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IB Physics Option A. Relativity Questions and Answers
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IB Physics Option A. Relativity
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IB Physics Option A. RelativityInertial Frame of Reference - answerA frame in which an object obeys Newton's first law
(travels at a constant velocity because no external force its on it)
Boost - answerOne frame moves relative to another frame with a constant relative
velocity
Galilean Transformations - answerthe set of equations that link two reference frames by
their relative velocity (x' = x - X, x = x' + vt, and u' = u - v)
Newton's Postulates - answerSpace and time are fixed and absolute (this is wrong)
Two observers in separate inertial frames must make the same observations of the
world, the laws of physics will hold for both frames (also postulated by Einstein)
Maxwell's Four Equations - answerIncorporate the value of the speed of light (in free
space) in a fundamental way, so that the speed of light is constant for all observers
Einstein's First Postulate (of Special Relativity) - answerThe laws of physics are the
same in all inertial reference frames
Einstein's Second Postulate (of Special Relativity) - answerThe speed of light (in a
vacuum) is the same in all inertial reference frames
Lorentz Factor - answer
Spacetime Interval - answer∆s: the quantity, ct, an invariant quantity that has
dimensions of length and is defined for motion in the x direction as ∆s² = (c∆t)² - ∆x²
Rest Mass - answerAn invariant quantity, m₀, the mass of a particle in the frame in
which the particle is at rest
Proper Time - answerAn invariant quantity, ∆t₀, the time interval in the stationary frame
(the frame where the events occur at the same position.) The shortest possible
measured time interval between two events.
Light Clock - answerConsists of two mirrors facing each other across a room. An
observer sits at rest in the room and watches light reflect between the mirrors. The time
light takes to pass between the mirrors is t=2L/c if the distance between the mirrors is L.
, Time Dilation - answerTime measured in a moving frame is always longer than the time
measured in a frame stationary relative to the clock t' = γt₀
Proper Length - answerAn invariant quantity, L₀, the length of an object measured by an
observer at rest relative to the object. The measurements of its ends must be made
simultaneously. it is the longest measured length that can be determined for an object
Length Contraction - answerLength measured in a moving frame is always shorter than
length measured in a frame stationary relative to the measuring device L₀ = L/γ
Muon Explanation (for time dilation and length contraction) - answerMuons are created
in the upper atmosphere when cosmic rays strike air molecules. They have very short
mean lifetimes (about 2.2µs) and travel at 0.98c. In one lifetime, they can travel about
660 m. Since the distance from Earth's surface to the upper atmosphere is 10 km, (on a
Newtonian basis,) very few muons would be expected to the reach the surface of Earth
(since that would take 15 lifetimes). However, many muons do make it.
With time dilation: at 0.98c, γ=5 so in Earth's reference frame, the mean lifetime
becomes 11µs. The time needed to travel 10 km is 33µs, so a significant number of
muons will remain undecided at the surface.
With length contraction: in the muon's reference frame, the 10 km/γ becomes 2 km,
which is only 3 mean lifetimes, so many more muons make it.
Clock Synchronization - answerSynchronize both clocks when they are close together
and then gradually move on to its final position so that they (approximately) share a
reference frame with each other. Or, have both clocks at their final positions and use a
third clock moving slowly between them to transfer the times from one to the other (<--
but this method is stupid)
Charges and Currents Explanation - answerA stationary observer sees a moving
positive test charge experience a repulsive force due to the magnetic field created by
the moving charges in the current-carrying wire.
From the test charge's frame of reference, the electrons in the wire are stationary, but
the positive charges are moving (but since the charge is "not moving" it won't
experience a magnetic force). Instead, the positive charges in the wire experience a
contraction in their spacing, creating a net positive, so a repulsive electrostatic force
acts on +q.
Spacetime Diagram (Minkowski Diagram) - answerA graphical representation of four
dimensional spacetime. They show the position of an object in one dimension (x) at a
time (t) in an inertial frame. The axes constitute the inertial frame. (Time on one axis,
position on the other, swag on both)
Worldline - answerTrajectory of a particle through spacetime
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