2 years, 2 months ago
How does the General theory of relativity affect the decay speed in time of a muon?
Do muons decay in 2.2 miliseconds according to the theory of relativity?
What does the time space topology look like for a muon?
What does the time space topology look like for a muon?
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M$1 Answer
That's special relativity, not general relativity.
Muons are affected by time dilation like other things moving at high speeds. Their decay time (as it appears in our frame of reference) depends on how fast they are going to relative to us.
See more info on time dilation here:
http://www.mahalo.com/answers/physics/a-man-is-driving-a-car-at-the-speed-of-light-he-turns-on-the-headlights-what-happens
http://www.fourmilab.ch/cship/timedial.html
Time dilation can also be caused by gravity, but that is very small on the Earth and makes little difference to a muon's observed lifetime.
Muons are affected by time dilation like other things moving at high speeds. Their decay time (as it appears in our frame of reference) depends on how fast they are going to relative to us.
See more info on time dilation here:
http://www.mahalo.com/answers/physics/a-man-is-driving-a-car-at-the-speed-of-light-he-turns-on-the-headlights-what-happens
http://www.fourmilab.ch/cship/timedial.html
Time dilation can also be caused by gravity, but that is very small on the Earth and makes little difference to a muon's observed lifetime.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$
At Brookhaven on a 14 meter ring a muon should make 15 laps, but in reality it completed 400 laps, a factor of 29, or 60 microseconds.
Solving of lamba
lamba= 1 / sqrt(1 - (v/c)^2) = 1 / sqrt(1-(.9994)^2) = 28.87 or 29
The prediction is that the muon should live 29 times longer than a muon that is still because of its kinetic energy and speed.
It seems the average speed of cosmic ray muons is thought to be about 99% of the speed of light.
http://web.mit.edu/woodson/Public/8.13finalpapers/Duarte_muons.pdf
http://www.eberkowitz.com/work/muons.pdf
http://physicsweb.phy.uic.edu/quarknet/experiment/experiment6.html
What percentage of the speed of light are muons moving?
Does the muon exist longer than most particles because of it's kinetic energy?
Muons travel at 99.94% of the speed of light. The 2 millisecond life span is predicted. However, the muon travels 29 times the distance than it should. Is time distorting?
Different particles have a different lifetimes even at rest. Some are a lot more unstable than others and decay into other particles much more quickly. The "everyday" particles like protons, electrons etc are highly stable for example.
This stability is only a probability. It's not a given that all muons decay in time X, only that by time X 50% of muons will have decayed.
Muons don't have an inherent speed any more than protons do. A proton could be sitting in a cup of coffee on your desk, or it could be accelerated up to a massive velocity in the large hadron collider.
Cosmic ray muons have been found to have the average speed I mentioned. But a muon in a particle accelerator could be accelerated or decelerated to other speeds as desired.
What determines the average observed lifetime of a particle is a) it's inherent stability at rest and b) it's speed relative to the observer.
Kinetic energy dioesn't come into it directly. It's just that if it's going faster it also has more kinetic energy.