[AST201H1] - Midterm Exam Guide - Ultimate 10 pages long Study Guide!

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AST201H1
MIDTERM EXAM
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AST101 Lecture 3: Time Dilation and the Twin Paradox
The speed of light
o Light always travels at c (in a vacuum, slightly slower in air)
o No object with mass can ever reach or exceed light speed
We can only measure motion relative to a given frame of reference
The speed of light is invariantit does not change with different frames of reference
o In all frames of reference, the speed of light is the same
Foundations of special relativity
o 1) We can only measure speeds of objects relative to one another (the laws of physics
apply equally in all reference frames)
o 2) The speed of light is invariant
The fact that the speed of light is invariant results in some complicated implications and
consequences
Time literally flows at different rates for any two people in motion relative to each other
o Because two observers moving relative to each other must agree about the speed of
light, they must disagree about the time between events
o If someone is moving relative to you, their clock will appear to run slower
o This is called time dilation
Observers in motion also disagree with each other about lengths and distances
o If someone is moving relative to you, their lengths will appear to be shorter
o This is called length contraction
o This means that space and time are not separate things
Space and time are bound together by the speed of light into a single entity called spacetime
Time dilation
If someone is moving relative to you, their clock will appear to run slower
o Someone in a different reference frame will always appear to run slower
Observers in motion relative to one another also disagree about lengths and distances
o This is another way to think about time dilation
o You may think about it either as time dilation or length contractionit is, in effect, the
same thing
The twin paradox (which is’t reall a parado; it just sees that a at first)
o A thought experiment in which one twin (Stayer) stays on Earth and one travels on a
rocket ship (Zoomer) and returns to Earth to find that the twin that stayed on Earth has
aged more
o Because obserers i otio ill alas thik that the other’s clock is ruig sloer
(i.e. the other is aging slower), it appears to be a paradox
Since each twin believes the other to be aging slower, they each expect that
when they reunite on Earth that the other will be younger
However, they cannot both be correct—this create the ti parado
o In each of their reference frames, they believe the other is ageing more slowly, and they
are both correct, within their own reference frames (which is why this is called the
special theory of relativity)
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o Observers in different equivalent reference frames will not agree on times, distances,
ages, etc.
o But Zoomer, to get back to Earth, has to turn around and decelerate, while Stayer has
not had to do anything
Zoomer has switched reference frames, but Stayer has not
Similar to driving a car quickly and then suddenly changing into reverse
(you experience a sudden jerk, when you switch reference frames)
When reference frames change, all the rules are broken
When reference frames change, the perception of time suddenly
changes
Once Zoomer settle back into her new reference frame, things go back to
oral, i.e. she sees “taer’s clock as ruig sloer, ad “taer sees
Zooer’s clock as ruig sloer
After the sudden jump in time, both clocks seem to run slowly once more
Resolving the twin paradox
o It is only a paradox if we pretend that the twins are interchangeable
o However, they are not interchangeable, because Zoomer changes reference frames
when she turns around to come back home, while Stayer did not
o As Zooer sitches referce fraes, hat she sees o Zooer’s clock is coplicated; at
other ties, the each see the other’s clock as ruig sloer tha their o
o Overall, Zoomer is the one whose clock accumulates less time (so she therefore ages
less than Stayer)
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