A PARADIGM SHIFT 219
Hendrik Lorentz, whose “Lorentz
factor” lay at the heart of Einstein’s
description of physics close to the
speed of light. It is defined
mathematically as:
Lorentz developed this equation to
describe the changes in time and
length measurements required in
order to reconcile the Maxwell
equations of electromagnetism
with the principle of relativity.
It was crucial to Einstein since it
provided a term for transforming
results as seen by one observer to
show what they look like to another
observer who is in motion relative
to the first observer. In the term
quoted above, v is the speed of one
observer compared to the other,
and c is the speed of light. In most
situations, v will be very small
compared to c, so v^2 /c^2 will be close
to zero, and the Lorentz factor
close to 1, meaning that it makes
almost no difference to calculations.
Lorentz’s work had been coolly
received, largely because it
could not be incorporated into
standard ether theories. Einstein
approached the problem from the
other direction, showing that
the Lorentz factor arose as an
inevitable consequence of the
principle of special relativity and
reexamining the true meaning
of measured time and distance
intervals. An important result of
this was the realization that events
that appeared simultaneous for an
observer in one reference frame
were not necessarily so for
someone in a different reference
frame (a phenomenon known as
the relativity of simultaneity).
Einstein also showed how from
the point of view of a distant
observer, the length of moving
objects in their direction of travel
became compressed as they
approached the speed of light, in
accordance with a simple equation
governed by the Lorentz factor.
Even more strangely, time itselfappears to run more slowly as
measured from the observer’s
reference frame.Illustrating relativity
Einstein illustrated special
relativity by asking us to consider
two frames of reference in motion
relative to each other: a moving
train and the embankment next
to it. Two flashes of lightning, at
points A and B, appear to occur
simultaneously to an observer
standing on the embankment at
a midpoint between them, M.
An observer on the train is at a
position M^1 in a separate frame
of reference. When the flashes
occur, M^1 may be passing right by
M. However, by the time the light
has reached the observer on the
train, the train has moved toward
point B and away from point A.
As Einstein puts it, the observer is
“riding ahead of the beam of light
coming from A.” The observer on
the train concludes that lightning
strike B occurred before strike A.
Einstein now insists that: “Unless
we are told the reference-body to
which the statement of time refers,
there is no meaning in a statement
of the time of an event.” Both time
and position are relative concepts.Mass-energy equivalence
The last of Einstein’s 1905 papers
was called Does the Inertia of a
Body Depend on its Energy
Content? Its three brief pages
expanded on an idea touched on in
the previous paper—that the mass
of a body is a measure of its energy.
Here, Einstein demonstrated that
if a body radiates away a certain
amount of energy (E) in the form
of electromagnetic radiation, its
mass will diminish by an amount
equivalent to E/c^2. This equation
is easily rewritten to show that the
energy of a stationary particle ❯❯1
√1 –– v^2 / c^2
In Einstein’s thought experiment,
for a stationary observer at point M,
two lightning flashes at A and B occur
simultaneously. However, to an observer
at point M^1 on a train moving at high
speed away from A and toward B, the
flash at B occurs before the flash at A.Near the speed of lightM^1BMA