Muons: Mysterious Time Travellers?

[Adam]

I am curious about muons. I've been told that they appear lower in the atmosphere than they should. Ie. that they should be gone within a short distance of passing through the atmosphere, being created at a certain height and having a very short lifespan, but instead are found much lower. I think I have that right, but feel free to correct me; I have not done much physics. Now, I am told that the commonly accepted idea is that these particles somehow do some mysterious spooky time-travelling to get so low. Or perhaps some relativity stuff I'm not aware of. Why not simply consider that they travel very, very fast?

 

[chroot]

You are correct in the behavior of the muons; they appear in greater numbers low in the atmosphere than you might expect. In short, the muons last longer than they're supposed to -- longer than they do when sitting still in a laboratory, for example.

The conclusion is not spooky time-travelling -- it is relativity. The particles are moving at very large fractions of the speed of light with respect to the earth, and thus suffer time dilation with respect to our clocks -- if a muon wore a watch, we'd see it running slowly. Muons do wear watches in a sense -- their own lifetimes are a timekeeping system. When the muons are traveling very fast with respect to an observer, the muons appear to decay much more slowly-- to live much longer -- than they should. This is called time dilation.

In fact, the same effect has been verified by countless experiments every since this early observation. Everytime particle physicists send their particles spinning around in their machines at speeds working up to the speed of light, they observe that the unstable particles live longer, and longer, and longer lives.

- Warren

 

[ahrkron]

There's not much I can add to Warren's post, but I just wanted to emphasize that, regarding your question abuot

Why not simply consider that they travel very, very fast?

The answer is that they live longer than expected, even after accoounting for their high speeds[/color].

 

[STAii]

I just want to add a little thing, in case you are not aware of it Adam, any object's speed has a maximum, which is the speed of light, no object (that has a (rest) mass) can reach the speed of light, and nothing in the universe (even energy) can have a speed bigger than the speed of light (seen by any observer).
So, if we want to explain the fact that there are muons lower in atmosphere than expected by saying that the muon's speed gets bigger, than the muons speed must be bigger than c (i assume), which is impossible.

 

[Adam]

Actually JamesR or Crisp from another forum showed me the maths once, but I forgot. However, I always have the feeling that there's something not qite right about it. Is it possible that the maths fit the observations for a reason other than that proposed? For example, what if particles simply have a longer lifespan at higher energy states, and this produces the results we see all the time? Would this not give the same result as explaining it in terms of time dilation?

 

[Adam]

Rest assured, I will work through the relativity chapter of my textbook sooner or later.

 

[quantumdude]

Originally posted by Adam
Is it possible that the maths fit the observations for a reason other than that proposed? For example, what if particles simply have a longer lifespan at higher energy states, and this produces the results we see all the time?

They do have a longer lifespan at higher energy states, and that is basically equivalent to the explanation already given![/color]. In the rest frame of the muon, it has lower energy (because its kinetic energy is zero), and it lives a shorter time.

The reason we talk about the lifetime varying with speed and not energy is that the effect of time dilation depends explicitly on v, and not E.