Download March 1

Einstein’s postulates
1. The laws of nature are the same for
everyone.
2. The speed of light in a vacuum is constant
for all observers.
Discussion
You and Jackie are each on separate trains
that will pass each other at high speed. Both
of you decide to measure how fast the trains
pass each other. How can you do this without
leaving your seat?
Discussion
Now that you and Jackie have the relative
speed of the trains, both of you decide to
measure the length of the other’s train. How
would you do this again without leaving your
seat?
Discussion
How can you measure the length of your train
without leaving your seat?
Discussion
Will the length of your train that you measure
be the same as the length of your train that
Jackie measures? Explain.
Discussion
How will your measurement of Jackie’s train
compare with her own measurement of her
train? Explain.
Length contraction
From your point of view, length of an object
moving by you (or distance between objects
moving by you) is shorter in the direction of
motion than it would be if it were at rest.
The faster the objects are moving, the shorter
the lengths.
Theory of Invariantness?
Length and time measurements depend on the
relative velocity of the observers in such a way
as to make the speed of light constant for all
observers in any reference frame.
Discussion
Suppose you have two identical space ships, one
is at rest with respect to you, the other is
moving at high velocity. As the ship passes you,
you give each ship an identical push for the
same duration of time. How do passengers on
the moving ship perceive the duration of push
you give them as compared to the duration of
the push you gave the stationary ship?
Discussion
If the moving ship observers you giving the
stationary ship a push for a longer duration,
how does this change the acceleration they
feel as compared to the acceleration they
observe you giving the stationary ship?
Explain.
Discussion
According to Newton’s second law F = ma. If the
force F applied is the same in both cases and the
acceleration is less in the case of the moving
ship, what does this mean for the mass of the
moving ship? Explain.
Mass increase
From your point of view, objects moving by you
have a greater mass than they have while at rest
with respect to you.
The bigger the velocity, the greater the effective
mass
E = mc2
As the speed of an object approaches the
speed of light, its mass tends toward infinity,
resisting any further increase in speed.
Kinetic energy added to a high speed object
gets converted into mass.
Special Theory of Relativity
No matter can travel at or faster than the
speed of light in a vacuum
Length contraction
Time dilation
Mass increase
Space fleet maneuvers
Consider three space ships moving in
formation. The flag ship is midway between
the lead ship and the rear ship.
The “go” order
The flag ship now signals to the other two
ships to fire their engines for exactly one
minute. The signal travels at the speed of
light to each ship which obeys the command.
The flag ship simply adjusts its own speed to
remain at the midpoint between the two
ships.
Because both ships are the same distance
from the flag ship, both ships fire their
engines at the same time. Because they are
all moving together at the same speed, they
all stop firing their engines at the same time
and the formation is preserved.
Eat lunch
The flag ship then signals to the other two
ships that it is time to eat lunch. From the
moving ships perspective they are all at rest
with the flagship at the midpoint. Thus both
ships received the “lunch” command at the
same time and lunch takes place on both
ships simultaneously.
The relativity of time
For someone at rest with respect to the
moving ships, the signals also travel at the
speed of light, but during the time it takes to
reach the back ship it moves forward, toward
the signal and thus receives the command a
little early. Also during the travel time for the
light the lead ship has moved forward, away
from the light and receives the signal a little
late.
Not simultaneous
Thus, from someone at rest with respect to
the moving ships, the last ship eats lunch first
and the lead ship eats lunch last.
Discussion
After lunch, the flagship again gives an
order for another engine burn. From the
perspective on someone at rest which ship
receives the order first? What happens to
the formation of the ships?
Desynchronized motion
Again the rear ship receives the order first and
fires its engine before the other two. Thus,
the rear ship for a time is going faster than the
other two ships and gets closer to the flag
ship. The lead ship gets the message last and
starts its engine burn later, allowing the other
two ships to catch up.
The formation length has shrunk
After the lead rocket shuts down its engine, all
ships will again be going the same velocity, but
the distance between them is now smaller than
it was before.
Desynchronized time causes length contraction
Discussion
How will this appear to the captains of the
ships flying in formation? Will they see their
ships as being closer? Why or why not?
Are the captains blind?
The ships can consider themselves at rest
before the second engine burn.
Therefore, from their perspective all the
ships fired their engines at the same time
and the distance between them did not
decrease.
Discussion
How could the ships get closer to each other
without the captains knowing it? Consider
doing another engine burn. The ships will
get closer still. Eventually, even if the fool
captains cannot see the difference won’t
they feel it as the run into each other?
Length contraction
No. The ships will never run into each
other. From the perspective of someone at
rest the distance between the ships will
decrease to 0 as the speed approaches the
speed of light. But the lengths of the ships
also decrease in size so that they never hit.
Space is contracting
It is not just objects that contract, but
space itself is contracting. The spaceships
contract because the space between their
atoms is contracted.
Width and height contraction?
Can’t happen because it is logically inconsistent
Example – firing a cannon
A fist fight
The force of a punch depends on how fast you
can throw a punch (the speed) and the mass
of your fist.
A high speed fight
Suppose two twin brothers get into a fight.
Each is traveling on a train going in opposite
directions with a constant velocity and each
tries to punch the other as the trains pass.
Time dilation again
But it takes time to throw a punch. Each
twin will consider himself at rest and he will
see the other twin as moving in slow motion.
Each will also conclude that the other’s slow
motion punch will have little effect on them,
and that their fast punch is going to knock
the other’s fist back in his mouth.
Who is right?
Which twin wins the fight?
Discussion
Neither. The punches will hit with equal
force and neither is able to shove the other’s
fist back into his brother’s mouth. How can
the other twin’s slow motion punch have as
much force as their own fast punch?
No magnetic fields
The Special theory of Relativity shows that the
magnetic field is just an electric field which
arises due to the relative motions of charged
particles.
Discussion
Given the results of the Special Theory of
Relativity, why did Einstein conclude that
Newton’s law of gravity needed to be revised?