Changes
Jump to navigation
Jump to search
Line 268:
Line 268: − + − + − + − + Line 296:
Line 296: + +
Theory of relativity (view source)
Revision as of 13:41, September 15, 2016
, 13:41, September 15, 2016Added some more detail to section on time dilation and muons
The length of an event <math>t</math>, as seen by a (relative) stationary observer observing an event is given by:
The length of an event <math>t</math>, as seen by a (relative) stationary observer observing an event is given by:
<math> t = \frac{t_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>
<math> t = \frac{t_{0}} {\sqrt{1 - \frac{u^{2}}{c^{2}}}}</math>
Where
Where
:<math>t_0</math> is the "proper time" or the length of the event in the observed frame of reference.
:<math>t_0</math> is the "proper time" or the length of the event in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>u</math> is the relative velocity between the [[inertial frame of reference|reference frames]].
:<math>c</math> is the speed of light (3x10<sup>8</sup> ms<sup>-1</sup>).
:<math>c</math> is the speed of light (3x10<sup>8</sup> ms<sup>-1</sup>).
Evidence for time dilation was discovered by studying [[muon decay]]. [[Muons]] are [[subatomic]] [[particles]] with a very short [[halflife]] (1.53 microseconds at rest) and a very fast speed (0.994c). By putting muon detectors at the top (D<sub>1</sub>) and bottom (D<sub>2</sub>) of a mountain with a separation of 1900m, scientists could measure accurately the proportion of muons reaching the second detector in comparison to the first. The proportion found was different to the proportion that was calculated without taking into account relativistic effects.
Evidence for time dilation was discovered by studying muon decay. [[Muons]] are [[subatomic particles]] with a short [[halflife]] of 1.53 microseconds. When produced by interactions of [[cosmic rays]] in the upper atmosphere, they have a speed around 0.994c. By putting muon detectors at the top (D<sub>1</sub>) and bottom (D<sub>2</sub>) of a mountain with a separation of 1900m, scientists could measure accurately the proportion of muons reaching the second detector in comparison to the first. The proportion found was different to the proportion that was calculated without taking into account relativistic effects.
Using the equation for [[exponential decay]], they could use this proportion to calculate the time taken for the muons to decay, relative to the muon. Then, using the time dilation equation they could then work out the dilated time. The dilated time showed a good correlation with the time it took the muons to reach the second sensor, thereby supporting the existence of time dilation.
Using the equation for [[exponential decay]], they could use this proportion to calculate the time taken for the muons to decay, relative to the muon. Then, using the time dilation equation they could then work out the dilated time. The dilated time showed a good correlation with the time it took the [[muons]] to reach the second sensor, thereby supporting the existence of time dilation.
The time taken for a muon to travel from D<sub>1</sub> to D<sub>2</sub> as measured by a stationary observer is:
The time taken for a muon to travel from D<sub>1</sub> to D<sub>2</sub> as measured by a stationary observer is:
This is in good agreement with the value calculated above, thereby providing evidence to support time dilation.
This is in good agreement with the value calculated above, thereby providing evidence to support time dilation.
Since either [[inertial frame of reference|reference frame]] is equally valid, from the [[muon]]'s point of view it sees the [[earth]] approach it at nearly the [[speed of light]]. Hence time passes faster for the muon (slower for an observer on the ground). This appears to be a contradiction. However, the [[muon]] sees the height of the mountain contracted and so travels a shorter distance in its own frame. See length contraction below.
====Time Dilation and Creation Science====
====Time Dilation and Creation Science====
(username removed)