Special Relativity: A Simple Matter of Perspective?

Popular belief has it that Eintein's Theory of Special Relativity is something difficult. It is not. Special Relativity is nothing more than what we usually call "Perspective", but applied to space and time, and not only to space. On this page, you will see how easy Relativity paradoxs appear once you have accepted this idea.

The Special Relativity "Paradoxs"

• The two rockets paradox: If two rockets cross, each emitting a pulse of light every second, then every rocket will see the pulses of light of the other rocket as separated by more than one second, even after taking into account the time it takes for light to travel from one rocket to the other. This effect is experimentally verified for instance when receiving data emitted from satellites.
• The red shift: In the above experiment, the light received by the other rocket will also have a lower frequency than the known frequency of emitted light. This effect is experimentally verified on distant stars, where the radiation spectrum of known elements is shifted down.
• The twins paradox: If a twin remains on earth while another twin travels at near light speed and returns to earth, the travelling twin will be younger when he returns. This effect is experimentally verified on particles with known average life in particle accelerators: particles last longer when they are moving. It is also the basis of the "Planet of the Apes" novel.
• The train paradox: If two lightning bolts strike the track simultaneously at both ends of a fast travelling train, the marks on the track will be shorter than the known length of the train at rest.
• The barn and the pole paradox: With sufficient speed, an object can go through a hole which is too short for the object.

The "magic recipe"

1. Plot all events in the experiment in a plane, where time is an axis, and space is the other axis, as measured by any given observer.
2. For any mobile in the diagram, the trajectory on the diagram is called the time line.
3. Any time measurement made by this mobile will be made along its own trajectory.
4. Any space measurement made by the mobile will be made perpendicular to this trajectory.
5. Any effect of perspective needs to be inverted. Where contractions happen on the diagram, special relativity will predict a dilatation. Where dilatations happen on the diagram, special relativity will predict a contraction.
6. Time and space don't mix. A rule of the thumb is to look suspiciously at any angle above 45° on your diagram.

The twins paradox

Our magic recipe, however, makes this paradox look quite simple. If we apply step 1 of the magic recipe, the twins paradox can be plotted as follows:

Step 2 indicates that the age of the travelling twin is represented by the length of the red curve, and the age of the twin remaining on earth by the length of the blue line.

It is a well known fact that the shortest path between two points is the straight line. So any trajectory the twin follows on our diagram is always longer. Applying step 3 of our recipe, the travelling twin will always age less than the twin remaining on earth.

The two rockets paradox

The big dots represent the events in space-time corresponding to each pulse of light, for each of the two rockets. Since the blue rocket is moving with respect to the red rocket, its trajectory is slanted (there is a displacement along space).

Applying step 2, and considering that the blue rocket emits a dot every second of its own time, we see that the plots are separated by the same distance along its trajectory, not along our time. However, if the red rockets tries to measure the interval between two pulses emitted by the blue rocket, it does so using the red dotted lines, which are perpendicular to its own red time. Conversely, the blue dotted lines show how the blue rockets measures the interval between two red pulses.

On the diagram, a contraction appears in both cases. Applying step 3, we discover that rocket red will see pulses emitted by rocket blue separated by a larger time interval, but that rocket blue will also see rocket red pulses separated by a larger time interval !

And that's it...

Red shift

Compared to the spectrum of the same element measured in a lab on earth, the spectrum of elements in distant stars appears shifted towards low frequencies. Since red is the lowest frequency in the visible spectrum, this is called the red shift.

See also the General Relativity FAQ on this topic.

The train paradox

Applying step 2, we can understand why the lightning bolts are not simultaneous for an observer in the train. The lightning at the front of the train will occur after the one at the rear of the train.

The distance d between the two bolts, measured in by an observer on the track (along the green dotted lines), is longer on our diagram than the length d’ of the train measured by an observer in the train. Applying step 3, we can deduce that the distance between the bolts in special relativity is shorter than the length of the train.

The barn and the pole paradox

See also the detailed explanation in the Relativity FAQ.