Title: InkPhysics / Turning points
On every note of this deck, unless a note says otherwise:
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Front: DEFINITION
Define: Proper time.
Back: The time between two events measured in the frame where they happen at the same place: the shortest time any observer records, t₀.

Front: CHECK YOURSELF
State the two postulates of special relativity, and explain which one the Michelson-Morley result supports and how.
Show a hint
The fringes that refused to move are a statement about one particular speed.
Back: One: physical laws have the same form in all inertial frames. Two: the speed of light in free space is invariant, the same for every inertial observer.
The null result supports the second. The two beams' round trips tied exactly, whatever the Earth's motion through space and however the arms were oriented.
So the measured speed of light does not depend on the motion of the apparatus carrying the source and detector, which is precisely the invariance the second postulate asserts.

Front: DEFINITION
Define: Specific charge of the electron.
Back: The electron's charge divided by its mass, e/m: Thomson measured it at about 1800 times hydrogen's, the first evidence for a particle smaller than an atom.

Front: CHECK YOURSELF
Explain why Young's 1801 experiment did not immediately overturn the corpuscular theory, and name the two later results that settled the wave theory's victory.
Show a hint
One reason is about people; the two results are a speed comparison and a prediction confirmed.
Back: Newton's authority kept the corpuscular theory respectable, and one experiment, however clean, was not enough to displace a century of consensus: acceptance of the wave picture was delayed for decades.
Measurements descended from Fizeau's method showed light travelling slower in water than in air, as the wave theory required and the corpuscular theory contradicted.
Maxwell's c = 1/√(μ_0ε_0) matched the measured speed of light, and Hertz then produced electromagnetic waves directly, at that same speed: light was a wave, and an electromagnetic one.

Front: DEFINITION
Define: Inertial frame of reference.
Back: A frame moving at constant velocity, in which Newton's first law holds.

Front: CHECK YOURSELF
A droplet weighing 3.84 × 10^−14 N hangs stationary between plates 6.0 mm apart with 480 V across them. Find the droplet's charge, and state how many electrons' worth it carries.
Show a hint
Rearrange QV/d = mg for Q; the weight mg is given whole.
Back: Q = (weight × d)/V = (3.84 × 10^−14 × 6.0 × 10^−3) / 480 = 4.8 × 10^−19 C.
4.8 × 10^−19 / 1.6 × 10^−19 = 3: the droplet carries three electrons' worth of charge.
A non-integer answer here means an arithmetic slip, and that check, whole numbers or nothing, is Millikan's discovery in miniature.

Front: CHECK YOURSELF
In a low-energy electron diffraction experiment the accelerating pd is doubled. Explain what happens to the ring pattern, and why an electron microscope can resolve detail no light microscope can reach.
Show a hint
Follow the chain pd, momentum, wavelength, and remember resolution follows wavelength.
Back: Doubling V multiplies the momentum by √2, so λ = h/p falls by a factor of √2, and the rings shrink by that factor: faster electrons, shorter waves, tighter pattern.
Resolution is limited to roughly the wavelength used. Electrons at even 150 V carry λ ≈ 10^−10 m, thousands of times shorter than visible light's 5 × 10^−7 m.
So an electron microscope resolves atomic-scale structure that no arrangement of glass lenses ever could: wave-particle duality, turned into an instrument.

Front: DEFINITION
Define: Rest mass.
Back: The mass of an object measured in the frame where it is at rest: m₀.

Front: CHECK YOURSELF
Show that the classical formula eV = ½mv² predicts electrons reaching the speed of light at an accelerating pd of about 260 kV, and comment on what this suggests.
Show a hint
Set v = c and solve for V using e/m = 1.76 × 10^11 C kg^−1.
Back: V = v^2/(2e/m) = (3.0 × 10^8)^2 / (2 × 1.76 × 10^11) = 2.6 × 10^5 V: about 260 kV.
Laboratory supplies exceed this easily, yet no electron has ever been observed at or beyond the speed of light.
So the classical formula must fail at high speeds. What actually happens near 260 kV, and why, is the business of this unit's relativity lessons.

Front: CHECK YOURSELF
A spacecraft passes Earth at 0.60c. Its on-board clock records 100 s between two ticks, and its proper length is 50 m. Find the time between those ticks and the craft's length as measured from Earth, and state which measurement each observer would call "correct".
Show a hint
The root is √(1 − 0.36) = 0.80; decide which quantity dilates and which contracts.
Back: Time: the ticks happen at the ship, so 100 s is proper time, and Earth measures t = 100/0.80 = 125 s: the moving clock runs slow.
Length: 50 m is proper length, and Earth measures l = 50 × 0.80 = 40 m, contracted along the motion.
Both are correct. Each observer's measurements are right in their own inertial frame; relativity's content is precisely that these quantities are frame-dependent, with the proper values belonging to the frame riding with the clock and the rule.

Front: EQUATION — NOT ON THE DATA SHEET
The balanced oil drop:
QVd = ?
Back: QVd = mg