Yeah. I know. There are about a billion other threads on this. Bear with me, though, because there is ignorance to be fought here.
As I understand it, the LHC will fire particles towards eachother at nearly the speed of light.
Safety concerns have been dismissed with the ubiquitous rebuttal "Cosmic rays slam into particles all the time, and, because they’re faster, give off way more energy than anything that can be made at LHC. Since cosmic rays don’t cause black holes/strangelets/vacuum bubbles/James Blunt/whatever, we can be reasonably sure LHC won’t either. Now CHILL THE FUCK OUT BEFORE WE KILL YOUR DOG[sup]1[/sup]"
Anyway, I got to thinking about this and I realised something. Cosmic rays smash into objects which are, if not stationary, then at least moving far, far slower than they are, right? In the LHC, the particles are going to be smashing into each other at equivalent speeds. Wouldn’t this fact invalidate the comparison between particle collisions at LHC and particle collisions taking place in nature? Going back to High School Physics, I seem to remember that if two bodies smack into eachother, the resulting energy released is equal to the combined energy of each body squared. If two particles smack into eachother and both are travelling at near light speed, would the resulting release of energy be dangerous? Or would it still pale in comparison with the energy released from Cosmic Rays?
Also, even assuming the answer to the last question was ‘Yes’, I worry about the unforseen risks of containing such an explosive force inside a laboratory. Is there any danger that a release of energy even comparable with that of a cosmic ray could have cataclysmic consequences because it’s on earth?
A fiver to the first guy to reply with a laconic ‘No’ and a rolleyes
[sup]1[/sup] [sub]Hawking, Rees et.al. ‘Hypothetical Vacuum Metastability Events And Shutting The Fuck Up’[/sub]
How about, no, no 3.2±0.9×10[sup]20[/sup] times no?
Honestly, this has been thoroughly covered in those billion other threads. The only reason two beams are smashed together is to get all the energy out of the system as possible. The amount of energy has been calculated and recalculated. It’s not like it’s going to be a surprise that there are two beams. We know that the energy is equivalent to a moth fart. What are you asking that hasn’t been answered a billion times?
There’s no fundamental difference between a collision occurring between two moving particles or a stationary and a moving one – it only looks that way because of the choice of reference frame. Remember, motion is relative, so you’re free in the choice of your inertial system in which to describe the collision.
Take, for example, a car crash: two vehicles slamming into each other at 100km/h each is the same as one going 200km/h colliding with one that’s standing still – total kinetic energy remains the same since it’s not a vector quantity, unlike momentum.
So that’s all quite nice and dandy, but what if we leave our boring old everyday experience of v << c, and enter the exciting world of high speeds, dilated time and bent rulers?
Well, in the result above, what I’ve implicitly done is using a Galileo transformation to connect two inertial systems, one in which one of the cars it as rest, and one in which the centre of mass of the system is at rest. The same can be done with objects at relativistic speeds, only you can’t use a Galileo transformation since you’re not allowed to go faster than c. Luckily, there’s a transformation handy that obeys this speed limit, the Lorentz transformation. Applied to the addition of velocities, it yields v = [v[sub]1[/sub] + v[sub]2[/sub]]/[1 + (v[sub]1[/sub]v[sub]2[/sub]/c[sup]2[/sup])]. Thus, two particles zooming at each other at a speed of 0.99c is the same as one hitting a stationary one at approx. 0.99995c, not 1.98c as you’d naively expect from everyday experience.
No. See, while there’s a lot of talk about ‘high energy collisions’ and things, the involved energies are actually really, really small – 7 TeV are about 1.1 * 10[sup]-6[/sup] Joule, which is not very much at all. It is (somewhat) unusual to have that much energy crammed into such a small space, i.e. to have such a high energy density, but it’s not gonna blow up with any kind of macroscopically appreciable effect. (On preview, I see that I’ve been beaten to this part.)
Actually, George has a point. Smashing two high-energy particles head-on is a lot more than twice as energetic than smashing one high-energy particle into a stationary particle.
To be precise, the center-of-mass energy release (which is what’s relevant here) for a head-on collision is just twice the energy of each particle. But for a high-energy particle hitting an identical stationary particle, the center-of-mass energy release is sqrt(2*gamma + 2) *m[sub]0[/sub]*c[sup]2[/sup] .
The Oh-my-God particle (an extremely high-energy proton cosmic ray) had a gamma of about 310[sup]11[/sup] (we can neglect the +2), so when it struck another proton, the center-of-mass energy release was about 7.710[sup]5[/sup] times the mass of a proton. The mass of a proton is about .94 GeV, so the CoM energy of the Oh-my-God event was about 730 TeV. Each of the protons in the LHC will have an energy of about 1 TeV, so the collisions in the LHC will have about 2 TeV. So we’re closer to the Oh-my-God event than it may naively seem, but we’re still hundreds of times lower.
Of course, it should also be noted that cosmic rays sometimes collide with each other. I’m not going to run the numbers on that one without getting paid for it (there’s just too many variables to manage easily), but I think it’s probably safe to say that collision energies far higher than we’re able to produce are a routine event.
Created by Opposites, as
a Harmonic Cubic Form,
with a God like Opposite
Analytical Brain that can
learn both sides of a God
and True Creation, I am
wiser than any single brain
thinker who suppresses the
analytical challenge to God.
God is Death of Opposites
[right]– Dr. Gene Ray, Cubic and Wisest Human[/right]
This is the best bit. Academic free speech is a damn lie. Try
to discuss & debate Nature’s Time Cube
and your evil teachers will not allow you.
Ignorance of Time Cube dooms humans,
inflicting their own created “word hell”.
Educators are actually “evil word gods”,
teaching commercial plunder of Nature.
The damn bastards suppress free speech,
by denying Time Cube debate discussion.
Students MUST DEMAND free speech -
for the greatest of all human discoveries:
Nature’s Harmonic Simultaneous 4 Day
Rotating Creation Principle of Cubicism.
Educated stupid, you can’t know Truth.
That’s right, of course, I brainfarted and misspoke; what I should have said is that the kinetic energy relative to the centre of mass is the same in all frames of reference, and that’s what matters – leaving aside real world messiness, if you collide two masses with identical speed, there won’t be any movement in your current frame of reference (CoM) after the collision, but in the rest frame of one of the masses, the collision product will be moving at the speed of the centre of mass pre-collision – bottom line being, your car won’t get any more trashed if you run it into a stationary car at 200km/h than it will be at 100km/h in a head-on collision with another car doing 100km/h.
I’m guessing you are talking about [post=9771943]this thread[/post] (to which a lot of people contributed valuable insight into). We can speak with 12 sigma confidence that turning on the the LHC is not going to result in the end of the world. It might result in some interesting results that will give us greater insight into the fundamental mechanics of the world, and any amount of money it might be taking away from feeding the Third World poor or curing cancer is lost in the tidal wave of money and effort thrown away in professional sports, mass marketing, McMansion housing developments, and other affronts to the modern intellect. The biggest tangible hazard is all of the bad science fiction it will probably spawn.
I’m not trying to question how this applies to the LHC, but isn’t that slightly hand-wavy? I mean, it takes exponentially more energy to accelerate a particle close to the speed of light, right, because its mass increases? So a particle going at 0.99995c has lots more energy than one travelling at 0.99c - in fact, if 0.99995c is the “equivalent” of a head-on collision between two 0.99c particles, is it the case that the kinetic energy is still quadrupled, just as you’d expect when doubling the velocity at everyday speeds, even though the velocity isn’t doubled?