3H project topic: A Relativistic Perspective

Paul Heslop

Description

What does the world actually look like if one is travelling close to the speed of light?
There are several weird effects. For example, below is a picture of some dice in a row.
The bottom row is stationary, the row above is identical but moving towards us at
90% of the speed of light. They're not physically rotating, yet you can see that effectively we
can actually see behind the cube.



Cubes moving at 90% of the speed of light 


Lorentz contraction means things get squashed but would we actually see this effect?
Surprisingly spheres will appear as spheres, they are not flattened as you might
expect from Lorentz contraction. The reason for this is that an observer does not
"see" her reference frame, but rather the photons reaching her eyes, and the photons
from the back of the sphere, having further to travel, left slightly earlier than from
the front, counteracting the effects of the Lorentz contraction. (see here ).

 

There are several relativistic flight simulators and animations on the web, for example:


or look here for more info.

There are several strange effects, collectively called relativistic beaming:

  1. Aberration: the scene is concentrated ahead, expanded behind; you can see things when looking forward that are in fact behind you
  2. Colour shifts: the scene is blue-shifted ahead, red-shifted behind;
  3. Brightness changes: the scene is brightened ahead, dimmed behind;
  4. Time changes: the scene is speeded up ahead, slowed down behind.

Mathematically, the fact that spheres appear as spheres property is related to the concept
of conformal (or more precisely Moebius) transformations (see here and refs therein.)
The conformal group has many applications throughout physics and mathematics.
For example, insights along these lines led Penrose directly to the concept of twistors, useful tools in physics.

In this project we will explore what a relativistic observer actually sees and the mathematics behind this with options to create your own pictures and animations.

Prerequisites

Special Relativity & Electromagnetism II (MATH2657)

Resources and references

Search the web, including the links above, there is lots out there. Some more links on the relativistic stuff...

  1. http://en.wikipedia.org/wiki/Lorentz_group
  2. http://math.ucr.edu/home/baez/physics/Relativity/SR/penrose.html and refs therein
  3. http://en.wikipedia.org/wiki/Mobius_transformation
  4. Physics world article
  5. Real-world relativity: Image-based special relativistic visualization
  6. More detailed thesis on which previous was based
  7. The apparent shape of a relativistically moving sphere Penrose paper
  8. Invisibility of the Lorentz contraction original paper by Terrell
  9. Apparent Shape of Large Objects at Relativistc Speeds Original paper by Boas
  10. Two-dimensional appearance of a relativistic Cube paper by Hickey