Muon - Revision history

KDort at 18:08, 17 April 2020

2020-04-17T18:08:35Z

2020-04-17T18:07:42Z

2020-04-17T18:01:28Z

2020-04-17T17:38:07Z

2020-04-17T17:33:23Z

2020-04-14T18:35:41Z

2020-04-14T18:35:26Z

2020-04-14T18:34:31Z

2020-04-14T18:34:21Z

2020-04-14T18:34:11Z

← Older revision		Revision as of 18:08, 17 April 2020
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	which effectively yields a longer mean path: <math> \gamma x = 40.83 \dot 660</math> m = 27 km.		which effectively yields a longer mean path: <math> \gamma x = 40.83 \dot 660</math> m = 27 km.
−	This relativistic '''time dilation''' (or equivalently '''length contraction''') enables the muons to reach the surface of the Earth before they decay. Our ability to measure muons on sea level is therefore direct evidence of the relativistic mechanisms that govern the ~~mean flight path~~ of ~~muons~~.	+	This relativistic '''time dilation''' (or equivalently '''length contraction''') enables the muons to reach the surface of the Earth before they decay. Our ability to measure muons on sea level is therefore direct evidence of the relativistic mechanisms that govern the propagation of particles travelling close to the speed of light.

← Older revision		Revision as of 18:07, 17 April 2020
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	<math> \tau = \gamma t = 40.83 \dot 2.2</math> μs = 90 μs		<math> \tau = \gamma t = 40.83 \dot 2.2</math> μs = 90 μs

−	which effectively yields a longer mean path: <math> \gamma x = 40.83 \dot 660</math> m = 27 km	+	which effectively yields a longer mean path: <math> \gamma x = 40.83 \dot 660</math> m = 27 km.
		+	This relativistic '''time dilation''' (or equivalently '''length contraction''') enables the muons to reach the surface of the Earth before they decay. Our ability to measure muons on sea level is therefore direct evidence of the relativistic mechanisms that govern the mean flight path of muons.

@@ Line 36: / Line 36: @@
 However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).
 The <math> \gamma </math>-factor is given by:
 <math>\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}</math>
 For a muon travelling close to the speed of light (v ~ 0.9997c) one obtains <math> \gamma \approx 40.83 </math>.
 This yields an Eigen time <math> \tau </math> of:
 <math> \tau = \gamma t = 40.83 \dot 2.2</math> μs = 90 μs

← Older revision		Revision as of 17:38, 17 April 2020
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	However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).		However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).
		+	The <math> \gamma </math>-factor is given by:
		+	<math>\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}</math>

−	<math>\gamma = \~~frac{1}{~~\~~sqrt{1 - v^~~2~~/c^~~2}}</math>	+	For a muon travelling close to the speed of light (v ~ 0.9997c) one obtains <math> \gamma \approx 40.83 </math>.
		+	This yields an Eigen time <math> \tau </math> of:
		+	<math> \tau = \gamma t = 40.83 \dot 2.2</math> μs = 90 μs

← Older revision		Revision as of 17:33, 17 April 2020
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	However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).		However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).
		+
		+	<math>\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}</math>

← Older revision		Revision as of 18:35, 14 April 2020
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	However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).		However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).
−	~~<math alt="Square root of pi">\sqrt{\pi}</math>~~

← Older revision		Revision as of 18:34, 14 April 2020
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	However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).		However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).
−
−	~~$\frac{2}{3}$~~

← Older revision		Revision as of 18:34, 14 April 2020
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	However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).		However, as the muons propagate with a velocity close to the speed of light, a relativistic correction to this calculation has to be applied. Namely, the mean lifetime has to be '''Lorentz transformed''' to the reference frame of a ''stationary'' observer (stationary with respect to Earth).

−	\frac{2}{3}	+	$\frac{2}{3}$