higher levels in nature question

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c.h.man
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higher levels in nature question

Post by c.h.man » Mon Mar 29, 2010 10:58 pm

I was just wondering, how is it possible for particles from the sun to hit nearly stationary particles in the atmosphere at higher energies than when two particles going near the speed of light in opposite directions hit? It seams counter-intuitive to me, cause the combined speed of the two particles is faster than the one particle from the sun can go.

JNW
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Re: higher levels in nature question

Post by JNW » Tue Mar 30, 2010 1:15 am

The ultra high energy cosmic rays that people compare the LHC to are from outside the solar system. In fact, the highest energy ones seem to be coming from galaxies with active nuclei.

Kasuha
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Re: higher levels in nature question

Post by Kasuha » Tue Mar 30, 2010 5:09 am

c.h.man wrote:cause the combined speed of the two particles is faster than the one particle from the sun can go.
Relativistics effects are not straightforward. A particle can never go faster than light from any frame of reference - if you watch highly energetic particle from a stationary position, you see it going at almost speed of light. If you watch the same particle from another particle going at almost speed of light against it, you still see it going at almost speed of light. If you watch a particle going at 99.99999% of light speed from a particle going "just" at 99.9% of light speed along its path (in the same direction) you also see it moving at almost speed of light (relative to you).
If you continue accelerating such a particle, it does not start to move significantly faster - you can accelerate it for instance from 99.99% of light speed to 99.999% of light speed. But the energy you used for it is not lost - the particle becomes "heavier", you can imagine it as if its inertia continues to grow.

c.h.man
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Re: higher levels in nature question

Post by c.h.man » Tue Mar 30, 2010 5:19 pm

So if you're a fast particle heading toward another fast particle, and despite you and the other particle traveling near the speed of light from a third persons perspective, it's like they're both only going just under half the speed of light in their relativistic world. So, why doesn't the fast particle heading toward a stationary particle experience the same thing?

Here's my thought process. In the head on collision scenario with two near speed of light particles, imagine the two particles (particle A, particle B) are a kilometer apart, and there is a stationary particle (particle C) in between them. The stationary particle is about 10 meters away from particle B. So, the two fast particles see each other as both moving just under half the speed of light for a combined speed that's almost the speed of light (so it doesn't violate the ftl rule), right? So in order for them to reach each other before particle A reaches particle C, particle A has to see the distance between itself and particle C closing at just under half the speed of light (the same speed particle A sees itself traveling at). Now remove particle B from the scenario, and you have the fast particle heading toward the stationary particle scenario. Why, all of the sudden, does particle A see the distance between itself and particle C closing near the speed of light?

You might have to draw it out to understand what I'm trying to say.

Kasuha
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Re: higher levels in nature question

Post by Kasuha » Tue Mar 30, 2010 6:33 pm

Um... no, sorry. That's not how it works. Normal speeds can combine this way but when you get close to speed of light things start to work very differently.

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chriwi
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Re: higher levels in nature question

Post by chriwi » Wed Mar 31, 2010 8:23 am

hello c.h.man,

you have to keep in mind that speed is traveled distance divided by time. In your scenario you forget that not only the distance seen by the different particles is different but also the perception a of time of the different particles is different likestated in Einsteins special theory of relativity (that is exactly the solution for the paradox you belive to see and also Einstein noticed this and came up with his theories as a solution for this paradox (later theese theories were prooven true)).
Since the perception of time changes as well asthe perception of distance traveled in the different systems of observation it is still possible and also necessary to see all veloceties allways smaller than the speed of light.
bye

chriwi

c.h.man
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Re: higher levels in nature question

Post by c.h.man » Wed Mar 31, 2010 3:47 pm

you have to keep in mind that speed is traveled distance divided by time. In your scenario you forget that not only the distance seen by the different particles is different but also the perception a of time of the different particles is different likestated in Einsteins special theory of relativity
I knew about the time perception part (though I don't really understand it). That was how I was reasoning to my self why the particles "perceived" themselves as going only half as fast. I didn't know that the particle's perception of distance was also different though.

:crazy: I'm so very confused :wtf:

Kasuha
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Re: higher levels in nature question

Post by Kasuha » Wed Mar 31, 2010 4:59 pm

I'd recommend you to read this Wikipedia article - yes it's confusing but may contain explanations you need.

Alexey Kruglov
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Re: higher levels in nature question

Post by Alexey Kruglov » Wed Mar 31, 2010 5:33 pm

In fact collision energy is not a matter of speed, it's rather matter of energies and momenta. Every ultrarelativistic particle travels almost at speed of light.

What people want from collisions is to put maximum energy into the rest energy of residues (that is their mass). That in turn depends on the total energy of the colliding particles. But if we are not in center of mass (COM) frame of reference of the colliding particles, some of this energy has to be put into kinetic energy due to momentum conservartion. In the COM frame the total momentum is 0, the collision energy is in fact defined as the total kinetic energy of the colliding particles in COM frame. When we collide two opposite beams with equal enegry (as in LHC) collision energy is just the sum of beam energies. If an ultrarelativistic particle with enegry E_1 hits a stationary particle of mass m_2 (in energy units), collision enegry is approximately sqrt(2 * m_2 * E_1), i.e. it's geometric mean between E_1 and 2m_2 (in case E_1 is much larger than m_1 and m_2). For example when a proton of energy 3500 GeV hits a carbon atom of mass ~11 GeV, collision energy is ~280 GeV, the rest (~3200 GeV) has to be put into kinetic energy.

As far as I remember, maximum enegry of particles observed in cosmic rays is several orders of magnitude larger than 10^20 eV, proton mass is about 1 GeV=10^9 eV, so collision energy > ~10^14 eV = 100 TeV (in fact more, it's just an estimate from below).

The full formula for collision energy is sqrt((E_tot+m_1+m_2)^2 - p_tot^2)-m_1-m_2, where E_tot and p_tot is total kinetic energy and vector sum of the momenta of the colliding patricles, and everything is expressed in energy units. Don't forget that E and p are different in different frames, while m (the rest mass) is invariant.

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