Special Theory of Relativity. Special Relativity I Einstein’s postulates Simultaneity Time...
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Transcript of Special Theory of Relativity. Special Relativity I Einstein’s postulates Simultaneity Time...
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
III: TIME DILATIONA light clock consists of two parallel mirrors and a photon bouncing back and forth over the distance D. An observerat rest with the clock will measure a click at times
to= 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…
• 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!
to=H/c
• Effect called Time Dilation.• Clock slows by a factor of
• This is called the Lorentz factor, or
22
22
/cv-1
1 /1
c
Hcvc
H
22/cv-1
1
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
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…
• 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?
221
21
1 cVV
VVVadd