 |
Project Context |
|
Getting a Handle on the Problem
We have two complementary approaches to the E, P and M question. In the first, we use historical data compiled at the beginning of the 20th century by Kaufmann and Bucherer for the energies and momenta of electrons (Shankland, Robert S., Atomic and Nuclear Physics, pp. 33-36, MacMillan, New York, 1955). Kaufmann and Bucherer did not have powerful accelerators available, however, owing to the low-rest energy of the electron, they were able to produce respectable graphs which illustrated the predications of relativity well. Note that Kaufmann did his work beforeEinstein announced the Special Theory of Relatvity in 1905!
We have also compiled Monte-Carlo data for a hypothetical test beam experiment in a GeV-range proton accelerator. In this experiment, protons of kinetic energies up to about 8 GeV are fired into a 3 Tesla magnetic field. (If you have the kinetic energy, how do you find total energy E?) By the amounts the protons are deflected in the magnetic field, we can determine their momenta. We provide both simulated tracks in the magnetic field and kinetic energy data. As in the Kaufmann-Bucherer experiment above, you ought to be able to use this data to relate E, P and M, provided you know the rest energy of the proton.
The links below direct you to the two complementary sets of data. To complete your study of the energy-momentum relationship, try to answer the questions below:
Questions to Consider
- Were the two sets of data consistent in showing the form of the relationship between E, P, and M?
- Are you able to write an equation that works for both data sets?
- In general, can you describe the relationship between E, P, and M?
- At low energies, is the rest energy of the accelerated particle important?
- Why do we often refer to momentum and energy almost interchangeably in discussing high-energy accelerators like the Tevatron and the LHC?
|
|
|