Measurements of the Speed and Mean Life of Cosmic-Ray Muons as a - PowerPoint PPT Presentation

Measurements of the Speed and Mean Life of Cosmic-Ray Muons as a Test of Special Relativity Fiz A. Cyst MIT - Department of Physics Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 1 / 15

Is there a relationship between velocity and time? Special Relativity In 1902 Einstein published his theory... Objects moving near the speed of light... Einstein - Circa 1912 Time dilation ... Muons Former MIT Professor Bruno Rossi observed cosmic ray muons... Rossi - Circa 1987 Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 2 / 15

Make Slide Titles Informative! ...and keep your audience focused. Summary of Key Physical Relationships - NO LONG DERIVATIONS! Identify assumptions, e.g. data are Poisson distributed, our calculations disregard 2nd order effects, etc... characterized by, σ i Maximizing the probability of the dataset ⇒ Mimimizing χ 2 � 2 � � y i − f ( x i ) χ 2 ν = σ i If you show present equations, you MUST identify every variable. Also try to tell what the equation MEANS!!! ◮ χ 2 ν >> 1 → Bad fit ◮ χ 2 ν << 1 → Probably overestimated errorbars on data Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 3 / 15

2nd Theory Slide...Describe limiting behaviors... A spin evolves in a magnetic field according to the µ · � Hamiltonian H = � B + H RF Free precession is R z = exp [ i ω z t σ z / 2 ] 0.7 0.6 operator distance 0.5 0.4 0.3 0.2 0.1 −0.5 0 0.5 fractional pulse error Note all text on plots should be at least 16 point! Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 4 / 15

Basic Elements of an NMR Spectrometer Don’t bombard your audience with too many details but DO identify critical elements. Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 5 / 15

Always present some of your raw data... subplot(2,2,1) subplot(2,2,2) 150 150 100 100 Counts 50 50 0 0 −50 −50 −100 0 100 200 300 −100 0 100 200 300 subplot(2,2,3) subplot(2,2,4) 150 150 100 100 Counts 50 50 0 0 −50 −50 −100 0 100 200 300 −100 0 100 200 300 Energy (MeV) Energy (MeV) Identify things like integration time, any instrumental gain and/or filtering... Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 6 / 15

And some reduced data... Fit Result Graphics Should Contain All Pertinent Information 140 a 4 = 111.7 ± 0.1 s 120 a 7 = 147.9 ± 0.1 s 100 80 Counts 60 40 2 /a 2 2 /a 2 ) y(x)=a 1 e −a 2 x +a 3 e −(x−a 4 ) + a 6 e −((x−a 7 ) 5 8 20 χ 2 ν −1 = 0.82 0 −50 0 50 100 150 200 250 300 Time(s) Explicitly state where your uncertainties come from! If residuals are significant, plot and discuss! Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 7 / 15

Muon Time of Flight Vs. Relativistic Prediction Always compare to a physical model! MCA Energy Calibration using 133 Ba 1000 Energy = (1.109 ± 0.025) × Channel − (2.149 ± 7.302) 800 Energy (MeV) 600 400 200 100 200 300 400 500 600 700 800 900 Channel Residuals 4 2 Energy (MeV) 0 −2 −4 100 200 300 400 500 600 700 800 900 Channel As you can see our data show a discrepancy at higher energies implying a poor calibration at these levels... Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 8 / 15

Results and Interpretation Give results as x = ( y . yy ± δ y s ys ± δ y r an ) 10 zz and compare to known values in terms of being so many standard deviations away... Description and Analysis of Errors, show how δ y is made up, discuss random and systematic contributions. If you’re more than 3 σ away from the known value, prepare to suggest possible systematics and persuasively argue their likely order of magnitude. What calibrations would you like to have performed... Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 9 / 15

Summary and Conclusions Does the data support your conclusions? If not, why not (speculate but be prepared to defend your reasoning!) Things you could have done better... The first main message of your talk in one or two lines. The second main message of your talk in one or two lines. Perhaps a third message, but not more than that. Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 10 / 15

Final Thoughts This template is just a guide. Slides may be added or removed based on length of talk, target audience or instructor advice. Bring a paper copy of your slides to your exam just in case you have AV difficulties. Arrive 10 minutes earlyand dress as you would for any other important public presentation. Practice, practice, practice! Fiz Cyst () 8.13/8.14 Presentation Template June 12, 2008 11 / 15