Albert Einstein published his special theory of relativity in 1905. Special relativity predicts strange sounding effects that occur when objects are traveling close to the speed of light. They include:
- Lorentz contraction
- time dilation
- mass increase with speed
- the speed of light is the ultimate speed limit
- mass energy equivalency, E=mc²
Speed of Light as a Fundamental Constant
Einstein assumed that the speed of light in a vacuum is a fundamental constant of the universe. All observers who are not accelerating measure the same value for the speed of light beams regardless of the observer's speed. This basis for special relativity contradicts what most physicists thought prior to Einstein's work or the Michelson-Morley experiment.
In order for observers moving at different velocities to measure the same value for the speed of a light beam, Einstein realized that something else must change. Speed is distance divided by time, so the length and time of moving objects must change as seen by outside observers. The changing time is called time dilation and the changing length is Lorentz contraction.
Time dilation
As Einstein liked to do, time dilation can be described with a thought experiment. Imagine an observer at rest and a passenger in a rocket moving at a significant fraction of the speed of light. Both the observer and the passenger have clocks easily readable by the other. As the rocket zips past, the rest observer sees the clock in the rocket moving more slowly and the observer's clock moving normally. To the rocket passenger, however, the clock in the rocket is moving normally.
The clocks are not broken. According to the time dilation effect in special relativity, an observer at rest sees time as moving more slowly for an object moving close to the speed of light. While time seems to move at a normal rate for anyone in the moving object.
The rocket passenger, however, thinks that the rocket is at rest and the observer is moving at the opposite direction at near the speed of light. Therefore the passenger sees the clock in the rocket as normal and the alleged rest clock as moving more slowly.
Both the rest observer and the rocket passenger are correct. The rate at which time flows, the order in which sequential events occur, and whether or not two events are simultaneous all depend on the observer's frame of reference. The disagreement between observers as to which one is in the rest frame leads to the famous twin paradox resulting from Einstein's special relativity theory.
Mathematical Formula for Time Dilation
The mathematical formulas for special relativity often use the factor gamma, which is defined by:
gamma = 1/(√(1-v²/c²))
In this formula, v is the speed of the moving object, c is the speed of light, and √ represents the square root of the quantity in parenthesis.
The time dilation effect is then given by:
t = gamma t'
Here t', which is called the proper time, is the time interval as measured by an observer in the reference frame that is moving along with the clock. The time interval t is the time measured by an observer who is in a different reference frame, which would be the rest frame if the clock is moving at a speed v. When v is less than c, gamma is greater than 1 and t is greater than t'. The proper time, as seen by an observer in the clock's reference frame is the shortest time interval measured on that clock. Observers in different reference frames from the clock will measure longer time intervals than the proper time because they see time as moving more slowly for that clock.
Experimental Verification of Time Dilation
Time dilation seems strange because the effects are only significant at speeds close to the speed of light, which we have never experienced. High energy physicists however frequently accelerate elementary particles to speeds near the speed of light. Many of these particles, such as muons, have very short lifetimes and quickly decay into other particles. When elementary particles are traveling close to the speed of light, their lifetimes, as seen in the laboratory at rest, are longer just as predicted by special relativity theory.
Time dilation is one of the strange effects predicted by Einstein's special theory of relativity.
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.
