# Is cosmic muon lifetime extension a valid test of relativity?

1. Aug 11, 2012

### arindamsinha

Experiments show that cosmic ray muons reach Earth surface in greater numbers than they should, unless relativistic time dilation is taken into consideration. It also seems to confirm the SR formula mathematically.

However, looking at a lot of different experiment records, I have some doubts about the validity of the experiments. I would like to get an opinion from those in this forum who are knowledgeable in this area.

My questions are:
1) Consensus looks as if the cosmic muons travel at about 98% of the speed of light, and therefore have a γ of about 5, and some experiments confirm this. This seems to confirm the SR time dilation formula with a very high precision.
• Now, there seem to be some different experiments showing different γ's ranging from about 5 to 189 (based on what I can find on the internet). Why this variation of γ? Is it because different experiments focus on different energy levels of muons?
• Which are the reliable/officially accepted experiments?

2) There also seems to be an assumption that the cosmic ray protons produce muons at an altitude of about 15 km (~ 9 miles) from the Earth surface.
• Is there any validation of this assumption? Where did this assumption come from?
• Should the protons not be creating muons at various altitudes (perhaps with some sort of Poisson distribution between altitude and muon numbers produced?)
• Is this assumption a necessary one for the purpose of validating the SR formula?

One overall question - how valid are the cosmic muon experiments as a proof of relativity theory (i.e. is it among the top proofs, or low down in the order)? I am not questioning the fact whether muon lifetime does get extended (which I accept), only how valid the "exact mathematical application" of SR formula is given what seems to be somewhat fuzzy assumptions?

Any insights will be greatly helpful.

2. Aug 11, 2012

### Mentz114

γ is a function of the velocity of the muon in question. The greater the speed, the greater the value of γ. I won't repeat the formula that gives γ in terms of velocity because I'm sure you've taken the trouble to look it up and understand what it means.

3. Aug 11, 2012

### Staff: Mentor

I would put them low down on the list for exactly the reasons you mention. They are produced by high energy particles interacting with the upper atmosphere. The high energy particles have a wide spread in energies, and the atmosphere particles have a wide spread in altitude, so you do get quite a bit of variation in starting altitude and speed for the muons. However, the number of these muons is also incredibly high, and the distribution is well studied, so you can do good statistics and get accurate results for the population.

However, I would consider lab measurements to be much more reliable. In particular, the Bailey muon experiments listed in section 5 here.

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

4. Aug 11, 2012

### bcrowell

Staff Emeritus
The history is similar to that of the 1938 Ives-Stilwell experiment with Doppler shifts, which was originally not very high in precision but was later made into one of the most high-precision tests of SR.

5. Aug 11, 2012

### arindamsinha

Thanks everyone for responses.

I am trying to understand if the assumption of 15 km altitude (for creation of almost all cosmic muons) is in any way experimentally verified.

I am giving below my thoughts on another possibility. Say that the muons are not all created at around 15 km altitude, but perhaps at all altitudes. Naturally, the lower the altitude, lesser the number of cosmic protons reaching there, and lesser the number of muons produced at that altitude. This could also account for the observed muon count ratio between sea level and higher altitudes, even with γ being a lot less that 5, or even being equal to 1. Is this line of reasoning incorrect?

So, my question is - γ having to be about 5 based on SR formula and observed average muon velocity - was the 15 km assumption retrofitted into the theory to square with the fact of muon counts?

6. Aug 11, 2012

### bcrowell

Staff Emeritus
Sounds like you need to look up the original reference, which is Bruno Rossi and David B. Hall, Phys Rev 59 (1941) 223. I believe they did experiments both in New England and in Colorado. Other people have studied this kind of thing using weather balloons. Since we have access to a lot of different altitudes, it seems like it would be straightforward to verify that the muons are not just getting produced at some very low altitude.

7. Aug 11, 2012

### arindamsinha

Thanks bcrowell. I am aware of the original reference you have suggested, but will look into it in some detail based on your inputs.

Are there any other reliable references you can suggest in cosmic muon experiments of this type? There are many on the Internet, but I am not sure which ones are really credible.

8. Aug 11, 2012

### Staff: Mentor

Note that cosmic rays aren't the only source of muons, just the first one historically. When we study muons nowadays, we produce them at particle accelerators. IIRC Fermilab has or had a beamline which produced beams of muons. The location of the production target is well-defined, and the momentum (and therefore the velocity) can be measured in a magnetic field before the muons decay.

9. Aug 11, 2012

### bcrowell

Staff Emeritus
I would go to a university library and find a book on cosmic ray physics, which is a big field.

Another possibility would be to find later papers that cite Rossi and Hall. I think you can do this, for example, on arxiv.org for papers that are on arxiv.

When you talk about "references" that are "on the internet," do you mean peer-reviewed papers, or just people's web pages?

10. Aug 12, 2012

### arindamsinha

@jtbell - absolutely. I have no doubts about the controlled muon experiments in labs. I am trying to understand only the reliability of cosmic muon experiments.

@bcrowell - thanks. That is exactly what I was thinking of doing.

The references I am talking about are in 3 categories - (a) papers on arxiv or elsewhere which seem to be properly written with references etc., though sometimes not easy to differentiate whether those are opinions of person(s) or whether acknowledged by the broad scientific community, (b) papers based on actual meticulous experiments, but not done by professional scientists (e.g. undergraduate experiments), (c) people's web pages.

Mostly I tend to ignore the third category. In the first two I am unable to always tell whether I can take the observations and conclusions as reliable or not (except for the few very well known papers, of course).