Accelerate to near the speed of light
Like Hans Solo on the Millenium Falcon,
or Captain Picard making it so,
you press the hyperlight button, and ... what happens?
In this movie,
you accelerate towards the Sun,
accelerating at the speed of light per 8 seconds,
equivalent to 4 million gees (ouch).
You accelerate for 16 seconds, then coast for another 16 seconds.
The clock shows your proper time (the time you actually experience) in seconds.
The planet is Mercury, not to scale.
The real Mercury is smaller and farther from the Sun.
The movie gives the impression that
initially you move away from the Sun,
but this is false.
As you accelerate towards the Sun,
relativistic aberration concentrates the scene more
and more ahead of you.
Notice several effects, collectively called relativistic beaming:
- Aberration: the scene is concentrated ahead, expanded behind;
- Color shifts: the scene is blueshifted ahead, redshifted behind;
- Brightness changes: the scene is brightened ahead, dimmed behind;
- Time changes: the scene is speeded up ahead, slowed down behind.
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The Rules of 4-Dimensional Perspective
The rules that govern the appearance of a scene
when you move through it at near the speed of light can be called
“The Rules of 4-Dimensional Perspective”.
These rules can be grasped,
much like the rules of 3-dimensional perspective,
without needing to understand intricate mathematics.
The Rules of 4-Dimensional Perspective
can be summarized as follows:
- Paint the scene at rest on the surface of a celestial sphere;
- Stretch the celestial sphere by Lorentz factor γ along the direction of motion into a celestial ellipsoid,
and displace the observer to a focus of the ellipsoid;
- Adjust the brightness, color, and clock speed at any point on the ellipsoid
in proportion to the length of the radius between the point and the observer.
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The diagram at left encapsulates these Rules.
In the left panel of the diagram,
you, the observer, are at the center of the celestial sphere.
The stars on the celestial sphere represent, well, stars on the celestial sphere.
In the right panel of the diagram,
you are moving through the scene to the right at 60% of the speed of light.
You, the observer,
are at a focus of the celestial ellipsoid.
The ellipsoid is stretched by Lorentz factor
γ = 1/√(1 − 0.6
2) = 1.25
along the direction of motion.
The scene appears relativistically aberrated,
which is to say concentrated ahead of you,
and expanded behind you.
The arrowed lines converging on you the observer
represent the energy-momenta of photons that you see.
The lengths of the arrows are proportional to the energies, or frequencies,
of the photons that you see.
The lengths are also proportional to the brightness,
the number of photons per unit time, that you see.
When you are moving through the scene at near light speed,
the arrows ahead are longer,
so you see the scene ahead is brighter,
and photons ahead are blueshifted, increased in energy,
increased in frequency.
Conversely, the arrows behind you are shorter,
so you see scene behind is dimmer,
and the photons behind are redshifted, decreased in energy, decreased in frequency.
Since photons are good clocks,
the change in photon frequency
also tells you how fast or slow clocks attached to the scene appear to you to run.
4D Perspective
Leonardo da Vinci's study for the "Adoration of the Magi",
seen at 0.995 times the speed of light.
In 4-dimensional perspective,
straight lines in general do not remain straight: they become arcs of circles.
Circles remain circles, although changed in radius.
Relativistically rotating box
This is a relativistically rotating box.
The angular velocity is such that corners of the box move at 1/2 the speed of light.
Despite appearance, the box is not flexing.
The box appears to be bent because the light travel time from the far side of the box
is longer than that from the near side.
