Special Relativity Physics 12 Adv

Einstein’s Postulates  In 1905, while working as a patent clerk in Switzerland, Einstein published his paper on Special Relativity  While the implications of this paper have been far reaching, the basis of the theory revolves around two postulates

Einstein’s Postulates 1.The laws of Nature, the ways in which things behave, are the same in all inertial systems regardless of their speeds. 2.The speed of light in a vacuum is completely independent of the motion of the source emitting it.

Thought Experiment 1  We have previously discussed the concept of a clock and will now use the nature of how we observe a clock to investigate the behaviour of special relativity  Draw a diagram that shows an observer watching a clock that is in their reference frame and determine the time it takes for the observer to see a given event to occur

Thought Experiment  Now, draw a picture that shows what a stationary observer would see if a clock is moving past them with some velocity v. Again, develop an equation for the time taken for an observer to be able to measure an event  Compare the result for the first and second clock

Time Measured by an Observer in the Frame of Reference of the Clock

Time Measured by an Observer outside the Frame of Reference of the Clock  Solve for the time taken for light to travel from A to B to C

Time Measured by an Observer outside the Frame of Reference of the Clock

Time Dilation Effects  For an object traveling at 30.0m/s  For a satellite traveling at 3.874x10 3 m/s  For an electron orbiting the nucleus at 2.7x10 8 m/s  1s:1s  1s: s  1s:0.44s

Wait a second…  Muons are particles that are created high in the atmosphere due to UV radiation and have a halflife of approximately 2μs  These particles are created about 9000m above the surface of the Earth and travel at about 0.998c  Determine the number of muons remaining from an original sample N at the surface of the Earth

Wait a second…  However, observations show that a significant number arrive at the surface of the Earth; approximately the number that should remain after one halflife  How fast would muons have to travel in order for this number of muons to arrive at the surface of the Earth  As this poses a problem, how could we fix it?

Length Contraction  A concept related to time dilation is that of length contraction  In a way that is similar to time changes depending on the frame of reference, length is also affected  This can be used to explain the behaviour of the muon

Muon  Time Dilation –According to time dilation, the muon’s half-life (measured in the frame of reference of the Earth) should be 30μs in the muon’s frame –As a result, the muon can travel a.998c for 30μs covering a distance of 9000m

Muon  Length Contraction –According to length contraction, the distance that the muon needs to move through (measured in the frame of reference of the Earth) should be 600m in the muon’s frame –As a result, the Earth rushes towards the muon at.998c for 2μs covering a distance of 600m

Problems  Page 819 –1-3  Page 824 –4-6