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Theory of relativity (view source)
Revision as of 14:01, September 19, 2016
, 14:01, September 19, 2016Added derivations of time dilation and length contraction
Creation scientists such as physicists Dr. [[Russell Humphreys]] and Dr. [[John Hartnett]] have used relativistic time dilation to explain how the earth can be only 6,000 years old even though cosmological data (background radiation, supernovae, etc.) set a much older age for the universe.
Creation scientists such as physicists Dr. [[Russell Humphreys]] and Dr. [[John Hartnett]] have used relativistic time dilation to explain how the earth can be only 6,000 years old even though cosmological data (background radiation, supernovae, etc.) set a much older age for the universe.
====Derivation of Time Dilation====
Time dilation is most easily derived using the [[Lorentz transformation]]s, though geometrical solution is also straight forward. Using the transformation relating [[time]] between two [[Inertial frame of reference|frames of reference]], <math>t</math> and <math>t'</math>. We can find the time difference between two events that occur at the '''same''' location in space. The events shall be called event one and event 2. This results in the equations:
<math>t'_1 = \gamma (t_1 - \frac{ux}{c^2}) </math><br/>
<math>t'_2 = \gamma (t_2 - \frac{ux}{c^2}) </math>
where
:<math>\gamma</math> is the [[Lorentz factor]]
:<math>u</math> is the relative [[speed]] between [[Inertial frame of reference|reference frames]]
:<math>c</math> is the [[speed of light]]
Subtracting the top equation from the bottom produces the time between the events as measured in each reference frame, so:
<math>t'_2 - t'_1 = \gamma (t_2 - t_1)</math>
This the equation for time dilation and is the same equation as earlier.
===Length contraction===
===Length contraction===
:<math>c</math> is the speed of light (<math>3 \times 10^8 </math> m s<sup>-1</sup>
:<math>c</math> is the speed of light (<math>3 \times 10^8 </math> m s<sup>-1</sup>
:<math>\gamma</math> is the [[Lorentz factor]]
:<math>\gamma</math> is the [[Lorentz factor]]
====Derivation====
Length contraction may be derived using the [[Lorentz transformation]]s as with time dilation. This time we use the equation for <math>x</math>. In this case, the time in the undashed frame must be the '''same'''. Following the same procedure as above we find that:
<math>x'_2 -x'_1 = \frac{x_2 - x_1}{\gamma}
This is the same as above with <math>x_2 - x_1</math> and <math>x'_2 - x'_1</math> being the lengths in the undashed and dashed frames respectively. Again, geometrical arguments may be used to achieve the same result.
===Mass increase===
===Mass increase===
:<math>F=\frac{d}{d\tau} p</math>
:<math>F=\frac{d}{d\tau} p</math>
where <math>p</math> is the momentum defined by <math>\gamma m v</math>, <math>\gamma</math> is the standard Lorentz factor, and <math>\tau</math> is the proper time. Force F defined this way is a vector and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.
where
:<math>p</math> is the momentum defined by <math>\gamma m v</math>
:<math>\gamma</math> is the standard Lorentz factor
:<math>\tau</math> is the proper time
Force F defined this way is a [[vector]] and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.
The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that
The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that
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