## Lesson 2: Time Dilation

## Overview:

It is difficult to believe in Einstein's theories, but you need to keep in mind that they are a logical proof that bullies you into agreeing with them. In this lesson, you will experience the awesomeness that is Einstein's thinking.

## Curriculum Expectations:

**Overall Expectations:**

**F2.**Investigate special relativity and quantum mechanics, and solve related problems.

**F3.**Demonstrate an understanding of the evidence that supports the basic concepts of quantum mechanics and Einstein’s theory of special relativity.

**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.

**F3.3**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).

## Success Criteria:

- Define time dilation.
- How does a light clock measure time? Draw a diagram in your explanation.
- How does the motion of a train moving at uniform motion of 0.95c train affect the operation of the light clock while inside the train's frame of reference?
- How does the motion of a train moving at uniform motion of 0.95c train affect the operation of the light clock relative to an observer who is at rest?
- Derive the mathematical expression for relativistic time.
- Explain the concept of relativistic time.
- Does the time dilation equation apply to biological processes.
- Describe how the time dilation equation changes as the speed of the moving frame is: (i) v=0, (ii) 0<v<c, (iii) v=c, and (iv) v>c.
- What does the term for proper time measure?
- Describe how the Hofde-Keating experiment is used to verify time dilation.
- Describe how GPS is used as an application of time dilation.

## Time Allocation: 3 hours

## Learning A

ctivities:**Read**pages 580 - 586 from Nelson 11.2 and

**copy the sample problems**into your notes.

In the playlist below, video:

- Will show you how to find how time changes for an observer traveling at 0.995c (speed of light).
- Will show you how to find the speed of a rocket traveling at 0.8c, speed of light, seen by an observer on Earth.
- Will show you how to find the relative speed of rocket B as seen by an observer on Earth when rocket A is traveling at 0.6c and rocket B is traveling at 0.8c.

**Practice**questions 1, 2 and 3 on page 585.

## Task:

**Solve**questions 2, 3, 6 and 7 from Nelson 11.2 Review on page 587.

## Reflect:

If the equation for time dilation is true (and experiments have conclusively shown that it is), why have you not noticed time dilation before now?