Relativistic Effects Help

By — McGraw-Hill Professional
Updated on Sep 18, 2011

Point Of View: Length

Relativistic speeds—that is, speeds high enough to cause significant time dilation—cause objects to appear foreshortened in the direction of their motion. As with time dilation, relativistic spatial distortion occurs only from the point of view of an observer watching an object speed by at a sizable fraction of the speed of light.

If we travel inside a space ship, regardless of its speed, everything appears normal as long as our ship is not accelerating. We can cruise along at 99.9 percent of the speed of light relative to the Earth, but if we are inside a space ship, it is always stationary relative to us. Time, space, and mass appear normal from the point of view of passengers on a relativistic space journey. However, as we watch the space ship sail by from the vantage point of Earth, its length decreases as its speed increases. Its diameter is not affected. The extent to which this happens is the same as the extent to which time slows down.

Let L be the apparent length of the moving ship as a fraction of its length when it is standing still relative to an observer. Let u be the speed of the ship as a fraction of the speed of light. Then

L = (1 – u 2)1/2

This effect is shown in Fig. 16-4 for various relative forward speeds. The foreshortening takes place entirely in the direction of motion. This produces apparent physical distortion of the ship and everything inside, including the passengers. It’s sort of like those mirrors in fun houses that are concave in only one dimension and reflect your image all scrunched up. As the speed of the ship approaches the speed of light, its observed length approaches zero.

Special and General Relativity
Simultaneity Point Of View: Length

Figure 16-4. As an object moves faster and faster, it grows shorter and shorter along the axis of its motion.

Suppositions And Cautions

Spatial distortion is a curious phenomenon. You might wonder, based on this result, about the shapes of photons. They are the particles of which visible light and all other EM radiation are comprised. Photons travel at the speed of light. Does that mean they are infinitely thin, flat disks or squares or triangles hurtling sidelong through space? No one has ever seen a photon, so no one knows how they are shaped. It is interesting to suppose that they are two-dimensional things and, as such, have zero volume. However, if they have zero volume, how can we say that they exist?

Scientists know a lot about what happens to objects as they approach the speed of light, but it’s intellectually dangerous to extrapolate and claim to know what would happen if the speed of light could be attained by a material thing. We will see shortly that no physical object (such as a space ship) can reach the speed of light, so the notion of a real object being squeezed down to zero thickness is nothing more than an academic fantasy. As for photons, comparing them with material particles such as bullets or baseballs is an unjustified intuitive leap. We cannot bring a photon to rest, nor can we shoot a bullet or throw a baseball at the speed of light. As they might say in certain places, “Baseballs and photons ain’t the same animals.”

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