Running the Relativistic Simulation
using the Twins with no Instant
Velocity Change example
This tutorial is an extension of the Twins
tutorial. It examines the behavior of
time and distance for a Twins example with a realistic change of velocity during
the astronaut’s turnaround.
Please
Note: Relativity is built on and
modifies Newtonian Physics. These
tutorials do not attempt to teach the user Newtonian Physics. They assume the user already knows Newtonian
Physics.
If you have not already gone through the regular
Twins tutorial you should. That tutorial
may be found at http://relativitysimulation.com/Tutorials/TutorialTwins.html. This tutorial assumes
you have a level of familiarity with the application that you will have gained
by running that tutorial. All of the
tutorials and the simulation application itself are accessible at http://relativitysimulation.com. This tutorial does not
implement relativistic acceleration. It
approximates the consequences of relativistic acceleration using a series of
small reference frame transformations.
(Acceleration will be implemented in a later version of the
Application.)
Selecting
the Predefined Example
Select “Twins,
no instant velocity change” from the Examples List.
The scene looks the same
as that for the regular Twins example.
And just as with the regular example you should zoom In
or Out till the scene on your computer looks like the one pictured
below.
Running the
Example
When you run this
example you will see the same behavior as the Twins example with the following
exceptions. During the astronaut’s
turnaround instead of a single jump from a reference frame moving at
relativistic speed to the right to a reference frame moving at relativistic
speed to the left, the turnaround will be done in increments. That will consume a little extra time and
distance so that the reunion times on both twins’ clocks will be different from
the regular Twins example.
Switching
Reference Frames
The value of this
example is the behavior you see when running with the astronaut as the observer
reference frame. So switch reference
frames to Astronaut-4.
Run the example several
times concentrating on the behavior of the Earth
clock during the astronaut’s turnaround.
Notice that the length
contraction of the row of clocks in the earth reference frame first loses its
contraction and then regains it. In
order to turn around, the astronaut must shrink relative velocity and come to rest
in the earth’s reference frame, then regain relative velocity in the opposite
direction. So length contraction of
objects in that reference frame first goes away and then comes back.
Also, instead of
jumping, the earth clock appears to run fast, in a choppy sort of way. (When real acceleration is implemented it
will be a smooth, fast running clock.)
The speed of the earth clock is so fast compared to the astronaut’s
clock that it catches up to and passes far ahead of the astronaut’s clock.
After the turnaround,
it is so far ahead that even its slower running during the return trip is not
enough and the trip ends with the earth clock reading ahead of the astronaut’s
clock. This situation (the other guy’s
clock running faster) will only occur when considering the example from the
reference frame of the accelerating astronaut.
In Special Relativity an inertial observer will always consider a clock
on a body in another reference frame to be running slow, whether the body is
accelerating or just coasting in an inertial frame of its own. But an accelerating body will always consider
the clock on an inertially moving body to be running
fast. And that’s the real resolution of
the Twins Paradox.
Further
Experimentation
There are
two examples and tutorials where the astronaut and earth exchange light
signals. Exchanging light signals is a
way for the twins to prove who is aging faster without having the astronaut land
back on earth and compare clocks.