Special Relativity
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1
What is the difference between the frames of reference S and S'?
S' moves in the +ve x direction with speed v relative to S
2
When can you use a galilean transform
When v is small
3
When can you use a lorentz transform?
When v is large
4
What are the formulas for x', y', z', t' in galilean relativity?
x' = x - vt
y' = y
z' = z
t' = t
y' = y
z' = z
t' = t
5
What is the formula for u' in galilean relativity?
u' = u - v
6
What is the formula for $\beta$ in special relativity?
$\beta = \frac{v}{c}$
7
What is the formula for $\gamma$ in special relativity?
$\gamma = (1 - \beta^2)^{-1/2}$
8
What are the formulas for x', y', z', t' in special relativity?
$x' = \gamma (x - vt)$
$y' = y$
$z' = z$
$t' = \gamma (t - \beta x)$
$y' = y$
$z' = z$
$t' = \gamma (t - \beta x)$
9
What is the formula for u' in special relativity?
$u' = \frac{u - v}{1 - \frac{uv}{c^2}}$
10
What is the assumption whe using galilean/lorentz transforms?
S and S' overlap at (0, 0, 0, 0)
11
Clock synchronisation?
Dont think this is assesed
12
What is an event on a spacetime diagram?
A point with an associated time and position
13
What do angled lines represent on a spacetime diagram?
World lines of moving objects
14
What do vertical lines represent on a spacetime diagram?
World lines of stationary objects
15
What angle does an obect moving with speed c, have on a spacetime diagram?
$\frac{\pi}{4}$
16
When are two events simultaneous in a spacetime diagram?
When they have the same ct coordinate
17
What does the relativity of simultaneity suggest?
Events simulataneous in one fram are not necessarily simultaneous in another frame
18
What is the formula for time dilation?
$\Delta t' = \gamma \Delta t$
19
What is the formula for proper time?
$\tau = t_B - t_A$
20
What is the formula for length contraction?
$L' = v \Delta t'$
21
What is the formula for proper length?
$L = L' \gamma$
22
What is the formula for the spacetime interval of 2 events in S?
$(\Delta S)^2 = (c\Delta t)^2 - (\Delta x)^2 - (\Delta y)^2 - (\Delta z)^2$
23
What is the formula for the spacetime interval of 2 events in S'?
$(\Delta S')^2 = (\Delta t')^2 - (\Delta x')^2 - (\Delta y')^2 - (\Delta z')^2$
24
What is the relation between $(\Delta S)^2$ and $(\Delta S')^2$?
$(\Delta S)^2$ = $(\Delta S')^2$
25
What do we call 2 events with spacetime interval > 0?
time-like interval
26
What do we call 2 events with spacetime interval = 0?
light-like interval
27
What do we call 2 events with spacetime interval < 0?
space-like interval
28
What question can be asked for this?
29
What is the formula for the recieved frequency in the receding longitudinal doppler effect?
$f = f_0 \sqrt{\frac{1 - \beta}{1 + \beta}}$
30
What is the formula for the recieved frequency in the approaching longitudinal doppler effect?
$f = f_0 \sqrt{\frac{1 + \beta}{1 - \beta}}$
31
What is the formula for the recieved frequency in the transverse doppler effect in observers rest frame?
$f = f_0 \sqrt{1 - \beta^2}$
32
What is the formula for the recieved frequency in the transverse doppler effect in emitters rest frame?
$f = f_0 \sqrt{1 - \beta^2}$