Certainty and Uncertainty in Physics Research

1
Certainty and Uncertainty in Physics Research

• Vocabulary of uncertainty
• The need to keep track of uncertainties
• Systematic vs statistical
• Some examples

2
The vocabulary of uncertainty

• Accuracy is correctness closeness to the truth
• Precision is relative uncertainty
• Error can be, without qualification, interpreted
  as a mistake (AKA blunder)
• Error can also be a type of uncertainty.
• Uncertainty is a measure of being unsure it
  gives a probability of being close to the truth

3
Some examples of sentences

• The calculation is accurate to 3 decimal
  places. (this means, not accurate at 4 or more)
• measured to 3.2 ppm precision. (this is how
  relatively well the authors think they have
  determined the quantity)
• The error from reading the dial is 0.2 V (this
  is not an uncertainty, this is an incorrect
  reading, a bias, which can be corrected for if it
  is understood)
• The uncertainty in the reading of the dial is
  0.2 V. (this is a systematic error, to be
  included in the final quoted result)
• Systematic and statistical errors are combined
  in quadrature. (see later, but possible if
  there is no correlation)

4
Things to consider as you perform your summer work

• Each time you measure something, try to repeat it
  and analyze the distribution of results
• This will give you a feeling of the
  reproducibility of your equipment or technique.
  If its really good, you dont have to keep doing
  this. If it varies a lot beware of physics
  conclusions you draw
• If you are doing statistical work for your
  summer projects, learn some of the basics
• There are many books (e.g., Bevingtons Data
  Reduction and Error Analysis for the Physical
  Sciences) and I wont go through these issues
  today
• Next semester, your senior theses should discuss
  the uncertainties associated with your work.
• Plan to keep track of these as you pursue your
  summer projects (use your new lab notebooks!)

5
In more detail

• Keep track of where the uncertainties are in your
  project as you go
• Are they in the assumptions associated with your
  model?
• Are they in the alignment of the apparatus?
• Are they in the counting statistics?
• Are they in the reproducibility of performing the
  same procedures?
• Are they in the optical element quality?
• Are they in the backgrounds?
• For the Fall Include a discussion of these
  issues in your senior theses
• We can discuss what you find together

6
Systematic uncertainties

• Laser alignment
• Laser power stability
• Optical alignment
• Temperature and equipment drift vs T
• Differences in sample quality
• difficulty in not having homogeneous solutions
  of nanoparticleseach one differs a bit from the
  last
• etc., etc.

7
Statistical errors

• Books exist on handling these and many recipes
  exist for propagating uncertainty
• Data Reduction and Error Analysis for the
  Physical Sciences, P. Bevington and K. Robinson,
  McGraw Hill
• Particle Data Group,
• Generally, is a benchmark to keep in
  mind as uncertainty
• Final errors often combine statistical and
  systematic
• Can it be done in quadrature ?
• This only works if the sources of errors are
  uncorrelated.

8
Conclusions

• Like it or not, your work has uncertainty
• Identify it
• Describe it
• Draw you conclusions based on your findings and
  on your uncertainties.
• INCLUDE a discussion of this in your thesis and
  in your future scientific writing