4-vectors:

1
4-vectors Four components that Lorentz transform
like ct, x, y, z.
2
The line is a worldline for a particle that is
(in this frame) A stationary B in constant
acceleration
3
The magnitude of the 4-velocity of this particle
(in this frame) is A zero B positive C
negative
4
The 4-velocity in this frame is (c, 0, 0, 0) The
magnitude of this (its length) is c.
5
In a different frame, this particle is moving. In
the primed frame shown, is the particle moving in
the A x or B-x direction?
6
In this primed frame, what is the magnitude (i.e.
length) of the particles 4-velocity? A larger
than c, because now it has an x-component B
smaller than c, because now it has an
x-component C c
7
The magnitude of a particles 4-velocity is
invariant. Moving to a different frame mixes up
the components, just as a cartesian rotation
mixes up components.
8
In the primed frame, the size of the x-component
of the 4-velocity increased. What happens to
the size of the ct component (compared to the
particles rest frame)? A it decreases to
compensate B it increases to compensate C
it is unchanged
9
In the primed frame, the size of the x-component
of the 4-velocity increased. What happens to
the size of the ct component (compared to the
particles rest frame)? B it increases to
compensate Because of the minus sign in our
length formula, d(ct)/d? must be larger than c.
In other words, t is larger than ? no
surprise, really, since the proper time is the
slowest clock.
10
Just as we sometimes draw velocity vectors on a
plot of object positions, we can draw
4-velocities on a spacetime diagram. What is
the direction of the 4-velocity vector for the
particle we have been discussing, on the diagram
shown? A straight down B straight up C
parallel to the ct axis for the unprimed frame,
but parallel to ct for the primed frame
11
A worldline is a worldline is a worldline -
Gertrude Stein (maybe?) Its the same worldline,
so a small piece of it, divided by an invariant
number, is the same 4-vector for all observers
straight up in this diagram.
12
Since the length of a 4-vector is invariant, the
length of your 4-velocity vector is the same
regardless of how fast you move!(That makes
sense there is always a frame where you are
stationary!)If you are moving, both the time
and the space components increase.
13
Which 4-vector is longest?Or choose E they
are the same length
14
4-momentum