Stop the LHC – until we know it’s SAFE!

That is what LHCDefense.org – the self-proclaimed “official site for citizens against the Large Hadron Collider” – exhorts us to do, through articles such as Curiosity killed the cat!, New paper contradicts Hawking, and Higgs vs. Hawking.

A hot new niche

Using everything from “expert” opinions, research papers on arxiv, and biblical verses, the website’s creator(s) have cunningly played upon the layperson’s paranoia of the “mad/evil scientist/Dr. Strangelove” cliché to sensationalize the issue and in the process have created a sizable following for the website, not to mention a good deal of publicity.

LHCDefense.org is by no means the only website cashing in on this hot new niche; there is a plethora of sites that have espoused LHC-bashing and proffer their myriad points of view to the anxious reader in exchange for some PR juice. lhcfacts.org and bigsciencenews.blogspot.com are good examples.

These websites’ main contentions are that the theory that black holes radiate is flawed, and if they do so, they do so at a very gentle rate even at the end-stage, and that Lord Hawking was daft after all. Or something like that. They tom-tom the fact that a guy with a masters’ degree in statistics did a Delphi study of a group of “physicists” and supposedly found that their estimates that Hawking radiation would fail ranged from 0% to 50%. Yeah, right. Let’s introduce democracy in physics.

Panic on the streets of Meyrin

We have been rushed into some hasty, ill-informed decisions in our time – we emailed our bank details to our new friend in Nigeria who had $26m to smuggle out of the country by midnight, switched from Google to Bing after seeing those TV adverts and just this May we stuck $225 on the Cape Caterpillars to win the International Premier League of cricket. But even those little jaunts look like feats of Socratic reasoning when you compare them to the rumors slouching out of LHCDefense.org. If they’re to be believed, a CERN scientist has predicted that a “miracle” will preclude the LHC from operating. This is the paper in which Holger Nielsen and Masao Ninomiya purportedly made the statement.

Which, is of course, ridiculous. Firstly, while the website states that “a” scientist has made the prediction, we find that the paper has two authors. Furthermore, a quick glance at the paper reveals that it has nothing to do with the production of micro black holes or strange matter at the LHC. Depending on your outlook, you could see this either as a case of clutching at straws; or that of stopping at nothing to further a machiavellian agenda to bring all scientific research to a grinding halt. Sadly, these stories are created for consumption by the lay public, not physicists. The effect of a constant slew of such stories could well be widespread panic on the streets of Meyrin, the picturesque and quiet (if you disregard Cointrin airport) Geneva suburb that abuts on CERN.

The truth about black holes

Like most physics departments worth their salt, Acta Physica Building has a fire alarm. When it goes off, everyone ignores it and stays put wherever they are until assorted do-gooders (fire marshals) herd them out of the building and across Big Road. Once out of harm’s way, everyone mills around trying to find somebody important to be seen talking to, then heads to the bar.

Everyone, that is, except us, who today morning took an asbestos blanket and traipsed back into a potential inferno to risk getting reduced to a carbon footprint for the sake of this incredibly important revelation.

Here goes. As always, we shall start at the beginning for the sake of clarity.

Black Hole basics

The decay rate of an isolated black hole is given by

$$!\frac{dm}{dt}=-\frac{\kappa}{m^{2}}\hspace{2 cm}(1)$$

where $$\kappa$$ is a constant:

$$!\kappa=\frac{g_{\ast}\hbar c^{4}}{7680\pi G^{2}}\hspace{2 cm}(2)$$

Solving Eq. (1), we can show that a black hole’s lifetime is given by

$$!\tau=\frac{m^{3}}{3\kappa}\hspace{2 cm}(3)$$.

Moreover, the temperature of a black hole is given by

$$!T=\frac{hc^{3}}{16\pi^{2}k_{B}Gm}\hspace{2 cm}(4)$$

A quick glance at Eq. (1) tells us that small black holes radiate more rapidly than more massive ones, and it explains why black holes end their lives in spectacular explosions.

At this juncture it is a good idea to emphasize on the word isolated.

Isolated – as in solitary, alone, removed, segregated, disengaged, sequestered, separated, insulated, undisturbed. Isolated – as opposed to connected.

A black hole in a box that contains vacuum is isolated. A black hole immersed in a radiation field is not isolated, neither is a black hole that is part of a population of black holes whose number density is large enough for them to reabsorb each other’s Hawking radiation. Consequently, a black hole lying in inter-stellar space cannot be considered to be isolated as it is immersed in the CMBR field, however weak it may be; and can also absorb inter-stellar gas and other material.

Hawking Radiation in brief

According to quantum field theory, there is no such thing as “nothing”. Vacuum itself has an underlying background energy that exists even in space devoid of matter. Virtual particle – antiparticle pairs are constantly created and annihilated in vacuum. These virtual particles exist for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle. They are “temporary” in the sense that they appear in calculations, but are not detectable as single particles due to their very brief existence. Indeed, they are detectable only as forces. The existence of these particles is no fiction. Though they cannot be directly observed, the effects they create are quite real.

Consider a virtual particle – antiparticle pair that is created right at the edge of a black hole’s event horizon. Usually, such a virtual pair will self-annihilate almost instantaneously. However in this case, there is a finite probability that one of the particles will cross the event horizon and disappear into the black hole. If this happens, the other particle/antiparticle will escape from the black hole. Conservation of energy requires that the particle that fell into the black hole must have had a negative energy. The black hole thus foots the bill of the escaped particle: it loses an amount of mass-energy equivalent to that of the escaped particle.

To a user at a distance, it will appear that the black hole is radiating a steady stream of particles and antiparticles; and is shrinking over time.

That, in brief, and in lay terms, is the mechanism of Hawking radiation. Hawking radiation is thermal in nature and has a black body spectrum. The rigorous theory of the mechanism of Hawking radiation involves quantum tunneling, which we will not delve into here.

How a black hole interacts with its environment

One way of looking at a black hole’s interaction with its environment is to compare it with heat flow (this is not entirely accurate, but works for the purpose of this illustration). Thermal energy flows from hot objects to cold ones. A hot metal rod immersed in a cool fluid such as water or air will lose heat to its environment. Similarly, a black hole radiates Hawking radiation or accretes mass-energy depending on its temperature and that of its environment.

For example, a solar-mass black hole ($$1.98892\times10^{30}\hspace{1 mm}kg$$ ≡ $$1.12\times10^{57}\hspace{1 mm}GeV$$) has a temperature of $$6.16\times10^{-8}\hspace{1 mm}K$$; while the interstellar medium has a temperature of $$\sim2.725\hspace{1 mm}K$$ (the CMBR temperature). The black hole is thus colder than its environment. This means that instead of emitting Hawking radiation, such a black hole will instead accrete the interstellar CMBR photons and increase in mass.

Conversely, a Planck-mass-sized ($$2.18\times10^{-8}\hspace{1 mm}kg\equiv1.22\times10^{19}\hspace{1 mm}GeV$$) micro black hole has a temperature of $$5.65\times10^{30}\hspace{1 mm}K$$ – which is far hotter than interstellar space. Such a black hole will radiate Hawking radiation and thereby decrease in mass.

Non-isolated black holes decay slower than their isolated counterparts, and Eq. (1) does not hold for them. The equation governing a non-isolated black hole’s decay has extra terms that account for heat sources and other factors in the black hole’s physical vicinity.

How fast (or slow) do black holes decay?

A black hole’s decay rate is inversely proportional to the square of its mass and is given by Eq. (1). In other words, small, hot black holes decay much faster then larger, colder ones. The below table makes this amply clear. Remember, this applies for isolated black holes.

Black hole lifetimes and decay rates. Note how black hole lifetimes increase dramatically with mass, while their decay rates and temperature decrease.

The above table tells some remarkable stories:

1. Micro black holes have incredibly short lifetimes; in stark contrast with their more massive counterparts. A black hole weighing 1 solar mass ($$1.12\times10^{57}\hspace{1 mm}GeV$$) has a lifetime of  $$2.8\times10^{93}\hspace{1 mm}s=8.88\times10^{85}\hspace{1 mm}years$$ – which is far greater than the universe’s lifetime! Large black holes are immortal, for all intents and purposes. Moreover, their temperatures are far too low for them to decay, they actually accrete the inter-stellar Cosmic Microwave Background Radiation and assorted inter-stellar material, and grow larger.
2. Micro black holes decay at an astonishing rate; again in stark contrast with their more massive colleagues. A Planck-mass ($$2.18\times10^{-8}\hspace{1 mm}kg\equiv1.22\times10^{19}\hspace{1 mm}GeV$$) micro black hole decays all its mass in $$3.63\times10^{-21}\hspace{1 mm}s$$, which means that it disintegrates in an explosion almost as soon as it is created. A 17.8 gram black hole takes only 2 milliseconds to spew forth the 382 kilotons of TNT in energy that it carries (conversion factor: 1 GeV $$\equiv3.824\times10^{-23}$$ kilotons of TNT). In contrast, the Hiroshima bomb had a blast yield of 18 kilotons of TNT, at best. To summarize, black holes decay faster as they grow smaller, and end their existence in spectacular explosions.

The revelation

Which finally brings us to the Large Hadron Collider. Let us first enumerate a few facts about the LHC:

1. Particle-particle collisions at the LHC will release a maximum of 14 TeV $$\equiv14\times10^{3}\hspace{1 mm}GeV$$ of energy per collision (each opposing particle beam will carry an energy of 7 TeV per particle).
2. The colliding particles will be traveling at 99.9999991% the speed of light, or $$\equiv3\times10^{10}\hspace{1 mm}cm/s$$.
3. The LHC’s tunnels are 3.8 m wide and contain the most perfect vacuum ever created.
4. The LHC is expected to be able to produce black holes at a rate as high as one per second.

So here’s the deal. Since the particle-particle collision yield is 14 TeV, the LHC will produce black holes no larger than $$14\times10^{3}\hspace{1 mm}GeV$$. That is sub-Planck mass. Since the LHC tunnels contain near-perfect vacuum, the black holes can be considered to be isolated, and Eq. (1) holds.

$$14\times10^{3}\hspace{1 mm}GeV$$ black holes have a lifetime of $$5.48\times10^{-66}\hspace{1 mm}s$$, which is shorter than the Planck time. At the maximum speed at which such a black hole can travel ($$\equiv3\times10^{10}\hspace{1 mm}cm/s$$), it will cover a distance of $$1.64\times10^{-55}\hspace{1 mm}cm$$ before it disintegrates, which is again shorter than the Planck length.

Assuming that the collisions occur at the center of the collision chamber, the black holes will be produced nearly 2 meters away from the collider’s walls. We can therefore say with 100% certainty that no black hole produced in the LHC will be able to hit the tunnel’s walls.

But what if micro black holes don’t decay?

That, after all, is what the LHCDefense folks et al have based their arguments on. Let’s humor them for once and consider this possibility to see where it takes us. We start by making the following observations:

1. A $$1.4\times10^{4}\hspace{1 mm}GeV$$ black hole has a radius of $$3.7\times10^{-48}\hspace{1 mm}m$$, which is less than the Planck length. This is $$\sim10^{37}$$ times smaller than the radius of a hydrogen atom (radius: $$\sim5.29\times10^{-11}\hspace{1 mm}m$$), $$\sim10^{33}$$ times smaller than the radius of a nucleon (radius: $$\sim5.29\times10^{-15}\hspace{1 mm}m$$), $$\sim10^{30}$$ times smaller than the radius of an electron (radius: $$\sim5.29\times10^{-18}\hspace{1 mm}m$$), and $$\sim10^{29}$$ times smaller than the radius of a quark – the most fundamental known particle (radius: $$\sim5.29\times10^{-19}\hspace{1 mm}m$$). A sub-planck-mass micro black hole would go right through atoms, atomic nuclei, and even nucleons without ever hitting anything.
2. Black holes interact only through the gravitational force, unlike other particles on earth that have most of the other three forces (strong, electromagnetic, and weak).  The gravitational force is by far the weakest among the forces, which is evident from the below comparison of their coupling constants:

Neutrinos interact through the aptly named weak force (the name says it all!). Trillions of solar neutrinos pass right through the earth every second (and right through you!) without interacting with any particle, which gives us a fair idea of just how incredibly weak the weak force is.

So let’s now ask ourselves a question:

Question: Will a micro black hole … – whose radius is more than a hundred trillion trillion trillion times smaller than the most fundamental known particle, and whose force is a million trillion trillion trillion times weaker than the neutrino’s weak force – … ever be able to interact with any particle in the earth?

The answer is: A RESOUNDING NO!

And therefore, Hallelujah ! We are saved !! Praise the Lord !!

In Conclusion

The Large Hadron Collider is sui generis; it will expand our understanding of the universe to an extent that no other instrument has done before.  It will give rise to several new theories, apart from proving or invalidating many theories that currently await judgment. The research done using this instrument will undoubtedly spawn several physics Nobel prizes, both in theoretical and experimental physics. Generations from today, we will enjoy the material fruits of our labor, much as we now enjoy GPS and other spin-offs of the theory of relativity that Einstein formulated over a hundred years ago.

Let us not be misled by people who do not know what they are talking about. Let us give the LHC a chance.

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