Exam 2 Flashcards
(33 cards)
What is the Lorentz Boost Factor ( gamma)
factor by which time, length and relativistic mass change for an object while it is moving
- What is the value of Lorentz boost factor when the speed of an object is small relative to the speed of light?
- when the speed gets larger than 0.5c?
- when the speed is actually 1.0c
- ?
- as velocity approaches the speed of light, denominator will be a # <1
- gamma will approach infinity
What is Tinker’s rule of thumb for measuring the time interval between 2 events?
When is it smallest?
Time between 2 events is smallest in the ref. frame where the 2 events happen in the same place (proper time)
which time (t or t prime) is the reference frame with the smallest time?
proper time ( t = t’ x gamma)
How can I go a distance of 20 years in only 15 years when my spacecraft travels at 80% the speed of light? How does this change the distance betwn the 2 planets in the ref frame of the spacecraft/
see notes
What is my rule of thumb for measuring the length of something? in which ref frame is it the longest
length of an object ( or distance) is alway maximal in the ref. frame where the object is at rest ( proper length)
proper time
proper length
t= t' x gamma L= L' x gamma
Does time dilation really occur? How does muon decay experiment provide evidence that time runs differently in different ref frames?
yes.
The half-life of a muon–> measure the # of fast moving muons there are at high altitude
-takes approx. 6 microseconds – approx. 3 half-lives – only 1/8 of muons survive reg time)
Result: when measuring high-velocity muons on the surface, # is nearly the same as # at altitude
t'= t / gamma t'= 6/10 = .6 microseconds
time dilation
2 observers disagree on time it takes for event
t’= t / gamma
length contraction
2 observers disagree on length/ distance between 2 objects
L’ = 1 x sqrt (1- (v/c)^2)
What is the twin paradox?
What is the age difference betwn the twins when they are reunited
resolution?
?
Resolution: special relativity…
Why is this a paradox? What ref. frame is moving and which is at rest? Why is time slower in one even than in the other?
?
observers on earth: non-inertial rf
observers on ship: inertial ref frame
How is length contraction relative? If two planes fly past one another, what will each pilot measure for the length of the other plane? What will they measure for the length of their own plane?
?
see notes
What is the ladder paradox? What is the resolution?
length of pole= 2x length of barn whose doors open and close simultaneously
- ladder moving nearly c –> length contraction
- its a paradox due to the ladders ref frame: ladder = stationary + barn is moving towar dit–> length contraction of barn where ladder cannot fit
Solution: both are true
Door A moving away from timer while B is moving toward.. so A opens 1st letting ladder in, and door B opens 2nd letting ladder out
What is relativity of simultaneity?
whether two spatially separated events occur at the same time – is not absolute, but depends on the observer’s reference frame.
spacetime diagram where a light ray would have a path on diagram
see notes
What is a lightcone?
What does it mean for an event to be outside the lightcone of a given object?
inside the lightcone but in the upper cone? lower cone?
lightcone= the path that a flash of light emannating from a single event (localized to a single point in space and a single moment in time traveling in all directions, would take through space and time
outside the lightcone: not causally connected
inside the light cone: causally connected
upper cone: future
lower cone: past
What is spacetime interval?
combines distances in space and in time. All observers who measure time and distance carefully will find the same spacetime interval between any two events
What is special about the quantity of the “spacetime interval”
all observers will calculate it to be the same number, no matter their reference frame.
What does E= mc^2 mean
“rest-mass energy” of a body
b/x energy + mass are interchangeable, no longer bound by “conservation of mass” & “conservation of energy” so we can convert from one to another
takes just a little bit of mass to yield a bunch of energy
*** When you burn a candle, is mass really conserves?
No
What sort of processes convert mass to energy? What are their “efficiencies”?
nuclear fusion: energy of the sun comes from small region in the center of sun –> only happens with a small fraction of those particles;; efficiency: .07 %
nuclear fission: nuclear weapons used fission of unstable heavy elements to release energy
How do I convert objects mass to energy with 100% efficiency?
when a particle encounters its anti-particles (anti-matter) the 2 particles annihlate and are converted completely to energy
electron —> positron
proton —> antiproton
What is the total energy of an object? What is the total energy when the speed of the object travels approaches the speed of light?
kinetic + rest-mass= total energy:
E= gamma x mc ^2
when body—> c, energy gets very large
v=c, energy would be infinite (why objects cant move at c
