Hello All!   
      
   I haven't posted this in quite awhile, but thought now would be a good time,   
   considering what scientists are doing with the super-collider.   
      
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   The Oh-My-God Particle, by John Walker, January 4, 1994   
      
   Fly's Eye   
      
   The University of Utah operates a cosmic ray detector called the Fly's Eye   
   II, situated at the Dugway Proving Ground about an hour's drive from Salt   
   Lake City. The Fly's Eye consists of an array of telescopes which stare   
   into the night sky and record the blue flashes which result when very high   
   energy cosmic rays slam into the atmosphere. From the height and intensity   
   of the flash, one can calculate the nature of the particle and its energy.   
      
   On the night of October 15, 1991, the Fly's Eye detected a proton with an   
   energy of 3.20.9x10^20 electron volts.[1,2] By comparison, the recently-   
   canceled Superconducting Super Collider (SSC) would have accelerated protons   
   to an energy of 20 TeV, or 2x10^13 electron volts -- ten million times less.   
   The energy of the Oh My God particle seen by the Fly's Eye is equivalent to   
   51 joules -- enough to light a 40 watt light bulb for more than a second --   
   equivalent, in the words of Utah physicist Pierre Sokolsky, to "a brick   
   falling on your toe." The particle's energy is equivalent to an American   
   baseball travelling fifty-five miles an hour.   
      
   All evidence points to these extremely high energy particles being protons   
   -- the nuclei of hydrogen atoms. Recalling that the rest mass of the proton   
   is 938.28 MeV -- roughly 1 GeV, 1x10^9 eV, all of the rest of the particle's   
   energy results from the kinetic energy resulting from its motion, which we   
   can calculate according to basic formulae of special relativity. So let's   
   crunch a few numbers.   
      
   Microbial Mass   
      
   First of all, noting that mass and energy are equivalent, we can calculate   
   the rest mass equivalent of a 3x10^20 eV particle to be about 5x10^-13 grams.   
   That doesn't sound like much until you recall that this is about 3x10^11   
   daltons (chemists measure molecular mass in daltons, where 1 dalton is the   
   mass of a hydrogen atom), just about the same as a single cell of the   
   intestinal bacterium E. coli (5x10^11 daltons). Thus this single subatomic   
   particle had a mass-energy equivalent to a bacterium.   
      
   How Fast?   
      
   How fast was it going? Pretty fast. The total mass-energy of a particle is   
   given in special relativity by the equation:   
      
    .             M_0   
    .    M  = ------------                   [1]   
    .                  v   
    .         Sqrt[1 - --]   
    .                  c   
      
   where M_0 is the particle's rest mass, 0, v is the particle's velocity, and   
   c is the speed of light. Okay, we know that the Oh My God proton has a rest   
   mass of about 1 GeV, and a total kinetic energy of 3x10^20 eV, so let's solve   
   equation [1] for v, setting c to 1 to obtain velocity as a fraction of the   
   speed of light:   
      
    v = Sqrt[m - M_0] / m   
      
    And thus, approximately:   
      
    v = 0.9999999999999999999999951 c   
      
   So taking 3x10^8 metres per second as the speed of light, we find that the   
   particle was traveling 2.9999999999999999999999853x10^8 metres per second,   
   thus 1.467x10^-15 metres per second slower than light -- one and a half   
   femtometres per second slower than light. If God's radar gun is slightly   
   out of calibration, this puppy's gonna be doin' hard time for speeding.   
   After traveling one light year, the particle would be only 0.15 femtoseconds   
   -- 46 nanometres -- behind a photon that left at the same time.   
      
   Quicktime   
      
   Recall also that time passes more slowly in a moving reference frame, by the   
   factor:   
      
    .             t0   
    .    t = ------------   
    .                 v   
    .        Sqrt[1 - --]   
    .                 c   
      
   Since we know v/c, we can immediately calculate:   
      
    .    t   
    .    -- = 3.197x10^11   
    .    t0   
      
   and thus, moving in the reference frame of the particle, time passes three   
   hundred billion times slower than in a rest frame. Thus, given that the   
   particle travels with essentially the speed of light, an observer traveling   
   along with the particle would perceive the flight time from the following   
   objects to the Earth.   
      
                       Distance[3]           Perceived   
     Object            (light years)         Travel Time   
    ===============    ==================    ===========   
    Alpha Centauri     4.36                  0.43 milliseconds   
    Galactic nucleus   32,000                3.2 seconds   
    Andromeda galaxy   2,180,000             3.5 minutes   
    Virgo cluster      42,000,000            1.15 hours   
    Quasar 3C273       2,500,000,000         3 days   
    Edge of universe   17,000,000,000        19 days   
      
   Thus, if you could accelerate yourself to the speed at which the Oh My God   
   particle was traveling, you'd be able to travel to the edge of the visible   
   universe in a couple of weeks. Unfortunately, even assuming you found a   
   source for the energy it would take and invented a means to accelerate   
   yourself and Intergalactic Vessel Omega Point to this velocity, you wouldn't   
   get far before being disrupted into subatomic goo due to interactions with   
   photons in the ubiquitous cosmic microwave background radiation. Sokolsky   
   has calculated that at 3x10^20 eV, even a single proton could travel no   
   farther than 10 megaparsecs, about the distance of the Virgo galaxy cluster,   
   before losing energy in this manner.   
      
   Warp Factor Oh-My-God -- Engage!   
      
   It is interesting to observe that a real particle, in our universe, subject   
   to all the laws of physics we understand, is a rather better interstellar   
   voyager than the best fielded in the 24th century by the United Federation   
   of Planets. Their much-vaunted Galaxy Class starships are capable of speeds   
   slightly in excess of Warp Factor 9, an apparent velocity of 1516 cochranes   
   (or 1516 times the speed of light).[4] At a velocity of 1516 c, traveling   
   to the centre of the galaxy would take, as perceived by the life forms on   
   board, a little more than 21 years. By contrast, an observer on board the   
   Oh-My-God particle would arrive at the nucleus of the Milky Way, according   
   to his clock, just about 3 seconds after leaving Starbase Terra. That's more   
   than 9,700,000 times faster than the starship. In the time the starship   
   spends vacuum-whooshing and rumbling its way to the nearby star Aldebaran,   
   the particle could travel to the edge of the visible universe.   
      
   Go Fast -- Grow Thin   
      
   Finally, let's consider the length contraction in the direction of motion   
   which results from the Lorentz transformation -- objects in the direction   
   of travel are seen to contract in that direction by a factor of:   
      
    .   l             v   
    .   -- = Sqrt[1 - --]   
    .   l0            c   
      
   And thus, paralleling the time dilation calculated above, in the frame of   
   the particle, oncoming objects are seen as contracted by a factor of   
   3x10^11, three hundred billion times, in thickness. Thus, seen from the   
   particle, the objects below will have the following thickness.   
      
    Object                  Rest Frame Thickness    Particle Frame Thickness   
    ================        ====================    ===========================   
      
    Earth's diameter        12,756 km               0.0399mm   
      
    Solar system            80 AU                   37 metres   
      
    Sun/Alpha Centauri      4.3 light years         127 km (79 mi)   
      
    30 kiloparsecs          2,895,000 km            Milky Way galaxy   
    .                                               about ten times the   
    .                                               distance from the   
    .                                               Earth to the Moon   
      
   But How?   
      
   How was such an extraordinary particle created? What cosmic process   
   accelerated a mundane proton to a brick-on-the-toe-energy?   
      
   Nobody knows. A particle with such energy would be deflected little by   
   galactic magnetic fields, and so its impact track should point right   
   back at the source.   
      
   Astronomers see nothing unusual in that direction.   
      
   Nature remains rich in mysteries.   
      
   References   
      
    [1]Physical Review Letters, 22 November 1993.   
      
    [2]G. Taubes, Science 262, 1649 (1993).   
      
    [3]Ottewell, G. The Astronomical Companion. Greenville SC: Astronomical   
    Workshop, 1979-1992. ISBN 0-93456-01-0.   
      
    [4]Sternbach, R. and M. Okuda. Star Trek: The Next Generation Technical   
    Manual.   
    New York: Pocket Books, 1991. ISBN 0-671-70427-3.   
      
   Disclaimer   
      
   These calculations involve some elementary but easy to mess up algebra and   
   some very demanding numerical calculations for which regular IEEE double   
   precision is insufficient. If you'd like to double-check these results, be   
   sure to use a multiple precision calculator with at least 30 significant   
   digits of accuracy. I generally use Mathematica for symbolic work and Mark   
   Hopkins' package C-BC for number crunching. It's entirely possible I've   
   made one or more mistakes of order-of-magnitude or greater significance.   
   But even so, (and please correct me!), this is, particle physics wise, a   
   genuine Oh Wow event.   
      
    by John Walker   
      
      
   Regards,   
      
   Roger    
   --- timEd/386 1.10.y2k+   
    * Origin: NCS BBS - Houma, LA - (1:3828/7)