Space and Time

Five Key Ideas from Special Theory of Relativity

1. No information can travel faster than light; no material object can ever reach the speed of light. 2. Something moving almost the speed of light - time will go slower for that person/object. 3. Simultaneous events are in the eye of beholder. A person moving close to the speed of light might not agree. 4. Length of something moving close to the speed of light is shorter than if it were not moving. 5. The mass of something moving close to the speed of light is more than if it were not moving.

What is absolute about relativity?

1. The laws of nature are the same for everyone, regardless of your reference frame. 2. The speed of light is the same for everyone.

Other proofs supporting Relativity

1. The lifetimes of subatomic particles --At rest, the pi+ meson has a lifetime of 18 nanoseconds. But when accelerated close to the speed of light, it has a much longer lifetime, in exact agreement with the time dilation equation. 2. Masses of particles increase when traveling close to the speed of light. 3. A 1971 experiment re: time dilation using airlines.

Mass increase. What is the thought experiment?

Al is moving by you at a high speed, while his brother is at rest in your reference frame. You give both Al and his brother the same push when Al is at the same spot as his brother. Because time is running slower for Al, he experiences the push for a shorter time and therefore undergoes a smaller acceleration than his brother.

You can never reach the speed of light. What is the Thought Experiment?

Although observers in different reference fames will measure your speed differently, they will all agree on two points: 1) Your headlight beams are moving out ahead of you and your spacecraft 2) The headlight beams are moving at a speed exactly equal to c.

Mass increase contributes to our understanding of why no object can ever reach the speed of light. How?

As an object's speed approaches the speed of light, you will find its mass to be heading towards infinity. No force can accelerate an infinite mass, so the object can never gain that last little bit of speed needed to push it to the speed of light.

Why is special relativity special?

Because we ignore the role of gravity.

Thought Experiments

Einstein performed no real live experiments -- he did all his experiments in his head. Gedanken experiments.

Time dilation

From your point of view, time runs more slowly in the reference frame of anyone moving relative to you. The faster the other reference frame is moving, the more slowly time passes within it.

What was the problem with Mercury's orbit?

It was not what it should have been. It was believed that a planet was causing Mercury to deviate from its predicted path (Vulcan).

Time dilation. What is the thought experiment?

Jackie sees her laser beam go straight up and down and accurately measures the time of travel from floor to the ceiling and back. On the other and, because you are moving 0.7c toward her, see her approaching you - much like the train moving past an observer on the side of the tracks. So to you, the laser beam moves in a slanted angle relative to the floor and ceiling. Thus you would say that the light beam traveled a longer path than just going up and down. You can't explain the light's longer path by saying that light is moving faster than if the beam was just going straight up/down. Both you and Jackie have to see the same speed for light. Says Einstein. So the only solution - assuming the speed is c in both cases and the distances are different - is that the `elapsed times must be different!

What is relative about relativity?

Motion is always relative in reference to whom or what something is being measured against.

How do time dilation and length contraction provide us a "ticket to the stars"?

People on earth see you travel from earth to vega and back at .999c, so the 25-light year trip takes just over 25 years in each direction. From your reference frame, you are stationary. Earth and Vega travel back and forth at .999c. Length contraction reduces the 25-light year rest length to only one light year, which means that for you, the trip takes about one year in each direction.

Reference frame

People share the same reference frame if they are not moving relative to one another.

Motion is relative. What is the thought experiment? What is the thought experiment close to the speed of light?

Same.

Michaelson-Morely experiment

The speed of light is not affected by the earth's motion around the sun.

James Maxwell and the rise of the aether theory.

Then came James Maxwell. He produced the theories of electricity and magnetism that are still current today. He proved that light was a wave traveling at 300,000 km/s. Some people said 'waves in what?' Water waves travel in water; sound waves travel in air. What is it that light waves travel in? There was no logical answer so an ancient idea was revived: the aether.

Simultaneity is always relative to the reference frame. What is the Thought experiment?

There is a red light and a green light that flash. One at the front end, one at the back end of Al's ship. Al is moving forward towards the red light, so it lights him up first. But because Al doesn't think he's moving (based on his reference frame), he thinks the red light happened first.

How did Michelson and Morley set up the river experiment for a beam of light?

They measured the speed of a light beam traveling parallel to the direction of the Earth's motion and compared that to a light beam traveling perpendicular to the Earth's motion. The aether idea predicted that light would have a slightly different speed in the two directions. They would, in fact, be measuring the Earth's speed against the aether. Michelson's great idea was to construct an exactly similar race for pulses of light, with the aether wind playing the part of the river. The scheme of the experiment is as follows: A pulse of light is directed at an angle of 45 degrees at a half silvered, half transparent mirror, so that half the pulse goes on through the glass, half is reflected. These two half-pulses are the two swimmers. The light beams both go on to distant mirrors which reflect them back to the half-silvered mirror. At this point, they are again half reflected and half transmitted. A telescope or detector is placed behind the half-silvered mirror as shown in the figure so that half of each half-pulse will arrive in this telescope/detector. Now, if there is an aether wind blowing, someone looking through the telescope should see the halves of the two half-pulses to arrive at slightly different times, since one would have gone more upstream and back, one more across stream in general. To maximize the effect, the whole apparatus, including the distant mirrors, was placed on a large turntable so it could be swung around. Their equipment would have been accurate enough to have measured this difference if the Earth had been traveling at a speed of 5 km/s around the Sun. The Earth actually travels around the Sun at nearly 30 km/s. Yet - Michelson and Morley found no difference in the speed of light in two perpendicular directions. So - Aether doesn't exist. Einstein knew about this result and this led him to consider the speed of light as a constant.

Explain the river experiment of Michelson and Morley.

Two swimmers • Same speed - v feet / second • River is flowing at a steady rate - 3 feet per second • Both swimmers start at the same point one one bank One swimmer: • Swims directly across the river to the closest point on the opposite bank - then turns around and swims back The other swimmer: • The other stays on one side of the river, swimming upstream a distance, then swims back to the start If the angle is correctly chosen so that the net movement is directly across, in one second the swimmer must have moved four feet across---the distances covered in one second will form a 3,4,5 triangle. So, at a crossing rate of 4 feet per second, the swimmer gets across in 25 seconds, and back in the same time, for a total time of 50 seconds. The cross-stream swimmer wins.

Length Contraction. What is the Thought experiment?

When someone's clock is shorter than yours, his/her length is contracted in the direction of motion. From your point of view, the lengths of objects moving by you (or the distances between objects moving by you) are sorter in their direction of motion than they would be if the objects were at rest. The faster the objects are moving, the shorter the lengths.

How can you measure speed?

You cannot measure it absolutely. You can only measure it relative to the earth and to the sun.

What is aether?

a weightless, transparent substance in space called aether that was the medium through which light waves waved. We should be able to see the speed of light because light moves through this aether. We should see this aether wind • Tried to detect aether to show that it was real As the earth revolved aroudn the sun, this aether blew the Earth.

Why does a ball thrown straight up and down inside a train appear to be moving faster to someone outside the train?

distance = velocity x t The observer outside the train sees the ball moving with this forward speed in addition to its up and down speed. Longer distance. Same time. Higher velocity.

What kind of reference frames do we use for the special theory of relativity?

inertial reference frames Since everything in and around these spaceships is weightless and floats freely.

Hypothesis about aether

postulated to be a medium that vibrated the light wave along. Aether had never been observed. If it was made of matter then it would slow down objects like the Earth and cause them to spiral into the Sun. The aether was thus solid enough to let light vibrate in...but light enough to let the Earth travel in space without hindrance. Colorless, odorless, weightless and hard to compress. But a "medium" through which light waves could travel.

Explain the equivalence of mass and energy.

• As you approach the speed of light, your effective mass increases, which implies that your kinetic energy ( ½ mv2) increases • This fact combined with conservation of energy lead to the conclusion that objects have a 'rest' mass energy, as the relativistic expression for kinetic energy is KE=mc2 + ½ mv2, hence we say E=mc2