Muon Tomography Evidence for Special Relativity?

[racerunner]

Muons are a popular way to provide evidence for Special Relativity. But, does Muon Tomography provide evidence for SR? Can you calibrate your muon detectors without reference to SR? Is there any need to refer to SR when interpreting the data?

I tutored a high school student who argued the affirmative (does provide evidence) in his research assignment – referencing articles about muon tomography and pyramids. I argued no – I said you don’t need to know about SR to watch a CRT TV. He argued yes and got 100% for his assignment. Where have I gone wrong?

 

[Sagittarius A-Star]

Muons are a popular way to provide evidence for Special Relativity. But, does Muon Tomography provide evidence for SR?

Practically, yes. Only because of SR time dilation, a significant number of cosmic ray muons can reach the surface of the earth.

The emergence of the muons is caused by the collision of cosmic rays with the upper atmosphere, after which the muons reach Earth. The probability that muons can reach the Earth depends on their half-life, which itself is modified by the relativistic corrections of two quantities: a) the mean lifetime of muons and b) the length between the upper and lower atmosphere (at Earth's surface). This allows for a direct application of length contraction upon the atmosphere at rest in inertial frame S, and time dilation upon the muons at rest in S′.[1][2]

Source:
https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation

Muon tomography or muography is a technique that uses cosmic ray muons to generate three-dimensional images of volumes using information contained in the Coulomb scattering of the muons.

Source:
https://en.wikipedia.org/wiki/Muon_tomography

 

[PeroK]

He argued yes and got 100% for his assignment. Where have I gone wrong?

What's your point? Why is it not evidence?

 

[Ibix]

I'd say the existence of usable numbers of cosmic ray muons at ground level is a test of SR, the same as anything that uses cosmic ray muons at ground level. Not sure that the tomography aspect adds anything, though, not from an SR test perspective.

 

[racerunner]

Not sure that the tomography aspect adds anything, though, not from an SR test perspective.

I'm not sure either. That's my question.

 

[Sagittarius A-Star]

Muons arrive at sea level with an average flux of about 1 muon per square centimeter per minute.

Source:
https://cosmic.lbl.gov/SKliewer/Cosmic_Rays/Muons.htm

In the current paper, however, we measured a flux of about 1 muon per minute per square-cm at Galveston Bay and a flux of about 100 muons per minute per square-cm at Mt. Hamilton (4200 ft).

Source:
https://arxiv.org/abs/1203.0101

Calculated without SR-time-dilation, only about 0.3 out of a million muons reach the surface of the earth.
Calculated with SR-time-dilation and assuming $\gamma = 5$, about 49,000 out of a million muons reach the surface of the earth.

Source:
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

Therefore, without SR time-dilation, the flux at sea-level would be (neglecting interaction with air-molecules)
$\frac{0.3}{49000} \frac{1}{cm^2min} \approx 6 \cdot 10^{-6} \frac{1}{cm^2min}$.

 

[racerunner]

I am very aware of the use of SR to explain the prevalence of muons at sea level.
Given that there's a significant quantity of muons at sea level, does the process of detecting muons that have traveled through (pyramid)rock and comparing them to muons that have not traveled through (pyramid)rock have to take account of relativistic effects?

 

[Ibix]

Actually, thinking about it, yes. The amount of scattering will depend on muon energy and momentum, and obviously these are relativistic muons. So you're testing your model of particle interactions at relativistic speeds, including your model of relativistic energy and momentum, over and above the mere existence of muons in large numbers.

 

[Vanadium 50]

Muons are a popular way to provide evidence for Special Relativity.

Um...not exactly.

The experiment was done in the 1960's, after which this sort of evidence was no longer needed and was certainly not the best evidence. It was popularized because films were made available to zillions of high schools and colleges.

What was actually done was measure the muon flux as a function of height, fit a lifetime to it, and infer that muons are typically time-dilated by a factor of 8 or 9.

The way the story is often presented is to say "2^-8 (or e^-9 or whatever) is a fraction of a percent, so the fact that we see muons at all is proof of relativity". This is a little strong, since we don't really know how many we started with. If we started out with a few hundred times as many, we would see the right number on the surface,.

While that's true, it's also true that if there were that many muons at altitude, air travel would be vastly more dangerous. Pilots and flight attendants would be dropping like flies from radiation exposure.[/sup][/sup]

 

[Sagittarius A-Star]

Given that there's a significant quantity of muons at sea level, does the process of detecting muons that have traveled through (pyramid)rock and comparing them to muons that have not traveled through (pyramid)rock have to take account of relativistic effects?

Yes. They measure the muon fluxes, coming in under different angles.

Atmospheric muons as an imaging tool
...
The angular distribution of the atmospheric muon intensity5 is found to be approximately proportional to $cos^n\Theta$, where θ is the zenith angle and n ≈ 2 [25], with mild dependence of n on energy, latitude, altitude and depth [26]. This strong dependence on the zenith angle implies a large difference in muon rate, and therefore much longer exposure times are needed when observing an object from a horizontal or quasi-horizontal line of sight (which is typically the case when imaging mountains and volcanoes from a distance) with respect to a vertical one.

Source:
https://www.sciencedirect.com/science/article/pii/S2405428320300010

The same is done in school SR-experiments to avoid, that a second experiment must be carried-out on top of a mountain.

Special relativity in the school laboratory: a simple apparatus for cosmic-ray muon detection
...
This is accomplished by measuring the flux of muons, I(θ), arriving at different angles, θ, to the vertical, having followed different path lengths through the atmosphere.

Source:
https://iopscience.iop.org/article/10.1088/0031-9120/50/3/317

 

[racerunner]

Actually, thinking about it, yes. The amount of scattering will depend on muon energy and momentum, and obviously these are relativistic muons. So you're testing your model of particle interactions at relativistic speeds, including your model of relativistic energy and momentum, over and above the mere existence of muons in large numbers.

Ibix: Thank you for hearing my question. Your answer is helpful to me. I would love to know if it's possible to shoot slow speed muons through rock as a comparison with atmospheric muons.

I still think that SR is not ESSENTIAL to making, calibrating and operating muon tomography. You could accidentally discover muons, measure their flux from all angles, calibrate flux loss through rock samples, and use that to probe the inside of pyramids without knowing what muons are. SR provides fruitful analysis and understanding but it is not essential to the task.

It worked for Rutherford. He fired alpha particles through gold foil at a time when "alpha" was a code word for "we don't actually know what this is".

 

[Vanadium 50]

You could accidentally discover muons, measure their flux from all angles, calibrate flux loss through rock samples, and use that to probe the inside of pyramids

Sort of.

In a non-SR world, these muons wouldn't exist. Sure you can posit another source of such muons, call it "sourcery" but once you go down that path you can quickly explain any experimental result whatever. "Yes, it looks like the water is boiling at 100C, but that's not what's really happening. It's magic instead..."

 

[racerunner]

To all above contributors: Thank you very much for taking the time to respond to my post.

 

[Mister T]

I still think that SR is not ESSENTIAL to making, calibrating and operating muon tomography. You could accidentally discover muons, measure their flux from all angles, calibrate flux loss through rock samples, and use that to probe the inside of pyramids without knowing what muons are. SR provides fruitful analysis and understanding but it is not essential to the task.

Your argument seems to be that you don't need to understand the explanation for how something works to be able to use it to make, calibrate, and operate machinery that makes use of that something. History is full of examples of that sort of thing.

 

[Ibix]

Your argument seems to be that you don't need to understand the explanation for how something works to be able to use it to make, calibrate, and operate machinery that makes use of that something. History is full of examples of that sort of thing.

I would agree - the lodestone predates Maxwell by quite a few centuries, for example. However, it's still a test of magnetism (or SR, in the muon tomography case) even if you only understand that it works, not how it works. If one (pre-Maxwell) came up with a theory of lodestone dynamics that predicted like poles of two lodestones to attract, for example, one could immediately dismiss it on the grounds of existing known behaviour. Similarly, I would say the existence of muon tomography data is a test of any theory of muon creation and deflection, whether one has such a theory at hand or not.