Welcome to Grad Lab - Astronomyspringer/phys6719/readings/lecture1.pdf · Experiment 1: Geiger...
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Welcome to Grad Lab John Belz, Hiroki Morishita January 10, 2012
Transcript of Welcome to Grad Lab - Astronomyspringer/phys6719/readings/lecture1.pdf · Experiment 1: Geiger...
Welcome to Grad Lab
John Belz, Hiroki MorishitaJanuary 10, 2012
10 January 2012 Physics 6719, Lecture 1 2
My View of this Course:
● Transition between classroom and “real-world” physics.
● Perform (to the extent possible) all aspects of the experimental cycle.
● We will– Research physics and equipment– Perform experiments– Write papers– Give talks
10 January 2012 Physics 6719, Lecture 1 3
10 January 2012 Physics 6719, Lecture 1 4
10 January 2012 Physics 6719, Lecture 1 5
3 Experiments● Experiment 1: Geiger Counter and Counting Statistics
● Experiments 2 and 3 chosen from:
– “High-Energy” Experiments:● Cosmic ray muon lifetime● Compton scattering● Alpha particle spectroscopy● Gamma-ray angular correlations
– “Low-Energy” Experiments:● Nuclear magnetic resonance● Low-temperature specific heat of copper● Hall effect● Zeeman effect
10 January 2012 Physics 6719, Lecture 1 6
Schedule for Lectures● 1/10; Course intro, lab guidelines, error
propagation● 1/13; Probability distributions
– Binomial – Poisson– Gaussian
● 1/17; 2 and interpretation of results
● 2/10; Exam review, practice problems● 2/14; Error and Data Analysis Exam
10 January 2012 Physics 6719, Lecture 1 7
Laboratory and Lab Report Guidelines
10 January 2012 Physics 6719, Lecture 1 8
Experiment Timetable● Week 1:
– Become familiar with experiment– Do “prelab” research– Begin taking data
● Week 2: – Perform experiment– Begin analysis
● Week 3: – Wrap up data taking– Write paper
10 January 2012 Physics 6719, Lecture 1 9
Week 1: Prelab Questions
● See overviews of experiments at: http://www.physics.utah.edu/~belz/phys6719/experiments.html
● Goal of prelab research: understand...
– physics motivation– understanding of analysis– sources of uncertainty
● Nothing to submit, but use as a guide in writing up experiment.
10 January 2012 Physics 6719, Lecture 1 10
Performing Experiment● Plan to work during assigned lab time.
Instructor availability will be limited otherwise.
● Allow for some “contingency time”. – Some experiments require a long time to
take data– You may find during analysis that you need
to take additional data
● All work, calculations, data should be recorded legibly in your lab notebooks
10 January 2012 Physics 6719, Lecture 1 11
Lab Notebooks● We will use large “blue books”
● Entries should be made according to the Rutherford Rules
– Dated– In ink– Strike out errors with a single line
● Notebook should be a record of all your doings in lab. All statements of fact in your papers must be substantiated either in your lab notebook or in an external reference.
● Turn in notebooks with final papers
10 January 2012 Physics 6719, Lecture 1 12
Final Week: Write Paper
● Four pages; Physical Review format (LaTex template and examples on course web page)
● Include the following sections
– Abstract (1 set-aside paragraph, summarizing paper)
– Introduction (1-2 paragraphs)
– Experiment (diagrams,schematics)
– Analysis (include data, figures, results)
– Discussion (evaluate your results, compare expectation)
– Conclusion (1 short paragraph)
– List of References/Citations
● Due first meeting after Week 3
10 January 2012 Physics 6719, Lecture 1 13
Experimental Errors and their Propagation
10 January 2012 Physics 6719, Lecture 1 14
Uncertainties in Experimental Physics
● Undergraduate physics:– 90% of time is spent measuring
central value– Compare to “accepted value”– Tack on experimental uncertainty as an
afterthought, if at all.
● Grad Lab (and the rest of your careers):– Most of time spent understanding uncertainty– Before you even touch equipment!– Is experiment worth doing? Will someone fund it?
10 January 2012 Physics 6719, Lecture 1 15
Terminology...
● Accuracy: How close to True value?
● Precision: What is the spread you'd see in repeated measurements?
10 January 2012 Physics 6719, Lecture 1 16
More terminology...
● Random or Statistical Error:
● Systematic Error:
10 January 2012 Physics 6719, Lecture 1 17
More terminology...
● Random or Statistical Error: Can be reduced by taking more measurements
● Systematic Error: Cannot be reduced by taking more measurements
● Q: When is an experiment “finished”?
10 January 2012 Physics 6719, Lecture 1 18
10 January 2012 Physics 6719, Lecture 1 19
Stop here!
10 January 2012 Physics 6719, Lecture 1 20
10 January 2012 Physics 6719, Lecture 1 21
10 January 2012 Physics 6719, Lecture 1 22
Quantifying Expected Deviation
Mean of N measurements of x
R.M.S. Or “Population Std. Dev.”
Error in the mean
“Sample Std. Dev.”
10 January 2012 Physics 6719, Lecture 1 23
● Calculate the RMS, SSD and Error in the Mean for the set of experimental measurements x = 7, 3, 6, 4, 5
● What value (with uncertainty) should be reported as the best estimate of the true value of x, given these experimental results?
10 January 2012 Physics 6719, Lecture 1 24
● “Error in the Mean”: Random uncertainty in your knowledge of the True value of x.
● “Standard Deviation” Random uncertainty in a single measurement of x.
10 January 2012 Physics 6719, Lecture 1 25
Propagation of Uncertainties
10 January 2012 Physics 6719, Lecture 1 26
Propagation of Uncertainties
Where is this from?
10 January 2012 Physics 6719, Lecture 1 27
● Consider function of one variable f(x)
● Assume errors small, so f(x) ~ linear
10 January 2012 Physics 6719, Lecture 1 28
● Consider function of one variable f(x)
● Assume errors small, so f(x) ~ linear
Generally we expresserrors as positive, so...
10 January 2012 Physics 6719, Lecture 1 29
● Now, what about multivariate functions e.g. f = f(x,y)?
● Assume errors small, so f(x) ~ linear
10 January 2012 Physics 6719, Lecture 1 30
● e.g. Measure the heights x and y of two people
● What is the uncertainty in the sum of heights q=x+y?
10 January 2012 Physics 6719, Lecture 1 31
● e.g. Measure the heights x and y of two people
● What is the uncertainty in the sum of heights q=x+y?
?
10 January 2012 Physics 6719, Lecture 1 32
Consider Two Cases:
● x and y have correlated errors (e.g. ruler is off)
● Expression above gives upper bound to errors
● x and y have uncorrelated errors
● Expression above overestimates error
?
10 January 2012 Physics 6719, Lecture 1 33
How do we correctly treat functions of two (or more)
variables?
10 January 2012 Physics 6719, Lecture 1 34
10 January 2012 Physics 6719, Lecture 1 35
Zero Covariance
Positive Covariance Negative Covariance
Covariance:
10 January 2012 Physics 6719, Lecture 1 36
Propagation of Uncertainty (neglecting correlations)
10 January 2012 Physics 6719, Lecture 1 37
10 January 2012 Physics 6719, Lecture 1 38
● QUICK: What is uncertainty in F?
10 January 2012 Physics 6719, Lecture 1 39
● QUICK: What is uncertainty in F?
● B has 10% relative uncertainty
10 January 2012 Physics 6719, Lecture 1 40
● QUICK: What is uncertainty in F?
● B has 10% relative uncertainty
● All others have 1% or less
10 January 2012 Physics 6719, Lecture 1 41
● QUICK: What is uncertainty in F?
● B has 10% relative uncertainty
● All others have 1% or less
● F has ~ same relative uncertainty as B: S
F ~ 15
10 January 2012 Physics 6719, Lecture 1 42
Additional Reading and Problems(Practice for E&DA Exam)
● Read in Taylor: – Ch 3: Propagation
of Uncertainties– Ch 4: Statistical
Analysis of Random Uncertainties
– Ch 9: Covariance and Correlation
● Try the problems:– Prove the relations
on slide #34, 36– 3.1, 3.2, 3.4, 3.15,
3.24– 4.6, 4.8, 4.19, 4.28– 9.2, 9.4, 9.8, 9.16
