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A common reaction to our model of mini black holes destroying the earth is "that will never work--because _____________(fill in the blank)." We would love to find a convincing way to fill that blank. But it has to be convincing--precautionary principle methodology applies here.

All limits suggested to date have been disappointing. But some are suggestive; a good limit may lie in their direction. We could use help with this. Why are we wrong? Please tell us. We will list all reasonable limits here (albeit we may reorganize and eliminate this section), and we will and try to be fair to all arguments. If requested, we will mention the name of the person making the suggestion. If appropriate, we will post submitted text. And let us know of relevant publications elsewhere. See our "Contact us" section on this website.

Limits we have heard to date are listed below. Comments on these limits are below the list

Potential model limits
1) Mini black hole creation requires more energy than available from colliders.
2) Mini black holes will evaporate via Hawking radiation.
3) Cosmic rays collisions, analogous to collider collisions, have not harmed us.
4) Mini black holes would accrete matter so slowly that they would not harm us for billions of years.
5) Mini black holes created in colliders would be moving faster than escape velocity from earth.
6) Cosmic ray creation of mini black holes implies a flux of mini black holes from all directions; some would be evident or would have harmed us.
7) The mechanism behind Hawking radiation requires some of the same principles as the mechanism behind mini black hole creation. If one is true, then the other must be true.
8) Heisenberg uncertainty requires that matter not be confined to a space the size of a mini black hole.
9) Time reversal invariance requires that the reaction forming the black hole reverse

Comments on potential model limits

1) Mini black holes require more energy than available from colliders

This is the position of the RHIC risk assessment by W. Busza et al [see our references section]. However, shortly after they asserted this limit, several papers appeared predicting mini black hole formation. [For example, Arkani-Hamed et al, Dimopoulos & Landsberg, Giddings & Thomas, Landsberg (see our references section)] This limit may well be true, but given published papers predicting otherwise, we need to acknowledge the possibility that it may not be true.

2) Mini black holes will evaporate via Hawking radiation

This is the position of the CERN risk assessment by J.-P. Blaizot et al [see our references section] They simply assert this limit, and stop there. However, Hawking radiation is theoretical, and has not been seen. There are published papers that assert that it does not exist. [For example, see the paper by V.A. Belinski. Helfer's paper also questions Hawking radiation. Both are cited in our reference section.] Fifteen physicists responding to our survey questions estimated an average of 10% probability that Hawking radiation would not work. [Survey results are forthcoming]

3) Cosmic rays collisions, analogous to collider collisions, have not harmed us

The analogy does not hold. In collider collisions, two particles moving in opposite directions collide. Momenta cancel. Mini black holes created this way would be moving slowly. (Some would be moving slowly--see 5) below for further discussion.) A slow mini black hole would drop into the earth, orbiting within the earth and eventually coming to rest at the center of earth, where it would have forever to accrete matter and grow exponentially. On the other hand, a mini black hole made by a collision between a cosmic ray particle and an earth particle would move at the average of the momenta of the particles creating it. Since one of these particles is a cosmic ray with enormous momentum, it would be moving at a reasonable fraction of the speed of light. To slow to less than escape velocity it would have to accrete thousands of particles. But there is reason to think that a mini black hole would be about as reactive as a neutrino, a particle that can zip right through the earth or the sun with little probability of a single collision. The probability of thousands of accretions in a single pass through the earth is so low that it is unlikely to happen in trillions of trials over billions of years. (This is also true for the faster escape velocity of the sun.) (We say "about as reactive as a neutrino," but reactivity could substantially exceed neutrino reactivity.) (Calculations available on request.)

4) Mini black holes would accrete matter so slowly that they would not harm us for billions of years.

This may be true. Our discussion of 3) above establishes that stable mini black holes must be extremely non-reactive. However, a mini black hole that falls into earth would have unlimited time to accrete. We are exploring several accretion mechanisms. Some of these mechanisms work better at low speed, and all increase exponentially. These mechanisms need to be explored in detail, but very little work is being done in this area. Absent a theory of quantum gravity, finding a definitive model will be difficult; when we look at new areas nature often has surprises that could not be predicted by classical methods. We would like to see at least a good approximation. If we invoke the precautionary principle, it is necessary to demonstrate that there is no accretion mechanism. We welcome and encourage any work on accretion.

(In developing theories of accretion, note that the radius of a mini black hole is orders of magnitude larger in theories of multiple dimensions. [cnfr Kanti, references section, his section 3] Also, capture effects work beyond the Schwarzschild radius.)

5) Mini black holes created in colliders would be moving faster than escape velocity from earth

The momenta of the two colliding particles cancel. However, the real collision of consequence is that of the quarks, which have substantial momentum in random directions. The probability of momentum less than escape velocity in a single collision is low. Greg Landsberg, in an e-mail exchange with us, calculated this probability as 10^-5. Given his prediction of a black hole produced each second, this implies creation of 158 per year that are moving at less than escape velocity.

6) Cosmic ray creation of mini black holes implies a flux of mini black holes from all over the universe; some would be evident or would have harmed us.

Fast mini black holes might come from all over the universe. However, fast mini black holes are not dangerous. [See 3) above.] Slow mini black holes which reach us would have to be created (or slowed) within the local group of galaxies. If slow, they would not have had time to come from further away within the life time of the universe. (Unless they were made by initial conditions, which seems not to be the case.) But few slow mini black holes could be made in the local group. A very high proportion of the mass in the local group is moving at astronomical but not relativistic speeds with respect to earth. Therefore, most mini black holes made by a collision between cosmic rays and local material must be moving at a reasonable fraction of the speed of light, for the same reason this is true on earth. There are a few exceptions. One exception is a cosmic ray hitting a cosmic ray going in the opposite direction. Another exception is a cosmic ray hitting something that is moving at equal but opposite relativistic velocity, for example the part of an accretion disk that is moving fastest and in the opposite direction from the cosmic ray. These and similar processes might produce a very low flux of slow mini black holes. Now consider a slow mini black hole as it approaches the solar system. The vast majority would travel in hyperbolic orbits and leave. Even if one does intersect a planet or the sun it would do so for only a short time, and these are objects that accrete at neutrino rates.

A model limit might be found here. What is needed is demonstration of a reliable and copious source of slow mini black holes, with calculations showing a high probability that they would be caught by earth.

7) The mechanism behind Hawking radiation requires some of the same principles as the mechanism behind mini black hole creation. If one is true, then the other must be true.

Black hole creation is enabled by the multidimensional models of string theory. String theorists have derived Hawking radiation based on principles of string theory. If both black hole creation and Hawking radiation are true, then mini black holes are not dangerous. At the moment, the extent to which one requires the other is not clear to us.

Until both are seen, it is always possible that the universe could allow one but not the other. What proponents can do is show that this would require strange physics, for example breaking parity principles or requiring conditional operation of effects. The fact that a parity principle would be violated does not automatically rule out the possibility of having one without the other. Physics has had to accept certain parity violations, and physicists regularly hypothesize such things. However, as we demonstrate that the necessary physics varies more and more from accepted versions, we reduce the probability of finding that the universe has that level of strangeness. The precautionary principle suggests that this probability should be very low before proceeding with an experiment that could lead to global disaster. On the other hand, the precautionary principle becomes extreme at the limit. We can not plan our day or our civilization while worrying about monsters in the closet, things that greatly distort present understandings.

We would like to see theorists address the question of the extent to which black hole creation is linked to Hawking radiation. We would like to see them put this into a formal risk assessment, laying out the demonstrations and certifying that they have carefully considered all reasonable possibilities that could permit one without the other, and found them to be implausible for good reasons.

Until they do, we agree that black hole creation and Hawking radiation are linked as part of a large amorphous body of theory. Therefore we accept that when computing the probabilities that one works and the other does not, that the probabilities should be considered conditional. If experiment shows that Hawking radiation works that shows support for the body of theory and increases the probability of black hole creation. However, because the body of theory is large and amorphous, we do not agree that, if one is true, the other must be true.

8) Heisenberg uncertainty requires that matter not be confined to a space the size of a mini black hole.

Heisenberg uncertainty opperates over short distances. The distance out of a black hole is in a sense infinite.

9) Time reversal invariance requires that the reaction forming the black hole reverse.

This is expressed in the following letter:

Dear Mr Blodgett,
There is another argument why microscopic black holes produced in high energy particle collisions cannot be stable or even long-lived. This is quite apart from evaporation by Hawking radiation (which I think will almost certainly happen). If we have the reaction proton + proton --> BH + some particles, by a basic principle called crossing symmetry the reaction proton + proton + some (anti-)particles --> BH must be able to happen, with a calculable probability. Then the principle of time reversal invariance, which we know to be true for the strong interaction and gravity, tells us that the reversed process: BH --> antiproton + antiproton + some particles must happen, and the time scale is as short as that of the BH creation reaction, less than a femtosecond.
I conclude that even if for some starnge reason Hawking evaporation does not occur, micro-black holes must still decay very rapidly (before they could move even a mm.)
If you want to put this argument on your web site, go ahead.
sincerely, Mike Albrow

We would like to see comment for or against this principle.

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