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 3.20.910^20 electron volts.[1,2] By comparison, the
recently-canceled Superconducting Super Collider (SSC) would have
accelerated protons to an energy of 20 TeV, or 210^13 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, 110^9 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 310^20 eV particle to be about 510^-13 grams.
That doesn't sound like much until you recall that this is about 310^11 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 (510^11 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 310^20 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 310^8 metres per second as the speed of light, we find that the 
particle was traveling 2.999999999999999999999985310^8 metres per second, 
thus 1.46710^-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
    -- = 3.19710^11
    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 310^20 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 310^11, 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                  0.0399 mm
Solar system                  80 AU                   37 metres
Sun/Alpha Centauri        4.3 light years            127 km (79 miles)
Milky Way galaxy          30 kiloparsecs          2,895,000 km, 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. I
f 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