"space" - SPECIAL RELATIVITY DEMONSTRATION (c) 1995 William J. Crilly Jr


This program was written by W.  J.  (Skip) Crilly on June 13, 1995 (James Clerk
Maxwell was born on this day in 1831).

Reference:  "Relativity" by Albert Einstein,  date, pub, etc.

The following text was updated on 2/20/99.

What this program shows you 
---------------------------

This program uses the Lorentz transformations to calculate the position, shape
and time of clocks that travel relative to a fixed reference frame.  You can set
an imaginary spaceship's speed and see two clocks at each end of the moving ship.
An identical spaceship is parked and has two clocks at each end of it.  On board
this stationary ship, we are able to examine the other ship as it scoots by.
Our ship has a LASER transmitter that sends light pulses out in two directions.
We can use this LASER to measure the speed of light.

The number in the upper left corner of the display is the spaceship speed as it
goes past our parked ship.  (1 = the speed of light, which as we know, we can
never reach.  I'll get to the reason for this.)

Two things will be evident from this demonstration.  

First, the speed of light measured on board each of the two ships comes out to
be the same number.  This is nice, because, for example, engineers don't know
how to use Maxwell's equations to build a radio that works with a changing speed
of light.  Wavelength times frequency is equal to the speed of light.  This
would get out of control.

Second, imagine that the clocks are "momentum clocks", e.g.  a nearly
frictionless mechanism that keeps masses going around in a circle.  Also imagine
that the circular clock surfaces are perpendicular to the direction of spaceship
motion, i.e.  ninety degrees off how they are drawn.  In this case, an amazing
thing becomes obvious, if you accept that the momentum of the clock masses
hasn't changed (the clock masses are moving perpendicular to the spaceship
velocity; Special Relativity says this momentum is a constant).  Momentum is
mass times velocity.  On board our ship, we will say that the clock masses must
be getting huge, because the (same-momentum) clock masses are moving very slowly.

How does the ship get propelled if it is getting so massive? Let's say we use
a LASER transmitter to push the ship along its way.  The LASER engineers will
complain that they can't push the huge mass anymore.  If the ship expels
mass/energy to increase speed, we are going to look at the expelled (and thus
slower) exhaust and say, "They're never going anywhere with that tiny bit of
expelled mass/energy!"

The speed of light is a tough obstacle, based on what we know.  We live with a
speed limit that we can't cross.  On the other hand, the speed limit is rather
nice, because it makes the long distance trip go very fast for the traveler!
Strange but true.

Many experiments have been performed to test Special Relativity.  For
example, the atomic clocks on board the moving GPS satellites change according
to Special Relativity.  GPS satellite clocks also change due to General
Relativity (mass curves the space around it).  The effects of General Relativity
are small and ignored in this program's demonstration.


Keys that do things 
-------------------

Use the up and down arrow keys to increase or decrease the spaceship speed.
Exit the program with the escape key or the space bar.


Calculating the speed of light on board each of the spaceships
--------------------------------------------------------------

Our reference frame is the stationary (lower) clocks.  Imagine that we have high
speed cameras that snap pictures of the ship clocks as they scoot by.

The LASER light pulses are transmitted by our left clock every time the clock
rotates once.  The light pulses travel to our second clock in one and a half
rotations of our clocks, so the speed of light is calculated, from the light
travel distance and time, to be the distance between the stationary clocks
divided by 1.5 rotations.  So the speed of light is distance between clocks per
1.5 clock revolutions.

From our point of view, the moving right clock always lags the moving 
left clock, due to the coupling between distance and time in Special
Relativity.  However, on board the ship carrying the clocks, the time on the two
clocks always indicates the same.

Set the spaceship speed to about 0.6 times the speed of light.  Notice that, in
our reference frame, we see the moving right clock to be close to one revolution
behind the moving left clock.  The right-going light pulses take 2.5 revolutions
of the moving clocks to go the distance between the clocks.  If we take
snapshots of the light speed measurement being made on board the moving ship, the
measured speed of light is calculated from the time 0 (left clock when pulse
arrives) to the time -1.0 (the lag) plus 2.5 revolutions = 1.5 (the same travel
time as the stationary clocks).  On board the ship, the speed of light
measurement result is the distance between clocks per 1.5 revolutions. 
So they get the same value that we got on board our ship.

What happens when the light goes the other way?  The left-going pulses arrive at
the moving right clock at 0, and at the moving left clock 0.5 revolutions later.
So the speed of this light is calculated from the time 0 (when the light arrives
at the right clock) to the time 1.0 (the left clock time lead) plus 0.5
revolutions = 1.5. Again, light speed is distance between clocks per 1.5 revolutions.

Squished slow-running clocks
----------------------------

Notice the squished, slow-running clocks as the speed increases.  This is really
what we will see.  The passengers are not squished when they look at each other,
but they do age very slowly, relative to us.  They travel to nearby stars in
weeks and can, in principle, visit anywhere in the universe during their lives.
When they return to Earth, a long time has passed.

Better ships will pick passengers up along the way
-------------------------------------------------- 

If we send a first ship at high speed on a mission to the stars, more advanced
ships will reach the first ship perhaps in weeks of ship time (decades of Earth
time).  The new ships will pick up the passengers, who will be youger than their
great-great grandchildren riding on the faster ships.  This process will continue
with more advanced ships.  Passengers will get a chance to view the Earth's future
in extreme fast forward, as they visit the stars. 

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