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Consequences of and evidence for special relativity

Consequences of and evidence for special relativity. By the end of this topic you should be able to: solve problems with relativistic energy , E = γ m 0 c 2 ; describe muon decay experiments as evidence for time dilation and length contraction ;

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Consequences of and evidence for special relativity

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  1. Consequences of and evidenceforspecialrelativity Bytheend of thistopicyoushould be able to: solveproblemswithrelativisticenergy, E = γm0c2; describe muon decayexperiments as evidencefor time dilation and lengthcontraction; Appreciatethesignificance of theMichelson-Morleyexperiment,

  2. Restenergy Thetheory of relativitypredictsthat, to a particle of mass m0thatis at restwithrespecttosomeinertialobserver, therecorrespondsanamount of energy E0thattheobservermeasurestobe E0=m0c2. Thisenergyiscalledtherestenergy of theparticle.

  3. Relativisticenergy Iftheparticlemoveswithspeed v relativetosomeinertialobserver, theenergycorrespondingtothemass of theparticlethatthisobserverwillmeasureisgivenby E = γm0c2 Thisisenergythattheparticle has becauseit has a mass and becauseitmoves. Iftheparticle has otherforms of energy, thenthe total energy of theparticlewillequalγm0c2 plus theotherforms of energy.

  4. Examplequestions

  5. In Newtonianmechanics, a constantforce produces a constantacceleration, and so thespeedincreasesuniformlywithoutlimit, exceedingthespeed of light. In relativisticmechanics, thespeedincreasesuniformly as long as thespeedissubstantiallylessthanthespeed of light. However, as thespeedincreases, so doestheenergy. Becauseittakesaninfiniteamount of energyfortheparticletoreachthespeed of light, weconcludethattheparticleneverreachesthespeed of light.

  6. Muon decay Lifetimewhenthe muon is at rest: 2.2 x 10-6s Lifetimefromthepoint of view of thelabframe: In this time the muon travels a distance: Withoutthe time dilationeffect, the muon wouldhavetravelled a distance of only:

  7. Muon decay Thedistance of 3 km measuredbytheobserversonEarthis a properlengthforthembutnotforanobserver in themuon’sframe of reference. TheEarth’ssurfaceiscoming up tothisobserverwith a speed of 0.99c and so the time whentheywillmeetis

  8. TheMichelson-Morleyexperiment

  9. Theconstancy of thespeed of light Thefirstconclusiveexperimentthatdemonstratedtheconstancy of thespeed of light withgreataccuracywasperformed at CERN in 1964. In thisexperiment, neutral pionsmoving at 0.99975c decayedinto a pair of photonsmoving in differentdirections.

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