Muon Lifetime and time dilation effect
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MUON LIFETIME AND TIME DILATION EFFECT Measuring the stopping rate of muons, as a function of depth in the atmosphere to demonstrate the time dilation effect of special relativity. Melinda Jolley THE MUON WAS SO UNEXPECTED THAT, REGARDING ITS DISCOVERY, NOBEL LAUREATE ISIDOR ISAAC RABI FAMOUSLY QUIPPED, “WHO ORDERED THAT?” Where do muons come from? • Not completely sure • Somewhere in deep space? • Very recent NASA research Muons were originally thought to be meson It’s name is a combination of mu and meson • • Femi Coupling Constant (πΊπ ) The Muon • • Nope, it is a Lepton Nicknamed ‘The Heavy Electron’ • π± →e± +2 ν THE GOALS OF MY EXPERIMENT Determine the Measured Lifetime of the Muon Muon Physics • • • • Moun.exe π π‘ = π0 π • Use the measured τ • π‘ π − Accepted τ = 2.20 µs Is there no Time Dilation? The Fermi Coupling Constant πΊπ = • β 192π3 ππ π5 • • Rates of Muon decays at one elevation Approximation for rate at second elevation Correction factors for Energy Loss over distance and Variations in the shape of the muon energy spectrum CORRECTING FOR ENERGY LOSS • • βπΈ = πΆπ ∗ βπ» ∗ ππππ ππππ • ππ£π = 1 β2 π βπ» β1 0 ππ£π ×π π0 = 1.28 × 10−3 −β 8400 π π . ππ3 THE MUON ENERGY SPECTRUM • π πππ€ = ππ‘ππππππ πππ‘π ππ‘ β1 ππ‘ππππππ πππ‘π ππ‘ β2 • π (ππππππ π βπππ) = π • π‘′ = ππ ππππ(ππ£π) πΆπ • • π π = −π‘′ π πΎ2 πΎ1 πΎ2 −1 πΎ1 = πΈ1 ππ 2 π πππ€ π (ππππππ π βπππ) ππΎ THE PREDICTIONS • π ππππ· = π π ∗ π (πππππππ‘ππ)π πππ ππ‘βππ β (ππ π‘πππ πππππ‘πππ) • =π 0 × π −π‘ π • π πππ· = π π ∗ π (πππππππ‘ππ)π πππ ππ‘βππ β (π‘πππ πππππ‘πππ) • =π 0 × π ( −π‘′ ) π THE EQUIPMENT USED • Scintillator is placed at the bottom of a black anodized aluminum alloy tube • Plastic Scintillator made of Organic Transparent Material HOW THE DATA LOOKS MY DATA • High Voltage set to -1154 Volts • Threshold Voltage set to 206 MeV • First location: Pueblo, CO, Elevation 1420 m • Second location: Monarch Mountain Base Summit, CO, Elevation 3290 m • ΔH= 1870 m • Much more Pueblo Data than Monarch Data FERMI COUPLING CONSTANT • • Mass of the Muon = 106 πππ π2 Reduced Planck’s Constant = 6.58 × 10−25 πΊππ ∗ π • Accepted value: 1.17 × 10−5 πΊππ −2 • Pueblo value : 1.18 × 10−5 πΊππ −2 • Monarch value : 1.19 × 10−5 πΊππ −2 STOPPING RATES • Pueblo’s Stopping Rate = 0.0284 • ππ’πππ π ππ Monarch’s Stopping Rate = 0.0644 ππ’πππ π ππ • t=6.28 µsec or π‘ = 2.85 π RATES ACCOUNTING FOR ENERGY LOSS • • Remember t is the transit time assuming no Time Dilation t’ assumes Time Dilation Effects • ππππ = 972 π . π3 • βπΈ = 364 πππ, πΈ1 = 508 πππ, πΎ1 = 4.9 • π‘ ′ = 2.38 π sec ππ π‘ = 1.08 π • π (πππππππ‘ππ)ππ’ππππ(ππ π‘πππ ππππππππππ) = π 0 × 0.0578 • π (πππππππ‘ππ)ππ’ππππ(π‘πππ πππππ‘πππ) = π 0 × 0.339 MUON ENERGY SPECTRUM CORRECTION AND PREDICTIONS • π (ππππππ π βπππ) = 0.339 • π πππ€ = • π π = 0.0284 0.0644 0.441 0.339 = 0.441 = 1.30 • π (πππππππ‘ππ)ππ’ππππ(ππ π‘πππ πππππ‘πππ) = 1.30 × 0.056 = 0.0749 • π (πππππππ‘ππ)ππ’ππππ(π‘πππ πππππ‘πππ) = 1.30 × 0.339 = 0.441 GREAT INCONSISTENCY OF THE MEASURED ANSWER WITH THE HYPOTHESIS THAT THERE IS NO RELATIVISTIC TIME DILATION EFFECTS ON THE MUON The data was consistent with the Relativistic Time Dilation Hypothesis. “ IF WE KNEW WHAT IT WAS WE WERE DOING, IT WOULD NOT BE CALLED RESEARCH, WOULD IT Einstein Thanks to: Dr. Brown Dr. Wallin My family Special thanks to Annika, Thomas, and Olivia ”
