Theory of Special Relativity
Time Dilation and Length Contraction
- Einstein published two main theories about space and time. These are his
SPECIAL THEORY OF RELATIVITY in 1905 and GENERAL THEORY OF RELATIVITY in 1915.
Both of these caused a radical change in how we view the universe.
- Both theories appear to be correct to the limits that we can measure so far.
Newton's Laws, on the other hand, do not predict observations in the extreme
limits: high velocity, high mass, and maybe even long distance (we will learn
latter that instead of invoking dark matter, some scientist suggest that Newton's
Laws are incorrect for large distances).
- One of the fundamentals of special relativity is that nothing can travel faster
than the speed of light (in a vacuum), and no object can be accelerated to the
speed of light.
- This fact causes many consequences: if we observe something moving at high speeds,
then time will run more slowly for that object (TIME DILATION). If we observe
the length of an object moving fast, then that object appears smaller (LENGTH
- In other words, measurements are relative.
- The mass of an object is related to its energy: Energy equals mass times the
speed of light squared (E=mc^2). We use the letter "c" to denote the speed
of light (300,000 km/s).
- A simple example is given in the book where they describe an airplane flying
from Africa to South America with the same speed as the Earth's rotation. For a
person here on Earth, it appears that the plane is traveling East to West. From
space, it appears that the plane is stationary and that the Earth is rotating
- There are two assumptions for special relativity that are not relative: 1) the
laws of nature are the same everywhere, and 2) the speed of light is the same
for everyone (it is a constant of nature). Do not get this confused with the
doppler shift (the doppler shift changes the wavelength of the light but not
- To help understand relativity, we need to define the frame of reference. This means
that we need to know where we are relative to other objects in order to understand
- The book goes through a series of thought experiments which we will discuss some
here. They use the examples of two rocketships in space. Similarly, we can use
two cars on Earth. If two cars are coming towards each other at 50 mi/hr each,
then the relative speed is 100 mi/hr. Now, if the cars are each moving at 0.99c (99%
of the speed of light) then their relative speed is NOT 1.98c (0.99 times 2) since
that would imply that something is traveling faster than the speed of light. In other
words, if you are in one of the cars, then you see the other car coming towards you
at a speed less than c.
- Does warp speed exist (the Star Trek fantasy of traveling faster than the speed
of light)? According to our physics, the answer is no. Since the speed of light is
constant for everyone, then if you turn on a flashight at any speed, you see the light
travel away from you at the speed of light. From an outside observer, they also see
the light travel at the speed of light. Thus, you must be traveling slower than c.
- The above example begs the question: Is the speed of light really constant everywhere?
As far as we can tell, the answer is yes - it has been experimentally validated.
The Speed of Light
- The book presents a good experiment to demonstrate time dilation. A light ray
travels a farther distance for a moving source from the point of view of an
outside observer compared to an observer in that frame of reference.
- Since the light travels farther, and since both observers see light travel at
the same speed, then time must run slower in the moving frame. In other words,
in a moving reference frame, time is dilated.
- Time dilation leads to length contraction. Because clocks run slower in a moving
frame, then it must record smaller distances (distance equals speed times time).
Thus, for very fast moving objects, we see them as shorter than if we were in that
reference frame. That means that we can fit a 15ft pole into a 10ft barn!
- The question of simultaneity arises often in relativity. Imagine two lights going off
at opposite ends of a ship. As we watch the ship go by us, the light reaches our eyes
at the same time, but they reach the center of the ship at different times because
the ship is moving. Thus to a person at the center of the ship, the light from one
end arrives before the other and they conclude that the light was emitted at different
- This website provides some
examples of length contraction.
- Plato and Aristotle thought that the speed of light was infinite, and this was
what everyone thought until the 1600s when scientists began experiments to measure
- Even Galileo tried to measure it by putting light sources on hills. Roemer in
1675 used the eclipses of Jupiter's moons to measure the speed of light. Eclipses
happened at different times depending on whether Earth was moving towards or away
from Jupiter. He got a value that was close to what the true value is today.
- The best experiment for measureing the absoluteness of the speed of light comes
from Michelson and Morley (in 1887). They determined that the speed of light is not affected
by the motion of the Earth around the Sun.
- Time dilation was measured in 1975 by using accurate clocks on an airplane moving
at a high velocity relative to a clock on the ground. The airplane's clock lost time
after 15 hours of travel.
- An example of the absoluteness of the speed of light comes from a paradox. If you
witness a collision of two cars, you see one car coming towards you and another going
away from you. If speed of light was relative then you would see the light from the
car coming towards before the light from the other. Thus, the cars would collide
at a point according to your frame of reference. This cannot be true and leads to a
- Einstein used these type of arguments to help formulate his relativity theories.
- Special Relativity tells us that we can time travel; in fact, it is very easy. The
example below is often called the twin paradox.
- Suppose you have two twins; one stays on Earth and one goes on a rocket to a nearby
star that is 25 light-years away. If the traveling twin flies at nearly the speed of
light, then they "see"
a smaller distance than the person on Earth due to length contraction. So, it takes
them a short time to travel there and back.
- However, back on Earth, it will take the amount of time that it would for light to
travel there and back, which would be 50 years. So, when the one twin returns they
will have aged only a short time compared to the twin on Earth. This is time travel.
- Special Relativity relates space and time. Einstein realized that this space-time
relation can be generalized to explain gravity. In other words, gravity is not due
to a force (as Newton described), but a change in the structure of space and time.