Einstein's Theory of Special Relativity - Revision history

Ecarder: Changed normal text math into LaTex

2022-09-29T01:44:45Z

Changed normal text math into LaTex

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	To determine whether Special Relativity is necessary to describe the motion of a particle, we must look at the ratio of its speed to that of the speed of light.		To determine whether Special Relativity is necessary to describe the motion of a particle, we must look at the ratio of its speed to that of the speed of light.

	If the ratio between the velocity of a particle, v, and the speed of light, c, is close to one, typically defined as v/c >= .1, then the particle is moving at relativistic speeds, and Special Relativity must be used to describe the motion of the object. If not, it is moving at non-relativistic speeds, then Newtonian mechanics is sufficient to describe the particle.		If the ratio between the velocity of a particle, <math>v</math>, and the speed of light, <math>c</math>, is close to one, typically defined as <math>\frac{v}{c} \geq .1 </math>, then the particle is moving at relativistic speeds, and Special Relativity must be used to describe the motion of the object. If not, it is moving at non-relativistic speeds, then Newtonian mechanics is sufficient to describe the particle.

	[[File:Relativistic_vs_nonrelativistic.png]]		[[File:Relativistic_vs_nonrelativistic.png]]

2022-04-24T01:50:14Z

Simulation

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	Graphical Glowscript Simulation: (because Trinket SUCKS!)		Graphical Glowscript Simulation: (because Trinket SUCKS!)

	[https://www.glowscript.org/#/user/mrheadhunter34/folder/MyPrograms/program/LengthContraction]		[https://www.glowscript.org/#/user/mrheadhunter34/folder/MyPrograms/program/LengthContraction]

2022-04-24T01:49:52Z

Length Contraction

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	[[File:tallball.jpg]]		[[File:tallball.jpg]]

			====Simulation====
			Trinket Simulation:
			[https://trinket.io/python/ca38e9a838]

			Graphical Glowscript Simulation: (because Trinket SUCKS!)

			[https://www.glowscript.org/#/user/mrheadhunter34/folder/MyPrograms/program/LengthContraction]

	===Relativistic Energy===		===Relativistic Energy===

2022-04-24T00:41:26Z

Mathematics of Special Relativity

2022-04-23T21:48:33Z

Length Contraction

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	Illustration of length contraction in direction of motion:		Illustration of length contraction in direction of motion:

	[[File:tallball.jpg]]		[[File:tallball.jpg]]

2022-04-23T21:48:18Z

Length Contraction

← Older revision		Revision as of 17:48, 23 April 2022
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	[[File:LC 3565.jpg]]		[[File:LC 3565.jpg]]

			Illustration of length contraction in direction of motion:
	[[File:tallball.jpg]]		[[File:tallball.jpg]]

2022-04-23T21:43:23Z

Length Contraction

← Older revision		Revision as of 17:43, 23 April 2022
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	[[File:LC 3565.jpg]]		[[File:LC 3565.jpg]]

	Instead of analyzing the motion of the tau from our frame of reference, we could ask what the tau would see in its reference frame. Its half-life in its reference frame is 3.05 x 10^-13 s. This does not change. The tau goes nowhere in this frame.

	~~How far would an observer, sitting in the tau rest frame, see an observer in our laboratory frame move while the tau lives [http://pages.towson.edu/zverev/conceptual/14.htm]~~

	We just calculated that the tau would travel 1.8 mm in our frame of reference. Surely we would expect the observer in the tau frame to see us move the same distance relative to the tau particle. Not so says the tau-frame observer -- you only moved 1.8 mm/gamma = 0.09 mm relative to me. This is length contraction.

	How long did the tau particle live according to the observer in the tau frame? We can rearrange d = v x t to read t = d/v . Here we use the same speed, Because the speed of the observer in the lab relative to the tau is just equal to (but in the opposite direction) of the speed of the tau relative to the observer in the lab, so we can use the same speed. So time = 0.09 x 10^-3 m/(3 x 10^8) m/sec = 3.0 x 10^-13 sec. This is the half-life of the tau as seen in its rest frame, just as it should be!

	[[File:tallball.jpg]]		[[File:tallball.jpg]]

2022-04-23T21:40:01Z

Mathematics of Special Relativity

← Older revision		Revision as of 17:40, 23 April 2022
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	===Length Contraction===		===Length Contraction===

			[[File:LC 3565.jpg]]

	Instead of analyzing the motion of the tau from our frame of reference, we could ask what the tau would see in its reference frame. Its half-life in its reference frame is 3.05 x 10^-13 s. This does not change. The tau goes nowhere in this frame.		Instead of analyzing the motion of the tau from our frame of reference, we could ask what the tau would see in its reference frame. Its half-life in its reference frame is 3.05 x 10^-13 s. This does not change. The tau goes nowhere in this frame.

2022-04-23T20:32:07Z

Relativistic Effects

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 [[File:gamma.GIF]]
-===Relativistic Effects===
+===Length Contraction===
 Instead of analyzing the motion of the tau from our frame of reference, we could ask what the tau would see in its reference frame. Its half-life in its reference frame is 3.05 x 10^-13 s. This does not change. The tau goes nowhere in this frame.

2022-04-23T20:31:05Z

Gamma(γ)

← Older revision		Revision as of 16:31, 23 April 2022
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	[[File:gamma.GIF]]		[[File:gamma.GIF]]

	[[File:Lorentz_factor.svg.png\|thumb\|Lorentz factor γ as a function of velocity. Its initial value is 1 (when v = 0); and as velocity approaches the speed of light (v → c) γ increases without bound (γ → ∞).]]

	===Relativistic Effects===		===Relativistic Effects===