most of the matter in the galaxy is moving at astronomical, but not relativistic, velocity with respect to earth. Unless a cosmic ray collides with the minute fraction of matter that is moving at relativistic velocity, in exactly the opposite direction, resulting black holes would still be relativistic. Therefore only a minuscule fraction of natural cosmic-ray-created black holes in the entire galaxy would be moving at less than relativistic velocity with respect to earth. Slow black holes created in other galaxies would not have time to reach earth. Even if a slow micro black hole did approach the solar system, in most cases it would zip around the sun like a comet and return to deep space. Even if its orbit intersected earth, it would only spend a few minutes within earth, not enough to slow it down.
We call this the collider/cosmic ray analogy. It appears to be a false analogy.
Mangano from CERN’s Large Hadron Collider Safety Analysis Group discussed these problems with the analogy in his recent talk at Berkeley, and agreed with most of them.
3. Neutron stars are much more heavy and dense, and so would collect them faster, and inside of them the miniblack holes would accrete matter much faster.
4. Neutron stars are long lived, so these stable black holes are doing it no harm. (from this, we can actually set upper bounds on how fast black holes can possibly accrete matter in a worst case scenario). 5. This worst case scenario shows the LHC to be absolutely safe in a worst case scenario.
The neutron star argument is relatively new. I have not had time to review it completely, and I am neither a physicist nor an astronomer. We will have to work on this one. It may be the definitive safety factor that collider advocates (and all of us really) would love to see.
However, the argument has obvious problems. Neutrinos easily transit stars. Neutron stars are generally formed in supernovas. The core of the star becomes a neutron star, and the outer layers of the star are blown away. Therefore neutron stars have less mass than their parent stars. Therefore a line through a neutron star is less likely to intersect mass than a line through a star. Therefore a neutron star is less likely to stop a black hole than its parent star. Astronomers, am I right about this? And, as I say above, almost all natural black holes are traveling at relativistic speeds. Therefore they do not spend much time inside neutron stars.
The question above claims a bunch of facts. Do we know them for sure? Since my group needs to work on this issue, I would appreciate citations. It is not only a matter of appreciate. Proper scientific discussion requires citation or demonstration. If you don’t have citations you lose the argument. But for me right now, the citations are more important than the argument, and I would appreciate them.
Let us go through your claims.
Neutron stars are long lived. If I am right above, this is as expected. However, how do we know this fact? Suppose an occasional neutron star does capture a black hole and explode. (I am assuming that the core is accreted, and the resulting energy blows off the outer layers.) We see many cosmic ray bursts. How do we know some are not exploding neutron stars? There may be a reason, but again my model is not ruled out if all neutron stars are long lived.
We can set upper limits on how fast black holes can accrete mater. What are those limits? Does their calculation assume slow black holes? I would appreciate citations.
This worst case scenario shows the LHC to be absolutely safe in a worst case scenario. I really do hope that this is true. But it needs to be demonstrated.
One similar argument that was cited by Mangano in his recent presentation at Berkeley is contained in [Dar, De Rujula, Heinz,http://arxiv.org/abs/hep-ph/9910471] They discuss strangelets being swept up in star formation. This would take millions of years. Therefore their scenario is applicable only if strangelets are stable for long periods. But strangelets are thought to be unstable. They even say that strangelets are unstable in their own paper. This alone seems to completely refute their argument. They also talk of a star being entirely converted into a strange remnant, and assert that this would produce a signature that is more energetic than a typical supernova. In a typical supernova, an energetic process in the core blows off the outer layers. They do not explain why the outer layers would not be blown off in the case of a strangelet-conversion supernova. If this does happen, the signature would not be more energetic. It appears that they are wrong twice.