* L0 = 45 m (length as measured by crew in rest frame) * v = 0.50c * c = 3×10^8 m/s * Using the Lorentz contraction formula: L = L0√(1-(v^2/c^2)) = 45√(1-(0.50c)2/c2) = 45√(1-0.25) = 45√0.75 = 33.75 m Therefore, the length of the spaceship as measured by mission control in Texas is 33.75 m.

1. TIME DILATION
LENGTH CONTRACTION
TWIN PARADOX

2.  Theory of relativity :
Encompasses two theories
of Albert Einstein special
relativity and general
relativity.

3. Albert
Einstein:
Description :
was a German
born theoretical
physicist who developed
the theory of general
relativity, effecting a
revolution in physics. For
this achievement, Einstein
is often regarded as the
father of modern
physics and one of the
most prolific intellects in
human history. He also
contribute the paper “On
the Electrodynamics of
Moving Bodies” (Annus
Mirabilis) that is publish in
the scientific journal in
1905.

4.  Special Relativity :  General Relativity:
Is a theory of the Is a theory of gravitation
structure of space develop by Einstein in
time. It was introduce the year 1907-1915.
by Albert Einstein’s the development of
1905 paper “On the general relativity
Electrodynamics of began with
Moving Bodies” equivalence principle
under which states of
accelerated motion
being at rest in
gravitational field are
physically identical

5.  The laws of physics are the same for
all observers in uniform motion relative
to one another. (Principle of relativity)
 The speed of light in a vacuum is the
same for all observation, regardless of
their relative motion or of the motion
of the source of light.

6.  Relativity of Simultaneity: two events,
simultaneous for one observer, may not be
simultaneous for another observers on relative
motion.
 Time Dilation: moving clocks are measured to
tick more slowly than an observers stationary
clock.
 Length contraction: objects are measured to be
shortened in the direction that they are moving
with respect to the observer.
 Mass-energy equivalence: E=mc2, energy and
mass equivalent and transmutation.
 Maximum speed is finite: No physical object,

7. Time:
Is not an
absolute but
is relative to
the motion
between the
observer
and the
event that is
being
observed.

8. Light
clock:
Light clock:
light will
bounce up
and down
between
parallel
mirrors and
tick-off equal
intervals of
time.

9. “The apparent
slowing down of
time for an object
moving at
relativistic speeds.”

11.  Formula:
to = time interval of flash to bounce between two
mirror.
v = velocity between the observer and the object
c = speed of light

12.  Leo and Christian are twins. At
the age of 30, Leo left for a
round trip to a distant star in a
spaceship with a speed of
0.95 c relative to earth. The
trip took 20 years according to
the ship.

13.  Isa experiment in special
relativity in which a twin makes
a journey into space in a high-
speed rocket and returns
home to find he has aged less
than his identical twin who
stayed on earth. TwinParadox

14. The apparent
shrinking of an
object moving at
relativistic speed

15. Lorentz-
FitzGerald
contraction
FitzGerald is better known
for his conjecture in his short
paper "The Ether and the
Earth's Atmosphere" (1889)
that if all moving objects
were foreshortened in the
direction of their motion, it
would account for the curious
null-results of the Michelson-
Morley experiment.
FitzGerald based this idea in
part on the way
electromagnetic forces were
known to be affected by
motion. In particular,
FitzGerald used some
equations that had been
derived a short time before
by his friend the electrical
engineer Oliver Heaviside.
The Dutch physicist Hendrik
Lorentz hit on a very similar
idea in 1892 and developed it
more fully into Lorentz
transformations, in
connection with his theory of
electrons.

16. Lorentz-
FitzGerald
contraction
Hendrick Lorentz In 1895,
with the attempt to explain
the Michelson-Morley
experiment, Lorentz
proposed that moving bodies
contract in the direction of
motion (see length
contraction; George
FitzGerald had already
arrived at this conclusion,
see FitzGerald-Lorentz
Contraction). Lorentz worked
on describing
electromagnetic phenomena
(the propagation of light) in
reference frames that moved
relative to each other. He
discovered that the transition
from one to another
reference frame could be
simplified by using a new
time variable which he
called local time.

17.  Formula:
 L0 is the proper length (the length of the object in its rest frame),
 L is the length observed by an observer in relative motion with
respect to the object,
 v is the relative velocity between the observer and the moving
object,
 c is the speed of light,

18. A spaceship travelling at 0.50
c relative to earth is 45 m
long as measured by its
crew. How long is the
spaceship as measured by
the mission control in
Texas?