Special Theory of Relativity

Special Relativity I Einstein’s postulates Simultaneity Time dilation Length contraction New velocity addition law

I: EINSTEIN’S POSTULATES OF RELATIVITY Postulate 1 – The laws of nature are the same in all inertial frames of reference Postulate 2 – The speed of light in a vacuum is the same in all inertial frames of reference. Let’s start to think about the consequences of these postulates. We will perform “thought experiments” (Gedankenexperiment)… For now, we will ignore effect of gravity – we suppose we are performing these experiments in the middle of deep space

I. Invariance of the speed of light

II. Simultaneity

III: TIME DILATION A light clock consists of two parallel mirrors and a photon bouncing back and forth over the distance D. An observer at rest with the clock will measure a click at times Dto= 2H/c

Now suppose we put one clock on a train or spaceship that is cruising (at constant velocity, v) past us. How long will it take the clock to “tick” when its in the moving spacecraft? Use Einstein’s postulates…

Now suppose that we put the clock on a platform sliding at constant speed v. d H vDt d2=H2+(vDt/2)2

Clock appears to run more slowly. But, suppose there’s an astronaut in the spacecraft the inside of the spacecraft is also an inertial frame of reference – Einstein’s postulates apply… So, the astronaut will measure a “tick” that lasts So, different observers see the clock going at different speeds! Time is not absolute! Dto=H/c

Effect called Time Dilation. Clock slows by a factor of This is called the Lorentz factor,  or G

Lorentz factor

Examples of time dilation [We will work through these examples on the white board during the class] Fast moving spacecraft The Apollo mission to the Moon Clocks flown in airliners Normal everyday life The Muon Experiment The jet in the galaxy M87

The jet in M87

IV: LENGTH CONTRACTION Consider two “markers” in space. Suppose spacecraft flies between two markers at velocity v. Compare what would be seen by observer at rest w.r.t. markers, and an astronaut in the spacecraft…

Length contraction… also called So, moving observers see that objects contract in the direction of motion. Length contraction… also called Lorentz contraction FitzGerald contraction Consider Muon experiment again, this time from point of view of the Muons i.e. think in frame of reference in which Muon is at rest Decay time in this frame is 2 s (2/1000,000 s) How to they get from top to bottom of Mountain before decaying?

From point of view of Muon, Mountain’s height contracts by factor of  Muons can then travel reduced distance (at almost speed of light) before decaying.

New velocity addition law Once we’ve taken into account the way that time and distances change, what’s the new law for adding velocities?