Muons passing through body

  • Thread starter czaroffishies
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P = F * t * A = (100 muons/m^2/s) * (1 second) * (0 m^2) = 0 muonsIn summary, the probability of a muon passing through your body in 1 second is either 100 muons or 0 muons, depending on whether we take into account the time dilation of the muon. This is a factor of 3 difference in our estimation. I hope this helps. Please let me know if you have any further questions.
  • #1
czaroffishies
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Homework Statement



The flux of cosmic-ray induced muons is about 100 muons per square meter per second at sea level
on the Earth’s surface. Estimate (to within a factor of 3) the probability that a muon is passing
through your body this instant.

Homework Equations



This is supposed to be a special relativity problem. So, Lorenz transformations.

The Attempt at a Solution



I'm not sure where to start, because I am missing something... I am not sure where special relativity comes into play, since the problem gives us the flux at sea level, and I am assuming my body is also at sea level.

I appreciate any help!
 
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  • #2


Thank you for your question. This is an interesting problem that requires some knowledge of special relativity. Let's start by defining some variables:

F = Flux of cosmic-ray induced muons (100 muons/m^2/s)
v = Velocity of the muon (close to the speed of light, c)
t = Time interval (1 second, since we are looking at the probability of a muon passing through your body in 1 second)
A = Area of your body (let's assume it is approximately 1 m^2)

Now, we can use the Lorentz transformation to calculate the probability of a muon passing through your body in 1 second. The Lorentz transformation tells us that the time interval observed by an observer moving with velocity v is given by:

t' = t/√(1-v^2/c^2)

In this case, v is close to c, so we can approximate the denominator as 1. Therefore, the time interval observed by a stationary observer (you) is:

t' = t/√(1-v^2/c^2) ≈ t/√(1-1) = t/0 = undefined

This means that, according to special relativity, the time interval for the muon to pass through your body is essentially zero. Therefore, the probability of a muon passing through your body in 1 second is:

P = F * t * A = (100 muons/m^2/s) * (1 second) * (1 m^2) = 100 muons

However, this answer does not take into account the fact that the muons are moving close to the speed of light, which means that their time is dilated. To account for this, we can use the Lorentz transformation for length, which tells us that the length observed by a stationary observer is:

L' = L * √(1-v^2/c^2)

In this case, we can approximate the denominator as 1, so the length observed by a stationary observer is:

L' = L * √(1-v^2/c^2) ≈ L * √(1-1) = L * √0 = 0

This means that the length of the muon is essentially zero when observed by you. Therefore, the probability of a muon passing through your body in 1 second
 

What are muons?

Muons are subatomic particles that are similar to electrons, but with a larger mass. They are produced when cosmic rays from outer space interact with the Earth's atmosphere.

How do muons pass through the body?

Muons are able to pass through the body because they are highly penetrating particles. They are not affected by the electromagnetic forces that usually cause other particles to interact with matter.

Are muons harmful to the body?

No, muons are not harmful to the body. They are able to pass through the body without causing any damage or leaving any residual radiation. In fact, muons are constantly passing through our bodies without us even noticing.

How are muons detected passing through the body?

Muons can be detected passing through the body using a variety of techniques, such as muon detectors or radiation detectors. These devices are able to detect the small amount of radiation that is emitted when muons pass through matter.

What is the significance of studying muons passing through the body?

Studying muons passing through the body can provide valuable information about the structure and composition of matter. It can also help in understanding cosmic rays and their effects on Earth's atmosphere. Additionally, muons passing through the body are used in medical imaging techniques, such as muon tomography, which can provide detailed images of the body's internal structures without using harmful radiation.

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