Albert Einstein's special theory of relativity, published in 1905, predicts unusual counterintuitive effects that occur when objects are traveling close to the speed of light, including:
- Lorentz contraction
- time dilation
- mass increase with speed
- the speed of light as the ultimate speed limit
- mass energy equivalency, E=mc²
Speed of Light as a Fundamental Constant
Einstein based his theory of special relativity on the assumption that the speed of light in a vacuum is a fundamental constant. Hence, all nonaccelerating observers measure the same value for the speed of a light beam regardless of their velocity.
Prior to Einstein's special relativity theory and the Michelson-Morley experiment, physicists thought that observers moving at different velocities would measure different values for the speed of light.
If, however, observers at different velocities measure the same value for the speed of light, then they must measure different values for some other quantities. Speed is distance over time. The mathematical proof is difficult, but different observers must measure different values for length and time so that they can measure the same value for the speed of light. Physicists call the shortening of moving objects Lorentz contraction.
Origin of Lorentz Contraction
In his special theory of relativity, Einstein showed that Lorentz contraction is a consequence of the constant value of the speed of light. H.A. Lorentz however suggested the idea prior to Einstein to explain the negative result of the Michelson-Morley experiment. Fitzgerald also independently suggested this idea, so Lorentz contraction is also sometimes called Lorentz-Fitzgerald contraction.
Understanding Lorentz Contraction
Einstein liked thought experiments about moving objects to understand and explain effects of relativity theory. A thought experiment with moving rockets can help explain Lorentz contraction. Keep in mind however that the Lorentz contraction effects do not become large enough to notice until the objects are moving at speeds of about 30,000 kilometers per second, which is 10% of the speed of light.
A rocket is 100 meters long when it is at rest. If the rocket zips past an observer at rest, then that observer measures the rocket's length as shorter than 100 meters. The precise length depends on how fast the rocket is moving. The rocket only appears shorter in the direction that the rocket is traveling; the other dimensions are the same as their normal values at rest.
To a passenger in the rocket however, all appears normal. The rocket is still 100 meters long. Remember that the passenger measures the length of the moving rocket with a meter stick that is also moving along with the rocket. This meter stick therefore shrinks by the same percentage as the moving rocket.
Summarizing the Lorentz contraction, an observer at rest sees a moving object as shorter than its actual length in the direction of motion. The passenger in the moving object however sees the length as normal.
Which Observer Is at Rest
Another principle of relativity is that there is no absolute reference frame at rest for the universe. Any observer in a nonaccelerating frame considers that frame as being at rest.
So the passenger in the rocket sees the rocket as being at rest and having its normal length. Furthermore the rocket passenger also sees the alleged rest observer as moving at the rocket's speed in the opposite direction. The rocket passenger sees the other observer is shorter than normal in the direction of the motion.
Mathematical Formula for Lorentz Contraction
In the mathematical formulas for special relativity the factor gamma arises frequently and is defined by:
gamma = 1/(√(1-v²/c²))
where v is the speed of the moving object, c is the speed of light, and √ indicates the square root of the quantity in parenthesis. Because v is less than c, gamma is greater than 1.
The Lorentz contraction formula for a moving object as seen by an observer at rest is:
L' = L/gamma
where L' is the contracted length as measured by the observer at rest and L is the rest length.
The idea that an object's length depends on how fast it is moving relative to the observer is counterintuitive and violates common sense. That is because these effects are only noticeable at speeds close to the speed of light. We have directly experienced neither these speeds nor these effects.
Further Reading
Einstein, A., "On the Electrodynamics of Moving Bodies" Annalen der Physik, 1905, Translated and reprinted in The Principle of Relativity, Dover, 1952.
Tipler, P.A., Modern Physics, Worth, 1978.
Serway, R.A., Moses, C.J., and Moyer, C.A., Modern Physics, Thomson, 2005.
Paul A. Heckert - I have a Ph.D. in astrophysics, over 30 years experience teaching physics and astronomy, and over 60 published research articles.
