The Greisen-Zatsepin-Kuzmin limit.

[inhahe]

So I'm reading http://digg.com/general_sciences/13_things_that_scientists_can_t_explain?t=5526450#c5526450 (a great read), and number 3 is this:

"""
3 Ultra-energetic cosmic rays

FOR more than a decade, physicists in Japan have been seeing cosmic rays that should not exist. Cosmic rays are particles - mostly protons but sometimes heavy atomic nuclei - that travel through the universe at close to the speed of light. Some cosmic rays detected on Earth are produced in violent events such as supernovae, but we still don't know the origins of the highest-energy particles, which are the most energetic particles ever seen in nature. But that's not the real mystery.

As cosmic-ray particles travel through space, they lose energy in collisions with the low-energy photons that pervade the universe, such as those of the cosmic microwave background radiation. Einstein's special theory of relativity dictates that any cosmic rays reaching Earth from a source outside our galaxy will have suffered so many energy-shedding collisions that their maximum possible energy is 5 × 1019 electronvolts. This is known as the Greisen-Zatsepin-Kuzmin limit.

Over the past decade, however, the University of Tokyo's Akeno Giant Air Shower Array - 111 particle detectors spread out over 100 square kilometres - has detected several cosmic rays above the GZK limit. In theory, they can only have come from within our galaxy, avoiding an energy-sapping journey across the cosmos. However, astronomers can find no source for these cosmic rays in our galaxy. So what is going on?

One possibility is that there is something wrong with the Akeno results. Another is that Einstein was wrong. His special theory of relativity says that space is the same in all directions, but what if particles found it easier to move in certain directions? Then the cosmic rays could retain more of their energy, allowing them to beat the GZK limit.

Physicists at the Pierre Auger experiment in Mendoza, Argentina, are now working on this problem. Using 1600 detectors spread over 3000 square kilometres, Auger should be able to determine the energies of incoming cosmic rays and shed more light on the Akeno results.

Alan Watson, an astronomer at the University of Leeds, UK, and spokesman for the Pierre Auger project, is already convinced there is something worth following up here. "I have no doubts that events above 1020 electronvolts exist. There are sufficient examples to convince me," he says. The question now is, what are they? How many of these particles are coming in, and what direction are they coming from? Until we get that information, there's no telling how exotic the true explanation could be.
“One possibility is that there is something wrong with the Akeno results. Another is that Einstein was wrong”
"""

Now I'm not a physicist, i have only rudimentary knowledge of relativity and so on, but the answer seems obvious to me:

Photons travel so fast that they travel only in space, not time, so in a sense they have no net velocity, because as a collective they don't move in a sense, they're just a part of the universe.

i know that doesn't make much sense, but here's the simpler way of looking at it:
if something's traveling through space and things are colliding with it, their net effect on its velocity will be net velocities of everything colliding with it. so if we were to *imagine* that this cosmic ray particle is traveling through a medium of slower (but still moving, in various directions) particles and hitting them, then since motion is relative, we could also look at this as though the cosmic ray particle starts out still, and the medium is ambushing it with its individual particles' speeds but also a general overall speed. this will cause the cosmic ray particle to accelerate (or, from the original point of view, to slow down).

but now imagine that all the medium's particles are moving at the speed of light. since they're all moving at the fastest possible speed, they have *no* net velocity compared to the cosmic ray. Relativity isn't exactly a MPH post on the highway that caps any particles (like photons) from attaining anything above 300000 km/second. it's the fastest possible speed by the very nature of time and space, so in a sense the speed of the cosmic ray (regardless of the fact that it's going "nearly the speed of light") is *infinitely* slower than the speeds of the photons, just like the highest possible number (or "idea") on an unlimited number line is infinity. the speed of photons must be infinite in one sense (such as that you can never catch up to them, and perhaps that a "rest mass" of 0 must be accelerated infinitely in order to become something non-zero), and yet limited in another sense, to 300000 km/s.

i think to put this in a more concrete form, if we look at the velocities that photons will impart onto the cosmic ray, they *can't* be dependent on speed. the reason for that is that all photons (by virtue of being "light") travel the same speed, and they all travel the same speed from *all* frames of reference velocitywise, such as the frame of reference of that cosmic ray. This leaves only *direction* to determine how much net velocity is imparted to the ray, and i would presume that the directions are evenly distributed. I.e. how can photons less frequently hit it from behind, just because it's moving away from them, if their relative speeds are not diminished by that forward motion, and thus it wouldn't take them any longer to catch up? I guess that's pretty much what I was saying from the beginning..

 

[PeterDonis]

if something's traveling through space and things are colliding with it, their net effect on its velocity will be net velocities of everything colliding with it.

No; the key is not velocity but momentum. That makes a difference; photons all have the same speed, but they can have the full range of possible momenta.

since motion is relative, we could also look at this as though the
cosmic ray particle starts out still, and the medium is ambushing it with its individual particles' speeds but also a general overall speed

Yes, you can look at things in the cosmic ray particle's rest frame, but the photons' momenta will look very different in this frame than they do in our (Earth) rest frame, even though technically their speeds will be the same. In our rest frame, the photons' momenta are more or less isotropic (i.e., the same in all directions). In the cosmic ray's rest frame, the photons' momenta are *highly* biased in the direction opposite to its motion (this should be obvious, but if it isn't, work through the Lorentz transformations and see it explicitly for yourself).

So even though the photons' speeds are all the same, their momenta, as seen by the cosmic ray, will always "push back" in the direction opposite to the ray's motion, slowing it down.

In other words, you can't get around the GZK limit the way you were thinking.

 

[inhahe]

No; the key is not velocity but momentum. That makes a difference; photons all have the same speed, but they can have the full range of possible momenta.



Yes, you can look at things in the cosmic ray particle's rest frame, but the photons' momenta will look very different in this frame than they do in our (Earth) rest frame, even though technically their speeds will be the same. In our rest frame, the photons' momenta are more or less isotropic (i.e., the same in all directions). In the cosmic ray's rest frame, the photons' momenta are *highly* biased in the direction opposite to its motion (this should be obvious, but if it isn't, work through the Lorentz transformations and see it explicitly for yourself).

So even though the photons' speeds are all the same, their momenta, as seen by the cosmic ray, will always "push back" in the direction opposite to the ray's motion, slowing it down.

In other words, you can't get around the GZK limit the way you were thinking.

ok, thanks. I was thinking after i posted that that maybe the energy a photon hits it with depends not only on the speed but of the wavelength, since low-frequency photos are called 'low-energy' photons iirc.. and since the doppler effect applies to light, that would make the impact relative to the ray's speed.. is that right?

 

[PeterDonis]

ok, thanks. I was thinking after i posted that that maybe the energy a photon hits it with depends not only on the speed but of the wavelength, since low-frequency photos are called 'low-energy' photons iirc.. and since the doppler effect applies to light, that would make the impact relative to the ray's speed.. is that right?

All the light rays travel at the same speed, so the impact can't depend on speed. :)

You're correct that the energy of the photons depends on their wavelength. Since the magnitude of a photon's momentum is equal to its energy (divided by the speed of light if you're using ordinary units), its momentum also depends on its wavelength. So you're also correct that the doppler effect, which changes the wavelength that you observe the photon to have, will also change the impact (momentum) you observe it to have. That's the same thing I was saying (photon momentum in the cosmic ray frame will be "biased" in the direction opposite to its motion), just in different words.

(Edit: I should clarify that the doppler effect is a function of the relative motion of the observer and the *source* of the photon. In the cosmic ray case, the sources of the photons that are impacting the cosmic ray are basically at rest with respect to the Earth frame, which is why I said the photon momenta were isotropic in that frame. In the cosmic ray's rest frame, the sources all appear to be moving in the opposite direction at a very high speed, which is what causes a doppler effect to be observed--which is just another way of saying that the photon momenta are biased in the direction opposite to the ray's motion.)