Special Relativity Unit 7

The first person to understand the relationship between space and time was Albert Einstein. Einstein went beyond common sense when he stated in 1905 that in moving through space we also change our rate of proceeding into the future- time itself is altered. This view was introduced to the world in his special theory of relativity.

Einstein reasoned that space and time are two parts of one whole called space-time. When you stand still, then all your traveling is through time. When you move a bit, then some of your travel is through space and most of it is still through time. If you were somehow able to travel through space at the speed of light, what changes would you experience in time?

The answer is that all your traveling would be through space, with no travel through time. You would be as ageless as light, for light travels through space only and is timeless.

Motion in space affects motion in time. Whenever we move through space, we to some degree alter our rate of moving into the future. This is time dilation, a stretching of time that occurs ever so slightly for everyday speeds, but significantly for speeds approaching the speed of light. If spacecraft of the future reach sufficient speed, people will be able to travel noticeably in time.

Speed is a relative quantity. An object may have different speeds relative to different frames of reference. Suppose your friend pitches a baseball at 60km/h. The ball is moving at 60km/h when you catch it. Now suppose your friend pitches a ball from the flatbed of a truck moving towards you at 40km/h. The speed of the ball will be 100km/h when it meets you. Now suppose the truck moves away from you at 40km/h and your friend again pitches the ball to you. This time the ball will be moving at 20km/h when it reaches you.

The speed of light is the only measurement that is an absolute. Every measurement of the speed of light in empty space gives the same value of 300,000km/s, regardless of the speed of the source or the speed of the receiver. Light from an approaching source reaches an observer at the same speed as light from a receding source. The constancy of the speed of light unifies space and time, according to Einstein.

Einstein reasoned that there is no stationary hitching post in the universe relative to which motion should be measured. Instead, all motion is relative and all frames of reference are arbitrary. A spaceship cannot measure its speed relative to empty space, but only relative to other objects. If, for example, spaceship A drifts past spaceship B in empty space, spaceman A and spacewoman B will each observe only the relative motion. From this observation each will be unable to determine who is moving and who is at rest, if either. This illustrates the first postulate of special relativity: All the laws of nature are the same in all uniformly moving frames of reference

The second postulate of relativity says: The speed of light in empty space will always have the same value regardless of the motion of the source or the motion of the observer. Consider a spaceship departing from the space station. A flash of light is emitted from the station at c. No matter what the speed of the space ship relative to the space station is, an observer on the space ship will measure the speed of the light passing her as c. If she sends a flash of her own to the space station, observers on the station will measure the speed of these flashes as c. The speed of the flashes will be no different if the space ship stops or turns around and approaches. The constancy of the speed of light is what unifies space and time.

Pretend you are in a space ship at rest in part of your town where a large public clock is displayed. Suppose the clock reads “12 noon.” To say it reads “12 noon” is to say that light reflects from the clock and carries that information towards you in the direction of your line of sight. If you suddenly move your head to the side, instead of meeting your eye, the light carrying the information will continue past, presumably out into space. Out there an observer who later receives the light could say, “Oh it’s 12 noon on Earth now.” But from our point of view it isn’t. You and a distant observer will see 12 noon at different times.

Now suppose your space ship is moving as fast as the speed of light. Then you’d keep up with clock’s information that says “12 noon.” Traveling at the speed of light, then, tells you it’s always 12 noon back home. Time at home is frozen.

So if your spaceship is not moving, you will see the hometown clock move into the future at a rate of 60 seconds per minute; if you could move at the speed of light, you’d see seconds on the clock taking infinite time. If you were moving less than the speed of light, the clock would be seen to run somewhere between the two extremes. From your high-speed moving frame of reference, the clock and all events in the reference frame of the clock will be seen in slow motion. Time will be stretched. How much depends on speed. This is time dilation.

A dramatic illustration of time dilation is the identical twins, one an astronaut who takes a high- speed round-trip journey while the other stays home on Earth. When the traveling twin returns, he is younger than the stay-at-home twin. How much younger depends on the relative speeds involved. If the traveling twin maintained a speed of 50% the speed of light for one year, 1.15 years will have elapsed on Earth. If the traveling twin maintains a speed of 87% the speed of light for a year, 2 years will have elapsed on Earth. At a speed of 99.5% the speed of light, 10 years would have passed on Earth.

Time as we know it travels only one way- forward. Here on Earth we constantly move into the future at a steady rate of 24 hours per day. An astronaut leaving on a deep- space voyage must live with the fact that, upon her return, much more time will have elapsed on Earth than she has experienced on her voyage. We can see into the past, but we cannot go into the past. When we look at stars in the night sky, the starlight we see left those stars dozens, hundreds, even millions of years ago.

Formula Δt= Δt o _______ √1-(v 2 /c 2 ) Δt= time interval between 2 events, as measured by an observer who is in motion with respect to the events Δt o = time interval between 2 events, as measured by an observer who is at rest with respect to the events (also called proper time) V= speed of moving object C= speed of light

Farmer MacGregor is throwing bales of hay off the back of his hay wagon with a speed of 3m/s relative to the wagon, which is pulled by a tractor moving forward with a speed of 7m/s. With what horizontal velocity do the bales of hay hit the ground?

Monty is being pulled in his wagon with a speed of 2m/s when he tosses in front of the wagon a Frisbee whose speed is 5m/s relative to the ground. Neglecting air resistance, how fast is the Frisbee moving when his dog, Snoopy, catches it in his mouth?

A light beam takes 3.0x10 -8 s to bounce back and forth vertically between two mirrors inside a moving spaceship, according to an observer on board the spaceship. How long would the beam take according to Gerard, a stationary observer on Earth, if the spacecraft were moving directly overhead in a direction perpendicular to the line of sight with a speed of 0.60c?