Extinction Risks and Particle Physics: When Are They Worth it?

The “one in a billion” calculation assumes black holes/strangelets created by cosmic rays would be as dangerous as black holes/strangelets created in colliders; some people dispute this (see http://www.risk-evaluation-forum.org/prob.htm , point 3).

Also:
“Imagine that there is a one in a billion chance that turning on the LHC destroys mankind, and otherwise makes every human life on average X times better. When is the expected benefit of taking the risk larger than the value of not taking the risk? It turns out X only needs to be 1.00000000100000008 – a minuscule amount better.”
The vast majority of people probably live in the far future, making this argument somewhat weaker than it looks.

Even when a fast particle hits a particle at rest it can produce a slow decay product (especially when the product is heavy); it is just much less likely. The large flux of cosmic rays over long time ought to have produced enough such cases to show up. Also, scattered fast-moving dangerous particles would seem to be very noticeable phenomena. But the key concern remains: could there be some property of colliders that is not found in nature?

Even if we take into account the value of future people the argument is the same. In the case of just the present N people, the expected value of doing the experiment is P*0 + (1-P)*N*X (where P is the chance of disaster). When this expression is larger than N (the value if we do not do anything) the experiment is worthwhile. This happens when X > 1/(1-P). But notice that N factors out: if we use all people there will ever be for N the result is the same. If the benefit X only accrues to the present generation, then concerns for future generations may swamp our risk-taking. But it seems unlikely that the benefits are only in the present; in fact, it seems likely that the biggest benefits will be further in the future rather than today.

I think the math has been done, although I’m not terribly up to date on the literature. A quick back-of-the-envelope estimation:

Calculating the risk from beam collisions is reasonably easy: Let’s call the mass of a dangerous remnant M. In order to be dangerous it has to move slower than Earth’s escape velocity v=11.2 km/s, so its energy has to be between Emin = Mc^2 and Emax = sqrt(M^2 c^4 + M^2 v^2 c^2/(1+v^2/c^2))
= Mc sqrt(c^2+v^2/(1+v^2/c^2)). Emax-Emin = 0.2092*Mc^2

When two particles collide with total energy E and produce N offspring particles, all different partitions of the energy between the N particles are going to be equally probable (from the equipartition principle in statistical mechanics). The sum of their energies has to be E, so one can view the individual energies as coordinate axes in a N dimensional coordinate system and the state located on a N-1 dimensional standard simplex sum_i E_i = E. The dangerous configurations are those where one of the coordinates is between Emin/E and Emax/E. The fraction of states where this occurs can be estimated as (Emax/E)^(N-1) – (Emin/E)^(N-1). (This leaves out momentum conservation, which becomes an issue when Emax/E starts to get close to 1)

E = 14 TeV (2.2428*10^-9 Joule) for the LHC. For strangelets, M is assumed to be on the order of a medium atomic mass. Setting M to 1e-26 kg (like a lithium atom) makes Emax about 40% of E (it cannot be much higher, or there will not be enough energy). Putting in these numbers for the case N=2 gives a probability P=6.3e-19. For N=3, P=1.1e-27, and so on. More particles means a few more ways a particle can get into the dangerous area, but the total space of mostly safe states grows much faster. The LHC will have about 8e7 collisions per second, so we should expect a “dangerous” interaction for N=2 every thousand year of experiment or so (and this assumes every collision to work!).

Now, in the stationary target case things get a bit messier. Assuming that the two colliding particles have equal mass and one moves ~c, we can work in a centre of mass coordinate system that moves at speed c/2. The total momentum is zero, and we are interested in how likely it is that reaction produces a particle of mass M moving at speed c/2 plus or minus 11.2 km/s in this coordinate system. Emax = sqrt(M^2 c^4 + M^2 (c/2+v)^2 c^2/(1+(c/2+v)^2/c^2)), Emin = sqrt(M^2 c^4 + M^2 (c/2-v)^2 c^2/(1+(c/2-v)^2/c^2)). The difference is just 0.0005 Mc^2, but more importantly both Emax and Emin are now (for the strangelet mass above) bigger than E – it would require a lot of energy to both create the particle and give it the fast velocity (in the center-of-mass frame) that corresponds to being at rest in the lab.

At least I think so, but the probability that I messed up a calculation is relatively high.

These calculations does seem to reinforce the estimate that it is pretty unlikely that particles get the relatively precise velocity needed to remain on Earth even in beam collisions (good for our security *), and that fixed targets are very inefficient in producing high energy reactions (bad for the moon argument). Maybe we ought to look for small black holes and strangelets whizzing around at high speed?

* This assumes that the cross section between the particle and the planet is not so large that it can gobble up enough mass while passing by to slow down and get trapped. A particle travelling at c/2 needs to absorb around 13,383 times its own mass before it gets below escape velocity.

It is, I think, a bit misleading to present the estimate in terms of benefits to individual people, since our assessment of how likely it is that the experiment will have an average benefit of X to each person will vary dramatically depending on the number of human beings that we believe will ever exist. And because we tend to underestimate how many such people would live if humanity did not become extinct prematurely, presenting the estimate in this manner will tend to downplay the expected costs of running the experiment. When readers of this blog consider how plausible is it that starting the LHC will expectedly increase the welfare of people by that tiny amount, they are likely to think about the people that currently exist, and perhaps a few extra generations into the future. If, however, we assume that the human species will expand in space and time constrained only by the availability of energy resources, then the number of future individuals becomes astronomically large–think about how many individuals will exist if, not implausibly, we assume that a trillion lives will be lived at any given time during the next trillion years. It is not at all clear that running the experiment is expected to benefit on average all these future people, even by a tiny amount. Such benefits may well be like ripples in a pond, diminishing in proportion to the distance from the origin. If the pond is large enough, it might be prudent not to throw the rock into it.

errata
‘x> (2+2p)/(1-p)’ should be ‘x>2/(1-p)’.
‘x = 2.000000004’ should be ‘x = 2.000000002’

CERNs web site states that we have not been destroyed by effects of cosmic rays and micro black holes will evaporate.

However, cosmic rays travel too fast to be captured by Earths gravity, and Hawking Radiation is disputed and contradicts Einsteins highly successful relativity theory. Collider particles smash head on like a car collision and can be captured by Earths gravity, and relativity predicts micro black holes will not decay (Hawking called Einstein doubly wrong, yet it is Einstein who is repeatedly found to have been correct in his theories). There is currently no reasonable proof of LHC safety, LSAG (LHC Safety Assessment Group) has been trying for months to prove safety without success. I hold the minority opinion that it may not be possible because it may in fact not be safe.

Cosmic Rays from the legal complaint.

any such novel particle created in nature by cosmic ray impacts would be left with a velocity at nearly the speed of light, relative to earth. At such speeds, . . . , is believed by most theorists to simply pass harmlessly through our planet with nary an impact, safely exiting on the other side. . . . Conversely, any such novel particle that might be created at the LHC would be at slow speed relative to earth, a goodly percentage would then be captured by earths gravity, and could possibly grow larger [accrete matter] with disastrous consequences of the earth turning into a large black hole.

Professor Dr. Otto E. Roessler estimates 50 months Earth accretion time from a single micro black hole captured by Earth’s gravity (www.golem.de/0802/57477-4.html, translation at http://www.lhcconcerns.com/LHCConcerns/Forums/phpBB3/viewtopic.php?f=10&t=52)

If this thing is so safe, why arent CERN scientists allowed to express any personal fears they might have about this Collider?

Alleged in the legal action: Chief Scientific Officer, Mr. Engelen passed an internal memorandum to workers at CERN, asking them, regardless of personal opinion, to affirm in all interviews that there were no risks involved in the experiments, changing the previous assertion of minimal risk.

(Statisticians generally consider minimal risk as 1-10%).

JTankers
LHCConcerns.com

JTankers: I am curious about what your standards for reasonable proof of LHC safety would be? It is after all proving a negative, something no amount of LSAG work will ever reach. What kind of physics or reasoning could it ever be based on?

The burden of proof in risk estimation is always a fraught issue. Normally we assume persons doing apparently safe things not to have to show they are safe, while for apparently unsafe things they have to do it. Maybe existential risks are sufficient to also force a burden of proof onto them, but then we need to have reason in the first place to think there is an existential risk. Since safety can never be proven, it would seem that the sceptic instead have to demonstrate a sufficiently serious risk. But in the case of physics disasters the real worry is always going to be about the least understood or unknown physics, not the known physics that could be used to derive solid risk estimates. Given the human tendency to regard uncertainty as threatening this will also cause a bias to regard uncertain risks as more serious than certain risks.

I’m also curious about Dr. Roessler’s calculation, since I have been doing accretion time calculations myself. To my knowledge they have not been published in any scientific paper?

Nick: I think argument 1 is probably false, but there are fascinating issues here about unequal distribution of the benefits in time and space as well as subjective benefits. I think 2 is a pretty good argument, and both 2-3 would be in line with Nick Bostrom’s “max-OK” principle. The problem with never doing anything that has the chance of justifying all goodness is that there seem to be such as background chance in any action and non-action (our actions plus quantum tunnelling can always produce planet-eating dragons). Saying that it is wrong to do actions that have a higher-than-default chance of ending goodness would as far as I see stop us from doing anything new or large-scale.

The particular peculiarity about physics disasters is that the actions necessary to learn what the risks are contribute to the risk. Since the uncertainty is model uncertainty rather than parameter uncertainty, we cannot rely on deduction to reduce the uncertainty. Is the only way forward sideways anthropic arguments like Nick’s and Max’s to bound risks?

I would like to echo Steven’s comments about delaying the experiments. It is clear that the CERN team either haven’t addressed many of the important issues, or haven’t been transparent about it. Either way, the experiments should not presently go ahead. We can gain almost all the same benefits at reduced risks if we have a decade or five to seriously think about the issues, collect more data on the intersection of relativity and quantum mechanics, and put together a safety report worthy of the stakes.

A serious reconsideration of the safety of the LHC, followed by the appropriate action is better than a blanket ban, or proceeding with our current level of ignorance.