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 Diploid
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Registered: 01/09/03
Posts: 19,274
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 The Oh-My-God Particle 
#3960029 - 03/23/05 02:27 PM (19 years, 28 days ago) |
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I dunno if this has been posted here before, but I thought this crowd would find it interesting:
http://www.fourmilab.ch/documents/ohmygodpart.html
--
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 3.2?0.9?10^20 electron volts.[1,2] By comparison, the recently-canceled Superconducting Super Collider (SSC) would have accelerated protons to an energy of 20 TeV, or 2?10^13 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, 1?10^9 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 3?10^20 eV particle to be about 5?10^-13 grams. That doesn't sound like much until you recall that this is about 3?10^11 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 (5?10^11 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 3?10^20 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 3?10^8 metres per second as the speed of light, we find that the particle was traveling 2.9999999999999999999999853?10^8 metres per second, thus 1.467?10^-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
-- = 3.197?10^11
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 3?10^20 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 3?10^11, 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. 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
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Republican Values:
1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.
4) We need a smaller, less-intrusive government.
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tak
geo's henchman
 
Registered: 11/20/00
Posts: 3,776
Loc: nowhereland
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 Re: The Oh-My-God Particle [Re: Diploid]
#3960785 - 03/23/05 04:46 PM (19 years, 28 days ago) |
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whoa
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The DJ's took pills to stay awake and play for seven days.
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newuser1492
Registered: 06/12/03
Posts: 3,104
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Re: The Oh-My-God Particle [Re: tak]
#3961846 - 03/23/05 08:49 PM (19 years, 28 days ago) |
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So taking 3?10^8 metres per second as the speed of light, we find that the particle was traveling 2.9999999999999999999999853?10^8 metres per second, thus 1.467?10^-15 metres per second slower than light
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.
It takes approx 7min for light to reach Earth from the Sun. How does it take 3 seconds for it to reach the center of our galaxy?
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 Boccherini
Trapped in aPr?lude
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Re: The Oh-My-God Particle [Re: newuser1492]
#3962458 - 03/23/05 10:27 PM (19 years, 28 days ago) |
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It takes 7 minutes for a photon to travel from the Sun to the Earth, but that time is relative to the Earth. The photon is travelling incredibly close to the speed of light, so there is a huge time dilation in that frame of reference. In the case of something moving as fast as this "Oh-My-God" particle, then the time to travel from the Sun to the Earth, from the particle's frame of reference is ~3 seconds. From the Earth, it will still appear that it takes 7 minutes for the photon to reach the Earth.
This time dilation leads to interesting things. There's something called the Twin Paradox that you can Google if you're interested. It's taking a pair of twins, and sending one in a spaceship travelling very fast (say .75c). The twin in space returns in 5 years, to be meeting his brother's great grandchildren or something like that. 100 years have passed according to the Earth, but for the twin only 5 years have passed (and he hasn't aged 100 years).
Edit: Here's a link that explains it better than I can.
http://members.tripod.com/wmhxbigguy/Theory/time.html
Edited by Boccherini (03/23/05 10:42 PM)
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Zekebomb
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Re: The Oh-My-God Particle [Re: Diploid]
#3963171 - 03/24/05 01:03 AM (19 years, 28 days ago) |
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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.
how does a particle travelling at almost the speed of light go faster than a space ship going 1516 times the speed of light?
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Seuss
Error: divide byzero
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Posts: 23,480
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Re: The Oh-My-God Particle [Re: Diploid]
#3963660 - 03/24/05 04:33 AM (19 years, 28 days ago) |
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> how does a particle travelling at almost the speed of light go faster than a space ship going 1516 times the speed of light?
Quote:
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.
I believe this part is incorrect. Within the reference frame of the particle, time passes normally with respect to itself. He is timing something in one frame of reference using a clock in another frame of reference.
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Just another spore in the wind.
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Diploid
Cuban
Registered: 01/09/03
Posts: 19,274
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 Re: The Oh-My-God Particle [Re: Zekebomb]
#3963947 - 03/24/05 08:17 AM (19 years, 28 days ago) |
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how does a particle travelling at almost the speed of light go faster than a space ship going 1516 times the speed of light?
He's comparing a trip to the center of the galaxy on the mythical starship Enterprise to the particle.
On the Enterprise, clocks run at the same rate as those in a rest frame of reference, say the Earth. So, if it takes the Enterprise 21 years, from Earth's point of view, then the occupants of the Enterprise will also experience 21 years.
In the real world, a clock in a spaceship traveling at the speed of the OMG particle will only tick off 3.2 seconds by the time it reaches the center of the Galaxy. Anyone on Earth looking at that clock will see it tick off those 3.2 seconds very, very slowly.
In other words, from the point of view of an observer on Earth, it will take 21 years for the clock on the ship to tick 3.2 seconds, but for a traveler on the ship, the 3.2 seconds will seem to pass normally, and the clocks on the Earth will tick off 21 years during the ship's 3.2 second trip.
This is an effect called time-dilation and is one prediction of Albert Einstein's Special Theory of Relativity. Time-dilation occurs whenever two frames of reference move with respect to each other, but the effect is very tiny at the ordinary speeds humans normally experience.
If you had two very accurate clocks, left one on the ground and took the other with you on an airliner, when you returned, you would find that the clock on the ground aged a few nanoseconds more than the clock you took flying with you. The faster the airplane, the greater the magnitude of the difference in time. This effect has actually been confirmed by flying atomic clocks, which are very accurate, on airplanes and the results agree precisely with Special Relativity Theory.
The OMG particle described in the article was traveling so fast that it's clock would seem to tick three hundred billion times slower than those on Earth and this difference accounts for the 3.2 second travel time to the center of the galaxy as observed by the particle and at the same time 21 years as observed by someone on the Earth.
An astonishing amount of energy is required for this to happen and this is why the OMG particle is so amazing.
--------------------
Republican Values:
1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.
4) We need a smaller, less-intrusive government.
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trendal
J♠
Registered: 04/17/01
Posts: 20,815
Loc: Ontario, Canada
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Re: The Oh-My-God Particle [Re: Diploid]
#3963965 - 03/24/05 08:26 AM (19 years, 28 days ago) |
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On the Enterprise, clocks run at the same rate as those in a rest frame of reference, say the Earth. So, if it takes the Enterprise 21 years, from Earth's point of view, then the occupants of the Enterprise will also experience 21 years.
Not quite true, I think 
They do travel at speeds in excess of 50% of the speed of light on the Enterprise. The warp engines compress the space in front of the ship, then the impulse drive pushes the ship over the compressed space, usually at 50% of c. So the ship travells MUCH faster than light over long distances, but never moves faster than light locally.
Because they are traveling at a substantial % of c, they have to re-adjust thier clocks with the nearest starbase quite often, or so I read somewhere (was it The Physics of Star Trek?).
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Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.
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Diploid
Cuban
Registered: 01/09/03
Posts: 19,274
Loc: Rabbit Hole
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Re: The Oh-My-God Particle [Re: trendal]
#3963986 - 03/24/05 08:34 AM (19 years, 28 days ago) |
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The warp engines compress the space in front of the ship...
Ah, I stand corrected.
--------------------
Republican Values:
1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.
4) We need a smaller, less-intrusive government.
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Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 23,480
Loc: Caribbean
Last seen: 2 months, 7 days
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Re: The Oh-My-God Particle [Re: Diploid]
#3963997 - 03/24/05 08:38 AM (19 years, 28 days ago) |
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Quote:
The OMG particle described in the article was traveling so fast that it's clock would seem to tick three hundred billion times slower than those on Earth and this difference accounts for the 3.2 second travel time to the center of the galaxy as observed by the particle and at the same time 21 years as observed by someone on the Earth.
Again, we are mixing clocks from different frames of reference. From the reference of the particle time is moving normally and it will still take 21 years to travel the distance. Don't forget the lorentz transforms when dealing with relativity... we have both time dilation and length contraction to worry about.
Where are Daba and Trendal when we need them...
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Just another spore in the wind.
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Diploid
Cuban
Registered: 01/09/03
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Re: The Oh-My-God Particle [Re: Seuss]
#3964020 - 03/24/05 08:47 AM (19 years, 28 days ago) |
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rom the reference of the particle time is moving normally and it will still take 21 years to travel the distance.
No it won't. You're missing the basal prediction of Special Relativity. There is no such thing as "time moving normally". This is one of the weird consequences of Special Relativity.
It will take 21 years for the trip, measured by someone on the Earth, however, someone riding along with the particle will have aged only 3.2 seconds when they reach their destination.
In other words, the person making the trip will arrive in about two heartbeats. That person's friends back on Earth will be 21 years older, but the traveler will only be 3.2 seconds older.
If the traveler immediately starts a trip back, when he arrives back on Earth, he will be 6.4 seconds older than when he left, but his friends will be 42 years older than when he left. Some of his friends will have died from old age in those 6.4 seconds the traveler experienced.
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Republican Values:
1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.
4) We need a smaller, less-intrusive government.
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trendal
J♠
Registered: 04/17/01
Posts: 20,815
Loc: Ontario, Canada
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Re: The Oh-My-God Particle [Re: Seuss]
#3964028 - 03/24/05 08:50 AM (19 years, 28 days ago) |
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No, from the perspective of the particle, only 3.2 seconds would pass during the trip to the center of the galaxy (I'm not sure if this figure is actually correct, as the author of the article doesn't seem to truly understand relativistic speeds).
Actually, the OMG particle would take nearly 28,000 years to reach the center of the galaxy (the earth is about 27,700 light years from the center).
He fucked up by trying to bring the Enterprise into the equation, as it moves MUCH faster than the speed of light over long distances and hence shouldn't be involved in a discussion about particles moving at close to c.
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Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.
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Diploid
Cuban
Registered: 01/09/03
Posts: 19,274
Loc: Rabbit Hole
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Re: The Oh-My-God Particle [Re: trendal]
#3964036 - 03/24/05 08:55 AM (19 years, 28 days ago) |
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Right, substitute 27,700 years for 21 years. The specific number isn't the issue, it's the fact that that time for the particle passes much more slowly than time for someone on Earth, even though to each observer, time seems to pass normally.
In the end, when the traveler returns to Earth, all his friends will be much older than he, even though he only experienced the passage of a few seconds' time.
--------------------
Republican Values:
1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.
4) We need a smaller, less-intrusive government.
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trendal
J♠
Registered: 04/17/01
Posts: 20,815
Loc: Ontario, Canada
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Re: The Oh-My-God Particle [Re: trendal]
#3964066 - 03/24/05 09:02 AM (19 years, 28 days ago) |
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http://en.wikipedia.org/wiki/Time_dilation
Td = Tn ( 1 - (v^2 / c^2))^1/2
Where Td is the time experienced by the particle, and Tn is the "normal" time experienced by an observer on Earth.
v = 0.9999999999999999999999951 c
so, with a lot of scribbling on my notepad here...I get an answer of ~ 2.7 seconds experienced by the particle during its 28000 year voyage.
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Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.
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Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 23,480
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Last seen: 2 months, 7 days
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Re: The Oh-My-God Particle [Re: trendal]
#3964201 - 03/24/05 09:47 AM (19 years, 28 days ago) |
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Ah, I see where my confusion was coming from...
T'=T/(1-(v^2/c^2)^1/2)
Time in the moving system will be observed by a stationary observer to be running slower by the factor T'. When v becomes very close to c, time virtually stands still for the outside observer.
... BUT ...
The Lorentz Contraction states that just as time expands from the perspective of the stationary observer, space contracts from the perspective of the moving observer by L'=L((1-v^2/c^2)^1/2). (where L is length)
The trip goes faster, from the perspective of the particle, not because of time dilation but because of space contraction.
--------------------
Just another spore in the wind.
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trendal
J♠
Registered: 04/17/01
Posts: 20,815
Loc: Ontario, Canada
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Re: The Oh-My-God Particle [Re: Seuss]
#3964241 - 03/24/05 09:59 AM (19 years, 28 days ago) |
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The trip goes faster, from the perspective of the particle, not because of time dilation but because of space contraction.
No it is due to the time dilation, and the length contraction is also due to the time dilation (think about it: if time is slowed down for you, the way you measure distance will also be affected so that distances appear shorter).
--------------------
Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.
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Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 23,480
Loc: Caribbean
Last seen: 2 months, 7 days
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Re: The Oh-My-God Particle [Re: trendal]
#3964356 - 03/24/05 10:37 AM (19 years, 28 days ago) |
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True... you cannot have one without the other... the two equations are simply reciprocals of each other... my problem was the reference point I chose to look at the problem was the exact opposite that everybody else is using. I was looking at the problem from the particle point of view rather than the stationary observer point of view. If I travel at 0.0001c or at .9999c, it takes me the same length of time, from my perspective, to tie my shoes. Time to dust the phys 2 book off and reread this stuff.
--------------------
Just another spore in the wind.
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trendal
J♠
Registered: 04/17/01
Posts: 20,815
Loc: Ontario, Canada
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Re: The Oh-My-God Particle [Re: Seuss]
#3964398 - 03/24/05 10:48 AM (19 years, 28 days ago) |
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Yeah, from the particle's point of view time still travels "normally", and it is the rest of the universe which moves in slow motion (as well as contracts in length).
Relativity is too much fun to play with 
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Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.
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Ego Death
Justadropofwaterinanendlesssea
Registered: 04/27/03
Posts: 10,447
Loc: The War Machine
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Re: The Oh-My-God Particle [Re: trendal]
#3964493 - 03/24/05 11:15 AM (19 years, 28 days ago) |
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Sorry for my randomness but what is it that would actually cause the person to be older than his friend?
I mean does one have to travel through space or could the same result come from someone being spun round on the spot?
I'm trying to understand why somebody accelerating is going forwards in time. I can imagine you could send a human into the future if you gyrated them fast enough? I suppose for the traveller it would be instaneous but the people not in a state of gyration would simply see the slow-ageing traveller in a state of suspended animation? Or maybe he would just dissappear and enter a different time-dimension?
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trendal
J♠
Registered: 04/17/01
Posts: 20,815
Loc: Ontario, Canada
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Re: The Oh-My-God Particle [Re: Ego Death]
#3964559 - 03/24/05 11:32 AM (19 years, 28 days ago) |
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Try to think of space and time as two different directions which you can travel in, at a right-angle to eachother.
Think of a square soccer field. The sidelines are "time" and the line down each end of the field is "space". You can run down the sidelines (time) and you will not be moving accross the field (space) at all...or you can run accross the field (through space) and not move at all down the field (through time). As well, you are ALWAYS limited to ONE speed and ONE speed only: the speed of light.
So lets say you put ALL your speed into running down the sidelines - moving through time. This means you cannot move through space AT ALL (or you would divert some of your speed to moving through space) so you must sit perfectly still. You would then be moving at the fastest possible speed through time. Now lets say you put all your speed into moving through space (accross the field). So you move through space at the speed of light, which means you aren't putting ANY of your speed into movement through time...so time doesn't "flow" at all for you.
And then of course there is everything in between: you can move diagonally down the field, so that you are moving through time AND space, but not through either one at the maximum speed (the speed of light). The more speed you divert into space, the less there is left for time.
--------------------
Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.
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