Lesson 3: Consequences of Special Relativity
Overview:
In the past two sections, you learned how special relativity contradicts the concept of absolute time in Newtonian mechanics. Measurements of time intervals are relative, in that they can be different for different observers. However, time is just one aspect of a reference frame; reference frames also involve measurements of position and length. How are these measurements affected by relativity?
Curriculum Expectations:
Overall Expectations:
F2. Investigate special relativity and quantum mechanics, and solve related problems.
Specific Expectations:
F2.1 Use appropriate terminology related to quantum mechanics and special relativity, including, but not limited to: quantum theory, photoelectric effect, matter waves, time dilation, and mass–energy transformation.
F2.3 Solve problems related to Einstein’s theory of special relativity in order to calculate the effects of relativistic motion on time, length, and mass (e.g., the half-life of cosmic ray muons, how far into the future a fast space ship would travel, the magnetic field strength necessary to keep protons in the Large Hadron Collider).
F2.4 Conduct a laboratory inquiry or computer simulation to analyse data (e.g., on emission spectra, the photoelectric effect, relativistic momentum in accelerators) that support a scientific theory related to relativity or quantum mechanics.
F2. Investigate special relativity and quantum mechanics, and solve related problems.
Specific Expectations:
F2.1 Use appropriate terminology related to quantum mechanics and special relativity, including, but not limited to: quantum theory, photoelectric effect, matter waves, time dilation, and mass–energy transformation.
F2.3 Solve problems related to Einstein’s theory of special relativity in order to calculate the effects of relativistic motion on time, length, and mass (e.g., the half-life of cosmic ray muons, how far into the future a fast space ship would travel, the magnetic field strength necessary to keep protons in the Large Hadron Collider).
F2.4 Conduct a laboratory inquiry or computer simulation to analyse data (e.g., on emission spectra, the photoelectric effect, relativistic momentum in accelerators) that support a scientific theory related to relativity or quantum mechanics.
Success Criteria:
- Define proper length.
- From the formula of time dilation, derive length contraction.
- Describe length contraction and include a picture and description along which direction contraction occurs.
- Define relativistic length.
- Describe what happens to the ratio of relativistic length to proper length as (i) v=0, (ii) v=c and (iii) v>c.
- How do muons help provide evidence of Einstein's theory of special relativity.
- Is the speed of light the universal speed limit?
Time Allocation: 4 hours
Learning Activities:
Read pages 588 - 596 from Nelson 11.3 and copy the sample problems into your notes.
In the playlist below, video:
- Will show you how to find the velocity of an 1m ruler that appears to be an 1ft ruler by an observer as it zooms by near the speed of light.
- Will show you how to find how long a particle of muon would exist on a spaceship traveling at 0.9c (speed of light).
Practice questions 2 and 3 on page 591.
Task:
Solve questions 1 Nelson 11.3 Review on page 597.
Quiz Chapter 11 on Moodle.
Quiz Chapter 11 on Moodle.
Reflect:
Identify Einstein’s two postulates for the theory of special relativity, and describe the evidence supporting the theory (e.g., thought experiments, half lives of elementary particles, relativistic momentum in accelerators, the conversion of matter into energy in a nuclear power plant).
Additional Resources:
Magnetism seems like a pretty magical phenomenon. Rocks that attract or repel each other at a distance - that's really cool - and electric current in a wire interacts in the same way. What's even more amazing is how it works. We normally think of special relativity as having little bearing on our lives because everything happens at such low speeds that relativistic effects are negligible. But when you consider the large number of charges in a wire and the strength of the electric interaction, you can see that electromagnets function thanks to the special relativistic effect of length contraction. In a frame of reference moving with the charges, there is an electric field that creates a force on the charges. But in the lab frame, there is no electric field so it must be a magnetic field creating the force. Hence we see that a magnetic field is what an electric field becomes when an electrically charged object starts moving.
